Related papers: The isotropic correlation function of plane figure…
The method for calculation of the correlation functions of the Ising-type systems with short-range interaction and with arbitrary value of spin is developed within cluster approximation. For the Ising model (spin $S^z=\pm1$) the expressions…
The spin-spin correlation function of the spherical model being precisely at an anisotropic Lifshitz point of arbitrary order is calculated exactly. The results are in agreement with scaling. The scaling function is shown to be universal.…
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
The dynamics of a hollow cylinder containing granules and rolling down an inclined plane was investigated. A theoretical approach for investigating the behaviour of such a cylinder was proposed. The critical angle of the plane that allows…
Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the…
We derive an analytic expression for the height correlation function of a rough surface based on the inverse wave scattering method of Kirchhoff theory. The expression directly relates the height correlation function to diffuse scattered…
In this article,we study theoretically and numerically the interaction of a vortex induced by a rotating cylinder with a perpendicular plane. We show the existence of weak solutions to the swirling vortex models by using the Hopf extension…
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
The anisotropic 2-point correlation function (2PCF) of galaxies measures pairwise clustering as a function of the pair separation's angle to the line of sight. The latter is often defined as either the angle bisector of the…
The problem of large-scale correlations of particles produced in high-energy collisions is discussed. Among them are, e.g., those correlations which lead to ring-like and elliptic flow shapes of individual high-multiplicity events in the…
Geometrical model of structure of the universe is examined to obtain analytical expression for the two points nonlinear correlation function. According to the model the objects (galaxies) are concentrated into two types of structure…
The correlation functions are calculated for the two dimensional Ising model with free boundary conditions and the two dimensional Ising model with periodic boundary conditions.
Occupation probabilities for primary-secondary-primary cell strings and correlation functions for primary sites of a decorated lattice model are expressed through the well-studied partition function and correlation functions of the Ising…
The classical correction to the velocity auto-correlation function of non-interacting particles due to memory effects, which are beyond the Boltzmann equation, is calculated both analytically and numerically for the case of isotropic…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
We investigate the QCD phase diagram as a function of isospin chemical potential at a fixed temperature by directly putting large numbers of \pi^+s into the system. Correlation functions of N \pi^+s systems involves N!N! contractions, and…
A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two- particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving…
A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual directions of rotation about their…
Over the past century, a correlation has been an essential mathematical technique utilized in engineering sciences, including practically every signal/image processing field. This paper describes an effective method of calculating the…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…