Related papers: Relaxation and 3d-2d passage with determinant type…
We construct lattice Hamiltonians with homogeneous interaction potentials which allow for explicit breather solutions. Especially we obtain exponentially localized solutions for $d$-dimensional lattices with $d=2,3$.
In this paper we apply both the procedure of dimension reduction and the incorporation of structured deformations to a three-dimensional continuum in the form of a thinning domain. We apply the two processes one after the other, exchanging…
We present a simple solution to enhance the separation ability of deterministic lateral displacement (DLD) systems by expanding the two-dimensional nature of these devices and driving the particles into size-dependent, fully…
We discuss the mechanism of truncations driven by the imposition of constraints. We show how the consistency of such truncations is controlled, and give general theorems that establish conditions for the correct uplifting of solutions. We…
The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
In [Bal18] a new method of constructing simplex designs based on cyclic group on $n$ elements has been proposed. One of the claims put forward therein is existence of 3-point simplex 3-design in dimension $d = 3$. In this manuscript we…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
We study an influence of the quenched extended defects on the critical dynamics of the d=3-dimensional systems with m-component non-conserved order parameter (model A dynamics). Considering defects to be correlated in \epsilon_d dimensions…
Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…
The determination of a dynamic law of cut is complex and often very difficult to develop. Several formulations were developed, in very complex ways being given that 3 AD crosses from there, the number of variables is much higher than out of…
On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence…
We consider a two-dimensional problem in nonlinear elasticity which corresponds to the cubic-to-tetragonal phase transformation. Our model is frame invariant and the energy density is given by the squared distance from two potential wells.…
We derive the quasiconvex relaxation of the Biot-type energy density $\lVert\sqrt{\operatorname{D}\varphi^T \operatorname{D}\varphi}-I_2\rVert^2$ for planar mappings $\varphi\colon\mathbb{R}^2\to \mathbb{R}^2$ in two different scenarios.…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…
Cooperative constraint solving is an area of constraint programming that studies the interaction between constraint solvers with the aim of discovering the interaction patterns that amplify the positive qualities of individual solvers.…
We show how reaction coordinate path lengths affect the relaxation efficiency of a complex system. To this purpose, we consider the metric contributions to the transition rates. These metric contributions preserve informations about the…