3,112 research outputs found
Random Time-Scale Invariant Diffusion and Transport Coefficients
Single particle tracking of mRNA molecules and lipid granules in living cells
shows that the time averaged mean squared displacement of
individual particles remains a random variable while indicating that the
particle motion is subdiffusive. We investigate this type of ergodicity
breaking within the continuous time random walk model and show that
differs from the corresponding ensemble average. In
particular we derive the distribution for the fluctuations of the random
variable . Similarly we quantify the response to a
constant external field, revealing a generalization of the Einstein relation.
Consequences for the interpretation of single molecule tracking data are
discussed.Comment: 4 pages, 4 figures.Article accompanied by a PRL Viewpoint in
Physics1, 8 (2008
Stable Equilibrium Based on L\'evy Statistics: Stochastic Collision Models Approach
We investigate equilibrium properties of two very different stochastic
collision models: (i) the Rayleigh particle and (ii) the driven Maxwell gas.
For both models the equilibrium velocity distribution is a L\'evy distribution,
the Maxwell distribution being a special case. We show how these models are
related to fractional kinetic equations. Our work demonstrates that a stable
power-law equilibrium, which is independent of details of the underlying
models, is a natural generalization of Maxwell's velocity distribution.Comment: PRE Rapid Communication (in press
Anomalous diffusion and generalized Sparre-Andersen scaling
We are discussing long-time, scaling limit for the anomalous diffusion
composed of the subordinated L\'evy-Wiener process. The limiting anomalous
diffusion is in general non-Markov, even in the regime, where ensemble averages
of a mean-square displacement or quantiles representing the group spread of the
distribution follow the scaling characteristic for an ordinary stochastic
diffusion. To discriminate between truly memory-less process and the non-Markov
one, we are analyzing deviation of the survival probability from the (standard)
Sparre-Andersen scaling.Comment: 5 pages, 3 figure
Thermodynamics and Fractional Fokker-Planck Equations
The relaxation to equilibrium in many systems which show strange kinetics is
described by fractional Fokker-Planck equations (FFPEs). These can be
considered as phenomenological equations of linear nonequilibrium theory. We
show that the FFPEs describe the system whose noise in equilibrium funfills the
Nyquist theorem. Moreover, we show that for subdiffusive dynamics the solutions
of the corresponding FFPEs are probability densities for all cases where the
solutions of normal Fokker-Planck equation (with the same Fokker-Planck
operator and with the same initial and boundary conditions) exist. The
solutions of the FFPEs for superdiffusive dynamics are not always probability
densities. This fact means only that the corresponding kinetic coefficients are
incompatible with each other and with the initial conditions
Comment on "Mean First Passage Time for Anomalous Diffusion"
We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)]
of the mean first passage time of a subdiffusive process to reach either end of
a finite interval in one dimension. The mean first passage time is in fact
infinite.Comment: To appear in Phys. Rev.
First passage behaviour of fractional Brownian motion in two-dimensional wedge domains
We study the survival probability and the corresponding first passage time
density of fractional Brownian motion confined to a two-dimensional open wedge
domain with absorbing boundaries. By analytical arguments and numerical
simulation we show that in the long time limit the first passage time density
scales as t**{-1+pi*(2H-2)/(2*Theta)} in terms of the Hurst exponent H and the
wedge angle Theta. We discuss this scaling behaviour in connection with the
reaction kinetics of FBM particles in a one-dimensional domain.Comment: 6 pages, 4 figure
Interactions of rod-like particles on responsive elastic sheets
What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive-repulsive rod-rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed
First passage time of N excluded volume particles on a line
Motivated by recent single molecule studies of proteins sliding on a DNA
molecule, we explore the targeting dynamics of N particles ("proteins") sliding
diffusively along a line ("DNA") in search of their target site (specific
target sequence). At lower particle densities, one observes an expected
reduction of the mean first passage time proportional to 1/N**2, with
corrections at higher concentrations. We explicitly take adsorption and
desorption effects, to and from the DNA, into account. For this general case,
we also consider finite size effects, when the continuum approximation based on
the number density of particles, breaks down. Moreover, we address the first
passage time problem of a tagged particle diffusing among other particles.Comment: 9 pages, REVTeX, 6 eps figure
Comment on "Why is the DNA denaturation transition first order?"
In this comment we argue that while the conclusions in the original paper (Y.
Kafri, D. Mukamel and L. Peliti, Phys. Rev. Lett. 85, 4988 (2000)) are correct
for asymptotically long DNA chains, they do not apply to the chains used in
typical experiments. In the added last paragraph, we point out that for real
DNA the average distance between denatured loops is not of the order of the
persistence length of a single-stranded chain but much larger. This
corroborates our reasoning that the double helix between loops is quite rigid,
and thereby our conclusion.Comment: 1 page, REVTeX. Last paragraph adde
Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
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 {\it biasing} and {\it decoupled} external fields is introduced.
Complementary to the recently established Langevin equations for anomalous
diffusion in a time-dependent external force-field [{\it Magdziarz et al.,
Phys. Rev. Lett. {\bf 101}, 210601 (2008)}] the Langevin formulation of
anomalous diffusion in a decoupled time-dependent force-field is derived
- …