159 research outputs found
Stick-slip motion of solids with dry friction subject to random vibrations and an external field
We investigate a model for the dynamics of a solid object, which moves over a
randomly vibrating solid surface and is subject to a constant external force.
The dry friction between the two solids is modeled phenomenologically as being
proportional to the sign of the object's velocity relative to the surface, and
therefore shows a discontinuity at zero velocity. Using a path integral
approach, we derive analytical expressions for the transition probability of
the object's velocity and the stationary distribution of the work done on the
object due to the external force. From the latter distribution, we also derive
a fluctuation relation for the mechanical work fluctuations, which incorporates
the effect of the dry friction.Comment: v1: 23 pages, 9 figures; v2: Reference list corrected; v3: Published
version, typos corrected, references adde
Exact power spectra of Brownian motion with solid friction
We study a Langevin equation describing the Brownian motion of an object
subjected to a viscous drag, an external constant force, and a solid friction
force of the Coulomb type. In a previous work [H. Touchette, E. Van der
Straeten, W. Just, J. Phys. A: Math. Theor. 43, 445002, 2010], we have
presented the exact solution of the velocity propagator of this equation based
on a spectral decomposition of the corresponding Fokker-Planck equation. Here,
we present an alternative, exact solution based on the Laplace transform of
this equation, which has the advantage of being expressed in closed form. From
this solution, we also obtain closed-form expressions for the Laplace transform
of the velocity autocorrelation function and for the power spectrum, i.e., the
Fourier transform of the autocorrelation function. The behavior of the power
spectrum as a function of the dry friction force and external forcing shows a
clear crossover between stick and slip regimes known to occur in the presence
of solid friction.Comment: v1: 14 pages, 5 figures; v2: new figures, some text added, typos
correcte
Calculation of the Voronoi boundary for lens-shaped particles and spherocylinders
We have recently developed a mean-field theory to estimate the packing
fraction of non-spherical particles [A. Baule et al., Nature Commun. (2013)].
The central quantity in this framework is the Voronoi excluded volume, which
generalizes the standard hard-core excluded volume appearing in Onsager's
theory. The Voronoi excluded volume is defined from an exclusion condition for
the Voronoi boundary between two particles, which is usually not tractable
analytically. Here, we show how the technical difficulties in calculating the
Voronoi boundary can be overcome for lens-shaped particles and spherocylinders,
two standard prolate and oblate shapes with rotational symmetry. By decomposing
these shapes into unions and intersections of spheres analytical expressions
can be obtained.Comment: 19 pages, 8 figure
Weak-noise limit of a piecewise-smooth stochastic differential equation
Y.C. was supported by the Chinese Scholarship Council,
the Hunan Provincial Innovation Foundation for Postgraduates
(Grant No. CX2011B011), and NUDT’s Innovation Foundation
(Grant No. B110205). W.J. gratefully acknowledges
support from EPSRC through Grants No. EP/H04812X/1 and
No. SFB91
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
Anomalous Processes with General Waiting Times: Functionals and Multipoint Structure
Many transport processes in nature exhibit anomalous diffusive properties
with non-trivial scaling of the mean square displacement, e.g., diffusion of
cells or of biomolecules inside the cell nucleus, where typically a crossover
between different scaling regimes appears over time. Here, we investigate a
class of anomalous diffusion processes that is able to capture such complex
dynamics by virtue of a general waiting time distribution. We obtain a complete
characterization of such generalized anomalous processes, including their
functionals and multi-point structure, using a representation in terms of a
normal diffusive process plus a stochastic time change. In particular, we
derive analytical closed form expressions for the two-point correlation
functions, which can be readily compared with experimental data.Comment: Accepted in Phys. Rev. Let
Path integral approach to random motion with nonlinear friction
Using a path integral approach, we derive an analytical solution of a
nonlinear and singular Langevin equation, which has been introduced previously
by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion
of a solid object on a vibrating horizontal surface. We show that the optimal
(or most probable) paths of this model can be divided into two classes of
paths, which correspond physically to a sliding or slip motion, where the
object moves with a non-zero velocity over the underlying surface, and a
stick-slip motion, where the object is stuck to the surface for a finite time.
These two kinds of basic motions underlie the behavior of many more complicated
systems with solid/solid friction and appear naturally in de Gennes' model in
the path integral framework.Comment: 18 pages, 3 figure
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
Space-time Phase Transitions in Driven Kinetically Constrained Lattice Models
Kinetically constrained models (KCMs) have been used to study and understand
the origin of glassy dynamics. Despite having trivial thermodynamic properties,
their dynamics slows down dramatically at low temperatures while displaying
dynamical heterogeneity as seen in glass forming supercooled liquids. This
dynamics has its origin in an ergodic-nonergodic first-order phase transition
between phases of distinct dynamical "activity". This is a "space-time"
transition as it corresponds to a singular change in ensembles of trajectories
of the dynamics rather than ensembles of configurations. Here we extend these
ideas to driven glassy systems by considering KCMs driven into non-equilibrium
steady states through non-conservative forces. By classifying trajectories
through their entropy production we prove that driven KCMs also display an
analogous first-order space-time transition between dynamical phases of finite
and vanishing entropy production. We also discuss how trajectories with rare
values of entropy production can be realized as typical trajectories of a
mapped system with modified forces
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