Related papers: Interaction-round-a-face and consistency-around-a-…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors.…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
This work lies at the intersection of Gibbs models and hyperuniform point processes. Classical Gibbs models, whether defined on lattices or in continuous space, provide flexible tools to describe interacting particle systems but are…
Calibration of fixtures in robotic work cells is essential but also time consuming and error-prone, and poor calibration can easily lead to wasted debugging time in downstream tasks. Contact-based calibration methods let the user measure…
A simple model to study interacting instabilities and textures of resulting patterns for thermal convection is presented. The model consisting of twelve-mode dynamical system derived for periodic square lattice describes convective patterns…
The fundamental tension between availability and consistency shapes the design of distributed storage systems. Classical results capture extreme points of this trade-off: the CAP theorem shows that strong models like linearizability…
A rational face cuboid is a cuboid that all of edges, two of three face diagonals and space diagonal have rational lengths. \[ E_{1,s}: y^2=x(x-(2s)^2)(x+(s^2-1)^2) \] for a rational number $s \neq 0, \pm 1$, and define $\tilde{A}$…
We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral…
We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We study equilibrium density and spin density profiles for a model of cold one-dimensional spin 1/2 fermions interacting via inverse square interaction and exchange in an external harmonic trap. This model is the well-known spin-Calogero…
We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
By solving the Young Laplace equation of capillary hydrostatics one can accurately determine equilibrium shapes of droplets on relatively smooth solid surfaces. The solution, however of the Young Laplace equation becomes tricky when a…
For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution of vector fields, the problem of its integration is considered. Among the many approaches to this problem, solvable structures provide a…
We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…
Finite volume multiple-particle interaction is studied in a two-dimensional complex $\phi^4$ lattice model. The existence of analytical solutions to the $\phi^4$ model in two-dimensional space and time makes it a perfect model for the…
The symmetry and topology of the coincidence structure, i.e. the locus of points in configuration space corresponding to particles in the same position, plays a critical role in extracting universal properties for few-body models with…
Interface localised interactions are studied for multiscalar universality classes accessible with the perturbative $\varepsilon$ expansion in $4-\varepsilon$ dimensions. The associated beta functions at one loop and partially at two loops…
We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although…