1,452 research outputs found
Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid
The Chapman-Enskog method of solution of kinetic equations, such as the
Boltzmann equation, is based on an expansion in gradients of the deviations fo
the hydrodynamic fields from a uniform reference state (e.g., local
equilibrium). This paper presents an extension of the method so as to allow for
expansions about \emph{arbitrary}, far-from equilibrium reference states. The
primary result is a set of hydrodynamic equations for studying variations from
the arbitrary reference state which, unlike the usual Navier-Stokes
hydrodynamics, does not restrict the reference state in any way. The method is
illustrated by application to a sheared granular gas which cannot be studied
using the usual Navier-Stokes hydrodynamics.Comment: 23 pages, no figures. Submited to PRE Replaced to correct misc.
errors Replaced to correct misc. errors, make notation more consistant,
extend discussio
Integration through transients for Brownian particles under steady shear
Starting from the microscopic Smoluchowski equation for interacting Brownian
particles under stationary shearing, exact expressions for shear-dependent
steady-state averages, correlation and structure functions, and
susceptibilities are obtained, which take the form of generalized Green-Kubo
relations. They require integration of transient dynamics. Equations of motion
with memory effects for transient density fluctuation functions are derived
from the same microscopic starting point. We argue that the derived formal
expressions provide useful starting points for approximations in order to
describe the stationary non-equilibrium state of steadily sheared dense
colloidal dispersions.Comment: 17 pages, Submitted to J. Phys.: Condens. Matter; revised version
with minor correction
Distinct telomere differences within a reproductively bimodal common lizard population
1. Different strategies of reproductive mode, either oviparity (eggâlaying) or viviparity (liveâbearing), will be associated with a range of other lifeâhistory differences that are expected to affect patterns of ageing and longevity. It is usually difficult to compare the effects of alternative reproductive modes because of evolutionary and ecological divergence. However, the very rare exemplars of reproductive bimodality, in which different modes exist within a single species, offer an opportunity for robust and controlled comparisons.
2. One trait of interest that could be associated with life history, ageing and longevity is the length of the telomeres, which form protective caps at the chromosome ends and are generally considered a good indicator of cellular health. The shortening of these telomeres has been linked to stressful conditions; therefore, it is possible that differing reproductive costs will influence patterns of telomere loss. This is important because a number of studies have linked a shorter telomere length to reduced survival.
3. Here, we have studied maternal and offspring telomere dynamics in the common lizard (Zootoca vivipara). Our study has focused on a population where oviparous and viviparous individuals coâoccur in the same habitat and occasionally interbreed to form admixed individuals.
4. While viviparity confers many advantages for offspring, it might also incur substantial costs for the mother, for example require more energy. Therefore, we predicted that viviparous mothers would have relatively shorter telomeres than oviparous mothers, with admixed mothers having intermediate telomere lengths. There is thought to be a heritable component to telomere length; therefore, we also hypothesized that offspring would follow the same pattern as the mothers.
5. Contrary to our predictions, the viviparous mothers and offspring had the longest telomeres, and the oviparous mothers and offspring had the shortest telomeres. The differing telomere lengths may have evolved as an effect of the lifeâhistory divergence between the reproductive modes, for example due to the increased growth rate that viviparous individuals may undergo to reach a similar size at reproduction
Segregation of an intruder in a heated granular dense gas
A recent segregation criterion [V. Garz\'o, Phys. Rev. E \textbf{78},
020301(R) (2008)] based on the thermal diffusion factor of an
intruder in a heated granular gas described by the inelastic Enskog equation is
revisited. The sign of provides a criterion for the transition
between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE).
The present theory incorporates two extra ingredients not accounted for by the
previous theoretical attempt. First, the theory is based upon the second Sonine
approximation to the transport coefficients of the mass flux of intruder.
Second, the dependence of the temperature ratio (intruder temperature over that
of the host granular gas) on the solid volume fraction is taken into account in
the first and second Sonine approximations. In order to check the accuracy of
the Sonine approximation considered, the Enskog equation is also numerically
solved by means of the direct simulation Monte Carlo (DSMC) method to get the
kinetic diffusion coefficient . The comparison between theory and
simulation shows that the second Sonine approximation to yields an
improvement over the first Sonine approximation when the intruder is lighter
than the gas particles in the range of large inelasticity. With respect to the
form of the phase diagrams for the BNE/RBNE transition, the kinetic theory
results for the factor indicate that while the form of these diagrams
depends sensitively on the order of the Sonine approximation considered when
gravity is absent, no significant differences between both Sonine solutions
appear in the opposite limit (gravity dominates the thermal gradient). In the
former case (no gravity), the first Sonine approximation overestimates both the
RBNE region and the influence of dissipation on thermal diffusion segregation.Comment: 9 figures; to be published in Phys. Rev.
Conformal compactification and cycle-preserving symmetries of spacetimes
The cycle-preserving symmetries for the nine two-dimensional real spaces of
constant curvature are collectively obtained within a Cayley-Klein framework.
This approach affords a unified and global study of the conformal structure of
the three classical Riemannian spaces as well as of the six relativistic and
non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, both
Newton-Hooke and Galilean), and gives rise to general expressions holding
simultaneously for all of them. Their metric structure and cycles (lines with
constant geodesic curvature that include geodesics and circles) are explicitly
characterized. The corresponding cyclic (Mobius-like) Lie groups together with
the differential realizations of their algebras are then deduced; this
derivation is new and much simpler than the usual ones and applies to any
homogeneous space in the Cayley-Klein family, whether flat or curved and with
any signature. Laplace and wave-type differential equations with conformal
algebra symmetry are constructed. Furthermore, the conformal groups are
realized as matrix groups acting as globally defined linear transformations in
a four-dimensional "conformal ambient space", which in turn leads to an
explicit description of the "conformal completion" or compactification of the
nine spaces.Comment: 43 pages, LaTe
Nonequilibrium fluctuation dissipation relations of interacting Brownian particles driven by shear
We present a detailed analysis of the fluctuation dissipation theorem (FDT)
close to the glass transition in colloidal suspensions under steady shear using
mode coupling approximations. Starting point is the many-particle Smoluchowski
equation. Under shear, detailed balance is broken and the response functions in
the stationary state are smaller at long times than estimated from the
equilibrium FDT. An asymptotically constant relation connects response and
fluctuations during the shear driven decay, restoring the form of the FDT with,
however, a ratio different from the equilibrium one. At short times, the
equilibrium FDT holds. We follow two independent approaches whose results are
in qualitative agreement. To discuss the derived fluctuation dissipation
ratios, we show an exact reformulation of the susceptibility which contains not
the full Smoluchowski operator as in equilibrium, but only its well defined
Hermitian part. This Hermitian part can be interpreted as governing the
dynamics in the frame comoving with the probability current. We present a
simple toy model which illustrates the FDT violation in the sheared colloidal
system.Comment: 21 pages, 13 figures, submitted to Phys. Rev.
Long Wavelength Instability for Uniform Shear Flow
Uniform Shear Flow is a prototype nonequilibrium state admitting detailed
study at both the macroscopic and microscopic levels via theory and computer
simulation. It is shown that the hydrodynamic equations for this state have a
long wavelength instability. This result is obtained first from the
Navier-Stokes equations and shown to apply at both low and high densities.
Next, higher order rheological effects are included using a model kinetic
theory. The results are compared favorably to those from Monte Carlo
simulation.Comment: 12 pages, including 2 figure
Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic
hard spheres can be identified, and calculated in the long wavelength limit.
Assuming they dominate at long times, formal expressions for the Navier-Stokes
transport coefficients are derived. They can be expressed in a form that
generalizes the Green-Kubo relations for molecular systems, and it is shown
that they can also be evaluated by means of -particle simulation methods.
The form of the hydrodynamic modes to zeroth order in the gradients is used to
detect the presence of inherent velocity correlations in the homogeneous
cooling state, even in the low density limit. They manifest themselves in the
fluctuations of the total energy of the system. The theoretical predictions are
shown to be in agreement with molecular dynamics simulations. Relevant related
questions deserving further attention are pointed out
Gaussian Kinetic Model for Granular Gases
A kinetic model for the Boltzmann equation is proposed and explored as a
practical means to investigate the properties of a dilute granular gas. It is
shown that all spatially homogeneous initial distributions approach a universal
"homogeneous cooling solution" after a few collisions. The homogeneous cooling
solution (HCS) is studied in some detail and the exact solution is compared
with known results for the hard sphere Boltzmann equation. It is shown that all
qualitative features of the HCS, including the nature of over population at
large velocities, are reproduced semi-quantitatively by the kinetic model. It
is also shown that all the transport coefficients are in excellent agreement
with those from the Boltzmann equation. Also, the model is specialized to one
having a velocity independent collision frequency and the resulting HCS and
transport coefficients are compared to known results for the Maxwell Model. The
potential of the model for the study of more complex spatially inhomogeneous
states is discussed.Comment: to be submitted to Phys. Rev.
Quantum transport and momentum conserving dephasing
We study numerically the influence of momentum-conserving dephasing on the
transport in a disordered chain of scatterers. Loss of phase memory is caused
by coupling the transport channels to dephasing reservoirs. In contrast to
previously used models, the dephasing reservoirs are linked to the transport
channels between the scatterers, and momentum conserving dephasing can be
investigated. Our setup provides a model for nanosystems exhibiting conductance
quantization at higher temperatures in spite of the presence of phononic
interaction. We are able to confirm numerically some theoretical predictions.Comment: 7 pages, 4 figure
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