We propose an energetic interpretation of stochastic processes described by Langevin equations with non-uniform temperature. In order to avoid Itô-Stratonovich dilemma, we start with a Kramers equation, and derive a Fokker-Plank equation by the renormalization group method. We give a proper definition of heat for the system. Based on our formulations, we analyze two examples, the Thomson effect...

To whom correspondence and requests for materials should be addressed: Bernd Nidetzky, Institute of Biotechnology and Biochemical Engineering, Graz University of Technology, Petersgasse 12, A-8010 Graz, Austria, Tel.: +43 (316) 873-8400; Fax: +43 (316) 873-108401, E-mail: [email protected], and Harald Plank, Institute for Electron Microscopy and Fine Structure Research, Graz University o...

It is a great honor for us to dedicate this paper to Professor Alfred Klemm on the occasion of his 100th birthday. M. Holovko remembers with pleasure his first meeting with Alfred Klemm during his first visit at the Max-Plank-Institut für Chemie in Mainz in 1986 together with Prof. Igor Yukhnovskii. They were invited to Klemm’s house. It is nice to recall now these discussions on science, art, ...

Running title: Structure of an Open Conformation of Cytochrome P450 Reductase These authors contributed equally to the work. Address correspondence to: Lucy Waskell, Department of Anesthesiology, University of Michigan and Veterans Affairs Medical Research Center, 2215 Fuller Rd. Ann Arbor, Michigan 48105, Tel: 734-8455858, E-mail: [email protected] or Jung-Ja P. Kim, Department of Biochemistry...

Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker–Plank model, with inhomogeneous diffusion and variable mobility parameters. We develop large time asymptotic analysis such nonstandard models reformulating extending classical entropy method, under assumption periodic boundary condition. In addition, illustrative numerical tests are presented t...

We consider the perturbation of Schwarzschild solution by perimeter action. The asymptotic behaviour at infinity and horizon are calculated analysed in first approximation. is characterised ratio Plank length to radius. It demonstrated that modified theory appear space-time regions radius scale unreachable test particles. These located places where standard gravity has singularities.