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- Rudolf Friedrich, Frank Jenko, Antonio Baule, Stephan 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)

- Rudolf Friedrich, Frank Jenko, Antonio Baule, Stephan 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)

- Stephan Eule, Rudolf Friedrich, Frank Jenko, Igor 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)

- David Lamouroux, Stephan Eule, Theo Geisel, Jan 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)

- Stephan Eule, V. Zaburdaev, Rudolf Friedrich, Theo 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)

- Stephan Eule, Rudolf Friedrich, Frank Jenko, David 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.

- David Lamouroux, Jan Nagler, Theo Geisel, Stephan Eule
- Proceedings. Biological sciences
- 2015

Spatial heterogeneity of a host population of mobile agents has been shown to be a crucial determinant of many aspects of disease dynamics, ranging from the proliferation of diseases to their persistence and to vaccination strategies. In addition, the importance of regional and structural differences grows in our modern world. Little is known, though, about… (More)

Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its… (More)

- Stephan Eule
- 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)