Understanding how the macroscopic parameters depend on the small-scale randomness of the environment and proving the Einstein Relation for this model is the ambitious aim of this project.
3) Establish the first rigorous Einstein Relation for a physically relevant model, the Variable Range Hopping.
The mathematical techniques we have at our disposal nowadays (such as the weak Einstein Relation and the control of long range models) are a solid basis for the investigation of the problem: This would be the first time an Einstein Relation is rigorously proven for a relevant physical model.
The viscosity of blood is varying according to Einstein relation.
The blood in central layer of blood vessel is a suspension of erythrocytes and is considered as Newtonian fluid with variable viscosity which varies according to Einstein relation.
The viscosity of blood in central layer is allowed to vary according to the Einstein relation
In fact, such an interaction can be expressed by a so-called Einstein relation implicating Hausdorff, spectral and walk dimension, expressing geometric, analytic and stochastic aspects of a set (see (GM83), (Tel06), and (Zho93) as related references).
Mandelbrot, Diffusion on fractal lattices and the fractal Einstein relation, J.