Related papers: Drift, diffusion, and third order derivatives in F…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
A new fourth partial derivative is introduced for the study of transport dynamics. It is a Lagrangian partial derivative following the path of diffusion, not the path of convection. Use of this derivative decouples the effect of diffusion…
We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional derivatives $\frac{\partial}{\partial t}P(x,t)=D \frac{\partial^{\gamma}}{\partial x^{\gamma}}[P(x,t) ]^{\nu}$. Exact time-dependent solutions are found for $ \nu =…
We present the Markovian quantum master equation describing rotational decoherence, friction, diffusion, and thermalization of planar, linear, and asymmetric rotors in contact with a thermal environment. It describes how an arbitrary…
We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift…
The drift and diffusion of a cloud of ions in a fluid are distorted by an inhomogeneous electric field. If the electric field carries the center of the distribution in a straight line and the field configuration is suitably symmetric, the…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
We consider a Fokker-Planck equation in a general domain in ${\mathbb{R}}^n$ with $L^p_{\mathrm{loc}}$ drift term and $W^{1,p}_{\mathrm{loc}}$ diffusion term for any $p>n$. By deriving an integral identity, we give several measure estimates…
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does…
The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation…
We study Brownian motion driven with both conservative and nonconservative external forces. By using the thermodynamic approach of the theory of Brownian motion we obtain the Fokker-Planck equation and derive expressions for the Fluctuation…
The generalized master equation with two times, introduced in earlier, applies to the problem of diffusion in an time-dependent (in general inhomogeneous) external field. We consider the case of the quasi Fokker-Planck approximation, when…
By investigating McKean-Vlasov SDEs, the order preservation and positive correlation are characterized for nonlinear Fokker-Planck equations. The main results recover the corresponding criteria on these properties established in [3, 5] for…
We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…
In this paper diffusion processes with changing modes are studied involving the variable order partial differential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…