Related papers: Mixing and tight polyhedra
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
Association Schemes and coherent configurations (and the related Bose-Mesner algebra and coherent algebras) are well known in combinatorics with many applications. In the 1990s, Mesner and Bhattacharya introduced a three-dimensional…
Using the Fundamental-Measure Density Functional Theory, we have studied theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting…
Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger…
Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to…
The influence of poor solvent quality on fluid demixing of a model mixture of colloids and nonadsorbing polymers is investigated using density functional theory. The colloidal particles are modelled as hard spheres and the polymer coils as…
One puzzle of neutrino masses and mixings is that they do not exhibit the kind of strong "hierarchy" that is found for the quarks and charged leptons. Neutrino mass ratios and mixing angles are not small. A possible reason for this is…
We use a microscopic density functional theory based on Wertheim's first order thermodynamic perturbation theory to study wetting behavior of athermal mixtures of colloids and excluded-volume polymers. In opposition to the wetting behavior…
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…
We propose a method for describing a phase behavior of a system consisting of particles of two sorts. The interaction of each species is described by interaction potentials containing the repulsive and attractive components. Asymmetry is…
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at…
The present work consists of a numerical study of the dynamics of irrational polygonal billiards. Our contribution reinforces the hypothesis that these systems could be Strongly Mixing, although never demonstrably chaotic, and discuss the…
In active matter, the lack of momentum conservation makes non-reciprocal interactions the rule rather than the exception. They lead to a rich set of emerging behaviors that are hard to account for and to predict starting from the…
Active systems are inherently out of equilibrium, as they collect energy from their surroundings and transform it into directed motion. A recent theoretical study suggests that binary mixtures of active particles with distinct effective…
The equilibrium phase behavior of a binary mixture of charged colloids and neutral, non-adsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere…
Polymer composites are ideal candidates for next generation biomimetic soft materials because of their exquisite bottom-up designability. However, the richness of behaviours comes at a price: the need for precise and extensive…
A Poisson system is a Poisson point process and a group action, together forming a measure-preserving dynamical system. Ornstein and Weiss proved Poisson systems over many amenable groups were isomorphic in their 1987 paper. We consider…
We consider extensions of the notion of topological transitivity for a dynamical system $(X,f)$. In addition to chain transitivity, we define strong chain transitivity and vague transitivity. Associated with each there is a notion of…