Related papers: On the low-dimensional solids and their melting

Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of…

The mathematical description of stable particle-like systems appearing in relativistic quantum field theory at large, respectively small scales or non-zero temperatures is discussed.

We study the duality of moduli of k- and (n-k)-dimensional slices of euclidean n-cubes, and establish the optimal upper bound 1.

Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.

We study melting in a two-dimensional system of classical particles with Gaussian-core interactions in disordered environments. The pure system validates the conventional two-step melting with a hexatic phase intervening between the solid…

We address the question of whether solids may be distinguished from fluids by their response to shear stress

A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects.

Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice…

Melting of two-dimensional (2D) equilibrium crystals, from superconducting vortex lattices to colloidal structures, is a complex phenomenon characterized by the sequential loss of positional and orientational order. Whereas melting…

We present single soliton states and soliton-antisoliton states with an adjoint Higgs field in 4D flat space. The action of a single soliton state diverges, while the action of soliton-antisoliton states converges. This means such solitons…

In this contribution we review a series of simple one dimensional lattice models that with an appropriate choice of parameters can account for various anomalous features of the behaviour of complex systems such as water. In particular, we…

The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…

We describe the quasi-static collapse of a radiating, spherical shell of matter in de Sitter space-time using a thermodynamical formalism. It is found that the specific heat at constant area and other thermodynamical quantities exhibit…

A model problem of magneto-elastic body is considered. Specifically, the case of a two dimensional circular disk is studied. The functional which represents the magneto-elastic energy is introduced. Then, the minimisation problem, referring…

We have studied, using molecular dynamics simulations, the pressure-induced melting in a monolayer of soft repulsive spherocylinders whose centers of mass are constrained to move on the surface of a sphere. We show that the orientational…

We show analytically and numerically the existence of double vortex solutions in two-Higgs systems. These solutions are generalizations of the \no vortices and exist for all values of the parameters in the Lagrangians considered. We derive…

Two-dimensional systems may admit a hexatic phase and hexatic-liquid transitions of different natures. The determination of their phase diagrams proved challenging, and indeed those of hard-disks, hard regular polygons, and inverse…

We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order $10^7$, convection takes the…

We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.

We review a number of topics germane to higher-dimensional solitons in Bose-Einstein condensates. For dark solitons, we discuss dark band and planar solitons; ring dark solitons and spherical shell solitons; solitary waves in restricted…