3,873 research outputs found
Towards deterministic equations for Levy walks: the fractional material derivative
Levy walks are random processes with an underlying spatiotemporal coupling.
This coupling penalizes long jumps, and therefore Levy walks give a proper
stochastic description for a particle's motion with broad jump length
distribution. We derive a generalized dynamical formulation for Levy walks in
which the fractional equivalent of the material derivative occurs. Our approach
will be useful for the dynamical formulation of Levy walks in an external force
field or in phase space for which the description in terms of the continuous
time random walk or its corresponding generalized master equation are less well
suited
Black-body furnace Patent
Development of black-body source calibration furnac
Optimal target search on a fast folding polymer chain with volume exchange
We study the search process of a target on a rapidly folding polymer (`DNA')
by an ensemble of particles (`proteins'), whose search combines 1D diffusion
along the chain, Levy type diffusion mediated by chain looping, and volume
exchange. A rich behavior of the search process is obtained with respect to the
physical parameters, in particular, for the optimal search.Comment: 4 pages, 3 figures, REVTe
High-response on-line gas analysis system for hydrogen-reaction combustion products
The results of testing an on-line quadrupole gas analyzer system are reported. Gas samples were drawn from the exhaust of a hydrogen-oxygen-nitrogen rocket which simulated the flow composition and dynamics at the combustor exit of a supersonic combustion ramjet engine. System response time of less than 50 milliseconds was demonstrated, with analytical accuracy estimated to be + or - 5 percent. For more complex chemical systems with interfering atom patterns, analysis would be more difficult. A cooled-gas pyrometer probe was evaluated as a total temperature indicator and as the primary mass flow measuring element for the total sample flow rate
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
Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
Anomalous diffusion is frequently described by scaled Brownian motion (SBM),
a Gaussian process with a power-law time dependent diffusion coefficient. Its
mean squared displacement is with
for . SBM may provide a
seemingly adequate description in the case of unbounded diffusion, for which
its probability density function coincides with that of fractional Brownian
motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a
significant amplitude scatter of the time averaged mean squared displacement.
More severely, we demonstrate that under confinement, the dynamics encoded by
SBM is fundamentally different from both fractional Brownian motion and
continuous time random walks. SBM is highly non-stationary and cannot provide a
physical description for particles in a thermalised stationary system. Our
findings have direct impact on the modelling of single particle tracking
experiments, in particular, under confinement inside cellular compartments or
when optical tweezers tracking methods are used.Comment: 7 pages, 5 figure
Fine structure of distributions and central limit theorem in diffusive billiards
We investigate deterministic diffusion in periodic billiard models, in terms
of the convergence of rescaled distributions to the limiting normal
distribution required by the central limit theorem; this is stronger than the
usual requirement that the mean square displacement grow asymptotically
linearly in time. The main model studied is a chaotic Lorentz gas where the
central limit theorem has been rigorously proved. We study one-dimensional
position and displacement densities describing the time evolution of
statistical ensembles in a channel geometry, using a more refined method than
histograms. We find a pronounced oscillatory fine structure, and show that this
has its origin in the geometry of the billiard domain. This fine structure
prevents the rescaled densities from converging pointwise to gaussian
densities; however, demodulating them by the fine structure gives new densities
which seem to converge uniformly. We give an analytical estimate of the rate of
convergence of the original distributions to the limiting normal distribution,
based on the analysis of the fine structure, which agrees well with simulation
results. We show that using a Maxwellian (gaussian) distribution of velocities
in place of unit speed velocities does not affect the growth of the mean square
displacement, but changes the limiting shape of the distributions to a
non-gaussian one. Using the same methods, we give numerical evidence that a
non-chaotic polygonal channel model also obeys the central limit theorem, but
with a slower convergence rate.Comment: 16 pages, 19 figures. Accepted for publication in Physical Review E.
Some higher quality figures at http://www.maths.warwick.ac.uk/~dsander
Helix untwisting and bubble formation in circular DNA
The base pair fluctuations and helix untwisting are examined for a circular
molecule. A realistic mesoscopic model including twisting degrees of freedom
and bending of the molecular axis is proposed. The computational method, based
on path integral techniques, simulates a distribution of topoisomers with
various twist numbers and finds the energetically most favorable molecular
conformation as a function of temperature. The method can predict helical
repeat, openings loci and bubble sizes for specific sequences in a broad
temperature range. Some results are presented for a short DNA circle recently
identified in mammalian cells.Comment: The Journal of Chemical Physics, vol. 138 (2013), in pres
Aging Scaled Brownian Motion
Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of
passive tracers in complex and biological systems. It is a highly
non-stationary process governed by the Langevin equation for Brownian motion,
however, with a power-law time dependence of the noise strength. Here we study
the aging properties of SBM for both unconfined and confined motion.
Specifically, we derive the ensemble and time averaged mean squared
displacements and analyze their behavior in the regimes of weak, intermediate,
and strong aging. A very rich behavior is revealed for confined aging SBM
depending on different aging times and whether the process is sub- or
superdiffusive. We demonstrate that the information on the aging factorizes
with respect to the lag time and exhibits a functional form, that is identical
to the aging behavior of scale free continuous time random walk processes.
While SBM exhibits a disparity between ensemble and time averaged observables
and is thus weakly non-ergodic, strong aging is shown to effect a convergence
of the ensemble and time averaged mean squared displacement. Finally, we derive
the density of first passage times in the semi-infinite domain that features a
crossover defined by the aging time.Comment: 10 pages, 8 figures, REVTe
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