Related papers: Boussinesq-like multi-component lattice equations …
We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…
The global regularity problem concerning the inviscid Boussinesq equations remains an open problem. In an attempt to understand this problem, we examine the damped Boussinesq equations and study how damping affects the regularity of…
We present a generic and systematic approach for constructing D-dimensional lattice models with exactly solvable d-dimensional boundary states localized to corners, edges, hinges and surfaces. These solvable models represent a class of…
The usual Cauchy matrix approach starts from a known plain wave factor vector $r$ and known dressed Cauchy matrix $M$. In this paper we start from a matrix equation set with undetermined $r$ and $M$. From the starting equation set we can…
We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. By mapping lattice Boltzmann schemes to Finite Difference schemes, we…
Systems of N = 1, 2, . . . first-order hyperbolic conservation laws feature N undamped waves propagating at finite speeds. On their own hand, multi-step Finite Difference and lattice Boltzmann schemes with q = N + 1, N + 2, . . . unknowns…
We are concerned with the long-time solvability for 2D inviscid Boussinesq equations for a larger class of initial data which covers the case of borderline regularity. First we show the local solvability in Besov spaces uniformly with…
We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz…
We describe how the usual supercharges of extended supersymmetry may be {\it twisted} to produce a BRST-like supercharge $Q$. The usual supersymmetry algebra is then replaced by a twisted algebra and the action of the twisted theory is…
We derive the Enskog equation utilizing orthonormal vielbein fields, enabling the utilization of arbitrary coordinate systems to characterize spatial geometry. Additionally, we employ an adapted coordinate system in the momentum space,…
A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and…
This article examines the dynamic phase transitions and pattern formations attributed to binary systems modeled by the Cahn-Hilliard equation. In particular, we consider a two-dimensional lattice structure and determine how different…
We study a harmonic triangular lattice, which relaxes in the presence of a weak, short-wavelength periodic potential. Monte Carlo simulations reveal that the elastic lattice has only short-ranged positional correlations, despite the absence…
The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained…
Theoretical and computational advances in lattice calculations are reviewed, with focus on examples relevant to the unitarity triangle of the CKM matrix. Recent progress in semi-leptonic form factors for B -> pi l nu and B -> D* l nu, as…
Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence,…
We consider the partial difference equations of the Adler-Bobenko-Suris classification, which are characterized as multidimensionally consistent. The latter property leads naturally to the construction of auto-B{\"a}cklund transformations…
We propose a class of auxetic three-dimensional lattice structures. The elastic microstructure can be designed in order to have omni-directional Poisson's ratio arbitrarily close to the stability limit -1. The cubic behavior of the periodic…
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…
In this article we initiate a systematic study of the well-posedness theory of the Einstein constraint equations on compact manifolds with boundary. This is an important problem in general relativity, and it is particularly important in…