4,183 research outputs found
Solvable model for spatiotemporal chaos
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a nontrivial spatial behavior. We also introduce and calculate a generalized spatiotemporal correlation function
Pinning control of spatiotemporal chaos
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Hu and Qu [Phys. Rev. Lett. 72, 68 (1994)]. A nonlinear generalization of the method for a 1D lattice is also presented
Robustness of predator-prey models for confinement regime transitions in fusion plasmas
Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help to identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. We study and compare the long-time behaviour of the three-equation and four-equation systems, their evolution towards the final state, and their attractive fixed points and limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an attractive fixed point of the three-equation system can become a limit cycle of the four-equation system. Addressing these questions which we together refer to as “robustness” for convenience is particularly important for models which, as here, generate sharp transitions in the values of system variables which may replicate some key features of confinement transitions. Our results help to establish the robustness of the zero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas
Nonlinear Transport and Current Fluctuation in an AB Ring with a Quantum Dot
Nonequilibrium steady states are explicitly constructed for a noninteracting
electron model of an Aharonov-Bohm (AB) ring with a quantum dot (QD) with the
aid of asymptotic fields. The Fano line shapes and AB oscillations are shown to
strongly depend on the bias voltage. Current fluctuations are studied as well.Comment: 4pages, 6figure
Which phase is measured in the mesoscopic Aharonov-Bohm interferometer?
Mesoscopic solid state Aharonov-Bohm interferometers have been used to
measure the "intrinsic" phase, , of the resonant quantum
transmission amplitude through a quantum dot (QD). For a two-terminal "closed"
interferometer, which conserves the electron current, Onsager's relations
require that the measured phase shift only "jumps" between 0 and .
Additional terminals open the interferometer but then depends on the
details of the opening. Using a theoretical model, we present quantitative
criteria (which can be tested experimentally) for to be equal to the
desired : the "lossy" channels near the QD should have both a
small transmission and a small reflection
Measuring the transmission of a quantum dot using Aharonov-Bohm Interferometers
The conductance G through a closed Aharonov-Bohm mesoscopic solid-state
interferometer (which conserves the electron current), with a quantum dot (QD)
on one of the paths, depends only on cos(phi), where Phi= (hbar c phi)/e is the
magnetic flux through the ring. The absence of a phase shift in the
phi-dependence led to the conclusion that closed interferometers do not yield
the phase of the "intrinsic" transmission amplitude t_D=|t_D|e^{i alpha}
through the QD, and led to studies of open interferometers. Here we show that
(a) for single channel leads, alpha can be deduced from |t_D|, with no need for
interferometry; (b) the explicit dependence of G(phi) on cos(phi) (in the
closed case) allows a determination of both |t_D| and alpha; (c) in the open
case, results depend on the details of the opening, but optimization of these
details can yield the two-slit conditions which relate the measured phase shift
to alpha.Comment: Invited talk, Localization, Tokyo, August 200
Broken unitarity and phase measurements in Aharonov-Bohm interferometers
Aharonov-Bohm mesoscopic solid-state interferometers yield a conductance
which contains a term , where relates to the magnetic
flux. Experiments with a quantum dot on one of the interfering paths aim to
relate to the dot's intrinsic Friedel transmission phase, .
For closed systems, which conserve the electron current (unitarity), the
Onsager relation requires that . For open systems, we show that
depends in general on the details of the broken unitarity. Although it
gives information on the resonances of the dot, is generally not equal
to . A direct relation between and requires
specific ways of opening the system, which are discussed.Comment: 4 pages, 3 figures(eps). Phys. Rev. Letters (in press
Local modes, phonons, and mass transport in solid He
We propose a model to treat the local motion of atoms in solid He as a
local mode. In this model, the solid is assumed to be described by the Self
Consistent Harmonic approximation, combined with an array of local modes. We
show that in the bcc phase the atomic local motion is highly directional and
correlated, while in the hcp phase there is no such correlation. The correlated
motion in the bcc phase leads to a strong hybridization of the local modes with
the T phonon branch, which becomes much softer than that obtained
through a Self Consistent Harmonic calculation, in agreement with experiment.
In addition we predict a high energy excitation branch which is important for
self-diffusion. Both the hybridization and the presence of a high energy branch
are a consequence of the correlation, and appear only in the bcc phase. We
suggest that the local modes can play the role in mass transport usually
attributed to point defects (vacancies). Our approach offers a more overall
consistent picture than obtained using vacancies as the predominant point
defect. In particular, we show that our approach resolves the long standing
controversy regarding the contribution of point defects to the specific heat of
solid He.Comment: 10 pages, 10 figure
Asexual and sexual replication in sporulating organisms
This paper develops models describing asexual and sexual replication in
sporulating organisms. Replication via sporulation is the replication strategy
for all multicellular life, and may even be observed in unicellular life (such
as with budding yeast). We consider diploid populations replicating via one of
two possible sporulation mechanisms: (1) Asexual sporulation, whereby adult
organisms produce single-celled diploid spores that grow into adults
themselves. (2) Sexual sporulation, whereby adult organisms produce
single-celled diploid spores that divide into haploid gametes. The haploid
gametes enter a haploid "pool", where they may recombine with other haploids to
form a diploid spore that then grows into an adult. We consider a haploid
fusion rate given by second-order reaction kinetics. We work with a simplified
model where the diploid genome consists of only two chromosomes, each of which
may be rendered defective with a single point mutation of the wild-type. We
find that the asexual strategy is favored when the rate of spore production is
high compared to the characteristic growth rate from a spore to a reproducing
adult. Conversely, the sexual strategy is favored when the rate of spore
production is low compared to the characteristic growth rate from a spore to a
reproducing adult. As the characteristic growth time increases, or as the
population density increases, the critical ratio of spore production rate to
organism growth rate at which the asexual strategy overtakes the sexual one is
pushed to higher values. Therefore, the results of this model suggest that, for
complex multicellular organisms, sexual replication is favored at high
population densities, and low growth and sporulation rates.Comment: 8 pages, 5 figures, to be submitted to Journal of Theoretical
Biology, figures not included in this submissio
A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient
We consider a simple mathematical model of gradual Darwinian evolution in
continuous time and continuous trait space, due to intraspecific competition
for common resource in an asexually reproducing population in constant
environment, while far from evolutionary stable equilibrium. The model admits
exact analytical solution. In particular, Gaussian distribution of the trait
emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1
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