Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW

Axiomatization of Finite Algebras

We show that the set of all formulas in n variables valid in a finite class A of finite algebras is always a regular tree language, and compute a finite axiom set for A. We give a rational reconstruction of Barzdins' liquid flow algorithm [BB91]. We show a sufficient condition for the existence of a class A of prototype algebras for a given theory e. Such a set allows us to prove theta satisfies phi simply by testing whether phi holds in A

Flat Holonomies on Automata Networks

We consider asynchronous dynamic networks of identical finite (independent of the network size) automata. A useful data structure on such networks is a partial orientation of its edges. It needs to be straight, i.e., have null holonomy (the difference between the number of up and down edges in each cycle). It also needs to be centered, i.e., have a unique node with no down edges. Using such orientation, any feasible computational task can be efficiently implemented with self-stabilization and synchronization. There are (interdependent) self-stabilizing asynchronous finite automata protocols assuring straight and centered orientation. Such protocols may vary in assorted efficiency parameters and it is desirable to have each replaceable with any alternative, responsible for a simple limited task. We describe an efficient reduction of any computational task to any such set of protocols compliant with our interface conditions