相关论文: On VC-density in VC-minimal theories

Fluids made of two-dimensional hard particles with polygonal shapes may stabilize symmetries which do not result directly from the particle shape. This is due to the formation of clusters in the fluid. Entropy alone can drive these effects,…

We prove a density version of the Carlson--Simpson Theorem. Specifically we show the following. For every integer $k\geq 2$ and every set $A$ of words over $k$ satisfying \[\limsup_{n\to\infty} \frac{|A\cap [k]^n|}{k^n}>0\] there exist a…

We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation…

The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…

We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the…

Recent progress on molecular theories of hydration of nonpolar solutes in aqueous solution has led to new ways of thinking about the old issue of free, or "available," volume in liquids. This article surveys the principal new results with…

We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions…

An accurate description of a columnar liquid crystal of hard disks at high packing fractions is presented using an improved free-volume theory. It is shown that the orientational entropy of the disks in the one-dimensional fluid direction…

We present the first measurement of the vortex free-energy order parameter at weak coupling for SU(2) in simulations employing multihistogram methods. The result shows that the excitation probability for a sufficiently thick vortex in the…

We consider the model of viscous compressible homogeneous multi-fluids with multiple velocities. We review different formulations of the model and the existence results for boundary value problems. We analyze crucial mathematical…

The classical double bubble theorem characterizes the minimizing partitions of $\mathbb{R}^n$ into three chambers, two of which have prescribed finite volume. In this paper we prove a variant of the double bubble theorem in which two of the…

We present a simple yet accurate numerical approach to compute the free energy of binding of multivalent objects on a receptor-coated surface. The method correctly accounts for the fact that one ligand can bind to at most one receptor. The…

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…

Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…

In this paper we derive a formula for the density of states in the presence of inelastic scattering in the quantum well of a double barrier structure as a function of a characteristic time of the motion of electrons (namely, the round trip…

We investigate the asymptotic rates of length-$n$ binary codes with VC-dimension at most $dn$ and minimum distance at least $\delta n$. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a…

We discuss minisuperspace models within the framework of varying physical constants theories including $\Lambda$-term. In particular, we consider the varying speed of light (VSL) theory and varying gravitational constant theory (VG) using…

The collective variable representation (CV) of classical statistical systems such as simple liquids has been intensively developed by the Ukrainian school after seminal works by Prof. Ihor Yukhnovskii. The basis and the structure of the CV…

We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…

We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the…