Anomalous diffusion with absorption: exact time-dependent solutions

Fractional rotational diffusion of rigid dipoles in an asymmetrical double-well potential.

The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar molecules rotating in an asymmetric double-well potential are evaluated using a fractional rotational diffusion equation (based on the diffusion limit of a fractal time random walk) for the distribution function of orientations of the molecules on the surface of the unit sphere. ...

Bimodal approximation for anomalous diffusion in a potential.

Exact and approximate solutions of the fractional diffusion equation for an assembly of fixed-axis dipoles are derived for anomalous noninertial rotational diffusion in a double-well potential. It is shown that knowledge of three time constants characterizing the normal diffusion, viz., the integral relaxation time, the effective relaxation time, and the inverse of the smallest eigenvalue of th...

Exact solutions for the flow of a generalized second grade due to a Longitudinal quadratic time-dependent shear stress

Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources.

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments, and find their corresponding long-time, asymptotic behaviors. The generally anomal...

Aixsymmetric Stagnation Point Flow of a Viscous Fluid on a Moving Cylinder with Time Dependent Axial Velocity

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity is investigated. The impinging free stream is steady with a strain rate k. An exact solution of the Navier-Stokes equations is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations. The general self-si...