We consider directed percolation processes for particle types A and B coupled unidirectionally by a transmutation reaction A -> B. It is shown that the strong coupling regime of this recently introduced problem defines a universality class with upper critical dimension d=6. Exact expressions are derived for the scaling dimensions in the inactive phase above d=4. Below d=4 the interactions of the normal directed percolation also get relevant.

Source: http://arxiv.org/abs/cond-mat/0402316v1

It is shown that the self inductance of a wire loop may be written as a curve integral akin to the Neumann formula for the mutual inductance of two wire loops. The only difference is that contributions where the two integration variables get too close to each other must be excluded from the curve integral and evaluated in detail. The contributions of these excluded segments depend on the distribution of the current in the cross section of the wire. They add to a simple constant proportional to...

Source: http://arxiv.org/abs/1204.1486v2

The formal derivation of Langevin equations (and, equivalently Fokker-Planck equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and others apparently not has widely found its way into textbooks. It has been reproduced dozens of times on the fly with many references to the literature and without adding much substantially new. Here we follow the tradition, but strive to produce a self-contained text. Furthermore, we address questions that naturally arise in the derivation....

Topics: Mathematical Physics, Mathematics, Physics, Classical Physics

Source: http://arxiv.org/abs/1506.02650

A tool to determine the critical dimension of field theories (physics).

Topics: Physics, field theory, critical dimension