1,724 research outputs found
Knotted Strange Attractors and Matrix Lorenz Systems
A generalization of the Lorenz equations is proposed where the variables take
values in a Lie algebra. The finite dimensionality of the representation
encodes the quantum fluctuations, while the non-linear nature of the equations
can describe chaotic fluctuations. We identify a criterion, for the appearance
of such non-linear terms. This depends on whether an invariant, symmetric
tensor of the algebra can vanish or not. This proposal is studied in detail for
the fundamental representation of . We find a knotted
structure for the attractor, a bimodal distribution for the largest Lyapunov
exponent and that the dynamics takes place within the Cartan subalgebra, that
does not contain only the identity matrix, thereby can describe the quantum
fluctuations.Comment: 10 pages Revtex, 3 figure
The effect of the range of interaction on the phase diagram of a globular protein
Thermodynamic perturbation theory is applied to the model of globular
proteins studied by ten Wolde and Frenkel (Science 277, pg. 1976) using
computer simulation. It is found that the reported phase diagrams are
accurately reproduced. The calculations show how the phase diagram can be tuned
as a function of the lengthscale of the potential.Comment: 20 pages, 5 figure
Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice: topology and boundary effects
The role of dimensionality (Euclidean versus fractal), spatial extent,
boundary effects and system topology on the efficiency of diffusion-reaction
processes involving two simultaneously-diffusing reactants is analyzed. We
present numerically-exact values for the mean time to reaction, as gauged by
the mean walklength before reactive encounter, obtained via application of the
theory of finite Markov processes, and via Monte Carlo simulation. As a general
rule, we conclude that for sufficiently large systems, the efficiency of
diffusion-reaction processes involving two synchronously diffusing reactants
(two-walker case) relative to processes in which one reactant of a pair is
anchored at some point in the reaction space (one walker plus trap case) is
higher, and is enhanced the lower the dimensionality of the system. This
differential efficiency becomes larger with increasing system size and, for
periodic systems, its asymptotic value may depend on the parity of the lattice.
Imposing confining boundaries on the system enhances the differential
efficiency relative to the periodic case, while decreasing the absolute
efficiencies of both two-walker and one walker plus trap processes. Analytic
arguments are presented to provide a rationale for the results obtained. The
insights afforded by the analysis to the design of heterogeneous catalyst
systems are also discussed.Comment: 15 pages, 8 figures, uses revtex4, accepted for publication in
Physica
Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid
The Chapman-Enskog method of solution of kinetic equations, such as the
Boltzmann equation, is based on an expansion in gradients of the deviations fo
the hydrodynamic fields from a uniform reference state (e.g., local
equilibrium). This paper presents an extension of the method so as to allow for
expansions about \emph{arbitrary}, far-from equilibrium reference states. The
primary result is a set of hydrodynamic equations for studying variations from
the arbitrary reference state which, unlike the usual Navier-Stokes
hydrodynamics, does not restrict the reference state in any way. The method is
illustrated by application to a sheared granular gas which cannot be studied
using the usual Navier-Stokes hydrodynamics.Comment: 23 pages, no figures. Submited to PRE Replaced to correct misc.
errors Replaced to correct misc. errors, make notation more consistant,
extend discussio
Growth states of catalytic reaction networks exhibiting energy metabolism
All cells derive nutrition by absorbing some chemical and energy resources
from the environment; these resources are used by the cells to reproduce the
chemicals within them, which in turn leads to an increase in their volume. In
this study, we introduce a protocell model exhibiting catalytic reaction
dynamics, energy metabolism, and cell growth. Results of extensive simulations
of this model show the existence of four phases with regard to the rates of
both the influx of resources and the cell growth. These phases include an
active phase with high influx and high growth rates, an inefficient phase with
high influx but low growth rates, a quasi-static phase with low influx and low
growth rates, and a death phase with negative growth rate. A mean field model
well explains the transition among these phases as bifurcations. The
statistical distribution of the active phase is characterized by a power law
and that of the inefficient phase is characterized by a nearly equilibrium
distribution. We also discuss the relevance of the results of this study to
distinct states in the existing cells.Comment: 21 pages, 5 figure
Oscillators and relaxation phenomena in Pleistocene climate theory
Ice sheets appeared in the northern hemisphere around 3 million years ago and
glacial-interglacial cycles have paced Earth's climate since then. Superimposed
on these long glacial cycles comes an intricate pattern of millennial and
sub-millennial variability, including Dansgaard-Oeschger and Heinrich events.
There are numerous theories about theses oscillations. Here, we review a number
of them in order to draw a parallel between climatic concepts and dynamical
system concepts, including, in particular, the relaxation oscillator,
excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all
theories of ice ages reviewed here feature a phenomenon of synchronisation
between internal climate dynamics and the astronomical forcing. However, these
theories differ in their bifurcation structure and this has an effect on the
way the ice age phenomenon could grow 3 million years ago. All theories on
rapid events reviewed here rely on the concept of a limit cycle in the ocean
circulation, which may be excited by changes in the surface freshwater surface
balance. The article also reviews basic effects of stochastic fluctuations on
these models, including the phenomenon of phase dispersion, shortening of the
limit cycle and stochastic resonance. It concludes with a more personal
statement about the potential for inference with simple stochastic dynamical
systems in palaeoclimate science.
Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages,
Dansgaard-Oeschger eventsComment: Published in the Transactions of the Philosophical Transactions of
the Royal Society (Series A, Physical Mathematical and Engineering Sciences),
as a contribution to the Proceedings of the workshop on Stochastic Methods in
Climate Modelling, Newton Institute (23-27 August). Philosophical
Transactions of the Royal Society (Series A, Physical Mathematical and
Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on
request to author and on http://www.uclouvain.be/ito
Diversity-induced resonance
We present conclusive evidence showing that different sources of diversity,
such as those represented by quenched disorder or noise, can induce a resonant
collective behavior in an ensemble of coupled bistable or excitable systems.
Our analytical and numerical results show that when such systems are subjected
to an external subthreshold signal, their response is optimized for an
intermediate value of the diversity. These findings show that intrinsic
diversity might have a constructive role and suggest that natural systems might
profit from their diversity in order to optimize the response to an external
stimulus.Comment: 4 pages, 3 figure
Lifting of Ir{100} reconstruction by CO adsorption: An ab initio study
The adsorption of CO on unreconstructed and reconstructed Ir{100} has been
studied, using a combination of density functional theory and thermodynamics,
to determine the relative stability of the two phases as a function of CO
coverage, temperature and pressure. We obtain good agreement with
experimentaldata. At zero temperature, the (1X5) reconstruction becomes less
stable than the unreconstructed (1X1) surface when the CO coverage exceeds a
critical value of 0.09 ML. The interaction between CO molecules is found to be
repulsive on the reconstructed surface, but attractive on the unreconstructed,
explaining the experimental observation of high CO coverage on growing (1X1)
islands. At all temperatures and pressures, we find only two possible stable
states: 0.05 ML CO c(2X2) overlayer on the (1X1) substrate, and the clean
(15) reconstructed surface.Comment: 31 page
Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production
Based on the Fokker-Planck and the entropy balance equations we have studied
the relaxation of a dissipative dynamical system driven by external
Ornstein-Uhlenbeck noise processes in absence and presence of nonequilibrium
constraint in terms of the thermodynamically inspired quantities like entropy
flux and entropy production. The interplay of nonequilibrium constraint,
dissipation and noise reveals some interesting extremal nature in the time
dependence of entropy flux and entropy production.Comment: RevTex, 17 pages, 9 figures. To appear in Phys. Rev.
Reentrance effect in the lane formation of driven colloids
Recently it has been shown that a strongly interacting colloidal mixture
consisting of oppositely driven particles, undergoes a nonequilibrium
transition towards lane formation provided the driving strength exceeds a
threshold value. We predict here a reentrance effect in lane formation: for
fixed high driving force and increasing particle densities, there is first a
transition towards lane formation which is followed by another transition back
to a state with no lanes. Our result is obtained both by Brownian dynamics
computer simulations and by a phenomenological dynamical density functional
theory.Comment: 4 pages, 2 figure
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