141 research outputs found
Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model
We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena et al., Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter lambda and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime
Statistical mechanics far from equilibrium: prediction and test for a sheared system
We report the complete statistical treatment of a system of particles
interacting via Newtonian forces in continuous boundary-driven flow, far from
equilibrium. By numerically time-stepping the force-balance equations of a
model fluid we measure occupancies and transition rates in simulation. The
high-shear-rate simulation data verify the invariant quantities predicted by
our statistical theory, thus demonstrating that a class of non-equilibrium
steady states of matter, namely sheared complex fluids, is amenable to
statistical treatment from first principles.Comment: 4 pages plus a 3-page pdf supplemen
Joint Probability Distributions for a Class of Non-Markovian Processes
We consider joint probability distributions for the class of coupled Langevin
equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)].
We generalize well-known results for the single time probability distributions
to the case of N-time joint probability distributions. It is shown that these
probability distribution functions can be obtained by an integral transform
from distributions of a Markovian process. The integral kernel obeys a partial
differential equation with fractional time derivatives reflecting the
non-Markovian character of the process.Comment: 13 pages, 1 figur
Brownian motion with dry friction: Fokker-Planck approach
We solve a Langevin equation, first studied by de Gennes, in which there is a
solid-solid or dry friction force acting on a Brownian particle in addition to
the viscous friction usually considered in the study of Brownian motion. We
obtain both the time-dependent propagator of this equation and the velocity
correlation function by solving the associated time-dependent Fokker-Planck
equation. Exact results are found for the case where only dry friction acts on
the particle. For the case where both dry and viscous friction forces are
present, series representations of the propagator and correlation function are
obtained in terms of parabolic cylinder functions. Similar series
representations are also obtained for the case where an external constant force
is added to the Langevin equation.Comment: 18 pages, 13 figures (in color
The Impact of Charcoal Production on Forest Degradation: a Case Study in Tete, Mozambique
Charcoal production for urban energy consumption is a main driver of forest degradation in sub-Saharan Africa. Urban growth projections for the continent suggest that the relevance of this process will increase in the coming decades. Forest degradation associated to charcoal production is difficult to monitor and commonly overlooked and underrepresented in forest cover change and carbon emission estimates. We use a multi-temporal dataset of very high-resolution remote sensing images to map kiln locations in a representative study area of tropical woodlands in central Mozambique. The resulting maps provided a characterization of the spatial extent and temporal dynamics of charcoal production. Using an indirect approach we combine kiln maps and field information on charcoal making to describe the magnitude and intensity of forest degradation linked to charcoal production, including aboveground biomass and carbon emissions. Our findings reveal that forest degradation associated to charcoal production in the study area is largely independent from deforestation driven by agricultural expansion and that its impact on forest cover change is in the same order of magnitude as deforestation. Our work illustrates the feasibility of using estimates of urban charcoal consumption to establish a link between urban energy demands and forest degradation. This kind of approach has potential to reduce uncertainties in forest cover change and carbon emission assessments in sub-Saharan Africa
Properties of a non-equilibrium heat bath
At equilibrium, a fluid element, within a larger heat bath, receives random
impulses from the bath. Those impulses, which induce stochastic transitions in
the system (the fluid element), respect the principle of detailed balance,
because the bath is also at equilibrium. Under continuous shear, the fluid
element adopts a non-equilibrium steady state. Because the surrounding bath of
fluid under shear is also in a non-equilibrium steady state, the system
receives stochastic impulses with a non-equilibrium distribution. Those
impulses no longer respect detailed balance, but are nevertheless constrained
by rules. The rules in question, which are applicable to a wide sub-class of
driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett.
{\bf 92}, 150601 (2004); J. Phys. A: Math. Gen. {\bf 38}, 293 (2005)] using
information-theoretic arguments. In the present paper, we provide a more
fundamental derivation, based on the uncontroversial, non-Bayesian
interpretation of probabilities as simple ratios of countable quantities. We
apply the results to some simple models of interacting particles, to
investigate the nature of forces that are mediated by a non-equilibrium
noise-source such as a fluid under shear.Comment: 14 pages, 7 figure
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
In the context of Markov evolution, we present two original approaches to
obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the
language of stochastic derivatives and by using a family of exponential
martingales functionals. We show that GFDT are perturbative versions of
relations verified by these exponential martingales. Along the way, we prove
GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the
usual proof for diffusion and pure jump processes. Finally, we relate the FR to
a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions,
new results in Section
On distributions of functionals of anomalous diffusion paths
Functionals of Brownian motion have diverse applications in physics,
mathematics, and other fields. The probability density function (PDF) of
Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger
equation in imaginary time. In recent years there is a growing interest in
particular functionals of non-Brownian motion, or anomalous diffusion, but no
equation existed for their PDF. Here, we derive a fractional generalization of
the Feynman-Kac equation for functionals of anomalous paths based on
sub-diffusive continuous-time random walk. We also derive a backward equation
and a generalization to Levy flights. Solutions are presented for a wide number
of applications including the occupation time in half space and in an interval,
the first passage time, the maximal displacement, and the hitting probability.
We briefly discuss other fractional Schrodinger equations that recently
appeared in the literature.Comment: 25 pages, 4 figure
Do Individual Investors Consciously Speculate on Reversals? Evidence from Leveraged Warrant Trading
Sensitivity of MEG and EEG to Source Orientation
An important difference between magnetoencephalography
(MEG) and electroencephalography (EEG)
is that MEG is insensitive to radially oriented sources. We
quantified computationally the dependency of MEG and
EEG on the source orientation using a forward model with
realistic tissue boundaries. Similar to the simpler case of a
spherical head model, in which MEG cannot see radial
sources at all, for most cortical locations there was a source
orientation to which MEG was insensitive. The median
value for the ratio of the signal magnitude for the source
orientation of the lowest and the highest sensitivity was
0.06 for MEG and 0.63 for EEG. The difference in the
sensitivity to the source orientation is expected to contribute
to systematic differences in the signal-to-noise ratio
between MEG and EEG.National Institutes of Health (U.S.) (Grant NS057500)National Institutes of Health (U.S.) (Grant NS037462)National Institutes of Health (U.S.) (Grant HD040712)National Center for Research Resources (U.S.) (P41RR14075)Mind Research Networ
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