Thermodynamic Properties of Generalized Exclusion Statistics

We analytically calculate some thermodynamic quantities of an ideal $g$-on gas obeying generalized exclusion statistics. We show that the specific heat of a $g$-on gas ($g \neq 0$) vanishes linearly in any dimension as $T \to 0$ when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at $g$ to the hole-statistics at $1/g$ at low temperatures. We derive the complete solution for the cluster coefficients $b_l(g)$ as a function of Haldane's statistical interaction $g$ in $D$ dimensions. We also find that the cluster coefficients $b_l(g)$ and the virial coefficients $a_l(g)$ are exactly mirror symmetric ($l$=odd) or antisymmetric ($l$=even) about $g=1/2$. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the $g$-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.Comment: 24 pages, Revtex, Corrected typo

Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces

Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all \tau. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small \tau, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite \tau, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.Comment: 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected and a footnote was added on the d-dimensional cas

Application of Bayesian model averaging to measurements of the primordial power spectrum

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale 0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper limit, depending on prior assumptions.Comment: 7 pages with 7 figures include

Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.Comment: 11 pages, 6 figure

Present and future evidence for evolving dark energy

We compute the Bayesian evidences for one- and two-parameter models of evolving dark energy, and compare them to the evidence for a cosmological constant, using current data from Type Ia supernova, baryon acoustic oscillations, and the cosmic microwave background. We use only distance information, ignoring dark energy perturbations. We find that, under various priors on the dark energy parameters, LambdaCDM is currently favoured as compared to the dark energy models. We consider the parameter constraints that arise under Bayesian model averaging, and discuss the implication of our results for future dark energy projects seeking to detect dark energy evolution. The model selection approach complements and extends the figure-of-merit approach of the Dark Energy Task Force in assessing future experiments, and suggests a significantly-modified interpretation of that statistic.Comment: 10 pages RevTex4, 3 figures included. Minor changes to match version accepted by PR

Multiscale modeling and simulation for polymer melt flows between parallel plates

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, visco-elastic liquid, and visco-elastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for $\omega\tau^R\lesssim 1$, and the crossover between the liquid-like and solid-like regime takes place around $\omega\tau^\alpha\simeq 1$ (where $\omega$ is the angular frequency of the plate and $\tau^R$ and $\tau^\alpha$ are Rouse and $\alpha$ relaxation time, respectively).Comment: 13pages, 12figure

Testing feasibility of scalar-tensor gravity by scale dependent mass and coupling to matter

We investigate whether there are any cosmological evidences for a scalar field with a mass and coupling to matter which change accordingly to the properties of the astrophysical system it "lives in", without directly focusing on the underlying mechanism that drives the scalar field scale-dependent properties. We assume a Yukawa type of coupling between the field and matter and also that the scalar field mass grows with density, in order to overcome all gravity constraints within the solar system. We analyse three different gravitational systems assumed as "cosmological indicators": supernovae type Ia, low surface brightness spiral galaxies and clusters of galaxies. Results show that: a) a quite good fit to the rotation curves of low surface brightness galaxies only using visible stellar and gas mass components is obtained; b) a scalar field can fairly well reproduce the matter profile in clusters of galaxies, estimated by X-ray observations and without the need of any additional dark matter; c) there is an intrinsic difficulty in extracting information about the possibility of a scale-dependent massive scalar field (or more generally about a varying gravitational constant) from supernovae type Ia.Comment: 30 pages, 15 figures, to appear in Phys. Rev.

Ignorance based inference of optimality in thermodynamic processes

We derive ignorance based prior distribution to quantify incomplete information and show its use to estimate the optimal work characteristics of a heat engine.Comment: Latex, 10 pages, 3 figure

Acceleration of the Universe driven by the Casimir force

We investigate an evolutional scenario of the FRW universe with the Casimir energy scaling like $(-)(1+z)^4$. The Casimir effect is used to explain the vacuum energy differences (its value measured from astrophysics is so small compared to value obtained from quantum field theory calculations). The dynamics of the FRW model is represented in terms of a two-dimensional dynamical system to show all evolutional paths of this model in the phase space for all admissible initial conditions. We find also an exact solution for non flat evolutional paths of Universe driven by the Casimir effect. The main difference between the FRW model with the Casimir force and the $\Lambda$CDM model is that their generic solutions are a set of evolutional paths with a bounce solution and an initial singularity, respectively. The evolutional scenario are tested by using the SNIa data, FRIIb radiogalaxies, baryon oscillation peak and CMB observation. We compare the power of explanation of the model considered and the $\Lambda$CDM model using the Bayesian information criterion and Bayesian factor. Our investigation of the information criteria of model selection showed the preference of the $\Lambda$CDM model over the model considered. However the presence of negative like the radiation term can remove a tension between the theoretical and observed primordial ${}^4$He and D abundance.Comment: RevTeX4, 17 pages, 9 figure

Tidal dissipation in rotating giant planets

[Abridged] Tides may play an important role in determining the observed distributions of mass, orbital period, and eccentricity of the extrasolar planets. In addition, tidal interactions between giant planets in the solar system and their moons are thought to be responsible for the orbital migration of the satellites, leading to their capture into resonant configurations. We treat the underlying fluid dynamical problem with the aim of determining the efficiency of tidal dissipation in gaseous giant planets. In cases of interest, the tidal forcing frequencies are comparable to the spin frequency of the planet but small compared to its dynamical frequency. We therefore study the linearized response of a slowly and possibly differentially rotating planet to low-frequency tidal forcing. Convective regions of the planet support inertial waves, while any radiative regions support generalized Hough waves. We present illustrative numerical calculations of the tidal dissipation rate and argue that inertial waves provide a natural avenue for efficient tidal dissipation in most cases of interest. The resulting value of Q depends in a highly erratic way on the forcing frequency, but we provide evidence that the relevant frequency-averaged dissipation rate may be asymptotically independent of the viscosity in the limit of small Ekman number. In short-period extrasolar planets, if the stellar irradiation of the planet leads to the formation of a radiative outer layer that supports generalized Hough modes, the tidal dissipation rate can be enhanced through the excitation and damping of these waves. These dissipative mechanisms offer a promising explanation of the historical evolution and current state of the Galilean satellites as well as the observed circularization of the orbits of short-period extrasolar planets.Comment: 74 pages, 12 figures, submitted to The Astrophysical Journa