uk: Математика, природничі науки

description: In this talk, we consider surfaces embedded in 4-manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary 4-manifold. This extends work of Swenton and Kearton-Kurlin in S4 . We consider applications of this result to bridge trisections of surfaces in 4-manifolds and Gluck twist in S4. This project is joint with Mark Hughes and Maggie Miller.

uk: вхід без авторизації

name: Surfaces and Isotopies in 4-manifolds via banded unlink diagrams


Vincent Longo

type: Person

cs: Matematika

de: Mathematik

fi: matematiikka

uk: Математика

en: Mathematics

fr: Mathématiques

da: Matematik

es: Matemáticas

nl: Wiskunde

de: Mathematik, Naturwissenschaften

uk: Математика, природничі науки

en: Mathematics, Natural Sciences

description: There have been examples provided in the past of connected sums of a knotted sphere with an unknotted projective plane which are isotopic to the unknotted projective plane. It is an open question as to whether the connected sum of an odd twist spun knot and an unknotted projective plane is isotopic to the unknotted projective plane, but in this talk we discuss when the result is known to be true after a trivial internal stabilization.

TIB AV-Portal

type: Service

type: WebContent

type: MediaObject

@language: en

cs: přihlášení není vyžadováno

de: keine Anmeldung erforderlich

uk: вхід без авторизації

en: no login required

nl: geen login vereist

name: On 2-knots and Connected Sums with Projective Planes

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

type: Organization

cs: Video

de: Video

fi: Video

uk: Відео

en: Video

fr: Vidéo

da: Video

nl: Video

es: Video


uk: Математика, природничі науки

description: Paul Melvin proved that 0-concordant 2-knots have diffeomorphic Gluck twists, but until recently there were no known proofs that there is more than one 0-concordance class. Now Sunukjian and Dai-Miller have found many examples using Heegaard Floer technology applied to the Seifert 3-manifolds which the 2-knots bound. In this talk we give another proof using Alexander ideals. The main theorem is that the Alexander ideal induces a homomorphism from the 0-concordance monoid of 2-knots to the ideal class monoid of Z[t,t−1]. A corollary is that any 2-knot with nonprincipal Alexander ideal cannot be 0-slice, and moreover has no inverse in the 0-concordance monoid. This is the first proof that the monoid is not a group, and gives another proof of the existence of infinitely many linearly independent 0-concordance classes. These techniques also apply to higher genus surfaces, where we give the first results on 0-concordance. Lastly, we show that under a mild condition on the knot group, the peripheral subgroup of a knotted surface is also a 0-concordance invariant.

uk: вхід без авторизації

name: 0-concordance of surface knots and Alexander ideals


uk: Математика, природничі науки

description: For smooth knots in the 3 sphere, concordance has a purely geometrical definition as the equivalence generated by genus 0 cobordisms in the sphere times an interval. For virtual knots, the relation is extended by using diagram-based definitions. Both framed and twisted virtual knots have a rigidity imbued by a choice of unit normal vector field to the knot. This talk presents combinatorial definitions for concordance of framed and twisted virtual knots and slice obstructions coming from self-linking numbers.

uk: вхід без авторизації

name: Concordance for framed and twisted virtual knots


Braiding branched coverings

uk: Математика, природничі науки

description: We will examine two and three fold branched coverings of a few classical knots and knotted surfaces, and demonstrate the method of charts that allows us to find immersed braidings of these in codimension 2. As much as possible, explicit constructions and recipes will be given.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We prove an analogue of the Kauffman-Murasugi-Thistlethwaite theorem for alternating links in surfaces. It states that any reduced alternating diagram of a link in a thickened surface has minimal crossing number, and any two reduced alternating diagrams of the same link have the same writhe. The proof holds more generally for links admitting adequate diagrams and the key ingredient is a two-variable generalization of the Jones polynomial for surface links defined by Krushkal. This result extends the first and second Tait conjectures to alternating links in thickened surfaces and also to alternating virtual links.

uk: вхід без авторизації

name: The Jones-Krushkal polynomial and minimal diagrams of surface links


uk: Математика, природничі науки

description: We discuss the standard and generalized robustness of k-coherence, which are shown to be equal when restricted to pure states. The resulting expression can be used to analyze the Schmidt rank k-entanglement for pure states.

uk: вхід без авторизації

name: The robustness of k-coherence and k-entanglement


uk: Математика, природничі науки

description: To describe certain facets of non-classicality, it is necessary to quantify properties of operations instead of states. This is the case if one wants to quantify how well an operation detects non-classicality, which is a necessary prerequisite for its use in quantum technologies. To do so rigorously, we build resource theories on the level of operations, exploiting the concept of resource destroying maps. We discuss the two basic ingredients of these resource theories, the free operations and the free super-operations, which are sequential and parallel concatenations with free operations. This leads to defining properties of functionals that are well suited to quantify the resources of operations. We introduce these concepts at the example of coherence. In particular, we present two measures quantifying the ability of an operation to detect, i.e. to use, coherence, one of them with an operational interpretation, and provide methods to evaluate them. We also present an application of these concepts to an experiment in quantum optics.

uk: вхід без авторизації

name: Quantifying operations with an application to coherence


uk: Математика, природничі науки

description: The most general (probabilistic) transformation of a quantum state is described by a quantum oper- ation. Quantum operations can be axiomatically defined as the most general map which are compatible with the probabilistic structure of the theory, and produce a legitimate output when applied locally on one side of a bipartite input. These admissibility requirements characterise quantum operations as com- pletely positive trace non increasing linear maps. What happens if we now consider maps from quantum operations to quantum operations? Can we give an axiomatic characterisation of these objects according to some generalised notion of admissibility? What happens if we recursively iterate the construction and we define a full hierarchy of higher order maps? Some special cases of higher order maps have been already studied in the literature. Causally ordered Quantum Networks, which encompass all conceivable quantum protocols, form a sub-hierarchy of maps which are endowed with a well ordered causal structure and they can be realised as quantum circuits. However, more general higher order maps may exhibit an indefinite causal structure which prevents a physical implementation as a quantum circuit. Non circuital higher order maps allow to accomplishing certain tasks that cannot be achieved by circuital maps, like the violation of causal inequalities, and can outperform circuital maps in certain quantum information pro- cessing tasks. The experimental realisation of non-circuital higher order maps has also been considered. Notwithstanding many results on the subject, a general mathematical framework is still missing. The aim of this contribution is to fill this critical gap by providing an axiomatic framework for higher order quantum theory. Higher order quantum theory is introduced axiomatically with a formulation based on the language of types of transformations. Complete positivity of higher order maps is derived from the general admissibility conditions instead of being postulated as in previous approaches. We will see that a complete mathematical characterisation of admissible maps is possible and that the set of admissible maps of a given type is in correspondence with a convex subset of the cone of positive operators. This result encompasses the analysis existing in the literature and gives them an axiomatic operational foundation. The present axioms for higher order quantum theory have an operational nature and do not refer to the specific mathematical structure of quantum theory. Therefore, with due care, our framework can be applied to general operational probabilistic theories.

uk: вхід без авторизації

name: Theoretical framework for Higher-Order Quantum Theory


uk: Математика, природничі науки

description: In this work, we develop resource-theoretic approaches to study the non-stabilizer resources in fault-tolerant quantum computation. First, we introduce a family of magic measures to quantify the amount of magic in a quantum state, several of which can be efficiently computed via convex optimization. Second, we show that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted asymptotically at a rate equal to one. This reveals the fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. Third, we establish efficiently computable benchmarks for the rate and efficiency of magic state distillation via our magic measures. Fourth, we introduce efficiently computable magic measures to quantify the magic of quantum channels, which can be applied to evaluate the magic generating capability and gate synthesis. Finally, we propose a classical algorithm for simulating noisy quantum circuits whose sample complexity is quantified by our channel measure. We further show by concrete examples that our algorithm can outperform previous approaches in simulating noisy quantum circuits.

uk: вхід без авторизації

name: Quantifying the magic resources for quantum computation


Resource theories of quantum channels

uk: Математика, природничі науки

description: We initiate the systematic study of resource theories of quantum channels, i.e. of the dynamics that quantum systems undergo by completely positive maps, in abstracto: Resources are in principle all maps from one quantum system to another, but some maps are deemed free. The free maps are supposed to satisfy certain axioms, among them closure under tensor products, under composition and freeness of the identity map (the latter two say that the free maps form a monoid). The free maps act on the resources simply by tensor product and composition. This generalizes the much-studied resource theories of quantum states, and abolishes the distinction between resources (states) and the free maps, which act on the former, leaving only maps, divided into resource-full and resource-free ones. We discuss the axiomatic framework of quantifying channel resources, and show two general methods of constructing resource monotones of channels. Furthermore, we show that under mild regularity conditions, each resource theory of quantum channels has a distinguished monotone, the robustness (and its smoothed version), generalizing the analogous concept in resource theories of states. We give an operational interpretation of the log-robustness as the amount of heat dissipation (randomness) required for resource erasure by random reversible free maps, valid in broad classes of resource theories of quantum channels. Technically, this is based on an abstract version of the recent convex-split lemma, extended from its original domain of quantum states to ordered vector spaces with sufficiently well-behaved base norms (which includes the case of quantum channels with diamond norm or variants thereof). Finally, we remark on several key issues concerning the asymptotic theory.

uk: вхід без авторизації


uk: Математика, природничі науки

description: Entanglement theory is usually formulated as a quantum resource theory in which the free operations are local operations and classical communication (LOCC). This defines a partial order among bipartite pure states that makes it possible to identify a maximally entangled state, which turns out to be the most relevant state in applications. However, the situation changes drastically in the multipartite regime. Not only do there exist inequivalent forms of entanglement forbidding the existence of a unique maximally entangled state, but recent results have shown that LOCC induces a trivial ordering: almost all pure entangled multipartite states are incomparable (i.e. LOCC transformations among them are almost never possible). In order to cope with this problem I will consider alternative resource theories in which I relax the class of LOCC to operations that do not create entanglement. In more detail, I will consider two possible theories depending on whether resources correspond to multipartite entangled or genuinely multipartite entangled (GME) states and I will show that they are both non-trivial: they induce a meaningful partial order since every pure state is deterministically transformable to more weakly entangled pure states. Moreover, I will also show that no inequivalent forms of entanglement exist in these theories (i.e. all resource states are interconvertible with non-zero probability). Last but not least, I will prove that the resource theory of GME that I formulate here has a unique maximally entangled state, the generalized GHZ state, which can be transformed deterministically to any other state by the allowed free operations.

uk: вхід без авторизації

name: A resource theory of entanglement with a unique multipartite maximally entangled state


uk: Математика, природничі науки

description: Resource theorists have racked up scores of theorems over the past decade. But can these abstract theories inform science beyond quantum information and quantum thermodynamics? Can resource theories answer other scientists’ questions about specific systems in the real physical world? We argue affirmatively, illustrating with photoisomers, or molecular switches. Photoisomers surface across nature and technologies, from our eyes to solar-fuel cells. How effectively can these switches switch? This question defies standard tools, because photoisomers are small, quantum and far from equilibrium. We answer by modeling a photoisomer within a thermodynamic resource theory. Using thermomajorization, we upper-bound the switching probability. Then, we compare the bound with detailed balance and Lindbladian evolution. Thermomajorization constrains the yield tightly if a laser barely excites the molecule, such that thermal fluctuations drive switching. We also quantify the coherence in the molecule’s postswitching electronic state. Electronic coherence cannot boost the yield in the absence of extra resources, we argue, because modes of coherence transform independently via thermal operations. This work illustrates how thermodynamic resource theories can illuminate nature, experiments, and synthetics. This work appears in "Fundamental limitations on photoisomerization from thermodynamic resource theories" and was undertaken with David Limmer.

uk: вхід без авторизації

name: How effectively can a molecular switch switch? A bound from thermodynamic resource theories


uk: Математика, природничі науки

description: We identify and explore the intriguing property of resource resonance arising within resource theories of entanglement, coherence and thermodynamics. While the theories considered are reversible asymptotically, the same is generally not true in realistic scenarios where the available resources are bounded. The finite-size effects responsible for this irreversibility could potentially prohibit small quantum information processors or thermal machines from achieving their full potential. Nevertheless, we show here that by carefully engineering the resource interconversion process any such losses can be greatly suppressed. Our results are predicted by higher order expansions of the trade-off between the rate of resource interconversion and the achieved fidelity, and are verified by exact numerical optimizations of the appropriate underlying approximate majorization conditions.

uk: вхід без авторизації

name: Finite size effects and resonances in resource interconversion


uk: Математика, природничі науки

description: One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks in which the resource can give an explicit advantage over all resourceless states. We show that this can always be accomplished for all convex resource theories. We establish in particular that any resource state enables an advantage in a channel discrimination task, allowing for a strictly greater success probability than any state without the given resource. Furthermore, we find that the generalized robustness measure serves as an exact quantifier for the maximal advantage enabled by the given resource state in a class of subchannel discrimination problems, providing a universal operational interpretation to this fundamental resource quantifier. We also consider a wider range of subchannel discrimination tasks and show that the generalized robustness still serves as the operational advantage quantifier for several well-known theories such as entanglement, coherence, and magic.

uk: вхід без авторизації

name: Every convex quantum resource is useful for channel discrimination


uk: Математика, природничі науки

description: How fast do infinite-dimensional quantum systems evolve? Do entropies of infinite-dimensional quantum systems satisfy continuity bounds? If so, what are the corresponding convergence rates? These are the questions that will addressed in this talk. By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite-dimensions, which are stronger than previously known bounds. Our results have interesting applications including quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. We also obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl’s law.

uk: вхід без авторизації

name: Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions.


uk: Математика, природничі науки

description: We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving two new versions of the convex-split lemma that use much smaller amount of additional resource (in comparison to previous version) and the second method being inspired by the technique of classical correlated sampling in computer science literature. These lead to a series of new consequences, as follows. First, we consider the task of quantum decoupling, where the aim is to apply an operation on a n-qubit register so as to make it independent of an inaccessible quantum system. Many previous works achieve decoupling with the aid of a random unitary. It is known that random unitaries can be replaced by random circuits of size O(nlog n) and depth poly(log n), or unitary 2-designs based on Clifford circuits of similar size and depth. We show that given any choice of basis such as the computational basis, decoupling can be achieved by a unitary that takes basis vectors to basis vectors. Thus, the circuit acts in a `classical' manner and additionally uses O(n) catalytic qubits in maximally mixed quantum state. Our unitary performs addition and multiplication modulo a prime and hence achieves a circuit size of O(n\log n) and logarithmic depth. This shows that the circuit complexity of integer multiplication (modulo a prime) is lower bounded by the optimal circuit complexity of decoupling. Next, we construct a new one-shot entanglement-assisted protocol for quantum channel coding that achieves near-optimal communication through a given channel. Furthermore, the number of qubits of pre-shared entanglement is exponentially smaller than that used in the previous protocol that was near-optimal in communication. We also achieve similar results for the one-shot quantum state redistribution. Joint work with Rahul Jain.

uk: вхід без авторизації

name: Efficient methods for one-shot quantum communication


uk: Математика, природничі науки

description: Given two sets of quantum states, is it possible to transform one to the other by a quantum channel? This question has been studied by many authors and recently fully settled by a set of entropic inequalities. We will consider an extension of this problem that can be formulated as follows: given two bipartite quantum channels, how precisely can one be approximated by applying a suitable supermap to a part of the other? Taking some inspiration from the classical randomization criterion by Le Cam, we study this question it the case when the precision of the approximation is measured by distance in the diamond norm.

uk: вхід без авторизації

name: Randomization theorems for quantum channels


uk: Математика, природничі науки

uk: вхід без авторизації

name: De Finetti Theorems for Quantum Channels


uk: Математика, природничі науки

description: We present a general framework of a resource theory based on the assumption of a) convexity and b) that the overlap of free states with maximally resourceful state is bounded. Using this structure, we derive bounds on the one-shot distillation rate for such a resource theory, thereby reproducing known bounds in coherence and entanglement. We use the free robustness and introduce a function Gmin related to overlap between states to express our bounds. To deal with resource theories where the free robustness in not finite we introduce the notion of imperfect free operations which we call ϵ-resource generating operations and generalize the free robustness toϵ-free robustness. We construct an ϵ-resource generating map that achieves pure state transformations and derive the conditions for such a transformation in terms of the ϵ-free robustness.

uk: вхід без авторизації

name: Common Structures in General Resource Theory


Embezzlement of Entanglement

uk: Математика, природничі науки

description: Embezzlement of entanglement was studied by van Dam and Hayden who showed that it was imposible to catylyically produce entanglement in the tensor product model, but that one could "nearly" acheive this goal. However, in the commuting operator model one can accomplish this task. We show that there is a parallel between this theory and Tsirelson's problems about the different models for conditional probability densities. In analogy there is a theory of "unitary correlations" that yields a set of matrices that allows one to study quantum input--classical output games.

uk: вхід без авторизації

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


How Zeno found the bomb

uk: Математика, природничі науки

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Resource theory of asymmetric distinguishability


uk: Математика, природничі науки

description: Bell inequalities were derived as conditions satisfied by local hidden-variable models. However, in recent years they have acquired a new status as device-independent certificates of relevant quantum properties. We provide several constructions in which Bell inequalities are constructed from the quantum states and/or measurements to certify, rather than from considerations concerning the geometry of classical correlations. In particular, we present Bell inequalities maximally violated by maximally entangled states or arbitrary dimension and also graph states.

uk: вхід без авторизації

name: Bell inequalities for quantum certification


uk: Математика, природничі науки

description: Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number N of ports, the error of the optimal protocol is proportional to the inverse square of N . We prove this by deriving an achievability bound, obtained by relating the corresponding optimization problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered simplex. We also give an improved converse bound of matching order in the number of ports. In addition, we determine the leading-order asymptotics of PBT variants defined in terms of maximally entangled resource states. The proofs of these results rely on connecting recently-derived representation-theoretic formulas to random matrix theory. Along the way, we refine a convergence result for the fluctuations of the Schur-Weyl distribution by Johansson, which might be of independent interest, joint work with M. Christandl, C. Majenz, G. Smith, F. Speelman, M. Walter

uk: вхід без авторизації

name: Asymptotic performance of port-based teleportation


uk: Математика, природничі науки

description: In this talk I discuss coherence distillation under Time translation Invariant operations. I show that although for a generic mixed state the distillation rate is zero, it is still possible to distill a sub-linear number of a pure coherent state, with fidelity approaching one, provided that we can consume asymptotically many copies of the mixed state. Furthermore, for a generic mixed input state, there is a tradeoff between the maximum achievable yield and the fidelity with pure coherent states. Interestingly, it turns out that Petz-Renyi relative entropy for alpha=2 gives a tight bound on the maximum achievable fidelity. Furthermore, coherence distillation provides an operational explanation for the violation of the monotonicity of Petz-Renyi relative entropy for the parameter range alpha>2. Finally, I talk about the limitations of measure-and-prepare (entanglement-breaking) processes for coherence distillation. If time allows, I also briefly discuss a new no-broadcasting theorem for coherence and asymmetry. The no-go theorem states that if two initially uncorrelated systems interact by symmetric dynamics and asymmetry is created at one subsystem, then the asymmetry of the other subsystem must be reduced. I also present a quantitative relation describing the tradeoff between the subsystems.

uk: вхід без авторизації

name: Sublinear Coherence Distillation (using Time-Translation Invariant Operations)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Human evolutionary history has shaped the genetic architecture of complex trait


uk: Математика, природничі науки

uk: вхід без авторизації

name: Performance of polygenic risk scores in diverse populations


uk: Математика, природничі науки

uk: вхід без авторизації

name: Unboxing a black box: Properties of phylogenetically-informed distances for microbiome data


uk: Математика, природничі науки

uk: вхід без авторизації

name: Zero-Inflated Generalized Dirichlet Multinomial (ZIGDM) Regression Model for Microbiome Compositional Data


uk: Математика, природничі науки

uk: вхід без авторизації

name: It’s just a matter of perspective - tuning-insensitive and robust sparse regression for microbiome data


uk: Математика, природничі науки

uk: вхід без авторизації

name: Balancing complexity in genetic studies of multifactorial diseases


uk: Математика, природничі науки

uk: вхід без авторизації

name: Methods to understand Disease Biology Using GWAS and Transcriptome Data


uk: Математика, природничі науки

uk: вхід без авторизації

name: Smooth modeling of covariate effects in bisulfite sequencing-derived measures of DNA methylation


uk: Математика, природничі науки

uk: вхід без авторизації

name: Empower Whole Genome Sequencing Association Analysis: Data Formats, Functional Annotation and Methods


uk: Математика, природничі науки

uk: вхід без авторизації

name: Virtual ChIP-seq: Predicting transcription factor binding by learning from the transcriptome


uk: Математика, природничі науки

uk: вхід без авторизації

name: Variance Components Estimation for Linear Mixed Models


uk: Математика, природничі науки

uk: вхід без авторизації

name: Racial Differences in Immune and Microbial Response in Colorectal Neoplasia


uk: Математика, природничі науки

uk: вхід без авторизації

name: Estimating the overall contribution of human oral microbiome to the risk of developing cancers based on prospective studies

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: Deep learning enables accurate clustering and batch effect removal in single-cell RNA-seq analysis


uk: Математика, природничі науки

uk: вхід без авторизації

name: Learning from the Transcriptome: analysis of single cell and bulk RNA sequencing data


uk: Математика, природничі науки

uk: вхід без авторизації

name: Inference of population structure from time-series genotype data


uk: Математика, природничі науки

uk: вхід без авторизації

name: Complex Traits: Leveraging Polygenecity to Inform Biology, Causality and Prediction


uk: Математика, природничі науки

uk: вхід без авторизації

name: Bayesian TWAS: a causal inference approach


uk: Математика, природничі науки

uk: вхід без авторизації

name: A Bayesian framework to address limitations of Mendelian Randomization


uk: Математика, природничі науки

uk: вхід без авторизації

name: Controlling and Testing Horizontal Pleiotropy with Probabilistic Mendelian Regression for Transcriptome-wide Association Studies


uk: Математика, природничі науки

uk: вхід без авторизації

name: Identifying cancer drivers at CTCF insulators


uk: Математика, природничі науки

uk: вхід без авторизації

name: Pathogen exposure and pathogen type moderate social status effects on gene regulation in adulthood


uk: Математика, природничі науки

uk: вхід без авторизації

name: Evolutionary genetic dissection of the genus Homo and its immune response


uk: Математика, природничі науки

uk: вхід без авторизації

name: Differential Co-Expression Analyses of Pathways


uk: Математика, природничі науки

uk: вхід без авторизації

name: Quantile Regression in the Post GWAS Secondary Phenotype Analysis


uk: Математика, природничі науки

uk: вхід без авторизації

name: Improved Pathogenic Variant Localization using a Hierarchical Model of Sub-regional Intolerance


uk: Математика, природничі науки

uk: вхід без авторизації

name: Determinants of differential gene expression in skeletal muscle and in adipose tissue


uk: Математика, природничі науки

uk: вхід без авторизації

name: Compositional Mediation Model for Binary Outcome


uk: Математика, природничі науки

uk: вхід без авторизації

name: Mediation analysis for zero-inflated mediators


uk: Математика, природничі науки

uk: вхід без авторизації

name: Testing mediation effect in high-dimensional compositional microbiome data

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: A powerful two-stage microbiome-wide association test


Ramsey complete sequences

uk: Математика, природничі науки

description: A sequence of positive integers A is said to be entirely Ramsey complete if, for any two-colouring of A, every positive integer can be written as the sum of distinct elements of A of the same colour. We show that there exists a constant C and an entirely Ramsey complete sequence A such that |A∩[n]|≤Clog2n for all n. This is best possible up to the constant and solves a problem of Burr and Erd\H{o}s. We also discuss several related problems stated by the same authors. Joint work with Jacob Fox.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The underlying philosophy of Ramsey Theory is that total disorder is impossible, and the underlying philosophy of Discrepancy Theory is that a totally equal distribution is impossible. In both theories we mainly try to find extremal configurations that satisfy some property or at least their magnitude. It is convenient to express these configurations as colored objects. Both theories can be extended from using colors to the use of vanishing (or almost vanishing) linear sums in several variables. Theorems in Ramsey Theory can be generalized using the Erdős Ginzburg Ziv theorem, by replacing a {0,1}-coloring by a coloring which uses the residues modulo a positive integer assuring a modular zero-sum. In Discrepancy Theory, many combinatorial problems can be expressed by a {-1,1}-coloring and the discrepancy from a uniform distribution is expressed as the deviation from zero. In the lecture we will discuss from a personal perspective, several Ramsey-type theorems and Discrepancy theorems in order to demonstrate the breadth of the subjects. Next we will survey recent developments of the EGZ theorem and other developments relating to integer-coloring. Finally, we will show how these developments relate to Ramsey Theory and Discrepancy Theory. The linear sums mentioned above can be generalized to symmetric polynomials. This suggests new avenues of research and many more problems.

uk: вхід без авторизації

name: Ramsey theory, Discrepancy Theory, Zero-Sums and Symmetric Functions


uk: Математика, природничі науки

uk: вхід без авторизації

name: Problem session: What about R(Kn, Z3)...


uk: Математика, природничі науки

description: The Erdos-Ginzburg-Ziv (EGZ) Theorem has an elegant proof due to Bailey and Richter that employs a 1935 result of Chevalley. Chevalley’s Theorem states that the number of shared zeros of a polynomial system over a finite field is not equal to one whenever the number of variables exceeds the sum of the degrees of the polynomials. In the same year, Warning generalized Chevalley’s Theorem and gave a lower bound on the number of shared zeros in such a system so long as one exists. We discuss our generalization of Warning’s Theorem and show how we can quantitatively refine existence theorems, such as EGZ, and simultaneously include the inhomogeneous case. Specifically, we show how one can apply our theorem to recover a 2012 result of Das Adhikari, Grynkiewicz and Sun that treats an analogue of the EGZ Theorem, one in which one considers the EGZ-problem for generalized zero-sum subsequences in any finite commutative p-group. Joint work with Pete L. Clark and Aden Forrow.

uk: вхід без авторизації

name: Counting zero-sum sequences with the polynomial method


uk: Математика, природничі науки

description: In this talk, we will present a new upper bound for the Davenport constant of finite Abelian groups of the form Crn

uk: вхід без авторизації

name: An asymptotically tight bound for the Davenport constant


Addition theorems in Fp

uk: Математика, природничі науки

description: In this talk, we will shortly present a direct and reverse way to develop the polynomial method that relies on the Combinatorial Nullstellensatz. The direct and usual way states that a multivariate polynomial of small degree cannot vanish on a large cartesian product provided that a specified coefficient is non zero. The reverse way relies on the coefficient formula and establishes an expression for this specified coefficient. This double interpretation of the polynomial method allows to shorten the proofs of the Cauchy-Davenport and the Dias da Silva-Hamidoune theorems and a new result on the cardinality of sets of subsums. Moreover tese proofs do not require any computations and do imply the critical cases of these three problems: arithmetical progressions.

uk: вхід без авторизації


Sequence Subsums in Zero-Sum Theory

uk: Математика, природничі науки

description: The last few years have seen the development and improvement of structural results in the area of sequence subsums over abelian groups. These results often have the flavor that either many elements can be represented as a sum of terms from a subsequence of the given sequence (possibly with length restrictions) or else the sequence must itself be highly structured. The Subsum Kneser's Theorem, giving the corresponding analog of the classical Kneser's Theorem for sumsets, is one such example. The statements of such results, particulary in their stronger forms, are often more challenging and technical in appearance, but they have been utilized to strong effect when searching for zero-sums in a variety of circumstances. In this talk, we will give an overview of several of these results, focussing on how they were successfully used in various concrete extremal problems involving zero-sums.

uk: вхід без авторизації


uk: Математика, природничі науки

description: For (G,+,0) a finite abelian group and S=g1…gk a sequence over G, we denote by σ(S) the sum of all terms of S. We call |S|=k the length of the sequence. If the sum of S is 0, we say that S is a zero-sum sequence. We denote by B(G) the set of all zero-sum sequences over G. This is a submonoid of the monoid of all sequences over G. We say that a zero-sum sequence is a minimal zero-sum sequence if it cannot be decomposed into two non-empty zero-sum subsequences. In other words, this means that it is an irreducible element in B(G). For S∈B(G) we say that ℓ is a factorization-length of S if there are minimal zero-sum sequences A1,…,Aℓ over G such that S=A1…Al. We denote the set of all ℓ that are a factorization-length of S by L(S).

uk: вхід без авторизації

name: Comparing system of sets of lengths over finite abelian groups


uk: Математика, природничі науки

uk: вхід без авторизації

name: EGZ-generalizations for linear equations and linear inequalities in three variables


Bounds for Folkman’s Theorem

uk: Математика, природничі науки

description: Folkman’s theorem asserts that in any red-blue colouring of [N], there is an n-set all of whose finite sums are the same colour. How large must N be in terms of n? Improving on Erdos—Spencer from the 80s, I’ll show that N must be at least doubly exponential in n.

uk: вхід без авторизації


uk: Математика, природничі науки

uk: вхід без авторизації

name: Constructions of high dimensional caps, sets without arithmetic progressions, and sets without zero sums


uk: Математика, природничі науки

uk: вхід без авторизації

name: Alternate minimization of matrices and problems in number theory


uk: Математика, природничі науки

description: In this talk we will discuss lower and upper bounds for the size of k-AP-free subsets of Znm, that is, for rk(Znm, in certain cases. Specifically, we will discuss some lower bounds given by Elsholtz and myself. In the case m=4,k=3 we present a construction which gives the tight answer up to n≤5 and point out some connection with coding theory. We will also mention some open questions (and some partial answers) about related linear algebraic problems.

uk: вхід без авторизації

name: Progression-free sets and rank of matrices


uk: Математика, природничі науки

description: In this talk, we consider problems and results that go in the opposite direction of the classical theorems in the discrepancy theory. The following statement gives a flavor of our approach. Let t, k and q be integers such that q≥0, 0≤t<k, and t≡k(mod2), and take s∈[0,t+1] as the unique integer satisfying s≡q+k−t−22(mod(t+2)).

uk: вхід без авторизації

name: Zero-sum subsequences in {−1,+1} bounded sum sequences


Lösung Fallstudie Controlling

keywords:
Strategieprozess
Hochschulmanagement
Wissenschaftsmanagement
Controlling
Controlling im Strategieprozess

de: Rechts-, Wirtschafts- und Sozialwissenschaften

uk: Право, економіка та суспільні науки

en: Law, Economics and Social Sciences

de: Wirtschaftswissenschaften

uk: Бізнес та економіка

en: Business and Economics

description: In diesem Video erklärt Professor Ziegele zunächst welche Rolle Controlling allgemein in Prozessen einnehmen kann. Anschließend bezieht er dies auf den speziellen Fall des Controllings innerhalb von Strategieprozessen an Hochschulen. Dabei geht er einerseits darauf ein, welche Rolle das Controlling im Informationsmanagement spielt und andererseits, welche Rolle Controlling im Prozessmanagement spielt.

@language: de

uk: вхід без авторизації

Hochschule Osnabrück

addressCountry: DE

addressLocality: Osnabrück

addressRegion: Lower Saxony


keywords: Ternnungsrechnung Wissenschaftsmanagement Kostenmanagement Finanzmanagement Bildungsmanagement Hochschulmanagement Overhead Gemeinkostenzuschlag

uk: Право, економіка та суспільні науки

description: In diesem Video erklärt Dr. Handel, wie eine Trennungsrechnung an Hochschulen funktioniert und warum diese in bestimmten Situationen eingesetzt werden kann. Dabei geht er auf die gesetzliche Grundlage ein und erläutert, wie eine Trennungsrechnung zu Berechnung verschiedener Overheads für Projekte an Hochschulen zum Einsatz kommen kann. In diesem Zusammenhang wird außerdem erläutert, wie wirtschaftliche und nicht-wirtschaftliche Tätigkeiten an Hochschulen voneinander zu trennen sind.

uk: вхід без авторизації

name: Trennungsrechnung: Begriffserläuterung und Einführung


uk: Математика, природничі науки

description: A countable group is said to have the Schmidt property if it admits an ergodic free p.m.p. action such that the full group of the associated orbit equivalence relation contains a non-trivial central sequence. It was originally asked by Klaus Schmidt whether any inner amenable group has this property. We show that any countable group with infinite FC-center has the Schmidt property, and as its consequence, any inner amenable, property (T) group has the Schmidt property. This is a joint work with Robin Tucker-Drob.

uk: вхід без авторизації

name: Groups with infinite FC-center have the Schmidt property


uk: Математика, природничі науки

description: Popa's intertwining theory is a very powerful tool to study inclusions of finite von Neumann algebras. This is in fact one of the most important technical ingredient in Popa's deformation/rigidity theory. Since this intertwining technique works only for finite von Neumann algebras, there have been many attempts to generalize it to inclusions of general von Neumann algebras. In this talk, I will give a survey of recent development for these attempts, which are mainly given by C. Houdayer, S. Vaes, Y. Ueda, A. Marrakchi, and myself. I also mention applications to the deformation/rigidity theory.

uk: вхід без авторизації

name: Popa's intertwining theory for type III factors


uk: Математика, природничі науки

description: We will present examples of equivalence relations without the Jones-Schmidt property, answering a question from Jones and Schmidt from 1985. We will then discuss its connections with structural properties of central sequence algebras, and implications for unique McDuff decompositions. This is based on joint works with Adrian Ioana.

uk: вхід без авторизації

name: The Jones-Schmidt property and central sequence algebras


uk: Математика, природничі науки

description: I will present recent joint work with Cyril Houdayer about a stationary version of characters on discrete groups. Our main result states that such stationary characters on lattices of semisimple Lie groups are actually genuine characters. I will present applications of this result to representation theory and operator algebras, as well as topological dynamics. I will also mention a result in non-commutative ergodic theory, which is the key to our approach and is of independent interest.

uk: вхід без авторизації

name: Stationary characters on lattices in semi-simple groups


uk: Математика, природничі науки

description: The free group factor L(Fd) can realized as the von Neumann algebra generated by d freely independent semicircular varables S1,…,Sd, the free probabilistic analogue of an independent family of Gaussians. We consider non-commutative random variables X1,…,Xm whose non-commutative distribution satisfy the integration-by-parts relation τ(DXjV(X)p(X))=τ⊗τ(∂Xjp(X)), where V is a suitably regular convex function. By studying "conditional transport of measure" for the associated N×N random matrix models in the large N limit, we show that there is an isomorphism W∗(X1,…,Xd)→W∗(S1,…,Sd) such that the W∗-algebra of the first k generators is mapped to the W∗-algebra of the first k generators for every k. In particular, W∗(X1) is sent to the generator MASA in L(Fd), so it is freely complemented. As an application, we deduce that for every non-commutative polynomial p, the algebra W∗(S1+ϵp(S)) is a freely complemented MASA in L(Fd) for sufficiently small ϵ.

uk: вхід без авторизації

name: Free Complementation of Certain MASAs in L(Fd) via Conditional Transport of Measure

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: In this talk we provide a natural complement to Monod and Shalom's orbit equivalence superrigidity theorem for irreducible actions of product groups by providing a large class of product actions whose orbit equivalence relation remember the product structure. More precisely, we show that if a product Γ1×⋯×Γn↷X1×⋯×Xn of measure preserving actions is stably orbit equivalent to a measure preserving action Λ↷Y, then Λ↷Y is induced from an action Λ0↷Y0 and there exists a direct product decomposition Λ0=Λ1×⋯×Λn into n infinite groups. Moreover, there exists a measure preserving action Λi↷Yi that is stably orbit equivalent to Γi↷Xi, for any 1≤i≤n, and the product action Λ1×⋯×Λn↷Y1×⋯×Yn is isomorphic to Λ0↷Y0.

uk: вхід без авторизації

name: Orbit equivalence rigidity for product actions


uk: Математика, природничі науки

description: It is a classical problem to recover a discrete group from various rings or algebras associated with it, such as the integral group ring. By analogy, in an operator algebraic framework we want to recover torsion-free groups from certain topological completions of the complex group ring, such as the reduced group C∗-algebra. Groups for which this is possible are called C∗-superrigid. My talk will discuss how a group can be recovered from its group rings, before I introduce the reduced group C∗-algebras and describe the state-of-the-art in C∗-superrigidity. I will end with a short account on other kinds of superrigidity for group operator algebras putting the subject into a bigger perspective.

uk: вхід без авторизації

name: Superrigidity for group operator algebras


uk: Математика, природничі науки

description: An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congruences include paradoxical decompositions and n-divisibility of actions. We consider the general question of when there are realizations of abstract systems of congruences satisfying various measurability constraints. We completely characterize which abstract systems of congruences can be realized by nonmeager Baire measurable pieces of the sphere under the action of rotations on the 2-sphere. This answers a question of Wagon. We also construct Borel realizations of abstract systems of congruences for the action of PSL2(Z) on P1(R).

uk: вхід без авторизації

name: Measurable realizations of abstract systems of congruence


Tensor products of matrix convex sets

uk: Математика, природничі науки

description: Following work of Kavruk et al. on tensor products of operator systems, we discuss the tensor theory of matrix convex sets. Among applications, we obtain a new formulation of Connes' embedding problem via noncommutative Choquet theory. This is joint work with Roy Araiza and Adam Dor-On.

uk: вхід без авторизації


Playing games with II1 factors

uk: Математика, природничі науки

description: In this talk, I will introduce several games that one can play with II1 factors and the connection between these games and other active areas of research, including the Connes Embedding Problem and the study of elementarily equivalent II1 factors (that is, II1 factors with isomorphic ultrapowers). Some of the work in this talk is joint with Thomas Sinclair.

uk: вхід без авторизації


uk: Математика, природничі науки

description: In the first part of my talk I will discuss the problems of reconstructing a countable discrete group from its von Neumann algebra (W*-superrigidity) and its reduced C*-algebra (C*-superrigidity) and I will survey several recent results in this direction. In the second part, using and interplay between von Neumann algebraic and C*-algebraic methods, I will introduce a new class of C*-superrigid groups which appear as wreath products with non-amenable core. As an application we obtain complete calculations of the symmetry groups of various group C*-algebras---a problem barely touched in the literature. This is based on a recent joint work with Alec Diaz-Arias.

uk: вхід без авторизації

name: Some rigidity aspects in von Neumann algebras and C*-algebras arising from groups


uk: Математика, природничі науки

description: We introduce a new equivalence relation on groups, which we call von Neumann equivalence, and which is coarser than both measure equivalence and W*-equivalnce. We introduce a general procedure for inducing actions in this setting and use this to show that the class of properly proximal groups is closed in this equivalence relation. In particular, proper proximality is preserved under both measure equivalence and W*-equivalence, and from this we obtain examples of non-inner amenable groups which are not properly proximal. This is based on joint work with Ishan Ishan and Jesse Peterson.

uk: вхід без авторизації

name: Von Neumann equivalence and properly proximal groups


uk: Математика, природничі науки

description: The classification program for von Neumann algebras witnessed remarkable progress which is in large part due to Popa's deformation/rigidity theory. We expand on the implications of the existence of maximal rigid algebras, provide concrete examples in the group setting, and applications when considering families of deformations as in L2 rigidity, in particular, further supporting the Peterson-Thom Conjecture. I will give some of the background that goes into our theorem, and Rolando will expand on the details in a follow up talk.

uk: вхід без авторизації

name: Maximal rigid subalgebras of deformations and L2-cohomology, I


uk: Математика, природничі науки

description: The classification program for von Neumann algebras witnessed remarkable progress which is in large part due to Popa's Deformation/Rigidity theory. Proceeding from where Ben Hayes ended in Part I, we expand on the implications of the existence of maximal rigid algebras, provide concrete examples in the group setting, and describe applications when considering families of deformations as in L2 rigidity; the latter result lends further support to the Peterson-Thom Conjecture.

uk: вхід без авторизації

name: Maximal Rigid Subalgebras of Deformations and L2 Cohomology, II


Matrix models for ε-independence

uk: Математика, природничі науки

description: I will discuss ε-independence, which is an interpolation of classical and free independence originally studied by Motkowski and later by Speicher and Wysoczanski. To be ε-independent, a family of algebras in particular must satisfy pairwise classical or free independence relations prescribed by a {0,1}-matrix ε, as well as more complicated higher order relations. I will discuss how matrix models for this independence may be constructed in a suitably-chosen tensor product of matrix algebras. This is joint work with Benoit Collins.

uk: вхід без авторизації


uk: Математика, природничі науки

description: The separably acting hyperfinite/amenable II1-factor R has the property that any two embeddings into its own ultrapower are unitarily conjugate. Jung showed in 2009 that the converse holds modulo the Connes Embedding Problem. In this talk we will discuss the recent result that amenability for tracial von Neumann algebras satisfying the Connes Embedding Problem is characterized by the weaker property that any two embeddings into an ultrapower of R are conjugate by unital completely positive maps. Time permitting, we will discuss other recent characterizations of amenability within this context. This is based on joint work with Srivatsav Kunnawalkam Elayavalli.

uk: вхід без авторизації

name: Ultraproduct embeddings and amenability for tracial von Neumann algebras


uk: Математика, природничі науки

description: Residual finite dimensionality is the C∗-algebraic analogue for maximal almost periodicity and residual finiteness for groups. Just as with the analogous group-theoretic properties, there is significant interest in when residual finite dimensionality is preserved under standard constructions, in particular amalgamated free products. In general, this question is quite difficult; however the answer is known when the amalgam is finite dimensional or when the two C∗-algebras are commutative. In moving beyond these cases, group theoretic restrictions suggest that we consider central amalgams. We generalize the commutative case to pairs of so-called ``strongly residually finite dimensional" C∗-algebras amalgamated over a central subalgebra. Examples of strongly residually finite dimensional C∗-algebras include group C∗-algebras associated to virtually abelian groups, certain just-infinite groups, and Lie groups with only finite dimensional irreducible unitary representations. Though this property may seem restrictive, a recent result of Thom indicates that it is in fact necessary. This is joint work with Tatiana Shulman.

uk: вхід без авторизації

name: Amalgamated Products of Strongly RFD C∗-algebras arising from locally compact groups


uk: Математика, природничі науки

description: Force-free electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arise on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In those regimes, the electromagnetic field obeys a modified nonlinear version of Maxwell equations, while the plasma only accommodates to locally cancel out the Lorentz force. The aim of the present talk is to discuss the initial/boundary value formulation of FFE at some given astrophysical settings. We start by showing that, when restricted to the correct constraint submanifold, the system is symmetric hyperbolic: we introduce here a particular hyperbolization for the FFE equations [1], following a covariant approach due to R. Geroch [2]. Then, we analyze the characteristic structure of the resulting evolution system and use this information to construct appropriate boundary conditions [3,4]. In particular, we focus on the treatment to mimic the perfectly conducting surface of a neutron star, where incoming and outgoing physical modes needs to be combined on a very precise way. We shall illustrate this procedure with the simpler vacuum (linear) electrodynamics. Also, we discuss the methods employed to deal with the constraints of the theory at the boundaries. And finally, we show some results from our 3D numerical simulations based on this approach [4,5,6]. [1] F. Carrasco, O. Reula. PRD (93), 2016. DOI: 10.1103/PhysRevD.93.085013 [2] R. Geroch. “Partial differential equations of physics”. In General Relativity, pp. 19-60. Routledge, 1996. [3] F. Carrasco, O. Reula. PRD (96), 2017. [4] F. Carrasco, C. Palenzuela, O. Reula. PRD (98), 2018. DOI: 10.1103/PhysRevD.98.023010 [5] F. Carrasco, D. Viganò. C. Palenzuela, J. Pons. MNRAS Letters (484), 2019. [6] R. Cayuso, F. Carrasco, B. Sbarato, O. Reula., 2019.

uk: вхід без авторизації

name: Initial/Boundary Value Formulation for Neutron Star Magnetospheres


uk: Математика, природничі науки

description: A short summary of the well-posed IBVP for the vacuum Einstein field equations in harmonic coordinates formulated in Comm. Math. Phys. 289, 1099-1129 (2009) will be provided.

uk: вхід без авторизації

name: Well-posed initial boundary value problem for the Einstein field equations in harmonic coordinates


uk: Математика, природничі науки

description: It is well known that gravitational waves interact in a non-linear way. This makes it difficult to describe them rigorously. The cleanest description is based on a certain conformal invariance of the Einstein equations — a fact which was established by R. Penrose and was used by H. Friedrich to prove several important global results for general relativistic space-times. The so called conformal field equations implement this conformal invariance on the level of partial differential equations. They provide various well-posed initial (boundary) value problems for use in different situations. The talk will give a computational perspective on the non-linear interaction of plane gravitational waves and also present preliminary results of a simulation of the behaviour of an initially spherically symmetric black hole under the impact of a gravitational wave burst.

uk: вхід без авторизації

name: Global simulation of the non-linear perturbations of a Schwarzschild black hole


uk: Математика, природничі науки

description: In the absence of time-like boundary, the classical initial value problem in GR verifies a geometric uniqueness property. In particular, isometric Cauchy data leads to (maximal globally hyperbolic) developments which are isometric. While there exists several well-posed formulation of the initial boundary value problem in GR, no such geometric uniqueness is known. This important issue was put forward by Helmut Friedrich. It is relevant not only for the local initial boundary value problem, but also for more global aspects, due to the possible breakdown of gauge choices. I will review the mathematical analysis of the initial boundary value problem in GR, with an emphasis on various aspects relevant to the geometric uniqueness problem. If time (and progress) permits, I will present work in progress with Grigorios Fournodavlos concerning an approach to the initial boundary value problem based on the wave equation satisfied by the second fundamental form of a foliation with prescribed mean curvature.

uk: вхід без авторизації

name: A review of the initial boundary problem in GR and geometric uniqueness


uk: Математика, природничі науки

description: The numerical computation of gravitational radiation emitted from binary black hole systems has been pivotal in the detection and characterization of 10 binary black hole astrophysical events since Sept. 14, 2015. However, the drive for more accurate waveforms remains, especially when computing higher-order spherical harmonic modes. The numerical relativity simulations currently used for LIGO / VIRGO detections solve Einstein’s field equations on a finite computational domain with an outer boundary. In order to obtain a unique Cauchy evolution, it is necessary to impose boundary conditions which should yield a well posed problem and ideally, be completely transparent to the physical problem on the unbounded domain. Short of achieving this ideal, one can try to develop so-called absorbing boundary conditions which form a well-posed problem and insure that only a very small amount of spurious gravitational radiation is reflected from the outer boundary into the computational domain. In this talk, I discuss the implementation of a hierarchy of such boundary conditions which hopefully will improve the accuracy of binary black hole numerical simulations.

uk: вхід без авторизації

name: Implementing higher-order absorbing boundary conditions for Numerical Relativity


uk: Математика, природничі науки

uk: вхід без авторизації

name: Hyperbolicity of constrained Hamiltonian systems with application to the IBVP in GR


uk: Математика, природничі науки

description: The mathematical study of the metric produced by compactly supported perfect fluid mass distributions governed by the Einstein-Euler equations is now developing. The main difficulty of the study comes from the situation that the boundary between the mass and the vacuum requires mathematically delicate treatise. This so called `physical vacuum boundary' is a kind of free boundary. The spherically symmetric evolution of the metric near spherically symmetric equilibria, say, solutions of the Tolman-Oppenheimer-Volkoff equation, is studied in [1] by application of the Nash-Moser theorem. The metric can be matched to the exterior Schwarrzschild metric in the vacuum region, but it turns out to be the boundary is of class C^2 if and only if the metric is static. The existence of the axially symmetric metric of slowly rotating mass under the weak gravitational field has been established in [2] in a bonded region containing the support of the density. But the global continuation of the metric beyond the bounded region has not yet been done. Actually we are not sure whether the matching can be done using the Kerr metric, and, what on earth, we are not sure whether the metric can be continued as asymptotically flat one or not. Much less the problem of time evolution near this rotating stationary metric is completely open. [1] T. Makino, Kyoto J. Math., 56 (2016). [2] T. Makino, J. Math. Physics., 59(2018).

uk: вхід без авторизації

name: Vacuum Boundary Problem of the Metric Produced by Perfect Fluid Mass Distributions


uk: Математика, природничі науки

description: In this talk, I will discuss a new approach to establishing the well-posedness of the relativistic Euler equations for liquid bodies in vacuum. The approach is based on a wave formulation of the relativistic Euler equations that consists of a system of non-linear wave equations in divergence form together with a combination of acoustic and Dirichlet boundary conditions. The equations and boundary conditions of the wave formulation differs from the standard one by terms proportional to certain constraints, and one of the main technical problems to overcome is to show that these constraints propagate, which is necessary to ensure that solutions of the wave formulation determine solutions to the Euler equations with vacuum boundary conditions. During the talk, I will describe the derivation of the wave equation and boundary conditions, the origin of the constraints, and how one shows that the constraints propagate. Time permitting, I will also discuss how energy estimates can be obtained from this new formulation paying particular attention to the role of the acoustic boundary conditions.

uk: вхід без авторизації

name: Dynamical relativistic liquid bodies: local-in-time existence and uniqueness

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

uk: вхід без авторизації

name: Asymptotic properties of linear field equations in anti-de Sitter space


uk: Математика, природничі науки

description: In theoretical physics, it is often conjectured that a correspondence exists between the gravitational dynamics of asymptotically Anti-de Sitter (aAdS) spacetimes and a conformal field theory of their boundaries. In the context of classical relativity, one can attempt to rigorously formulate such a correspondence statement as a unique continuation problem for PDEs: Is an aAdS solution of the Einstein equations uniquely determined by its data on its conformal boundary? In this talk, we report on recent progress in this direction, and we highlight the connections between correspondence conjectures in physics, unique continuation theory for wave equations, and the geometry of aAdS spacetimes. We discuss recent unique continuation theorems for waves on aAdS spacetimes that form the key step toward correspondence results, as well as novel geometric obstructions to these results. As an application, we provide an answer to the following question: when can a symmetry on the conformal boundary be extended into the interior? This is mostly joint work with Gustav Holzegel (Imperial College London).

uk: вхід без авторизації

name: Correspondence and Rigidity Results on Asymptotically Anti-de Sitter Spacetimes


uk: Математика, природничі науки

uk: вхід без авторизації

name: Uniform boundedness and continuity at the Cauchy horizon for linear waves on Reissner--Nordström--AdS black holes


uk: Математика, природничі науки

description: When investigating quantum or semiclassical phenomena in a general relativistic context one usually resorts to quantum field theory in curved spacetime. However, traditional quantization methods rely on foliating spacetime into spacelike hypersurfaces or on fixing asymptotic boundary conditions in time. This is a serious limitation if for the problem of interest no suitable Cauchy hypersurfaces exist and/or if boundary conditions are naturally given on timelike hypersurfaces, either at finite locations or asymptotically. I will outline methods of quantization adapted to such situations and the conceptual insights on which they are based. If time permits I will comment on how this may contribute to the search for a quantum theory of gravity.

uk: вхід без авторизації

name: Quantization on timelike hypersurfaces in curved spacetime


Orthogonality of Kerr quasinormal modes

uk: Математика, природничі науки

description: For linear perturbations of black hole spacetimes, the ringdown is described by quasinormal modes. Quasinormal modes are resonance states, defined by ingoing and outgoing radiation conditions at the horizon and infinity. Their wavefunctions do not lie in a Hilbert space, and they do not in general form a complete basis. In particular, there is a priori no obvious inner product under which they are orthonormal. In contrast to normal modes, this limits efforts to carry out higher order perturbation theory in terms of quasinormal modes. In this work, we show that for type D spacetimes with a t-φ reflection symmetry, gravitational quasinormal modes are in fact orthogonal. We work in terms of Weyl scalars. On this space we define a symmetric bilinear form ⟨⟨·, ·⟩⟩ in terms of the symplectic form for the Teukolsky equation on a Cauchy surface Σ and the t-φ reflection operator. (Our bilinear form is motivated by earlier work of Leung, Liu, and Young [Phys. Rev. A 49, 3057 (1994)].) The bilinear form is complex-linear in both entries, it is independent of the precise choice of Σ, and the time-evolution operator is symmetric with respect to ⟨⟨·, ·⟩⟩. It follows that quasinormal modes are orthogonal with respect to ⟨⟨·, ·⟩⟩ and have finite norm. We also relate the bilinear form on Weyl scalars to bilinear forms on the spaces of metric perturbations and Hertz potentials. The formula for a quasinormal mode excitation coefficient emerges naturally as the projection of initial data onto the quasinormal mode, however this projector also extends to data consisting of quasinormal modes. By projecting with the bilinear form, our goal is to develop a framework for higher order black hole perturbation theory in terms of quasinormal modes.

uk: вхід без авторизації


keywords:
Vegeted Filter Strip
Macropores
Preferential Flow
Undisturbed soil monolith

de: Geowissenschaften (ohne Geographie)

uk: Науки про Землю(крім географії)

en: Geosciences (excl. Geography)

uk: Математика, природничі науки

description: Artificial runoff experiments revealed high share of macropores and, thus, preferential flow in vegeted filter strip (VFS) soils. These are most likely due to higher organismal activity, e.g., earthworm channels. They cause a rapid transport of parts of the surface runoff to subsoil layers, but may also cause a complete bypass of VFS. Accordingly, the type and extent of flow pathways needs to be acknowledged and accounted for in VFS designs.

uk: вхід без авторизації

name: Macropore Outlet: Earthworm channel outlest drain most of the colected percolating and laterally exported water


de: Geschichte

uk: Історія

en: History

de: Geisteswissenschaften

uk: Гуманітарні науки

en: Humanities

description: Das Gebiet zwischen Maas im Westen und Harz im Osten, zwischen Main im Süden und Cloppenburger Hochgeest im Norden ist vom 3.-1. Jh. v. Chr. zwar stark von der gemeinhin als "keltisch" angesehenen Latènekultur beeinflusst, ist dieser aber nicht zuzurechnen. Es gilt traditionell als Kontakt- oder Zwischenzone zwischen Kelten und Germanen. Bernhard Sicherl behandelt in seinem Montagsvortrag die Fragen der regionalen Differenzierung – und deren Interpretation, Fragen nach der sozialen Gliederung sowie nach der Funktion der für die nördlichen Mittelgebirge typischen Wallanlagen. Dabei soll einerseits der Forschungsstand skizziert werden, anderseits sollen Entwicklungen der letzten Dekate benannt werden, die Fragen die zukünftige Forschung aufwerfen.

uk: вхід без авторизації

name: Zwischen vielen Fragezeichen. Zum Nordrand der Mittelgebirgszone im 3.–1. Jahrhundert v. Chr.

name: Niedersächsisches Landesamt für Denkmalpflege (NLD)


uk: Математика, природничі науки

uk: вхід без авторизації

name: Rigidity and flexibility of periodic frameworks: Recent progress and open questions


uk: Математика, природничі науки

description: In materials science, auxetic behavior refers to the rather unusual property of a material to laterally expand, rather than shrink, when stretched in some direction. Only sporadic examples are known. I will present a brief survey of the geometric theory of auxetic behavior for periodic bar-and-joint frameworks, as introduced in a series of recent papers by Ciprian Borcea and myself. The theory leads to new principles for designing an abundance of frameworks that provably support auxetic deformations. It also leads to effective algorithms for deciding when a given framework allows, infinitesimally, an auxetic deformation. We have developed code to effectively test for the auxetic property on frameworks built from crystal databases. I will conclude with a summary of the current challenges and some preliminary results. This is joint work with Ciprian Borcea (Rider U.) and Juan Castillo (Harvard U.). Our project was supported by a 2018-19 Harvard Radcliffe IAS Fellowship.

uk: вхід без авторизації

name: Searching for auxetic behavior in periodic frameworks


uk: Математика, природничі науки

description: Authors: Sangmin Lee, Erin G. Teich, Michael Engel, and Sharon C. Glotzer Complex crystallization pathways occur in a variety of systems both in nature and in simulations and experiments. These systems transition from the fluid phase to the solid phase, not via classical nucleation and growth, but rather through the emergence of single or multiple structural precursors in the fluid, which then give rise to the crystallization of the solid phase. The influence of these precursors on the solid phase crystallization, and the structural characteristics of the prenucleation phases, have yet to be fully elucidated. Here, we report three instances of two-step crystallization of hard-particle fluids, in which crystallization proceeds via a high-density precursor fluid phase with prenucleation motifs in the form of clusters, fibers and layers, and networks, respectively. These are motifs of varying dimension and complexity. We explore the influence that the dimension of these prenucleation motifs has on the crystallization process, and we structurally and dynamically characterize each crystallization event. The crystals that form are complex, including, notably, a crystal with 432 particles in its cubic unit cell. Our results establish the existence of two-step crystallization pathways in entropic systems and showcase the accompanying variety of prenucleation structures that are possible.

uk: вхід без авторизації

name: Multi-step entropic colloidal crystallization pathways


Soft packings

uk: Математика, природничі науки

description: A {\it soft ball packing of unit balls with outer radius λ>0}, is a family of pairs of concentric closed balls, one with radius 1+λ, called a {\it soft ball}, and the other one with unit radius, called the {\it core} of the soft ball. In this talk I review results related to soft ball packings of unit balls, and some related concepts. Most of the presented results are joint work with K. Bezdek.

uk: вхід без авторизації


uk: Математика, природничі науки

description: We study combinatorial properties of families of simple 3-dimensional polytopes defined by their cyclic and strongly cyclic k-edge-connectivity. Among them are flag polytopes and Pogorelov polytopes, which are polytopes realizable in the Lobachevsky (hyperbolic) space L3 as bounded polytopes of finite volume with right dihedral angles. The latter class contains fullerenes — simple 3-dimensional polytopes with only pentagonal and hexagonal faces. We focus on combinatorial constructions of families of polytopes from a small set of initial polytopes by a given set of operations. Here we will present the classical result by V.Eberhard (1891) for all simple 3-polytopes, more recent results by A.Kotzig (1969), D.Barnette (1974, 1977), J.Butler (1974), T.Inoue (2008), and V.D.Volodin (2011), and their improvements by V.M.Buchstaber and the author (2017-2019). For fullerenes we have a more strong result. We also study polytopes realizable in L3 as polytopes of finite volume with right dihedral angles. On the base of E.M. Andreev's theorem (1970) we prove that cutting off ideal vertices defines a one-to-one correspondence with strongly cyclically 4-edge-connected polytopes different from the cube and the pentagonal prism. We show that any polytope of the latter family is obtained by cutting off a matching of a polytope from the same family or the cube with at most two nonadjacent orthogonal edges cut producing all the quadrangles. We refine D.Barnette's construction of this family of polytopes and give its application to right-angled polytopes. We refine the construction of ideal right-angled polytopes by edge-twists described in the survey by A.Yu.Vesnin (2017) on the base of results by I.Rivin (1996) and G.Brinkmann, S.Greenberg, C.Greenhill, B.D.McKay , R.Thomas, and P.G.Wollan (2005), and analyse its connection to D.Barnette's construction via perfect matchings. We make a conjecture on behaviour of volume under operations generalizing results by T.Inoue (2008) and give arguments confirming it.

uk: вхід без авторизації

name: Combinatorics and hyperbolic geometry of families of 3-dimensional polytopes: fullerenes and right-angled polytopes


uk: Математика, природничі науки

description: As early as 1985, Landau free-energy models [1-3] and density-functional mean-field theories [4] were introduced in an attempt to explain the stability of quasicrystals, with only partial success if any. It is only in recent years, that great progress has been made in understanding the thermodynamic stability of quasicrystals in such simple isotropic classical field theories. Much of this has happened thanks to insight from the experimental observation of quasicrystalline order in diverse systems ranging from fluid dynamics to soft condensed matter. The key to unlocking the stability puzzle was in the realization that more than a single length scale was required, but more importantly in figuring out how to introduce these multiple scales into the models, and identifying the remaining requirements [5,6]. We and others have since managed to produce Landau and other mean-field theories with a wide range of quasicrystals as their minimum free-energy states, and have also confirmed some of these theories using molecular dynamics simulations with appropriately designed inter particle potentials [7-12]. I shall give a quick overview of the quasicrystals that can be stabilized in these theories—in systems of one or two types of particles, in two and in three dimensions—and attempt to identify a trend that might be emerging in going from Landau theories to more realistic density-functional mean-field theories. It remains an open question whether this trend may eventually lead to understanding the stability of quasicrystals in complex metallic alloys. This research is supported by Grant No. 1667/16 from the Israel Science Foundation. [1] P. Bak, Phys. Rev. Lett. 54, 1517 (1985). [2] N.D. Mermin, S.M. Troian, Phys. Rev. Lett. 54, 1524 [Erratum on p. 2170] (1985). [3] P.A. Kalugin, A.Yu. Kitaev, L.C. Levitov, JETP Lett. 41, 145 (1985). [4] S. Sachdev, D.R. Nelson, Phys. Rev. B 32, 4592 (1985). [5] R. Lifshitz, H. Diamant. Phil. Mag. 87, 3021 (2007). [6] R. Lifshitz, D. Petrich, Phys. Rev. Lett. 79, 1261 (1997). [7] K. Barkan, H. Diamant, R. Lifshitz, Phys. Rev. B 83, 172201 (2011). [8] A.J. Archer, A.M. Rucklidge, E. Knobloch, Phys. Rev. Lett. 111, 165501 (2013). [9] K. Barkan, M. Engel, R. Lifshitz, Phys. Rev. Lett. 113, 098304 (2014). [10] C. V. Achim, M. Schmiedeberg, and H. Löwen, Phys. Rev. Lett. 112, 255501 (2014). [11] P. Subramanian, A.J. Archer, E. Knobloch, A.M. Rucklidge, Phys. Rev. Lett. 117, 075501 (2016). [12] S. Savitz, M. Babadi, R. Lifshitz, IUCrJ 5, 247 (2018). [13] M.C. Walters, P. Subramanian, A.J. Archer, R. Evans, Phys. Rev. E 98, 012606 (2018). [14] S. Savitz, R. Lifshitz, “Self-assembly of body-centered icosahedral cluster crystals”, presentation at this conference (2019).

uk: вхід без авторизації

name: Thermodynamic stability of quasicrystals: From fluid dynamics to soft condensed matter


uk: Математика, природничі науки

description: Authors: Jaeuk Kim and Salvatore Torquato\\ Disordered hyperuniform packings (or dispersions) are unusual amorphous states of two-phase materials that are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in disordered hyperuniform materials, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a “bounded-cell” condition, hard particles are placed inside each cell such that the volume fraction of this cell occupied with these particles becomes identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit. We numerically implement this procedure to two distinct types of initial tessellations; Voronoi and sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in two and three dimensions. Application to sphere tessellations establishes the hyperuniformity of the classical Hashin-Shtrikman coated-spheres structures that possess optimal effective transport and elastic properties.

uk: вхід без авторизації

name: Tessellation-Based Procedure to Construct Perfectly Hyperuniform Disordered Two-Phase Packings


uk: Математика, природничі науки

description: Jean Taylor, currently at University of California, Berkeley. Marjorie and I are interested in how crystals grow, especially how quasicrystals grow. In the case of multi-element alloys, it is highly likely to be by formation and then aggregation of clusters. There are many reasons to suspect icosahedral order may be important in forming many clusters; periodicity or quasiperiodicity would then arise from how these local clusters aggregate. Overlapping rhombic triacontahedra (RTs) are central to describing physical crystals with local or global icosahedral symmetry; structures derived from these overlapping RTs are a key to understanding how such crystals might grow and to unifying their presentations. Might overlapping rhombic icosahedra (RIs) also be useful to understanding how crystals and quasicrystals with local or global 5-fold symmetry can be described? Perhaps they could also be a key to how they might grow? I will describe both our suggestions as to how this might all work out and our search for evidence in physical crystals and quasicrystals.

uk: вхід без авторизації

name: A hunt for new descriptions of old quasicrystals via soft-packing


uk: Математика, природничі науки

description: Zeolites (zeo = boil; lithos = stone) are microporous, aluminosilicate minerals commonly used as commercial adsorbents and catalysts. In 1973 the book "Zeolite molecular sieves: structure, chemistry and use" (771pp) by Donald W. Breck appeared. At that time 27 zeolite framework types were known. In 2007, the 6'th edition of the Atlas of Zeolite Framework Types describes 176 known distinct approved types. Zeolites occur naturally but are also produced industrially on a large scale. Combinatorially, zeolites are line graphs of 4-regular graphs and may be finite. However, it is not always possible to realize a combinatorial zeolite as a unit distance graph in 3-space. Mike Winkler found a saturated tetrahedral packing consisting of only 12 tetrahedra. It is not known yet if the packing is rigid. A 16 vertex model was shown to have at least two degrees of freedom. We try to give an overview of recent results and open problems.

uk: вхід без авторизації

name: From combinatorial zeolites to geometric realizations


Log-optimal spherical configuration

uk: Математика, природничі науки

description: We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attains its relative minima at configurations that consist of two orthogonal to each other regular simplices of cardinality m and n, where m+n=d+2. The global minimum occurs when m=n if d is even and m=n+1 otherwise. This characterizes a new class of configurations that minimize the logarithmic energy on the (d-1)-sphere for all d. The other two classes known in the literature, the regular simplex and the cross polytope, are both universally optimal configurations. This is a joint work with Peter Dragnev.

uk: вхід без авторизації


Gordian Unlinks

uk: Математика, природничі науки

description: Given a sufficiently nice embedded space curve, we can thicken it into a physical rope. A pair of physical configurations is Gordian if there is no physical isotopy that takes one to the other. It is an (old) open problem to describe a Gordian unknot. We will explore some special configurations of physical links by considering extrusion along with various packing constraints. This is a dual perspective to the topological sweep-out procedure Coward and Hass used to first describe a Gordian split link. There are some advantages that appear with our shifted view; we trade a general statement about knots and surfaces for tighter area bounds and rigidity, severely constraining the character of certain physical isotopies. In the end, we claim this is sufficient to describe a Gordian Unlink. Related to work with Rob Kusner, Greg Buck.

uk: вхід без авторизації


uk: Математика, природничі науки

description: One of the methods in the design of new materials is to predict the crystal structure of a new compound from it’s molecular composition. This process involves generating many hypothetical structures based on lattice energy optimization. A different approach based only on the geometry of a molecule with it’s potential to speed up classical crystal structure prediction computations will be presented. Our preliminary results with regard to the periodic packing of a geometric representations of the pentacene molecule using Monte-Carlo molecular dynamic simulations will be also shown. Limitations and downsides of presented approach will be discussed, and future directions will be proposed.

uk: вхід без авторизації

name: Dense periodic packings in the light of crystal structure prediction


uk: Математика, природничі науки

description: The spreading of bacterial colonies at solid–air interfaces is determined by the physico-chemical properties of the involved interfaces and bioactive growth processes. The production of surfactant molecules by bacteria is a widespread strategy that allows the colony to efficiently expand over the substrate. On the one hand, surfactant molecules lower the surface tension of the colony, effectively increasing the wettability of the substrate, which facilitates spreading. On the other hand, gradients in the surface concentration of surfactant molecules result in Marangoni flows that drive spreading. These flows may cause an instability of the circular colony shape and the subsequent formation of fingers. In this work, we study the effect of bacterial surfactant production and substrate wettability on colony growth and shape within the framework of a hydrodynamic thin film model. We show that variations in the wettability and surfactant production are sufficient to reproduce four different types of colony growth, which have been described in the literature, namely, arrested and continuous spreading of circular colonies, slightly modulated front lines and the formation of pronounced fingers.

uk: вхід без авторизації

name: Spreading strategies and morphology of bacterial colonies: Interplay between passive physico-chemical effects and bioactive growth

name: Banff International Research Station (BIRS) for Mathematical Innovation and Discovery


uk: Математика, природничі науки

description: We discuss the use of feedback control in suppressing the inertial instabilities of a falling liquid film. In this setup, an input to the system, e.g. local fluid injection, is chosen in response to real time observations of the interface shape. If the control scheme is designed with perfect knowledge of the governing equations and implemented with access to instantaneous observations of the entire system state, feedback control offers almost unlimited scope to change the system dynamics. Both of these requirements fail in any practical implementation, but we would hope to be able to achieve effective control strategies based on reasonably accurate models and observations of only a few key variables. Falling liquid films have a hierarchy of long-wave models of increasing complexity, which offers an ideal environment to explore robustness to model choice. We find that the success of control schemes based on low order models is dependent on the method of actuation chosen; injection of fluid has a direct effect on interface dynamics and simple control strategies work well across many models, while selective substrate heating has a much more subtle effect on dynamics and control schemes are correspondingly more sensitive to details of the flow.

uk: вхід без авторизації

name: Feedback control of falling liquid films


uk: Математика, природничі науки

description:
Colloidal forces are known to influence the pattern deposition of nanoparticles off a volatile carrier liquid. Several experimental studies suggest a direct connection between colloidal forces and the morphology of the particulate deposit [1,2,3]. Specifically, variations in the zeta potential of the suspended particles and substrate; and variations in the ionic strength in the suspension were found to alter the geometry of the deposit. We use theory and experiment to investigate the connection between colloidal forces and the pattern deposition of colloidal particles off a volatile carrier liquid. We connect between colloidal forces and pattern deposition by considering the adhesion of particles to the solid substrate and the coagulation of particles in the suspension [4,5]. Our initial theoretical approach is based on an asymptotic – long wave type – model for the deposition process. In this model we employ the interaction–force boundary layer theorem to account for the rate of adhesion of particles to the solid substrate. The theorem allows for manifesting the dynamic process of adhesion in a form that is reminiscent of a first order chemical reaction in a dynamic advection-diffusion equation for the transport of particle mass in the liquid. Similarly, we employ the augmented Smoluchowski theorem to account for particle aggregation. Hence, the rate of aggregation is manifested in a form that is reminiscent of multiple second order chemical reactions. The coefficients of the reaction terms are associated with the energy barriers for adhesion or coagulation. Comparing the predictions of our asymptotic model to experiment, we find that the rate of adhesion, coagulation, and diffusion of particles in the volatile liquid as well as the rate of liquid evaporation govern the deposition of particles. Moreover, fast adhesion of particles to the solid substrate and fast diffusion of particles in the liquid disperse the spatial distribution of the particulate deposit. Fast coagulation and fast evaporation support the deposition of denser patterns of particles of sharper spatial boundaries. A different theoretical approach for modelling the deposition problem, which we currently pursue, is to employ phase change type energy functional to account for particle coagulation and adsorption in the volatile liquid film. Such an approach should naturally incorporate the physics associated with concentrated particulate systems and particle volume effects that are not accounted for in the current asymptotic model. References 1. R. Bhardwaj, X. Fang, et al. Self-Assembly of Colloidal Particles from Evaporating Droplets: Role of DLVO Interactions and Proposition of a Phase Diagram, Langmuir 26 (7833–7842) 2010 2. M. Anyfantakis, Z. Geng, et al. Modulation of the Coffee-Ring Effect in Particle/Surfactant Mixtures: the Importance of Particle−Interface Interactions
. Langmuir 31 ( 4113–4120) 2015 3. E. Homede, A. Zigelman, et al. Signatures of van der Waals and electrostatic forces in the deposition of nanoparticle assemblies; J. Phys. Chem. Lett. 9 (5226–5232) 2018 4. A. Zigelman and O Manor. Simulations of the dynamic deposition of colloidal particles from a volatile sessile drop, J. Colloids Interface Sci. 525 (282-290) 2018 5. A. Zigelman and O. Manor. The deposition of colloidal particles from a sessile drop of a volatile suspension subject to particle adsorption and coagulation, J. Colloids Interface Sci. 509 (195) 2018

uk: вхід без авторизації

name: Pattern deposition of colloidal particles


uk: Математика, природничі науки

description: We will describe the derivation of a nonlinear evolution equation that describes space-time self-organization at the free surface of a solid target undergoing irradiation by an energetic ion beam. Under this type of driving, for many materials the outermost surface layer of the target responds as a highly viscous fluid, displaying formation of nanoscale ripples in macroscopic time scales. In spite of the irrelevance of gravity at these small distances, the weakly nonlinear limit of the equation resembles the well known description of a macroscopic incompressible viscous thin film flowing down an incline, which is a paradigmatic instance of free surface flow systems for which the morphological instability responsible for pattern formation is controlled by inertial effects. The predictive power of the evolution equation for ion-beam surface nanopatterning underscores nonlinear effects that might have been expected to be of a secondary importance in such a nanoscopic-scale, Stokes-flow system. The content of this talk is joint work with Mario Castro (Universidad Pontificia Comillas) and Javier Muñoz-García (UC3M).

uk: вхід без авторизації

name: Nanofluid down an incline: nonlinear description of ion-induced solid flow


uk: Математика, природничі науки

description: This talk focuses on the flow of a solidifying liquid film on a solid surface subject to a complex kinematics, a process relevant to pancake making or surface coating. The key question this study aims to address is: what is the optimal surface kinematics in order to spread the liquid layer uniformly on the surface? We present an optimal control method based on an adjoint formulation of governing partial differential equation. Key benefits of this method are that no assumption is required on the functional form of the controls and that significant improvement in thickness uniformity can be achieved at a low computational cost.

uk: вхід без авторизації

name: Pancake making and surface coating: optimal control of a liquid film


uk: Математика, природничі науки

description: Asymptotic methods yield an efficient leading-order model of flow along a thin curved duct. The flow consists of a primary axial component along the duct and, because of the curvature, a secondary “Dean flow” in the cross section. Such flows are used in microfluidics to sort suspended particles by size; an important application is “liquid biopsy”, the isolation of a particular cell type within a (dilute) cell suspension. A description of the background flow, in the absence of particles, is pre-requisite to modelling the perturbation caused by a particle and the migration of the particle within the duct cross-section. I will discuss the suitability of a thin-film model for this purpose. Time permitting, I will also discuss the use of asymptotic methods for modelling of particle migration.

uk: вхід без авторизації

name: Thin film flow and particle sorting in a curved duct


uk: Математика, природничі науки

description: Modeling of partial differential equations is an art that leaves the scientists with a choice of what is deemed important, e.g., mathematical well-posendess, conservation laws, thermodynamic consistency, … ,or just simplicity - in multiphysics settings this calls for appropriate modeling strategies. In this talk, a thermodynamics inspired strategy for the modeling of free boundary flows with moving contact lines will be revisited. It will be argued that this mathematical structure is not just useful for modeling but also for the numerical approximation of solutions. Furthermore, possible strategies for their extension to non-smooth settings will be shortly motivated, e.g., hysteresis and particulate flows.

uk: вхід без авторизації

name: Dynamic contact angles via generalized gradient flows


uk: Математика, природничі науки

description: The long-wave dynamics of an elastic sheet lubricated by a thin layer of viscous fluid on a wetting substrate is examined using both numerical simulations and a quasistatic model. As a continuum model for a lipid bilayer, the elastic sheet has a electric capacitance that stores changes across the membrane. Within the lubrication framework we investigate the electrohydrodynamics of the thin film coupled to the capacitive elastic membrane. Novel nonlinear dynamics is found and results are useful to understand electroformation, a standard experimental procedure to fabricate unilamellar vesicles from planar lipid bilayer membrane. We also extend this theoretical framework to investigate the rupture of vesicles when settled onto a glass substrate in an ionic solution.

uk: вхід без авторизації

name: Long-wave dynamics of a lubrication layer under an inextensible elastic membrane


uk: Математика, природничі науки

description: The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. Solitary-pulse solutions exist under certain conditions. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.

uk: вхід без авторизації

name: Two dimensional pulse dynamics on electrified falling films


uk: Математика, природничі науки

description: Catalysts are usually made of a dense but porous material such as activated carbon, zeolites, etc. that provide a large surface area. Liquids that are produced as a by-product of a gas reaction at the catalyst site transport to the surface of the porous material, slowing down transport of the gaseous reactants to the catalyst active site. Understanding the dynamics of the liquid films in the gas channel is critical to maintain performance and durability of the catalyst assembly. We develop a mathematical model for liquid films dynamics and study different regimes.

uk: вхід без авторизації

name: Motion of Liquid Films in the Gas Channels