Understanding the statistics of bedload particle motions is great importance. To model hop events which are defined as trajectories particles moving successively from start to end their motions, recently, Wu et al. ( Water Resour. Res. , vol. 56, 2020, p. e2019WR025116) have successfully performed individual-based simulations according Fokker–Planck equation for velocities. However, analytical ...

This paper is intended to provide a mathematical model about mass transfer of natural medicinal components in production process of andrographolide as a medical plant. An inverse problem that included a partial differential equation in conjunction with initial and boundary conditions is introduced to estimate diffusivity of andrographolide during production of solvent extraction. To solve the i...

A new model to calculate heat eddy diffusivity in separating and reattaching flows based on modification of constant Prt is proposed. This modification is made using an empirical correlation between maximum Nusselt number and entrance Reynolds number. The model includes both the simplicity of Prt=0.9 assumption and the accuracy of two-equation heat-transfer models. Furthermore, an appropriate l...

The theory of mean field electrodynamics for diffusive processes in Electron Magnetohydrodynamic (EMHD) model is presented. In contrast to Magne-tohydrodynamics (MHD) the evolution of magnetic field here is governed by a nonlinear equation in the magnetic field variables. A detailed description of diffusive processes in two dimensions are presented in this paper. In particular , it has been sho...

Analytical solutions are derived for a pressure transmission experiment of a saturated charged compressible porous medium. The governing equations describe infinitesimal deformations of charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoup...

We analyzed the effect of strains on material transport in a typical dual damascene copper interconnect via under electromigration stress. The electromigration model incorporates all important driving forces for atom migration coupled with the solution of the electrical and thermal problems. Our approach differs from others by considering a diffusivity tensor in the transport equation taking in...

*Correspondence: [email protected] 2School of Aerospace Engineering and Applied Mechanicas, Tongji University, Shanghai, China Full list of author information is available at the end of the article Abstract We apply a series expansion technique to estimate the water content distribution and front position in finite boundary conditions. We derive an approximate analytical solution of the Richard...

In this paper we, apply the classical control theory to a parabolic partial differential equation in a bounded domain with diffusivity-interior-boundary actuation. We first we study the existence of the solution of the parabolic partial differential equation, then we study the solution bound estimate which are used to prove the existence of the solution of the optimal control problem in a Banac...

also known as the diffusion equation, describes in typical applications of the evolution in time of the density u u x, t of some quantities such as heat and chemical concentration 1, page 44 . In this case, the thermal diffusivity and thermal conductivity of the medium are assumed to be constant. However, in some media such as gases, the parameters are proportional to the temperature of the med...

We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for t...