2,610 research outputs found
Escalation of error catastrophe for enzymatic self-replicators
It is a long-standing question in origin-of-life research whether the
information content of replicating molecules can be maintained in the presence
of replication errors. Extending standard quasispecies models of non-enzymatic
replication, we analyze highly specific enzymatic self-replication mediated
through an otherwise neutral recognition region, which leads to
frequency-dependent replication rates. We find a significant reduction of the
maximally tolerable error rate, because the replication rate of the fittest
molecules decreases with the fraction of functional enzymes. Our analysis is
extended to hypercyclic couplings as an example for catalytic networks.Comment: 6 pages, 4 figures; accepted at Europhys. Let
Records and sequences of records from random variables with a linear trend
We consider records and sequences of records drawn from discrete time series
of the form , where the are independent and identically
distributed random variables and is a constant drift. For very small and
very large drift velocities, we investigate the asymptotic behavior of the
probability of a record occurring in the th step and the
probability that all entries are records, i.e. that . Our work is motivated by the analysis of temperature time series in
climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure
Bottleneck-induced transitions in a minimal model for intracellular transport
We consider the influence of disorder on the non-equilibrium steady state of
a minimal model for intracellular transport. In this model particles move
unidirectionally according to the \emph{totally asymmetric exclusion process}
(TASEP) and are coupled to a bulk reservoir by \emph{Langmuir kinetics}. Our
discussion focuses on localized point defects acting as a bottleneck for the
particle transport. Combining analytic methods and numerical simulations, we
identify a rich phase behavior as a function of the defect strength. Our
analytical approach relies on an effective mean-field theory obtained by
splitting the lattice into two subsystems, which are effectively connected
exploiting the local current conservation. Introducing the key concept of a
carrying capacity, the maximal current which can flow through the bulk of the
system (including the defect), we discriminate between the cases where the
defect is irrelevant and those where it acts as a bottleneck and induces
various novel phases (called {\it bottleneck phases}). Contrary to the simple
TASEP in the presence of inhomogeneities, many scenarios emerge and translate
into rich underlying phase-diagrams, the topological properties of which are
discussed.Comment: 14 pages, 15 figures, 1 tabl
Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations
We present a comprehensive analysis of a linear growth model, which combines
the characteristic features of the Edwards--Wilkinson and noisy Mullins
equations. This model can be derived from microscopics and it describes the
relaxation and growth of surfaces under conditions where the nonlinearities can
be neglected. We calculate in detail the surface width and various correlation
functions characterizing the model. In particular, we study the crossover
scaling of these functions between the two limits described by the combined
equation. Also, we study the effect of colored and conserved noise on the
growth exponents, and the effect of different initial conditions. The
contribution of a rough substrate to the surface width is shown to decay
universally as , where is
the time--dependent correlation length associated with the growth process,
is the initial roughness and the correlation length of the
substrate roughness, and is the surface dimensionality. As a second
application, we compute the large distance asymptotics of the height
correlation function and show that it differs qualitatively from the functional
forms commonly used in the intepretation of scattering experiments.Comment: 28 pages with 4 PostScript figures, uses titlepage.sty; to appear in
Phys. Rev.
Coarsening of Sand Ripples in Mass Transfer Models with Extinction
Coarsening of sand ripples is studied in a one-dimensional stochastic model,
where neighboring ripples exchange mass with algebraic rates, , and ripples of zero mass are removed from the system. For ripples vanish through rare fluctuations and the average ripples mass grows
as \avem(t) \sim -\gamma^{-1} \ln (t). Temporal correlations decay as
or depending on the symmetry of the mass transfer, and
asymptotically the system is characterized by a product measure. The stationary
ripple mass distribution is obtained exactly. For ripple evolution
is linearly unstable, and the noise in the dynamics is irrelevant. For the problem is solved on the mean field level, but the mean-field theory
does not adequately describe the full behavior of the coarsening. In
particular, it fails to account for the numerically observed universality with
respect to the initial ripple size distribution. The results are not restricted
to sand ripple evolution since the model can be mapped to zero range processes,
urn models, exclusion processes, and cluster-cluster aggregation.Comment: 10 pages, 8 figures, RevTeX4, submitted to Phys. Rev.
Epitaxial Growth of Thin Films -- a Statistical Mechanical Model
A theoretical framework is developed to describe experiments on the structure
of epitaxial thin films, particularly niobium on sapphire. We extend the
hypothesis of dynamical scaling to apply to the structure of thin films from
its conventional application to simple surfaces. We then present a
phenomenological continuum theory that provides a good description of the
observed scattering and the measured exponents. Finally the results of
experiment and theory are compared.Comment: 10 pages, 3 figures, minor revisions. accepted for publication in J
Phys Condense Matte
Stretched exponentials and power laws in granular avalanching
We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion.
Comment: 8 pages, more concise and some points clarified
Evolutionary trajectories in rugged fitness landscapes
We consider the evolutionary trajectories traced out by an infinite
population undergoing mutation-selection dynamics in static, uncorrelated
random fitness landscapes. Starting from the population that consists of a
single genotype, the most populated genotype \textit{jumps} from a local
fitness maximum to another and eventually reaches the global maximum. We use a
strong selection limit, which reduces the dynamics beyond the first time step
to the competition between independent mutant subpopulations, to study the
dynamics of this model and of a simpler one-dimensional model which ignores the
geometry of the sequence space. We find that the fit genotypes that appear
along a trajectory are a subset of suitably defined fitness \textit{records},
and exploit several results from the record theory for non-identically
distributed random variables. The genotypes that contribute to the trajectory
are those records that are not \textit{bypassed} by superior records arising
further away from the initial population. Several conjectures concerning the
statistics of bypassing are extracted from numerical simulations. In
particular, for the one-dimensional model, we propose a simple relation between
the bypassing probability and the dynamic exponent which describes the scaling
of the typical evolution time with genome size. The latter can be determined
exactly in terms of the extremal properties of the fitness distribution.Comment: Figures in color; minor revisions in tex
Dynamic Scaling in a 2+1 Dimensional Limited Mobility Model of Epitaxial Growth
We study statistical scale invariance and dynamic scaling in a simple
solid-on-solid 2+1 - dimensional limited mobility discrete model of
nonequilibrium surface growth, which we believe should describe the low
temperature kinetic roughening properties of molecular beam epitaxy. The model
exhibits long-lived ``transient'' anomalous and multiaffine dynamic scaling
properties similar to that found in the corresponding 1+1 - dimensional
problem. Using large-scale simulations we obtain the relevant scaling
exponents, and compare with continuum theories.Comment: 5 pages, 4 ps figures included, RevTe
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