Related papers: Modified-Bloch Equation Based on Fractal Derivativ…
Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal…
The studying of anomalous diffusion by pulsed field gradient (PFG) diffusion technique still faces challenges. Two different research groups have proposed modified Bloch equation for anomalous diffusion. However, these equations have…
Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. An general PFG signal…
Pulsed field gradient (PFG) has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is complicated. In this…
Anomalous diffusion exists widely in polymer and biological systems. Pulsed field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in NMR and MRI. However, the interpretation of PFG anomalous diffusion is…
Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In…
Anomalous diffusion has been investigated in many systems. Pulsed field gradient (PFG) anomalous diffusion is much more complicated than PFG normal diffusion. There have been many theoretical and experimental studies for PFG isotropic…
This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…
Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
A Fokker Planck equation on fractal curves is obtained, starting from Chapmann-Kolmogorov equation on fractal curves. This is done using the recently developed calculus on fractals, which allows one to write differential equations on…
We consider the propagation of galactic cosmic rays under assumption that the interstellar medium is a fractal one. An anomalous diffusion equation in terms of fractional derivatives is used to describe of cosmic ray propagation. The…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
Equation for anomalous diffusion in momentum space, recently obtained in the recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16 July 2009) is solved for the stationary and non-stationary cases on basis of the…
The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
Accurately analyzing NMR and MRI diffusion experimental data relies on the theoretical expression used for signal attenuation or phase evolution. In a complex system, the encountered magnetic field is often inhomogeneous, which may be…