7,922 research outputs found
Analytical study of the effect of recombination on evolution via DNA shuffling
We investigate a multi-locus evolutionary model which is based on the DNA
shuffling protocol widely applied in \textit{in vitro} directed evolution. This
model incorporates selection, recombination and point mutations. The simplicity
of the model allows us to obtain a full analytical treatment of both its
dynamical and equilibrium properties, for the case of an infinite population.
We also briefly discuss finite population size corrections
Absorbing-state phase transitions in fixed-energy sandpiles
We study sandpile models as closed systems, with conserved energy density
playing the role of an external parameter. The critical energy density,
, marks a nonequilibrium phase transition between active and absorbing
states. Several fixed-energy sandpiles are studied in extensive simulations of
stationary and transient properties, as well as the dynamics of roughening in
an interface-height representation. Our primary goal is to identify the
universality classes of such models, in hopes of assessing the validity of two
recently proposed approaches to sandpiles: a phenomenological continuum
Langevin description with absorbing states, and a mapping to driven interface
dynamics in random media. Our results strongly suggest that there are at least
three distinct universality classes for sandpiles.Comment: 41 pages, 23 figure
Novel charges in CFT's
In this paper we construct two infinite sets of self-adjoint commuting
charges for a quite general CFT. They come out naturally by considering an
infinite embedding chain of Lie algebras, an underlying structure that share
all theories with gauge groups U(N), SO(N) and Sp(N). The generality of the
construction allows us to carry all gauge groups at the same time in a unified
framework, and so to understand the similarities among them. The eigenstates of
these charges are restricted Schur polynomials and their eigenvalues encode the
value of the correlators of two restricted Schurs. The existence of these
charges singles out restricted Schur polynomials among the number of bases of
orthogonal gauge invariant operators that are available in the literature.Comment: 58 page
Gravitational Dynamics of an Infinite Shuffled Lattice: Particle Coarse-grainings, Non-linear Clustering and the Continuum Limit
We study the evolution under their self-gravity of infinite ``shuffled
lattice'' particle distributions, focussing specifically on the comparison of
this evolution with that of ``daughter'' particle distributions, defined by a
simple coarse-graining procedure. We consider both the case that such
coarse-grainings are performed (i) on the initial conditions, and (ii) at a
finite time with a specific additional prescription. In numerical simulations
we observe that, to a first approximation, these coarse-grainings represent
well the evolution of the two-point correlation properties over a significant
range of scales. We note, in particular, that the form of the two-point
correlation function in the original system, when it is evolving in the
asymptotic ``self-similar'' regime, may be reproduced well in a daughter
coarse-grained system in which the dynamics are still dominated by two-body
(nearest neighbor) interactions. Using analytical results on the early time
evolution of these systems, however, we show that small observed differences
between the evolved system and its coarse-grainings at the initial time will in
fact diverge as the ratio of the coarse-graining scale to the original
inter-particle distance increases. The second coarse-graining studied,
performed at a finite time in a specified manner, circumvents this problem. It
also makes more physically transparent why gravitational dynamics from these
initial conditions tends toward a ``self-similar'' evolution. We finally
discuss the precise definition of a limit in which a continuum (specifically
Vlasov-like) description of the observed linear and non-linear evolution should
be applicable.Comment: 21 pages, 8 eps figures, 2 jpeg figures (available in high resolution
at http://pil.phys.uniroma1.it/~sylos/PRD_dec_2006/
Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations
We present a computational study of finite-time mixing of a line segment by
cutting and shuffling. A family of one-dimensional interval exchange
transformations is constructed as a model system in which to study these types
of mixing processes. Illustrative examples of the mixing behaviors, including
pathological cases that violate the assumptions of the known governing theorems
and lead to poor mixing, are shown. Since the mathematical theory applies as
the number of iterations of the map goes to infinity, we introduce practical
measures of mixing (the percent unmixed and the number of intermaterial
interfaces) that can be computed over given (finite) numbers of iterations. We
find that good mixing can be achieved after a finite number of iterations of a
one-dimensional cutting and shuffling map, even though such a map cannot be
considered chaotic in the usual sense and/or it may not fulfill the conditions
of the ergodic theorems for interval exchange transformations. Specifically,
good shuffling can occur with only six or seven intervals of roughly the same
length, as long as the rearrangement order is an irreducible permutation. This
study has implications for a number of mixing processes in which
discontinuities arise either by construction or due to the underlying physics.Comment: 21 pages, 10 figures, ws-ijbc class; accepted for publication in
International Journal of Bifurcation and Chao
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