2,714 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
Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes
We study the effect of quenched spatial disorder on the steady states of
driven systems of interacting particles. Two sorts of models are studied:
disordered drop-push processes and their generalizations, and the disordered
asymmetric simple exclusion process. We write down the exact steady-state
measure, and consequently a number of physical quantities explicitly, for the
drop-push dynamics in any dimensions for arbitrary disorder. We find that three
qualitatively different regimes of behaviour are possible in 1- disordered
driven systems. In the Vanishing-Current regime, the steady-state current
approaches zero in the thermodynamic limit. A system with a non-zero current
can either be in the Homogeneous regime, chracterized by a single macroscopic
density, or the Segregated-Density regime, with macroscopic regions of
different densities. We comment on certain important constraints to be taken
care of in any field theory of disordered systems.Comment: RevTex, 17pages, 18 figures included using psfig.st
Mutation supply and the repeatability of selection for antibiotic resistance
Whether evolution can be predicted is a key question in evolutionary biology.
Here we set out to better understand the repeatability of evolution. We
explored experimentally the effect of mutation supply and the strength of
selective pressure on the repeatability of selection from standing genetic
variation. Different sizes of mutant libraries of an antibiotic resistance
gene, TEM-1 -lactamase in Escherichia coli, were subjected to different
antibiotic concentrations. We determined whether populations went extinct or
survived, and sequenced the TEM gene of the surviving populations. The
distribution of mutations per allele in our mutant libraries- generated by
error-prone PCR- followed a Poisson distribution. Extinction patterns could be
explained by a simple stochastic model that assumed the sampling of beneficial
mutations was key for survival. In most surviving populations, alleles
containing at least one known large-effect beneficial mutation were present.
These genotype data also support a model which only invokes sampling effects to
describe the occurrence of alleles containing large-effect driver mutations.
Hence, evolution is largely predictable given cursory knowledge of mutational
fitness effects, the mutation rate and population size. There were no clear
trends in the repeatability of selected mutants when we considered all
mutations present. However, when only known large-effect mutations were
considered, the outcome of selection is less repeatable for large libraries, in
contrast to expectations. Furthermore, we show experimentally that alleles
carrying multiple mutations selected from large libraries confer higher
resistance levels relative to alleles with only a known large-effect mutation,
suggesting that the scarcity of high-resistance alleles carrying multiple
mutations may contribute to the decrease in repeatability at large library
sizes.Comment: 31pages, 9 figure
Extremal statistics of curved growing interfaces in 1+1 dimensions
We study the joint probability distribution function (pdf) of the maximum M
of the height and its position X_M of a curved growing interface belonging to
the universality class described by the Kardar-Parisi-Zhang equation in 1+1
dimensions. We obtain exact results for the closely related problem of p
non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M)
where \tau_M is there the time at which the maximal height M is reached. Our
analytical results, in the limit p \to \infty, become exact for the interface
problem in the growth regime. We show that our results, for moderate values of
p \sim 10 describe accurately our numerical data of a prototype of these
systems, the polynuclear growth model in droplet geometry. We also discuss
applications of our results to the ground state configuration of the directed
polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics
Letters. New results added for non-intersecting excursion
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
The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions
We study irreversible dimer nucleation on top of terraces during epitaxial
growth in one and two dimensions, for all values of the step-edge barrier. The
problem is solved exactly by transforming it into a first passage problem for a
random walker in a higher-dimensional space. The spatial distribution of
nucleation events is shown to differ markedly from the mean-field estimate
except in the limit of very weak step-edge barriers. The nucleation rate is
computed exactly, including numerical prefactors.Comment: 22 pages, 10 figures. To appear in Phys. Rev.
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.
Roughness of Sandpile Surfaces
We study the surface roughness of prototype models displaying self-organized
criticality (SOC) and their noncritical variants in one dimension. For SOC
systems, we find that two seemingly equivalent definitions of surface roughness
yields different asymptotic scaling exponents. Using approximate analytical
arguments and extensive numerical studies we conclude that this ambiguity is
due to the special scaling properties of the nonlinear steady state surface. We
also find that there is no such ambiguity for non-SOC models, although there
may be intermediate crossovers to different roughness values. Such crossovers
need to be distinguished from the true asymptotic behaviour, as in the case of
a noncritical disordered sandpile model studied in [10].Comment: 5 pages, 4 figures. Accepted for publication in Phys. Rev.
Design and fabrication of highly efficient non-linear optical devices for implementing high-speed optical processing
We present the design and fabrication of micro-cavity semiconductor devices for enhanced Two-Photon-Absorption response, and demonstrate the use of these devices for implementing sensitive autocorrelation measurements on pico-second optical pulses
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