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We study the steady state of an assembly of microtubules in a confined volume, analogous to the situation inside a cell where the cell boundary forms a natural barrier to growth. We show that the dynamical equations for growing and…
We consider for a small parameter $\varepsilon >0$ a parabolic convection-diffusion problem with P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in a three-dimensional graph-like junction consisting of thin curvilinear cylinders…
We study the bound states of two-dimensional bright solitons in nonlocal nonlinear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady…
A model of strongly inhomogeneous medium with simultaneous perturbation of rigidity and mass density is studied. The medium has strongly contrasting physical characteristics in two parts with the ratio of rigidities being proportional to a…
We analytically study plasma solitary waves, or solitons, in a two-dimensional (2D) electron system (ES) placed in close proximity to and between two ideal metallic gates. As a rule, solitons are described using a perturbative approach…
We study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori…
Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…
In a two-band system, both conventional sign-preserving $s_{++}$ and unconventional sign-changing $s_{\pm}$ superconducting state may appear at low temperatures. Moreover, they may transform from one to another due to the impurity…
We consider a prototypical "stretching plus bending" functional of an elastic shell. The shell is modeled as a d-dimensional Riemannian manifold endowed, in addition to the metric, with a reference second fundamental form. The shell is…
Here we present an explicit counterexample to a bimodality concept as the unique signal of first order phase transition. Using an exact solution of the simplified version of the statistical multifragmentation model we demonstrate that the…
We consider a two-dimensional (2D) nonlinear Schrodinger equation with self-focusing nonlinearity and a quasi-1D double-channel potential, i.e., a straightforward 2D extension of the well-known double-well potential. The model may be…
A semi-linear parabolic problem is considered in a thin $3D$ star-shaped junction that consists of several thin curvilinear cylinders that are joined through a domain (node) of diameter $\mathcal{O}(\varepsilon).$ The purpose is to study…
Consider the projection of an $n$-dimensional random vector onto a random $k_n$-dimensional basis, $k_n \leq n$, drawn uniformly from the Haar measure on the Stiefel manifold of orthonormal $k_n$-frames in $\mathbb{R}^n$, in three different…
We study the asymptotic behaviour of eigenvalues and eigenfunctions of 2D vibrating systems with mass density perturbed in a vicinity of closed curves. The threshold case in which resonance frequencies of the membrane and thin inclusion…
We consider a disordered two-dimensional electronic system in the limit of high magnetic field at the metal-insulator transition. Density of states close to the Fermi level acquires a divergent correction to the lowest order in…
In this paper we consider a family of three-dimensional problems in thermoelasticity for linear elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero.We fully characterize with strong…
We propose a dynamical protocol to probe the rigidity and phase coherence of dipolar supersolids by merging initially separated fragments in quasi-one-dimensional (1D) double-well potentials. Simulations based on the extended…
This paper investigates the asymptotic behaviors of time-harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high-contrast material parameters. We derive sharp asymptotic estimates and…
We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…