We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.

We constructed an analog circuit generating fluctuations of which a probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by tuning the resistance. A theory of a differential equation with both multiplicative and additive noises which describes the circuit is introduced. The circuit is composed of a noise genera...

We determine the relations of power product of physical quantities (PQs) by the generalized relation. Assuming the relations with two, three and four PQs to generalized relation separately, we find the corresponding general formulas. By ordering the exponent of physical constant in relations being zero or fit number, we gain many famous equations without factors such as mass-energy relation, fo...

– The porous media equation has been proposed as a phenomenological “nonextensive” generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming nonlinear response, i.e. that the diffusive flux depends on gradients of a power of the concentration. The present equation distinguishes from the porous medi...

The signal generated by a weak impulse propagates in an oscillatory way and dispersively in a gravitationally compacted granular chain. For the power-law type contact force, we show analytically that the type of dispersion follows power-laws in depth. The power-law for grain displacement signal is given by h − 1 4 (1− 1 p ) where h and p denote depth and the exponent of contact force, and the p...

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The no...

Fractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and w...