114 research outputs found
Thermostatting by deterministic scattering
We present a mechanism for thermalizing a moving particle by microscopic
deterministic scattering. As an example, we consider the periodic Lorentz gas.
We modify the collision rules by including energy transfer between particle and
scatterer such that the scatterer mimics a thermal reservoir with arbitrarily
many degrees of freedom. The complete system is deterministic, time-reversible,
and provides a microcanonical density in equilibrium. In the limit of the disk
representing infinitely many degrees of freedom and by applying an electric
field the system goes into a nonequilibrium steady state.Comment: 4 pages (revtex) with 4 figures (postscript
Thermostating by deterministic scattering: the periodic Lorentz gas
We present a novel mechanism for thermalizing a system of particles in
equilibrium and nonequilibrium situations, based on specifically modeling
energy transfer at the boundaries via a microscopic collision process. We apply
our method to the periodic Lorentz gas, where a point particle moves
diffusively through an ensemble of hard disks arranged on a triangular lattice.
First, collision rules are defined for this system in thermal equilibrium. They
determine the velocity of the moving particle such that the system is
deterministic, time reversible, and microcanonical. These collision rules can
systematically be adapted to the case where one associates arbitrarily many
degrees of freedom to the disk, which here acts as a boundary. Subsequently,
the system is investigated in nonequilibrium situations by applying an external
field. We show that in the limit where the disk is endowed by infinitely many
degrees of freedom it acts as a thermal reservoir yielding a well-defined
nonequilibrium steady state. The characteristic properties of this state, as
obtained from computer simulations, are finally compared to the ones of the
so-called Gaussian thermostated driven Lorentz gas.Comment: 13 pages (revtex) with 10 figures (encapsulated postscript
The Nose-hoover thermostated Lorentz gas
We apply the Nose-Hoover thermostat and three variations of it, which control
different combinations of velocity moments, to the periodic Lorentz gas.
Switching on an external electric field leads to nonequilibrium steady states
for the four models with a constant average kinetic energy of the moving
particle. We study the probability density, the conductivity and the attractor
in nonequilibrium and compare the results to the Gaussian thermostated Lorentz
gas and to the Lorentz gas as thermostated by deterministic scattering.Comment: 7 pages (revtex) with 10 figures (postscript), most of the figures
are bitmapped with low-resolution. The originals are many MB, they can be
obtained upon reques
Fluctuation formula for nonreversible dynamics in the thermostated Lorentz gas
We investigate numerically the validity of the Gallavotti-Cohen fluctuation
formula in the two and three dimensional periodic Lorentz gas subjected to
constant electric and magnetic fields and thermostated by the Gaussian
isokinetic thermostat. The magnetic field breaks the time reversal symmetry,
and by choosing its orientation with respect to the lattice one can have either
a generalized reversing symmetry or no reversibility at all. Our results
indicate that the scaling property described by the fluctuation formula may be
approximately valid for large fluctuations even in the absence of
reversibility.Comment: 6 pages, 6 figure
CORG: a database for COmparative Regulatory Genomics
Sequence conservation in non-coding, upstream regions of orthologous genes from man and mouse is likely to reflect common regulatory DNA sites. Motivated by this assumption we have delineated a catalogue of conserved non-coding sequence blocks and provide the CORG-'COmparative Regulatory Genomics'-database. The data were computed based on statistically significant local suboptimal alignments of 15 kb regions upstream of the translation start sites of, currently, 10 793 pairs of orthologous genes. The resulting conserved non-coding blocks were annotated with EST matches for easier detection of non-coding mRNA and with hits to known transcription factor binding sites. CORG data are accessible from the ENSEMBL web site via a DAS service as well as a specially developed web service (http://corg.molgen.mpg.de) for query and interactive visualization of the conserved blocks and their annotation
Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering
In recent work a deterministic and time-reversible boundary thermostat called
thermostating by deterministic scattering has been introduced for the periodic
Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the
nonlinear properties of this new dynamical system by numerically calculating
its Lyapunov exponents. Based on a revised method for computing Lyapunov
exponents, which employs periodic orthonormalization with a constraint, we
present results for the Lyapunov exponents and related quantities in
equilibrium and nonequilibrium. Finally, we check whether we obtain the same
relations between quantities characterizing the microscopic chaotic dynamics
and quantities characterizing macroscopic transport as obtained for
conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript
Rotor interaction in the annulus billiard
Introducing the rotor interaction in the integrable system of the annulus
billiard produces a variety of dynamical phenomena, from integrability to
ergodicity
Systems biologists seek fuller integration of systems biology approaches in new cancer research programs
Systems biology takes an interdisciplinary approach to the systematic study of complex interactions in biological systems. This approach seeks to decipher the emergent behaviors of complex systems rather than focusing only on their constituent properties. As an increasing number of examples illustrate the value of systems biology approaches to understand the initiation, progression, and treatment of cancer, systems biologists from across Europe and the United States hope for changes in the way their field is currently perceived among cancer researchers. In a recent EU-US workshop, supported by the European Commission, the German Federal Ministry for Education and Research, and the National Cancer Institute of the NIH, the participants discussed the strengths, weaknesses, hurdles, and opportunities in cancer systems biology
On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems
We discuss the transient and steady state fluctuation relation for a
mechanical system in contact with two deterministic thermostats at different
temperatures. The system is a modified Lorentz gas in which the fixed
scatterers exchange energy with the gas of particles, and the thermostats are
modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the
system. The transient fluctuation relation, which holds only for a precise
choice of the initial ensemble, is verified at all times, as expected. Times
longer than the mesoscopic scale, needed for local equilibrium to be settled,
are required if a different initial ensemble is considered. This shows how the
transient fluctuation relation asymptotically leads to the steady state
relation when, as explicitly checked in our systems, the condition found in
[D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity
of the steady state fluctuation relation, is verified. For the steady state
fluctuations of the phase space contraction rate \zL and of the dissipation
function \zW, a similar relaxation regime at shorter averaging times is
found. The quantity \zW satisfies with good accuracy the fluctuation relation
for times larger than the mesoscopic time scale; the quantity \zL appears to
begin a monotonic convergence after such times. This is consistent with the
fact that \zW and \zL differ by a total time derivative, and that the tails
of the probability distribution function of \zL are Gaussian.Comment: Major revision. Fig.10 was added. Version to appear in Journal of
Statistical Physic
Coherent States Measurement Entropy
Coherent states (CS) quantum entropy can be split into two components. The
dynamical entropy is linked with the dynamical properties of a quantum system.
The measurement entropy, which tends to zero in the semiclassical limit,
describes the unpredictability induced by the process of a quantum approximate
measurement. We study the CS--measurement entropy for spin coherent states
defined on the sphere discussing different methods dealing with the time limit
. In particular we propose an effective technique of computing
the entropy by iterated function systems. The dependence of CS--measurement
entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail:
[email protected]). Submitted to J.Phys.
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