65 research outputs found
A quasi-elastic regime for vibrated granular gases
Using simple scaling arguments and two-dimensional numerical simulations of a
granular gas excited by vibrating one of the container boundaries, we study a
double limit of small and large , where is the restitution
coefficient and the size of the container. We show that if the particle
density and where is the particle diameter, are
kept constant and small enough, the granular temperature, i.e. the mean value
of the kinetic energy per particle, , tends to a constant whereas the
mean dissipated power per particle, , decreases like when
increases, provided that . The relative fluctuations
of , and the power injected by the moving boundary, , have simple
properties in that regime. In addition, the granular temperature can be
determined from the fluctuations of the power injected by the moving
boundary.
Injected Power Fluctuations in 1D Dissipative Systems
Using fermionic techniques, we compute exactly the large deviation function
(ldf) of the time-integrated injected power in several one-dimensional
dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics
supplemented by an injection mechanism, which is taken as a Poissonian flipping
of one particular spin. We discuss the physical content of the results,
specifically the influence of the rate of the Poisson process on the properties
of the ldf.Comment: 18 pages, 8 figure
Energy fluctuations in vibrated and driven granular gases
We investigate the behavior of energy fluctuations in several models of
granular gases maintained in a non-equilibrium steady state. In the case of a
gas heated from a boundary, the inhomogeneities of the system play a
predominant role. Interpreting the total kinetic energy as a sum of independent
but not identically distributed random variables, it is possible to compute the
probability density function (pdf) of the total energy. Neglecting correlations
and using the analytical expression for the inhomogeneous temperature profile
obtained from the granular hydrodynamic equations, we recover results which
have been previously observed numerically and which had been attributed to the
presence of correlations. In order to separate the effects of spatial
inhomogeneities from those ascribable to velocity correlations, we have also
considered two models of homogeneously thermostated gases: in this framework it
is possible to reveal the presence of non-trivial effects due to velocity
correlations between particles. Such correlations stem from the inelasticity of
collisions. Moreover, the observation that the pdf of the total energy tends to
a Gaussian in the large system limit, suggests that they are also due to the
finite size of the system.Comment: 13 pages, 10 figure
Effects of the low frequencies of noise on On-Off intermittency
A bifurcating system subject to multiplicative noise can exhibit on-off
intermittency close to the instability threshold. For a canonical system, we
discuss the dependence of this intermittency on the Power Spectrum Density
(PSD) of the noise. Our study is based on the calculation of the Probability
Density Function (PDF) of the unstable variable. We derive analytical results
for some particular types of noises and interpret them in the framework of
on-off intermittency. Besides, we perform a cumulant expansion for a random
noise with arbitrary power spectrum density and show that the intermittent
regime is controlled by the ratio between the departure from the threshold and
the value of the PSD of the noise at zero frequency. Our results are in
agreement with numerical simulations performed with two types of random
perturbations: colored Gaussian noise and deterministic fluctuations of a
chaotic variable. Extensions of this study to another, more complex, system are
presented and the underlying mechanisms are discussed.Comment: 13pages, 13 figure
Critical exponents in zero dimensions
In the vicinity of the onset of an instability, we investigate the effect of
colored multiplicative noise on the scaling of the moments of the unstable mode
amplitude. We introduce a family of zero dimensional models for which we can
calculate the exact value of the critical exponents for all the
moments. The results are obtained through asymptotic expansions that use the
distance to onset as a small parameter. The examined family displays a variety
of behaviors of the critical exponents that includes anomalous exponents:
exponents that differ from the deterministic (mean-field) prediction, and
multiscaling: non-linear dependence of the exponents on the order of the
moment
Fluctuations of energy flux in wave turbulence
We report that the power driving gravity and capillary wave turbulence in a
statistically stationary regime displays fluctuations much stronger than its
mean value. We show that its probability density function (PDF) has a most
probable value close to zero and involves two asymmetric roughly exponential
tails. We understand the qualitative features of the PDF using a simple
Langevin type model.Comment: submitted to PR
High natural erosion rates are the backdrop for enhanced anthropogenic soil erosion in the Middle Hills of Nepal
Although agriculturally accelerated soil erosion is implicated in the unsustainable environmental degradation of mountain environments, such as in the Himalaya, the effects of land use can be challenging to quantify in many mountain settings because of the high and variable natural background rates of erosion. In this study, we present new long-term denudation rates, derived from cosmogenic 10Be analysis of quartz in river sediment from the Likhu Khola, a small agricultural river basin in the Middle Hills of central Nepal. Calculated long-term denudation rates, which reflect background natural erosion processes over 1000+ years prior to agricultural intensification, are similar to present-day sediment yields and to soil loss rates from terraces that are well maintained. Similarity in short- and long-term catchment-wide erosion rates for the Likhu is consistent with data from elsewhere in the Nepal Middle Hills but contrasts with the very large increases in short-term erosion rates seen in agricultural catchments in other steep mountain settings. Our results suggest that the large sediment fluxes exported from the Likhu and other Middle Hills rivers in the Himalaya are derived in large part from natural processes, rather than from soil erosion as a result of agricultural activity. Catchment-scale erosional fluxes may be similar over short and long timescales if both are dominated by mass wasting sources such as gullies, landslides, and debris flows (e.g., as is evident in the landslide-dominated Khudi Khola of the Nepal High Himalaya, based on compiled data). As a consequence, simple comparison of catchment-scale fluxes will not necessarily pinpoint land use effects on soils where these are only a small part of the total erosion budget, unless rates of mass wasting are also considered. Estimates of the mass wasting contribution to erosion in the Likhu imply catchment-averaged soil production rates on the order of ~ 0.25–0.35 mm yr−1, though rates of mass wasting are poorly constrained. The deficit between our best estimates for soil production rates and measurements of soil loss rates supports conclusions from previous studies that terraced agriculture in the Likhu may not be associated with a large systematic soil deficit, at least when terraces are well maintained, but that poorly managed terraces, forest, and scrubland may lead to rapid depletion of soil resources
Fluctuations in granular gases
A driven granular material, e.g. a vibrated box full of sand, is a stationary
system which may be very far from equilibrium. The standard equilibrium
statistical mechanics is therefore inadequate to describe fluctuations in such
a system. Here we present numerical and analytical results concerning energy
and injected power fluctuations. In the first part we explain how the study of
the probability density function (pdf) of the fluctuations of total energy is
related to the characterization of velocity correlations. Two different regimes
are addressed: the gas driven at the boundaries and the homogeneously driven
gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of
homogeneity in hydrodynamics profiles, even in the absence of velocity
correlations, the fluctuations of total energy are non-trivial and may lead to
erroneous conclusions about the role of correlations. In the second part of the
chapter we take into consideration the fluctuations of injected power in driven
granular gas models. Recently, real and numerical experiments have been
interpreted as evidence that the fluctuations of power injection seem to
satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an
alternative interpretation of such results which invalidates the
Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and
using techniques from large deviation theory, the general validity of a
Fluctuation Relation for power injection in driven granular gases is
questioned. Finally a functional is defined using the Lebowitz-Spohn approach
for Markov processes applied to the linear inelastic Boltzmann equation
relevant to describe the motion of a tracer particle. Such a functional results
to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure
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