1,011 research outputs found
Supercoil formation in DNA denaturation
We generalize the Poland-Scheraga (PS) model to the case of a circular DNA,
taking into account the twisting of the two strains around each other. Guided
by recent single-molecule experiments on DNA strands, we assume that the
torsional stress induced by denaturation enforces formation of supercoils whose
writhe absorbs the linking number expelled by the loops. Our model predicts
that, when the entropy parameter of a loop satisfies , denaturation
transition does not take place. On the other hand for a first-order
denaturation transition is consistent with our model and may take place in the
actual system, as in the case with no supercoils. These results are in contrast
with other treatments of circular DNA melting where denaturation is assumed to
be accompanied by an increase in twist rather than writhe on the bound
segments.Comment: 4 pages, 3 figures, accepted for publication in PRE Rapid Com
Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model
The recently discovered phenomenon of nonlinear supratransmission consists in
a sudden increase of the amplitude of a transmitted wave triggered by the
excitation of nonlinear localized modes of the medium. We examine this process
for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at
the other. The supratransmission regime occurs for driving frequencies above
the upper band-edge and originates from direct moving discrete breather
creation. We derive approximate analytical estimates of the supratransmission
threshold, which are in excellent agreement with numerics. When analysing the
long-time behavior, we discover that, below the supratransmission threshold, a
conducting stationary state coexists with the insulating one. We explain the
bistable nature of the energy flux in terms of the excitation of quasi-harmonic
extended waves. This leads to the analytical calculation of a
lower-transmission threshold which is also in reasonable agreement with
numerical experiments.Comment: 8 pages, 9 figures. Phys. Rev. E (accepted
The grand canonical ABC model: a reflection asymmetric mean field Potts model
We investigate the phase diagram of a three-component system of particles on
a one-dimensional filled lattice, or equivalently of a one-dimensional
three-state Potts model, with reflection asymmetric mean field interactions.
The three types of particles are designated as , , and . The system is
described by a grand canonical ensemble with temperature and chemical
potentials , , and . We find that for
the system undergoes a phase transition from a
uniform density to a continuum of phases at a critical temperature . For other values of the chemical potentials the system
has a unique equilibrium state. As is the case for the canonical ensemble for
this model, the grand canonical ensemble is the stationary measure
satisfying detailed balance for a natural dynamics. We note that , where is the critical temperature for a similar transition in
the canonical ensemble at fixed equal densities .Comment: 24 pages, 3 figure
Time-, Frequency-, and Wavevector-Resolved X-Ray Diffraction from Single Molecules
Using a quantum electrodynamic framework, we calculate the off-resonant
scattering of a broad-band X-ray pulse from a sample initially prepared in an
arbitrary superposition of electronic states. The signal consists of
single-particle (incoherent) and two-particle (coherent) contributions that
carry different particle form factors that involve different material
transitions. Single-molecule experiments involving incoherent scattering are
more influenced by inelastic processes compared to bulk measurements. The
conditions under which the technique directly measures charge densities (and
can be considered as diffraction) as opposed to correlation functions of the
charge-density are specified. The results are illustrated with time- and
wavevector-resolved signals from a single amino acid molecule (cysteine)
following an impulsive excitation by a stimulated X-ray Raman process resonant
with the sulfur K-edge. Our theory and simulations can guide future
experimental studies on the structures of nano-particles and proteins
Phase diagram of the ABC model with nonconserving processes
The three species ABC model of driven particles on a ring is generalized to
include vacancies and particle-nonconserving processes. The model exhibits
phase separation at high densities. For equal average densities of the three
species, it is shown that although the dynamics is {\it local}, it obeys
detailed balance with respect to a Hamiltonian with {\it long-range
interactions}, yielding a nonadditive free energy. The phase diagrams of the
conserving and nonconserving models, corresponding to the canonical and
grand-canonical ensembles, respectively, are calculated in the thermodynamic
limit. Both models exhibit a transition from a homogeneous to a phase-separated
state, although the phase diagrams are shown to differ from each other. This
conforms with the expected inequivalence of ensembles in equilibrium systems
with long-range interactions. These results are based on a stability analysis
of the homogeneous phase and exact solution of the hydrodynamic equations of
the models. They are supported by Monte-Carlo simulations. This study may serve
as a useful starting point for analyzing the phase diagram for unequal
densities, where detailed balance is not satisfied and thus a Hamiltonian
cannot be defined.Comment: 32 page, 7 figures. The paper was presented at Statphys24, held in
Cairns, Australia, July 201
Analytical study of an exclusive genetic switch
The nonequilibrium stationary state of an exclusive genetic switch is
considered. The model comprises two competing species and a single binding site
which, when bound to by a protein of one species, causes the other species to
be repressed. The model may be thought of as a minimal model of the power
struggle between two competing parties. Exact solutions are given for the
limits of vanishing binding/unbinding rates and infinite binding/unbinding
rates. A mean field theory is introduced which is exact in the limit of
vanishing binding/unbinding rates. The mean field theory and numerical
simulations reveal that generically bistability occurs and the system is in a
symmetry broken state. An exact perturbative solution which in principle allows
the nonequilibrium stationary state to be computed is also developed and
computed to first and second order.Comment: 28 pages, 6 figure
A dynamically extending exclusion process
An extension of the totally asymmetric exclusion process, which incorporates
a dynamically extending lattice is explored. Although originally inspired as a
model for filamentous fungal growth, here the dynamically extending exclusion
process (DEEP) is studied in its own right, as a nontrivial addition to the
class of nonequilibrium exclusion process models. Here we discuss various
mean-field approximation schemes and elucidate the steady state behaviour of
the model and its associated phase diagram. Of particular note is that the
dynamics of the extending lattice leads to a new region in the phase diagram in
which a shock discontinuity in the density travels forward with a velocity that
is lower than the velocity of the tip of the lattice. Thus in this region the
shock recedes from both boundaries.Comment: 20 pages, 12 figure
Motion of condensates in non-Markovian zero-range dynamics
Condensation transition in a non-Markovian zero-range process is studied in
one and higher dimensions. In the mean-field approximation, corresponding to
infinite range hopping, the model exhibits condensation with a stationary
condensate, as in the Markovian case, but with a modified phase diagram. In the
case of nearest-neighbor hopping, the condensate is found to drift by a
"slinky" motion from one site to the next. The mechanism of the drift is
explored numerically in detail. A modified model with nearest-neighbor hopping
which allows exact calculation of the steady state is introduced. The steady
state of this model is found to be a product measure, and the condensate is
stationary.Comment: 31 pages, 9 figure
Nonlinear optical spectroscopy of single, few, and many molecules; nonequilibrium Green's function QED approach
Nonlinear optical signals from an assembly of N noninteracting particles
consist of an incoherent and a coherent component, whose magnitudes scale \sim
N and \sim N(N-1), respectively. A unified microscopic description of both
types of signals is developed using a quantum electrodynamical (QED) treatment
of the optical fields. Closed nonequilibrium Green's function expressions are
derived that incorporate both stimulated and spontaneous processes. General
(n+1)-wave mixing experiments are discussed as an example of spontaneously
generated signals. When performed on a single particle, such signals cannot be
expressed in terms of the nth order polarization, as predicted by the
semiclassical theory. Stimulated processes are shown to be purely incoherent in
nature. Within the QED framework, heterodyne-detected wave mixing signals are
simply viewed as incoherent stimulated emission, whereas homodyne signals are
generated by coherent spontaneous emission.Comment: article: 33 pages (preprint format!) ''paper.tex'' figures: 17
figures (.eps) in folder ``figures'
Cooperating or Fighting with Decoherence in the Optimal Control of Quantum Dynamics
This paper explores the use of laboratory closed-loop learning control to
either fight or cooperate with decoherence in the optimal manipulation of
quantum dynamics. Simulations of the processes are performed in a Lindblad
formulation on multilevel quantum systems strongly interacting with the
environment without spontaneous emission. When seeking a high control yield it
is possible to find fields that successfully fight with decoherence while
attaining a good quality yield. When seeking modest control yields, fields can
be found which are optimally shaped to cooperate with decoherence and thereby
drive the dynamics more efficiently. In the latter regime when the control
field and the decoherence strength are both weak, a theoretical foundation is
established to describe how they cooperate with each other. In general, the
results indicate that the population transfer objectives can be effectively met
by appropriately either fighting or cooperating with decoherence
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