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An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…
We provide a comprehensive overview of the current theoretical understanding of the dynamic structure factor of stiff polymers in semidilute solution based on the wormlike chain (WLC) model. We extend previous work by computing exact…
Assuming that a plane partition of the positive integer $n$ is chosen uniformly at random from the set of all such partitions, we propose a general asymptotic scheme for the computation of expectations of various plane partition statistics…
Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the…
We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and…
Inspired by the works of Dewar, Murty and Kot\v{e}\v{s}ovec, we establish some useful theorems for asymptotic formulas. As an application, we obtain asymptotic formulas for the numbers of skew plane partitions and cylindric partitions. We…
We study cumulants of numbers of $q$-step walks on Erd\"os-R\'enyi-type random graphs of long-range percolation radius model in the limit when the number of vertices $N$, concentration $c$, and the interaction radius $R$ tend to infinity.…
One of the most promising routes to non-fermi liquids and strange metals has been through SYK models \cite{Sachdev:2010um}, which necessarily involve large flavor degrees of freedom and interactions with imposed disorder. We introduce an…
A general expression was obtained for the dynamic energy of the van der Waals interaction of a neutral atom with a flat slit whose walls are characterized by a frequency-dependent dielectric permittivity. The interaction of cesium atoms…
This study considers the spreading of a Newtonian and perfectly wetting liquid in a square array of cylindric micropillars confined between two plates. We show experimentally that the dynamics of the contact line follows a Washburn-like law…
Interfacial properties of colloid--polymer mixtures are examined within an effective one--component representation, where the polymer degrees of freedom are traced out, leaving a fluid of colloidal particles interacting via polymer--induced…
Multifractal analysis of multiplicative random cascades is revisited within the framework of {\em mixed asymptotics}. In this new framework, statistics are estimated over a sample which size increases as the resolution scale (or the…
The propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally…
Condensates of active particles such as cells form almost-crystalline lattices which play a central role in many biological systems. Typically, their properties have been determined merely by analogy to the rather trivial one-dimensional…
In this paper, starting from the Born-Green-Yvon (BGY) equation, we derive a general expression for the contact value of the singlet distribution function near a hard wall for anisotropic fluids. This relation includes two separate…
This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…
We consider a recurrent random walk of i.i.d. increments on the one-dimensional integer lattice and obtain a formula relating the hitting distribution of a half-line with the potential function, $a(x)$, of the random walk. Applying it, we…
We study oscillatory integrals in several variables with analytic, smooth, or $C^k$ phases satisfying a nondegeneracy condition attributed to Varchenko. With only real analytic methods, Varchenko's estimates are rediscovered and…
Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
We perform a Monte Carlo study of $N$-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions ($d=2$), or the tip of an impenetrable cone in $d=3$, of sizes ranging up to $N=10^6$ steps. We find that the…