660 research outputs found
Dynamics of Annealed Systems under External Fields: CTRW and the Fractional Fokker-Planck Equations
We consider the linear response of a system modelled by continuous-time
random walks (CTRW) to an external field pulse of rectangular shape. We
calculate the corresponding response function explicitely and show that it
exhibits aging, i.e. that it is not translationally invariant in the
time-domain. This result differs from that of systems which behave according to
fractional Fokker-Planck equations
Small-World Rouse Networks as models of cross-linked polymers
We use the recently introduced small-world networks (SWN) to model
cross-linked polymers, as an extension of the linear Rouse-chain. We study the
SWN-dynamics under the influence of external forces. Our focus is on the
structurally and thermally averaged SWN stretching, which we determine both
numerically and analytically using a psudo-gap ansatz for the SWN-density of
states. The SWN stretching is related to the probability of a random-walker to
return to its origin on the SWN. We compare our results to the corresponding
ones for Cayley trees.Comment: 14 pages, 4 figures. Preprint version, submitted to JC
Kinetic description of diffusion-limited reactions in random catalytic media
We study the kinetics of bimolecular, catalytically-activated reactions
(CARs) in d-dimensions. The elementary reaction act between reactants takes
place only when these meet in the vicinity of a catalytic site; such sites are
assumed to be immobile and randomly distributed in space. For CARs we develop a
kinetic formalism, based on Collins-Kimball-type ideas; within this formalism
we obtain explicit expressions for the effective reaction rates and for the
decay of the reactants' concentrations.Comment: 15 pages, Latex, two figures, to appear in J. Chem. Phy
Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations
We consider the linear response of systems modelled by continuous-time random
walks (CTRW) and by fractional Fokker-Planck equations under the influence of
time-dependent external fields. We calculate the corresponding response
functions explicitely. The CTRW curve exhibits aging, i.e. it is not
translationally invariant in the time-domain. This is different from what
happens under fractional Fokker-Planck conditions
The subdiffusive target problem: Survival probability
The asymptotic survival probability of a spherical target in the presence of
a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a
continuous Euclidean medium is calculated. In one and two dimensions the
survival probability of the target in the presence of a single trap decays to
zero as a power law and as a power law with logarithmic correction,
respectively. The target is thus reached with certainty, but it takes the trap
an infinite time on average to do so. In three dimensions a single trap may
never reach the target and so the survival probability is finite and, in fact,
does not depend on whether the traps move diffusively or subdiffusively. When
the target is surrounded by a sea of traps, on the other hand, its survival
probability decays as a stretched exponential in all dimensions (with a
logarithmic correction in the exponent for ). A trap will therefore reach
the target with certainty, and will do so in a finite time. These results may
be directly related to enzyme binding kinetics on DNA in the crowded cellular
environment.Comment: 6 pages. References added, improved account of previous results and
typos correcte
Relaxation Properties of Small-World Networks
Recently, Watts and Strogatz introduced the so-called small-world networks in
order to describe systems which combine simultaneously properties of regular
and of random lattices. In this work we study diffusion processes defined on
such structures by considering explicitly the probability for a random walker
to be present at the origin. The results are intermediate between the
corresponding ones for fractals and for Cayley trees.Comment: 16 pages, 6 figure
Dynamics of end-linked star polymer structures
In this work we focus on the dynamics of macromolecular networks formed by
end-linking identical polymer stars. The resulting macromolecular network can
then be viewed as consisting of spacers which connect branching points (the
cores of the stars). We succeed in analyzing exactly, in the framework of the
generalized Gaussian model, the eigenvalue spectrum of such networks. As
applications we focus on several topologies, such as regular networks and
dendrimers; furthermore, we compare the results to those found for regular
hyperbranched structures. In so doing, we also consider situations in which the
beads of the cores differ from the beads of the spacers. The analytical
procedure which we use involves an exact real-space renormalization, which
allows to relate the star-network to a (much simpler) network, in which each
star is reduced to its core. It turns out that the eigenvalue spectrum of the
star-polymer structure consists of two parts: One follows in terms of
polynomial equations from the relaxation spectrum of the corresponding
renormalized structure, while the second part involves the motion of the spacer
chains themselves. Finally, we show exemplarily the situation for copolymeric
dendrimers, calculate their spectra, and from them their storage and the loss
moduli.Comment: 15 pages, 11 eps-figures include
Quantum transport on two-dimensional regular graphs
We study the quantum-mechanical transport on two-dimensional graphs by means
of continuous-time quantum walks and analyse the effect of different boundary
conditions (BCs). For periodic BCs in both directions, i.e., for tori, the
problem can be treated in a large measure analytically. Some of these results
carry over to graphs which obey open boundary conditions (OBCs), such as
cylinders or rectangles. Under OBCs the long time transition probabilities
(LPs) also display asymmetries for certain graphs, as a function of their
particular sizes. Interestingly, these effects do not show up in the marginal
distributions, obtained by summing the LPs along one direction.Comment: 22 pages, 11 figure, acceted for publication in J.Phys.
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