In this paper we discuss some thermoelastic and thermoviscoelastic models obtained from the Gurtin theory, based on invariance of entropy under time reversal. We derive differential systems where temperature velocity are ruled by generalized versions Moore-Gibson-Thompson equation. one-dimensional case, provide a complete analysis evolution, establishing an existence uniqueness result valid for...

We investigate through a generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor λ. We obtain as well an exact expression for λ for all kinds of diffusion. Moreover, we show that λ is ...

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze d...

The Fokker-Planck equation for the probability f(r,t) to find a random walker at position r at time t is derived for the case that the probability to make jumps depends nonlinearly on f(r,t) . The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in...

Diffusion weighted imaging (DWI) techniques have been used to study human brain white matter fiber structures in vivo. Commonly used standard diffusion tensor magnetic resonance imaging (DTI) tractography derived from the second order diffusion tensor model has limitations in its ability to resolve complex fiber tracts. We propose a new fiber tracking method based on the generalized diffusion t...

1 Introduction Disorder leads to important physical effects which are of quantum mechanical origin. This has been revealed by Anderson [1] in the study of a disordered tight-binding model. The problem has attracted great attention over many decades [2]. Subsequent to the ideas presented in our previous papers [3,4], we discuss here a new analytical approach to calculate the phase-diagram for th...

The thermoelastic properties of ferropericlase Mg(1-x)Fe(x)O (x = 0.1875) throughout the iron high-to-low spin cross-over have been investigated by first principles at Earth's lower mantle conditions. This cross-over has important consequences for elasticity such as an anomalous bulk modulus (K(S)) reduction. At room temperature the anomaly is somewhat sharp in pressure but broadens with increa...