We demonstrate how the Laplace operator can be combined with a stochastic jump process to describe the evolution of a polymer network. Growth processes in polymer networks can proceed through the transfer of rather large oligomeric subunits from a pool of soluble molecules into the laments forming the network. In such a situation stochastic jump processes are a natural tool for the description ...

The transport of a condensing passive scalar is studied as a prototype model for the kinematics of moisture transport on isentropic surfaces. Condensation occurs whenever the scalar concentration exceeds a specified local saturation value. Since condensation rates are strongly nonlinear functions of moisture content, the mean moisture flux is generally not diffusive. To relate the mean moisture...

in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

We introduce a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the McKean–Vlasov type describing Markov processes and Hamilton–Jacobi–Bellman–Isaacs equation stochastic control games. This allows for unified analysis these equations, which leads to an effective theory coupled forward–backward systems (forward evolution backward evolution)...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on h̄-scaling of an equation for time evolution of the Wigner’s quasiprobability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvat...

A model of genome evolution is proposed. Based on several general assumptions the evolutionary theory of a genome is formulated. Both the deterministic classical equation and the stochastic quantum equation are proposed. The classical equation is written in a form of of second-order differential equations on nucleotide frequencies varying in time. It is proved that the evolutionary equation can...

Treating the motion of a dust particle suspended in a liquid as a random walk, Einstein in 1905 derived an equation describing the diffusion of the particle’s probability distribution in configuration space. Fokker and Planck extended this work to describe the velocity distribution of the particles. Their equation and its solutions have been applied to many problems in nature starting with the ...

‎in this paper lie symmetry analysis is applied in order to find new solutions for fokker plank equation of ornstein-uhlenbeck process‎. ‎this analysis classifies the solutions format of the fokker plank equation by using the lie algebra of the symmetries of our considered stochastic process‎.