10 research outputs found
Tagged particle in single-file diffusion
Single-file diffusion is a one-dimensional interacting infinite-particle
system in which the order of particles never changes. An intriguing feature of
single-file diffusion is that the mean-square displacement of a tagged particle
exhibits an anomalously slow sub-diffusive growth. We study the full statistics
of the displacement using a macroscopic fluctuation theory. For the simplest
single-file system of impenetrable Brownian particles we compute the large
deviation function and provide an independent verification using an exact
solution based on the microscopic dynamics. For an arbitrary single-file
system, we apply perturbation techniques and derive an explicit formula for the
variance in terms of the transport coefficients. The same method also allows us
to compute the fourth cumulant of the tagged particle displacement for the
symmetric exclusion process.Comment: 34 pages, to appear in Journal of Statistical Physics (2015
Island Distance in One-Dimensional Epitaxial Growth
The typical island distance in submonlayer epitaxial growth depends on
the growth conditions via an exponent . This exponent is known to
depend on the substrate dimensionality, the dimension of the islands, and the
size of the critical nucleus for island formation. In this paper we study
the dependence of on in one--dimensional epitaxial growth. We
derive that for and confirm this result
by computer simulations.Comment: 5 pages, 3 figures, uses revtex, psfig, 'Note added in proof'
appende
Random Fibonacci Sequences
Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1}
decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently
small (large) B. In the limits B --> 0 and B --> infinity, we expand the
Lyapunov exponent lambda(B) in powers of B and B^{-1}, respectively. For the
classical case of we obtain exact non-perturbative results. In
particular, an invariant measure associated with Ricatti variable
r_n=x_{n+1}/x_{n} is shown to exhibit plateaux around all rational.Comment: 11 Pages (Multi-Column); 3 EPS Figures ; Submitted to J. Phys.
A preferential attachment model with Poisson growth for scale-free networks
We propose a scale-free network model with a tunable power-law exponent. The
Poisson growth model, as we call it, is an offshoot of the celebrated model of
Barab\'{a}si and Albert where a network is generated iteratively from a small
seed network; at each step a node is added together with a number of incident
edges preferentially attached to nodes already in the network. A key feature of
our model is that the number of edges added at each step is a random variable
with Poisson distribution, and, unlike the Barab\'{a}si-Albert model where this
quantity is fixed, it can generate any network. Our model is motivated by an
application in Bayesian inference implemented as Markov chain Monte Carlo to
estimate a network; for this purpose, we also give a formula for the
probability of a network under our model.Comment: 18 pages with 2 figures; correction to a proof in the appendi
Signatures of arithmetic simplicity in metabolic network architecture
Metabolic networks perform some of the most fundamental functions in living
cells, including energy transduction and building block biosynthesis. While
these are the best characterized networks in living systems, understanding
their evolutionary history and complex wiring constitutes one of the most
fascinating open questions in biology, intimately related to the enigma of
life's origin itself. Is the evolution of metabolism subject to general
principles, beyond the unpredictable accumulation of multiple historical
accidents? Here we search for such principles by applying to an artificial
chemical universe some of the methodologies developed for the study of genome
scale models of cellular metabolism. In particular, we use metabolic flux
constraint-based models to exhaustively search for artificial chemistry
pathways that can optimally perform an array of elementary metabolic functions.
Despite the simplicity of the model employed, we find that the ensuing pathways
display a surprisingly rich set of properties, including the existence of
autocatalytic cycles and hierarchical modules, the appearance of universally
preferable metabolites and reactions, and a logarithmic trend of pathway length
as a function of input/output molecule size. Some of these properties can be
derived analytically, borrowing methods previously used in cryptography. In
addition, by mapping biochemical networks onto a simplified carbon atom
reaction backbone, we find that several of the properties predicted by the
artificial chemistry model hold for real metabolic networks. These findings
suggest that optimality principles and arithmetic simplicity might lie beneath
some aspects of biochemical complexity