2,810 research outputs found
Diffusion-Limited One-Species Reactions in the Bethe Lattice
We study the kinetics of diffusion-limited coalescence, A+A-->A, and
annihilation, A+A-->0, in the Bethe lattice of coordination number z.
Correlations build up over time so that the probability to find a particle next
to another varies from \rho^2 (\rho is the particle density), initially, when
the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic
limit. As a result, the particle density decays inversely proportional to time,
\rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant
value.Comment: To be published in JPCM, special issue on Kinetics of Chemical
Reaction
Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model
The quantum phase transition from a spin-Peierls phase with a small Fermi
surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is
studied in the framework of a one-dimensional Kondo-Heisenberg model that
consists of an electron gas away from half filling, coupled to a spin-1/2 chain
by Kondo interactions. The Kondo spins are further coupled to each other with
isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic
Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing
on three-eighths filling and using the density-matrix renormalization-group
(DMRG) method, we show that the zero-temperature transition between the phases
with small and large Fermi momenta appears continuous, and involves a new
intermediate phase where the Fermi surface is not well defined. The
intermediate phase is spin gapped and has Kondo-spin correlations that show
incommensurate modulations. Our results appear incompatible with the local
picture for the quantum phase transition in heavy fermion compounds, which
predicts an abrupt change in the size of the Fermi momentum.Comment: 9 pages, 8 figure
Exact mean first-passage time on the T-graph
We consider a simple random walk on the T-fractal and we calculate the exact
mean time to first reach the central node . The mean is performed
over the set of possible walks from a given origin and over the set of starting
points uniformly distributed throughout the sites of the graph, except .
By means of analytic techniques based on decimation procedures, we find the
explicit expression for as a function of the generation and of the
volume of the underlying fractal. Our results agree with the asymptotic
ones already known for diffusion on the T-fractal and, more generally, they are
consistent with the standard laws describing diffusion on low-dimensional
structures.Comment: 6 page
Designer Nets from Local Strategies
We propose a local strategy for constructing scale-free networks of arbitrary
degree distributions, based on the redirection method of Krapivsky and Redner
[Phys. Rev. E 63, 066123 (2001)]. Our method includes a set of external
parameters that can be tuned at will to match detailed behavior at small degree
k, in addition to the scale-free power-law tail signature at large k. The
choice of parameters determines other network characteristics, such as the
degree of clustering. The method is local in that addition of a new node
requires knowledge of only the immediate environs of the (randomly selected)
node to which it is attached. (Global strategies require information on finite
fractions of the growing net.
Percolation in Hierarchical Scale-Free Nets
We study the percolation phase transition in hierarchical scale-free nets.
Depending on the method of construction, the nets can be fractal or small-world
(the diameter grows either algebraically or logarithmically with the net size),
assortative or disassortative (a measure of the tendency of like-degree nodes
to be connected to one another), or possess various degrees of clustering. The
percolation phase transition can be analyzed exactly in all these cases, due to
the self-similar structure of the hierarchical nets. We find different types of
criticality, illustrating the crucial effect of other structural properties
besides the scale-free degree distribution of the nets.Comment: 9 Pages, 11 figures. References added and minor corrections to
manuscript. In pres
Facilitated diffusion of proteins on chromatin
We present a theoretical model of facilitated diffusion of proteins in the
cell nucleus. This model, which takes into account the successive
binding/unbinding events of proteins to DNA, relies on a fractal description of
the chromatin which has been recently evidenced experimentally. Facilitated
diffusion is shown quantitatively to be favorable for a fast localization of a
target locus by a transcription factor, and even to enable the minimization of
the search time by tuning the affinity of the transcription factor with DNA.
This study shows the robustness of the facilitated diffusion mechanism, invoked
so far only for linear conformations of DNA.Comment: 4 pages, 4 figures, accepted versio
Fractal and Transfractal Recursive Scale-Free Nets
We explore the concepts of self-similarity, dimensionality, and
(multi)scaling in a new family of recursive scale-free nets that yield
themselves to exact analysis through renormalization techniques. All nets in
this family are self-similar and some are fractals - possessing a finite
fractal dimension - while others are small world (their diameter grows
logarithmically with their size) and are infinite-dimensional. We show how a
useful measure of "transfinite" dimension may be defined and applied to the
small world nets. Concerning multiscaling, we show how first-passage time for
diffusion and resistance between hub (the most connected nodes) scale
differently than for other nodes. Despite the different scalings, the Einstein
relation between diffusion and conductivity holds separately for hubs and
nodes. The transfinite exponents of small world nets obey Einstein relations
analogous to those in fractal nets.Comment: Includes small revisions and references added as result of readers'
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