Search PubMed⌕ Search

Biomedical subjects

W Horsthemke

Publications and source records attributed to W Horsthemke.

17 recordsLinked to original sources
PubMed2006

Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources.

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments, and find their corresponding long-time, asymptotic behaviors. The generally anomalous diffusive regimes of the particles are classified, and their dependence on the friction coefficient and the characteristics of the noises is analyzed in detail. The asymptotic predictions are confirmed by exact solutions for two examples.

Journal Article↗
PubMed2000

Mean first-passage time for an overdamped particle in a disordered force field

We derive a rigorous expression for the mean first-passage time of an overdamped particle subject to a constant bias in a force field with quenched disorder. Depending on the statistics of the disorder, the disorder-averaged mean first-passage time can undergo a transition from an infinite value for small bias to a finite value for large bias. This corresponds to a depinning transition of the particle. We obtain exact values for the depinning threshold for Gaussian disorder and also for a class of piecewise constant random forces, which we call generalized kangaroo disorder. For Gaussian disorder, we investigate how the correlations of the random force field affect the average motion of the particle. For kangaroo disorder, we apply the general results for the depinning transition to two specific examples, viz., dichotomous disorder and random fractal disorder.

Journal Article↗
PubMed2000

Anomalous diffusion of particles driven by correlated noise

We study the effect of an arbitrary stationary random force on the motion of damped particles. Using a Langevin description, we derive exact expressions for the dispersion of the particle position, of the particle velocity, and their cross dispersion. The particles can exhibit anomalous diffusion, and the connection between this behavior and the functional form of the noise correlations is investigated in detail. We also study anomalous diffusion for the special cases of overdamped and undamped particles.

Journal Article↗
PubMed1999

Spatial instabilities in reaction random walks with direction-independent kinetics.

We study spatial instabilities in reacting and diffusing systems, where diffusion is modeled by a persistent random walk instead of the usual Brownian motion. Perturbations in these reaction walk systems propagate with finite speed, whereas in reaction-diffusion systems localized disturbances affect every part instantly, albeit with heavy damping. We present evolution equations for reaction random walks whose kinetics do not depend on the particles' direction of motion. The homogeneous steady state of such systems can undergo two types of transport-driven instabilities. One type of bifurcation gives rise to stationary spatial patterns and corresponds to the Turing instability in reaction-diffusion systems. The other type occurs in the ballistic regime and leads to oscillatory spatial patterns; it has no analog in reaction-diffusion systems. The conditions for these bifurcations are derived and applied to two model systems. We also analyze the stability properties of one-variable systems and find that small wavelength perturbations decay in an oscillatory manner.

Journal Article↗
PubMed1981

Voltage-noise-induced transitions in electrically excitable membranes.

A quantitative study of the steady-state behavior of the sodium and potassium conductance for the Hodgkin-Huxley axon under the influence of an externally driven voltage noise is reported. The dichotomous Markov noise (random telegraph signal) considered allows for an exact evaluation of the stationary probability density of the conductances. Phase diagrams are constructed to represent the response of the system as a function of the amplitude and the correlation time of the noise. The results obtained for the Hodgkin-Huxley axon are compared with some molecular models used in the literature.

Animals↗
PubMed1979

Multiple transitions induced by light intensity fluctuations in illuminated chemical systems.

The influence of external noise on the steady-state properties of a chemical system with very simple kinetics was studied. We dealt with an isomerization reaction, in a closed system, coupled to a light absorption and radiationless deexcitation process involving only one of the isomers. The theoretical analysis established that external noise deeply modified the macroscopic properties of the system and even induced transition phenomena that are totally unexpected from the usual deterministic description.

Journal Article↗