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- R Friedrich, F Jenko, A Baule, S Eule
- Physical review. E, Statistical, nonlinear, and…
- 2006

In order to describe non-Gaussian kinetics in weakly damped systems, the concept of continuous time random walks is extended to particles with finite inertia. One thus obtains a generalized Kramers-Fokker-Planck equation, which retains retardation effects, i.e., nonlocal couplings in time and space. It is shown that despite this complexity, exact solutions… (More)

- Jakob J. Metzger, Stephan Eule
- PLoS Computational Biology
- 2013

Muller's ratchet is a paradigmatic model for the accumulation of deleterious mutations in a population of finite size. A click of the ratchet occurs when all individuals with the least number of deleterious mutations are lost irreversibly due to a stochastic fluctuation. In spite of the simplicity of the model, a quantitative understanding of the process… (More)

- R Friedrich, F Jenko, A Baule, S Eule
- Physical review letters
- 2006

The anomalous (i.e., non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of "random kicks" is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a new fractional equation of the Kramers-Fokker-Planck type is derived. The associated collision operator necessarily… (More)

- S Eule, R Friedrich, F Jenko, I M Sokolov
- Physical review. E, Statistical, nonlinear, and…
- 2008

We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for… (More)

- S Eule, R Friedrich, F Jenko, D Kleinhans
- The journal of physical chemistry. B
- 2007

In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby (Fogedby, H. C. Phys. Rev. E 1994, 50, 041103), we show how these equations are related to Langevin equations via the procedure of subordination.

- D Lamouroux, S Eule, T Geisel, J Nagler
- Physical review. E, Statistical, nonlinear, and…
- 2012

We introduce a population model for species under cyclic competition. This model allows individuals to coexist and interact on single cells while migration takes place between adjacent cells. In contrast to the model introduced by Reichenbach, Mobilia, and Frey [Reichenbach, Mobilia, and Frey, Nature (London) 448, 1046 (2007)], we find that the emergence of… (More)

- S Eule, R Friedrich
- 2005

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic… (More)

- S Eule, V Zaburdaev, R Friedrich, T Geisel
- Physical review. E, Statistical, nonlinear, and…
- 2012

The description of diffusion processes is possible in different frameworks such as random walks or Fokker-Planck or Langevin equations. Whereas for classical diffusion the equivalence of these methods is well established, in the case of anomalous diffusion it often remains an open problem. In this paper we aim to bring three approaches describing anomalous… (More)

- S Eule, R Friedrich
- 2009

The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of biasing and decoupled external fields is introduced. Complementary to the recently established Langevin equations for… (More)

- Dmitry Tsigankov, Stephan Eule
- BMC Neuroscience
- 2010

We present a model of stochastic molecular transport in spiny dendrites. In this model the molecules perform a random walk between the spines that trap the walkers. If the molecules interact with each other inside the spines the trapping time in each spine depends on the number of molecules in the respective trap. The corresponding mathematical problem has… (More)