Related papers: Lattice Model with Nearest-Neighbor and Next-Neare…
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…
The equilibrium properties of the lattice fluid with the repulsion between the nearest neighbors on the two-level planar triangular lattice are investigated. The numerical results obtained from the analytical expressions are compared with…
In this paper we propose a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The two lattices have slightly different lattice parameters and there is a small…
The result of 2-dimensional Gaussian lattice fit to a speckle intensity pattern based on a linear model that includes nearest-neighbor interactions is presented. We also include a Monte Carlo simulation of the same spatial speckle pattern…
Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and predict the emergence…
In the present work, we highlight the significant effect that the simplest beyond nearest neighbor interactions can have on two-dimensional dynamical lattices. To do so, we select as our case example the closest further neighbor, namely the…
We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, crystal, in characteristic relationship to each other. As the parameters of the model are varied one obtains characteristic patterns of phase…
We present a simple model which allows to investigate equilibrium aspects of molecular recognition between rigid biomolecules on a generic level. Using a two-stage approach, which consists of a design and a testing step, the role of…
A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential…
For an interacting system of N electrons, we study the conditions under which a lattice model of size L with nearest neighbor hopping t and U/r Coulomb repulsion has the same ground state as a continuum model. For a fixed value of N, one…
We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais…
Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…
Using Monte Carlo Simulation and fundamental measure theory we study the phase diagram of a two-dimensional lattice gas model with a nearest neighbor hard core exclusion and a next-to-nearest neighbors finite repulsive interaction. The…
Lattice model with long-range interaction of power-law type that is connected with difference of non-integer order is suggested. The continuous limit maps the equations of motion of lattice particles into continuum equations with fractional…
We establish the most general form of the discrete elasticity of a 2D triangular lattice embedded in three dimensions, taking into account up to next-nearest neighbour interactions. Besides crystalline system, this is relevant to biological…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrodinger equation. Our approach offers a systematic way of analyzing the existence and…
With the maturation of differentiable physics, its role in various downstream applications: such as model predictive control, robotic design optimization, and neural PDE solvers, has become increasingly important. However, the derivative…
Recently, graph (network) data is an emerging research area in artificial intelligence, machine learning and statistics. In this work, we are interested in whether node's labels (people's responses) are affected by their neighbor's features…