11,765 research outputs found
Dynamics of Competitive Evolution on a Smooth Landscape
We study competitive DNA sequence evolution directed by {\it in vitro}
protein binding. The steady-state dynamics of this process is well described by
a shape-preserving pulse which decelerates and eventually reaches equilibrium.
We explain this dynamical behavior within a continuum mean-field framework.
Analytical results obtained on the motion of the pulse agree with simulations.
Furthermore, finite population correction to the mean-field results are found
to be insignificant.Comment: 4 pages, 2 figures, revised, to appear in Phys. Rev. Let
Nonlinear lattice model of viscoelastic Mode III fracture
We study the effect of general nonlinear force laws in viscoelastic lattice
models of fracture, focusing on the existence and stability of steady-state
Mode III cracks. We show that the hysteretic behavior at small driving is very
sensitive to the smoothness of the force law. At large driving, we find a Hopf
bifurcation to a straight crack whose velocity is periodic in time. The
frequency of the unstable bifurcating mode depends on the smoothness of the
potential, but is very close to an exact period-doubling instability. Slightly
above the onset of the instability, the system settles into a exactly
period-doubled state, presumably connected to the aforementioned bifurcation
structure. We explicitly solve for this new state and map out its
velocity-driving relation
The Universal Gaussian in Soliton Tails
We show that in a large class of equations, solitons formed from generic
initial conditions do not have infinitely long exponential tails, but are
truncated by a region of Gaussian decay. This phenomenon makes it possible to
treat solitons as localized, individual objects. For the case of the KdV
equation, we show how the Gaussian decay emerges in the inverse scattering
formalism.Comment: 4 pages, 2 figures, revtex with eps
Microscopic Selection of Fluid Fingering Pattern
We study the issue of the selection of viscous fingering patterns in the
limit of small surface tension. Through detailed simulations of anisotropic
fingering, we demonstrate conclusively that no selection independent of the
small-scale cutoff (macroscopic selection) occurs in this system. Rather, the
small-scale cutoff completely controls the pattern, even on short time scales,
in accord with the theory of microscopic solvability. We demonstrate that
ordered patterns are dynamically selected only for not too small surface
tensions. For extremely small surface tensions, the system exhibits chaotic
behavior and no regular pattern is realized.Comment: 6 pages, 5 figure
Two-finger selection theory in the Saffman-Taylor problem
We find that solvability theory selects a set of stationary solutions of the
Saffman-Taylor problem with coexistence of two \it unequal \rm fingers
advancing with the same velocity but with different relative widths
and and different tip positions. For vanishingly small
dimensionless surface tension , an infinite discrete set of values of the
total filling fraction and of the relative
individual finger width are selected out of a
two-parameter continuous degeneracy. They scale as
and . The selected values of differ from
those of the single finger case. Explicit approximate expressions for both
spectra are given.Comment: 4 pages, 3 figure
Velocity selection problem for combined motion of melting and solidification fronts
We discuss a free boundary problem for two moving solid-liquid interfaces
that strongly interact via the diffusion field in the liquid layer between
them. This problem arises in the context of liquid film migration (LFM) during
the partial melting of solid alloys. In the LFM mechanism the system chooses a
more efficient kinetic path which is controlled by diffusion in the liquid
film, whereas the process with only one melting front would be controlled by
the very slow diffusion in the mother solid phase. The relatively weak
coherency strain energy is the effective driving force for LFM. As in the
classical dendritic growth problems, also in this case an exact family of
steady-state solutions with two parabolic fronts and an arbitrary velocity
exists if capillary effects are neglected. We develop a velocity selection
theory for this problem, including anisotropic surface tension effects. The
strong diffusion interaction and coherency strain effects in the solid near the
melting front lead to substantial changes compared to classical dendritic
growth.Comment: submitted to PR
Quantum network of neutral atom clocks
We propose a protocol for creating a fully entangled GHZ-type state of
neutral atoms in spatially separated optical atomic clocks. In our scheme,
local operations make use of the strong dipole-dipole interaction between
Rydberg excitations, which give rise to fast and reliable quantum operations
involving all atoms in the ensemble. The necessary entanglement between distant
ensembles is mediated by single-photon quantum channels and collectively
enhanced light-matter couplings. These techniques can be used to create the
recently proposed quantum clock network based on neutral atom optical clocks.
We specifically analyze a possible realization of this scheme using neutral Yb
ensembles.Comment: 13 pages, 11 figure
Precision Measurement of the 29Si, 33S, and 36Cl Binding Energies
The binding energies of 29Si, 33S, and 36Cl have been measured with a
relative uncertainty using a flat-crystal spectrometer.
The unique features of these measurements are 1) nearly perfect crystals whose
lattice spacing is known in meters, 2) a highly precise angle scale that is
derived from first principles, and 3) a gamma-ray measurement facility that is
coupled to a high flux reactor with near-core source capability. The binding
energy is obtained by measuring all gamma-rays in a cascade scheme connecting
the capture and ground states. The measurements require the extension of
precision flat-crystal diffraction techniques to the 5 to 6 MeV energy region,
a significant precision measurement challenge. The binding energies determined
from these gamma-ray measurements are consistent with recent highly accurate
atomic mass measurements within a relative uncertainty of .
The gamma-ray measurement uncertainties are the dominant contributors to the
uncertainty of this consistency test. The measured gamma-ray energies are in
agreement with earlier precision gamma-ray measurements.Comment: 13 pages, 4 figure
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