The Steady State Distribution of the Master Equation

The steady states of the master equation are investigated. We give two expressions for the steady state distribution of the master equation a la the Zubarev-McLennan steady state distribution, i.e., the exact expression and an expression near equilibrium. The latter expression obtained is consistent with recent attempt of constructing steady state theormodynamics.Comment: 6 pages, No figures. A mistake was correcte

An expression for stationary distribution in nonequilibrium steady state

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths and/or driven by an external force. Starting from the detailed fluctuation theorem we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate $\eta$ is proportional to $\exp[{\Phi}(\eta)]$ where ${\Phi}(\eta)=-\sum_k\beta_k\mathcal{E}_k(\eta)$ is the excess entropy change. Here $\mathcal{E}_k(\eta)$ is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the $k$-th heat bath whose inverse temperature is $\beta_k$. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.Comment: 4 pages, 2 figure

A dynamical theory of homogeneous nucleation for colloids and macromolecules

Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal or macromolecular system in the strong damping limit the most likely path for nucleation can be determined by gradient descent in density space governed by a nontrivial metric fixed by the dynamics. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to liquid-vapor nucleation where it is shown that, in contrast to most free energy-based studies, the smallest clusters correspond to long wavelength, small amplitude perturbations.Comment: final version; 4 pages, 2 figure

Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models

The revised Enskog approximation for a fluid of hard spheres which lose energy upon collision is discussed for the case that the energy is lost from the normal component of the velocity at collision but is otherwise arbitrary. Granular fluids with a velocity-dependent coefficient of restitution are an important special case covered by this model. A normal solution to the Enskog equation is developed using the Chapman-Enskog expansion. The lowest order solution describes the general homogeneous cooling state and a generating function formalism is introduced for the determination of the distribution function. The first order solution, evaluated in the lowest Sonine approximation, provides estimates for the transport coefficients for the Navier-Stokes hydrodynamic description. All calculations are performed in an arbitrary number of dimensions.Comment: 27 pages + 1 figur

Phase diagram and universality of the Lennard-Jones gas-liquid system

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexsisting density, the critical exponent of the order parameter is estimated to be $\beta = 0.3285(7)$. Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be $\nu = 0.63 (4)$. The obtained values of $\beta$ and $\nu$ are consistent with those of the Ising universality class.Comment: 8 pages, 8 figures, new results are adde

Distinct telomere differences within a reproductively bimodal common lizard population

1. Different strategies of reproductive mode, either oviparity (egg‐laying) or viviparity (live‐bearing), will be associated with a range of other life‐history 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 co‐occur 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 life‐history 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

Surviving the effects of barotrauma: assessing treatment options and a ‘natural’ remedy to enhance the release survival of line caught pink snapper (Pagrus auratus)

A new technique to ameliorate the effects of barotrauma was tested based on observations of pink snapper, Pagrus auratus (Forster), inadvertently piercing their everted stomach with their teeth and releasing trapped swim bladder gases. This technique was termed buccal venting and involved piercing the everted stomach protruding into the buccal cavity or out of the mouth with a 16-gauge hypodermic needle (a practice previously not encouraged). Short-term (~3 days) survival of buccal-vented fish was not significantly different from laterally vented fish nor untreated controls. Both buccal and lateral venting techniques were shown to cause no harm and allowed fish to return to depth. The short-term (1–3 days) post-release survival of line caught snapper was 88% with no significant difference in survival across three depth ranges tested (37–50, 51–100 and 101–180 m). Survival of sublegal pink snapper ( 0.05) from that of legal-sized fish (≥35 cm TL). Healing of the swim bladder was observed in 27% of pink snapper dissected after ≤3 days in captivity, and healing of stomachs was observed in 64% of pink snapper that had been buccal vented. Relatively high post-release survival rates of line caught pink snapper may offer some protection for snapper stocks where high fishing pressure and legal size restrictions result in the majority of the catch having to be released

Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid

The response functions for small spatial perturbations of a homogeneous granular fluid have been described recently. In appropriate dimensionless variables, they have the form of stationary state time correlation functions. Here, these functions are expressed in terms of reduced single particle functions that are expected to obey a linear kinetic equation. The functional assumption required for such a kinetic equation, and a Markov approximation for its implementation are discussed. If, in addition, static velocity correlations are neglected, a granular fluid version of the linearized Enskog kinetic theory is obtained. The derivation makes no a priori limitation on the density, space and time scale, nor degree of inelasticity. As an illustration, recently derived Helfand and Green-Kubo expressions for the Navier-Stokes order transport coefficients are evaluated with this kinetic theory. The results are in agreement with those obtained from the Chapman-Enskog solution to the nonlinear Enskog kinetic equation.Comment: Submitted to J. Stat. Mec

Hot Brownian Motion

We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a practical rational basis for emerging photothermal technologies.Comment: 10 pages, 5 figure

Short-term survival of discarded pearl perch (Glaucosoma scapulare Ramsay, 1881) caught by hook-and-line in Queensland, Australia

Post-release survival of line-caught pearl perch (Glaucosoma scapulare) was assessed via field experiments where fish were angled using methods similar to those used by commercial, recreational and charter fishers. One hundred and eighty-three individuals were caught during four experiments, of which >91% survived up to three days post-capture. Hook location was found to be the best predictor of survival, with the survival of throat- or stomach-hooked pearl perch significantly (P < 0.05) lower than those hooked in either the mouth or lip. Post-release survival was similar for both legal (≥35 cm) and sub-legal (<35 cm) pearl perch, while those individuals showing no signs of barotrauma were more likely to survive in the short term. Examination of the swim bladders in the laboratory, combined with observations in the field, revealed that swim bladders rupture during ascent from depth allowing swim bladder gases to escape into the gut cavity. As angled fish approach the surface, the alimentary tract ruptures near the anus allowing swim bladder gases to escape the gut cavity. As a result, very few pearl perch exhibit barotrauma symptoms and no barotrauma mitigation strategies were recommended. The results of this study show that pearl perch are relatively resilient to catch-and-release suggesting that post-release mortality would not contribute significantly to total fishing mortality. We recommend the use of circle hooks, fished actively on tight lines, combined with minimal handling in order to maximise the post-release survival of pearl perch