1,445 research outputs found
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
Logarithmic oscillators: ideal Hamiltonian thermostats
A logarithmic oscillator (in short, log-oscillator) behaves like an ideal
thermostat because of its infinite heat capacity: when it weakly couples to
another system, time averages of the system observables agree with ensemble
averages from a Gibbs distribution with a temperature T that is given by the
strength of the logarithmic potential. The resulting equations of motion are
Hamiltonian and may be implemented not only in a computer but also with
real-world experiments, e.g., with cold atoms.Comment: 5 pages, 3 figures. v4: version accepted in Phys. Rev. Let
Separation of trajectories and its Relation to Entropy for Intermittent Systems with a Zero Lyapunov exponent
One dimensional intermittent maps with stretched exponential separation of
nearby trajectories are considered. When time goes infinity the standard
Lyapunov exponent is zero. We investigate the distribution of
,
where is determined by the nonlinearity of the map in the vicinity of
marginally unstable fixed points. The mean of is determined
by the infinite invariant density. Using semi analytical arguments we calculate
the infinite invariant density for the Pomeau-Manneville map, and with it
obtain excellent agreement between numerical simulation and theory. We show
that \alpha \left is equal to Krengel's entropy and
to the complexity calculated by the Lempel-Ziv compression algorithm. This
generalized Pesin's identity shows that \left and
Krengel's entropy are the natural generalizations of usual Lyapunov exponent
and entropy for these systems.Comment: 12 pages, 10 figure
Anomalous diffusion in viscosity landscapes
Anomalous diffusion is predicted for Brownian particles in inhomogeneous
viscosity landscapes by means of scaling arguments, which are substantiated
through numerical simulations. Analytical solutions of the related
Fokker-Planck equation in limiting cases confirm our results. For an ensemble
of particles starting at a spatial minimum (maximum) of the viscous damping we
find subdiffusive (superdiffusive) motion. Superdiffusion occurs also for a
monotonically varying viscosity profile. We suggest different substances for
related experimental investigations.Comment: 15 page
Neutron-induced background in the CONUS experiment
CONUS is a novel experiment aiming at detecting elastic neutrino nucleus
scattering in the fully coherent regime using high-purity Germanium (Ge)
detectors and a reactor as antineutrino () source. The detector setup
is installed at the commercial nuclear power plant in Brokdorf, Germany, at a
very small distance to the reactor core in order to guarantee a high flux of
more than 10/(scm). For the experiment, a good
understanding of neutron-induced background events is required, as the neutron
recoil signals can mimic the predicted neutrino interactions. Especially
neutron-induced events correlated with the thermal power generation are
troublesome for CONUS. On-site measurements revealed the presence of a thermal
power correlated, highly thermalized neutron field with a fluence rate of
(74530)cmd. These neutrons that are produced by nuclear
fission inside the reactor core, are reduced by a factor of 10 on
their way to the CONUS shield. With a high-purity Ge detector without shield
the -ray background was examined including highly thermal power
correlated N decay products as well as -lines from neutron
capture. Using the measured neutron spectrum as input, it was shown, with the
help of Monte Carlo simulations, that the thermal power correlated field is
successfully mitigated by the installed CONUS shield. The reactor-induced
background contribution in the region of interest is exceeded by the expected
signal by at least one order of magnitude assuming a realistic ionization
quenching factor of 0.2.Comment: 28 pages, 28 figure
The challenge of non-Markovian energy balance models in climate
We first review the way in which Hasselmann’s paradigm, introduced in 1976 and recently honored with the Nobel Prize, can, like many key innovations in complexity science, be understood on several different levels. It can be seen as a way to add variability into the pioneering energy balance models (EBMs) of Budyko and Sellers. On a more abstract level, however, it used the original stochastic mathematical model of Brownian motion to provide a conceptual superstructure to link slow climate variability to fast weather fluctuations, in a context broader than EBMs, and led Hasselmann to posit a need for negative feedback in climate modeling. Hasselmann’s paradigm has still much to offer us, but naturally, since the 1970s, a number of newer developments have built on his pioneering ideas. One important one has been the development of a rigorous mathematical hierarchy that embeds Hasselmann-type models in the more comprehensive Mori-Zwanzig generalized Langevin equation (GLE) framework. Another has been the interest in stochastic EBMs with a memory that has slower decay and, thus, longer range than the exponential form seen in his EBMs. In this paper, we argue that the Mori-Kubo overdamped GLE, as widely used in statistical mechanics, suggests the form of a relatively simple stochastic EBM with memory for the global temperature anomaly. We also explore how this EBM relates to Lovejoy et al.’s fractional energy balance equation
Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
Using methods of stochastic dynamics, we have studied stationary states in
the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape
of stationary states depend both on the potential type and the damping. If the
damping is strong enough, for potential wells which in the overdamped regime
produce multimodal stationary states, stationary states in the underdamped
regime can be multimodal with the same number of modes like in the overdamped
regime. For the parabolic potential, the stationary density is always unimodal
and it is given by the two dimensional -stable density. For the mixture
of quartic and parabolic single-well potentials the stationary density can be
bimodal. Nevertheless, the parabolic addition, which is strong enough, can
destroy bimodlity of the stationary state.Comment: 9 page
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
Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions
We study the long-time behavior of decoupled continuous-time random walks
characterized by superheavy-tailed distributions of waiting times and symmetric
heavy-tailed distributions of jump lengths. Our main quantity of interest is
the limiting probability density of the position of the walker multiplied by a
scaling function of time. We show that the probability density of the scaled
walker position converges in the long-time limit to a non-degenerate one only
if the scaling function behaves in a certain way. This function as well as the
limiting probability density are determined in explicit form. Also, we express
the limiting probability density which has heavy tails in terms of the Fox
-function and find its behavior for small and large distances.Comment: 16 pages, 1 figur
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