196,564 research outputs found
Universality of Long-Range Correlations in Expansion-Randomization Systems
We study the stochastic dynamics of sequences evolving by single site
mutations, segmental duplications, deletions, and random insertions. These
processes are relevant for the evolution of genomic DNA. They define a
universality class of non-equilibrium 1D expansion-randomization systems with
generic stationary long-range correlations in a regime of growing sequence
length. We obtain explicitly the two-point correlation function of the sequence
composition and the distribution function of the composition bias in sequences
of finite length. The characteristic exponent of these quantities is
determined by the ratio of two effective rates, which are explicitly calculated
for several specific sequence evolution dynamics of the universality class.
Depending on the value of , we find two different scaling regimes, which
are distinguished by the detectability of the initial composition bias. All
analytic results are accurately verified by numerical simulations. We also
discuss the non-stationary build-up and decay of correlations, as well as more
complex evolutionary scenarios, where the rates of the processes vary in time.
Our findings provide a possible example for the emergence of universality in
molecular biology.Comment: 23 pages, 15 figure
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Stochastic stability of viscoelastic systems under Gaussian and Poisson white noise excitations
As the use of viscoelastic materials becomes increasingly popular, stability of viscoelastic structures under random loads becomes increasingly important. This paper aims at studying the asymptotic stability of viscoelastic systems under Gaussian and Poisson white noise excitations with Lyapunov functions. The viscoelastic force is approximated as equivalent stiffness and damping terms. A stochastic differential equation is set up to represent randomly excited viscoelastic systems, from which a Lyapunov function is determined by intuition. The time derivative of this Lyapunov function is then obtained by stochastic averaging. Approximate conditions are derived for asymptotic Lyapunov stability with probability one of the viscoelastic system. Validity and utility of this approach are illustrated by a Duffing-type oscillator possessing viscoelastic forces, and the influence of different parameters on the stability region is delineated
Probing the high-density behavior of symmetry energy with gravitational waves
Gravitational wave (GW) astronomy opens up an entirely new window on the
Universe to probe the equations of state (EOS) of neutron-rich matter. With the
advent of next generation GW detectors, measuring the gravitational radiation
from coalescing binary neutron star systems, mountains on rotating neutron
stars, and stellar oscillation modes may become possible in the near future.
Using a set of model EOSs satisfying the latest constraints from terrestrial
nuclear experiments, state of the art nuclear many-body calculations of the
pure neutron matter EOS, and astrophysical observations consistently, we study
various GW signatures of the high-density behavior of the nuclear symmetry
energy, which is considered among the most uncertain properties of dense
neutron-rich nucleonic matter. In particular, we find the tidal polarizability
of neutron stars, potentially measurable in binary systems just prior to
merger, is more sensitive to the high density component of the nuclear symmetry
energy than the symmetry energy at nuclear saturation density. We also find
that the upper limit on the GW strain amplitude from elliptically deformed
stars is very sensitive to the density dependence of the symmetry energy. This
suggests that future developments in modeling of the neutron star crust, and
direct gravitational wave signals from accreting binaries will provide a wealth
of information on the EOS of neutron-rich matter. We also review the
sensitivity of the -mode instability window to the density dependence of the
symmetry energy. Whereas models with larger values of the density slope of the
symmetry energy at saturation seem to be disfavored by the current
observational data, within a simple -mode model, we point out that a
subsequent softer behavior of the symmetry energy at high densities (hinted at
by recent observational interpretations) could rule them in.Comment: 14 pages, 11 figures, 3 tables; submitted to EPJA Special Volume on
Nuclear Symmetry Energ
A Solvable Sequence Evolution Model and Genomic Correlations
We study a minimal model for genome evolution whose elementary processes are
single site mutation, duplication and deletion of sequence regions and
insertion of random segments. These processes are found to generate long-range
correlations in the composition of letters as long as the sequence length is
growing, i.e., the combined rates of duplications and insertions are higher
than the deletion rate. For constant sequence length, on the other hand, all
initial correlations decay exponentially. These results are obtained
analytically and by simulations. They are compared with the long-range
correlations observed in genomic DNA, and the implications for genome evolution
are discussed.Comment: 4 pages, 4 figure
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