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A mathematical model of the distribution function for the discrete 3-disk is proposed in order to utilize in the statistical evolution equation of the 3-dimensional Universe. The model distribution is constructed based on analyses in known…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
We study the spectral and magnetic properties of one-dimensional lattices filled with 2 to 4 fermions (with spin 1/2) per lattice site. We use a generalized Hubbard model that takes account all interactions on a lattice site, and solve the…
We explore a technique for probing energy spectra in synthetic lattices that is analogous to scanning tunneling microscopy. Using one-dimensional synthetic lattices of coupled atomic momentum states, we explore this spectroscopic technique…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
Non-equilibrium quantum phenomena are ubiquitous in nature. Yet, theoretical predictions on the real-time dynamics of many-body quantum systems remain formidably challenging, especially for high dimensions, strong interactions or disordered…
We present Monte Carlo simulation results for the three dimensional Thirring model on moderate sized lattices using a hybrid molecular dynamics algorithm which permits an odd or non-integer number Nf of fermion flavors. We find a continuous…
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice with Laplacian and potential terms modulated by a primitive invertible two-letter substitution. We investigate the spectrum and the spectral type, the…
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…
The propagation and refraction of a cylindrical wave created by a line current through a slab of backward wave medium, also called left-handed medium, is numerically studied with FDTD. The slab is assumed to be uniaxially anisotropic.…
A three dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices,…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
We present a quantitative benchmark of multiscale models for dendritic growth simulations. We focus on approaches based on phase-field, dendritic needle network, and grain envelope dynamics. As a first step, we focus on isothermal growth of…
We study the problem of "phantom" folding of the two-dimensional square lattice, in which the edges and diagonals of each face can be folded. The non-vanishing thermodynamic folding entropy per face $s \simeq .2299(1)$ is estimated both…
The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with…
This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the…