527 research outputs found
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
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
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
Coagulation reaction in low dimensions: Revisiting subdiffusive A+A reactions in one dimension
We present a theory for the coagulation reaction A+A -> A for particles
moving subdiffusively in one dimension. Our theory is tested against numerical
simulations of the concentration of particles as a function of time
(``anomalous kinetics'') and of the interparticle distribution function as a
function of interparticle distance and time. We find that the theory captures
the correct behavior asymptotically and also at early times, and that it does
so whether the particles are nearly diffusive or very subdiffusive. We find
that, as in the normal diffusion problem, an interparticle gap responsible for
the anomalous kinetics develops and grows with time. This corrects an earlier
claim to the contrary on our part.Comment: The previous version was corrupted - some figures misplaced, some
strange words that did not belong. Otherwise identica
Quantum walk approach to search on fractal structures
We study continuous-time quantum walks mimicking the quantum search based on
Grover's procedure. This allows us to consider structures, that is, databases,
with arbitrary topological arrangements of their entries. We show that the
topological structure of the database plays a crucial role by analyzing, both
analytically and numerically, the transition from the ground to the first
excited state of the Hamiltonian associated with different (fractal)
structures. Additionally, we use the probability of successfully finding a
specific target as another indicator of the importance of the topological
structure.Comment: 15 pages, 14 figure
Quantum transport on small-world networks: A continuous-time quantum walk approach
We consider the quantum mechanical transport of (coherent) excitons on
small-world networks (SWN). The SWN are build from a one-dimensional ring of N
nodes by randomly introducing B additional bonds between them. The exciton
dynamics is modeled by continuous-time quantum walks and we evaluate
numerically the ensemble averaged transition probability to reach any node of
the network from the initially excited one. For sufficiently large B we find
that the quantum mechanical transport through the SWN is, first, very fast,
given that the limiting value of the transition probability is reached very
quickly; second, that the transport does not lead to equipartition, given that
on average the exciton is most likely to be found at the initial node.Comment: 8 pages, 8 figures (high quality figures available upon request
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