Related papers: On the Distribution function of area and perimeter…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
A natural model for the approximation of a convex body $K$ in $\mathbb{R}^d$ by random polytopes is obtained as follows. Take a stationary Poisson hyperplane process in the space, and consider the random polytope $Z_K$ defined as the…
The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A…
We consider consecutive random subdivision of polygons described as follows. Given an initial convex polygon with $d\ge 3$ edges, we choose a point at random on each edge, such that the proportions in which these points divide edges are…
The number of plane partitions contained in a given box was shown by MacMahon to be given by a simple product formula. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in cyclic…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a `slice' defined by minimizing the distance to a single generic `template' intersects the group orbit of every…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
We construct random dynamics on collections of non-intersecting planar contours, leaving invariant the distributions of length- and area-interacting polygonal Markov fields with V-shaped nodes. The first of these dynamics is based on the…
When a chordwise Reynolds number (Re) falls below about $10^5$ the performance of wings and aerodynamic sections become sensitive to viscous phenomena, including boundary layer separation and possible reattachment. Here, detailed…
Assuming that a plane partition of the positive integer $n$ is chosen uniformly at random from the set of all such partitions, we propose a general asymptotic scheme for the computation of expectations of various plane partition statistics…
In this note, we construct a $3$-dimensional generalisation of the Pascal's triangle that we named Pascal's cube, as it has the construction of a cube with entries given by extended binomial coefficients ${}^cC^{a}_{b}$. The Pascal's cube…
Counting how many particles pass through a specific space within a specific time is an interesting question in applied physics and social science. Here a logistic model is developed to estimate the total number of flowing particles. This…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…