3,517 research outputs found
Residual mean first-passage time for jump processes: theory and applications to L\'evy flights and fractional Brownian motion
We derive a functional equation for the mean first-passage time (MFPT) of a
generic self-similar Markovian continuous process to a target in a
one-dimensional domain and obtain its exact solution. We show that the obtained
expression of the MFPT for continuous processes is actually different from the
large system size limit of the MFPT for discrete jump processes allowing
leapovers. In the case considered here, the asymptotic MFPT admits
non-vanishing corrections, which we call residual MFPT. The case of L/'evy
flights with diverging variance of jump lengths is investigated in detail, in
particular, with respect to the associated leapover behaviour. We also show
numerically that our results apply with good accuracy to fractional Brownian
motion, despite its non-Markovian nature.Comment: 13 pages, 8 figure
Measurement techniques for cryogenic Ka-band microstrip antennas
The measurement of cryogenic antennas poses unique logistical problems since the antenna under test must be embedded in a cooling chamber. A method of measuring the performance of cryogenic microstrip antennas using a closed cycle gas cooled refrigerator in a far field range is described. Antenna patterns showing the performance of gold and superconducting Ka-band microstrip antennas at various temperatures are presented
Topologically Driven Swelling of a Polymer Loop
Numerical studies of the average size of trivially knotted polymer loops with
no excluded volume are undertaken. Topology is identified by Alexander and
Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration
radius, and probability density distributions as functions of gyration radius
are generated for loops of up to N=3000 segments. Gyration radii of trivially
knotted loops are found to follow a power law similar to that of self avoiding
walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200
Subdiffusion-limited reactions
We consider the coagulation dynamics A+A -> A and A+A A and the
annihilation dynamics A+A -> 0 for particles moving subdiffusively in one
dimension. This scenario combines the "anomalous kinetics" and "anomalous
diffusion" problems, each of which leads to interesting dynamics separately and
to even more interesting dynamics in combination. Our analysis is based on the
fractional diffusion equation
Diffusion mechanisms of localised knots along a polymer
We consider the diffusive motion of a localized knot along a linear polymer
chain. In particular, we derive the mean diffusion time of the knot before it
escapes from the chain once it gets close to one of the chain ends.
Self-reptation of the entire chain between either end and the knot position,
during which the knot is provided with free volume, leads to an L^3 scaling of
diffusion time; for sufficiently long chains, subdiffusion will enhance this
time even more. Conversely, we propose local ``breathing'', i.e., local
conformational rearrangement inside the knot region (KR) and its immediate
neighbourhood, as additional mechanism. The contribution of KR-breathing to the
diffusion time scales only quadratically, L^2, speeding up the knot escape
considerably and guaranteeing finite knot mobility even for very long chains.Comment: 7 pages, 2 figures. Accepted to Europhys. Let
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
Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins
We investigate the translocation of a stiff polymer consisting of M monomers
through a nanopore in a membrane, in the presence of binding particles
(chaperones) that bind onto the polymer, and partially prevent backsliding of
the polymer through the pore. The process is characterized by the rates: k for
the polymer to make a diffusive jump through the pore, q for unbinding of a
chaperone, and the rate q kappa for binding (with a binding strength kappa);
except for the case of no binding kappa=0 the presence of the chaperones give
rise to an effective force that drives the translocation process. Based on a
(2+1) variate master equation, we study in detail the coupled dynamics of
diffusive translocation and (partial) rectification by the binding proteins. In
particular, we calculate the mean translocation time as a function of the
various physical parameters.Comment: 22 pages, 5 figures, IOP styl
Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion
We study the translocation dynamics of a polymer chain threaded through a
nanopore by an external force. By means of diverse methods (scaling arguments,
fractional calculus and Monte Carlo simulation) we show that the relevant
dynamic variable, the translocated number of segments , displays an {\em
anomalous} diffusive behavior even in the {\em presence} of an external force.
The anomalous dynamics of the translocation process is governed by the same
universal exponent , where is the Flory
exponent and - the surface exponent, which was established recently
for the case of non-driven polymer chain threading through a nanopore. A closed
analytic expression for the probability distribution function , which
follows from the relevant {\em fractional} Fokker - Planck equation, is derived
in terms of the polymer chain length and the applied drag force . It is
found that the average translocation time scales as . Also the corresponding time dependent
statistical moments, and reveal unambiguously the anomalous nature of the translocation
dynamics and permit direct measurement of in experiments. These
findings are tested and found to be in perfect agreement with extensive Monte
Carlo (MC) simulations.Comment: 6 pages, 4 figures, accepted to Europhys. Lett; some references were
supplemented; typos were correcte
DNA bubble dynamics as a quantum Coulomb problem
We study the dynamics of denaturation bubbles in double-stranded DNA on the
basis of the Poland-Scheraga model. We demonstrate that the associated
Fokker-Planck equation is equivalent to a Coulomb problem. Below the melting
temperature the bubble lifetime is associated with the continuum of scattering
states of the repulsive Coulomb potential, at the melting temperature the
Coulomb potential vanishes and the underlying first exit dynamics exhibits a
long time power law tail, above the melting temperature, corresponding to an
attractive Coulomb potential, the long time dynamics is controlled by the
lowest bound state. Correlations and finite size effects are discussed.Comment: 4 pages, 3 figures, revte
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