TY  - JOUR
A1  - Eliazar, Iddo
A1  - Metzler, Ralf
T1  - The RARE model a generalized approach to random relaxation processes in disordered systems
JF  - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2  - This paper introduces and analyses a general statistical model, termed the RAndom RElaxations (RARE) model, of random relaxation processes in disordered systems. The model considers excitations that are randomly scattered around a reaction center in a general embedding space. The model's input quantities are the spatial scattering statistics of the excitations around the reaction center, and the chemical reaction rates between the excitations and the reaction center as a function of their mutual distance. The framework of the RARE model is versatile and a detailed stochastic analysis of the random relaxation processes is established. Analytic results regarding the duration and the range of the random relaxation processes, as well as the model's thermodynamic limit, are obtained in closed form. In particular, the case of power-law inputs, which turn out to yield stretched exponential relaxation patterns and asymptotically Paretian relaxation ranges, is addressed in detail.
KW  - chemical relaxation
KW  - Pareto analysis
KW  - reaction kinetics theory
KW  - reaction rate constants
KW  - stochastic processes
Y1  - 2012
U6  - https://doi.org/10.1063/1.4770266
SN  - 0021-9606
SN  - 1089-7690
VL  - 137
IS  - 23
PB  - American Institute of Physics
CY  - Melville
ER  -