scholarly journals INTERACTING CONSTITUENTS IN COSMOLOGY

2008 ◽  
Vol 17 (06) ◽  
pp. 857-879 ◽  
Author(s):  
R. ALDROVANDI ◽  
R. R. CUZINATTO ◽  
L. G. MEDEIROS
Keyword(s):  
Energy Density ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Source Terms ◽  
Systematic Method ◽  
Usual Approach ◽  
Interaction Terms ◽  
Real Fluids ◽  
Universe Evolution ◽  
Source Fluid

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure × energy density equations of state p(ρ). The usual approach in cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the statistical mechanics of real fluids, is proposed to include them. A toy model is presented which shows how such interaction terms could be applied to engender significant cosmological effects.

scholarly journals Cosmic Evolution of Viscous QCD Epoch in Causal Eckart Frame

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 112
Author(s):  
Eman Abdel Hakk ◽  
Abdel Nasser Tawfik ◽  
Afaf Nada ◽  
Hayam Yassin
Keyword(s):  
Energy Density ◽  
Energy Flow ◽  
Equations Of State ◽  
Temporal Evolution ◽  
Particle Diffusion ◽  
Cosmic Evolution ◽  
Bulk Viscous ◽  
Viscous Pressure ◽  
Bulk Viscous Pressure ◽  
Particle Current

It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic evolution of viscous hadron and parton epochs in casual and non-casual Eckart frame is analyzed. By proposing equations of state deduced from recent lattice QCD simulations including pressure p, energy density ρ, and temperature T, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter H˙, the cosmic energy density ρ˙, and the share η˙ and the bulk viscous coefficient ζ˙. We also suggest how the bulk viscous pressure Π could be related to H. We conclude that the relativistic theory of fluids, the Eckart frame, and the finite viscous coefficients play essential roles in the cosmic evolution, especially in the hadron and parton epochs.

RELATIVISTIC NUCLEAR ENERGY DENSITY FUNCTIONALS

2010 ◽  
Vol 19 (04) ◽  
pp. 548-557 ◽  
Author(s):  
D. VRETENAR ◽  
T. NIKŠIĆ ◽  
P. RING
Keyword(s):  
Energy Density ◽  
Degrees Of Freedom ◽  
Nuclear Energy ◽  
Effective Interaction ◽  
Binding Energies ◽  
Large Set ◽  
Density Functionals ◽  
Heavy Nuclei ◽  
Interaction Terms ◽  
Range Dynamics

A class of relativistic nuclear energy density functionals is explored, in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance correlations, as well as intermediate and long-range dynamics, are encoded in the nucleon-density dependence of the strength functionals of an effective interaction Lagrangian. The resulting phenomenological effective interaction, adjusted to experimental binding energies of a large set of axially deformed nuclei, together with a new separable pairing interaction adjusted to reproduce the pairing gap in nuclear matter calculated with the Gogny force, is applied in triaxial relativistic Hartree-Bogoliubov calculations of sequences of heavy nuclei: Th , U , Pu , Cm , Cf , Fm , and No .

The theory of rubber elasticity

1976 ◽  
Vol 351 (1666) ◽  
pp. 397-406 ◽  
Keyword(s):  
Equation Of State ◽  
Statistical Mechanics ◽  
Equations Of State ◽  
Rubber Elasticity ◽  
Elastic Behaviour ◽  
Excluded Volume ◽  
Simple Pattern ◽  
Dynamical Approach ◽  
Equilibrium Approach ◽  
The Future

It is argued that since statistical mechanics has developed in two ways, the dynamical approach of Boltzmann and the equilibrium approach of Gibbs, both should be valuable in rubber elasticity. It is shown that this is indeed the case, and the generality of these approaches allows one to study the problem in greater depth than hitherto. In particular, damping terms in the elastic behaviour of rubber can be calculated, and also the effect of entanglements and excluded volume on the equation of state. It is noticeable that although the calculated equations of state are quite complex, they do not fit into a simple pattern of invariants. The future for these developments is briefly discussed.

Equations of state for fluids based on hard sphere repulsion

2015 ◽  
Vol 29 (13) ◽  
pp. 1550089 ◽  
Author(s):  
Minhui Shan ◽  
Jianxiang Tian
Keyword(s):  
Equation Of State ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Equations Of State ◽  
The Past ◽  
Complex Interactions ◽  
Structures And Properties ◽  
The One ◽  
Real Fluids

As is well-known, the structures and thermodynamic properties of fluids are determined by the complex interactions, i.e., the repulsive one and the attractive one, among particles. The simplest equation-of-state (EOS) model maybe the one of hard sphere repulsion plus or multiplying some attraction. Followed by the rapid promotion of the accuracy of hard sphere EOS in the past dozens of years, one question rises as whether more accurate hard sphere repulsion derives better prediction of the structures and properties of fluids with a special attraction. In this work, we used two repulsions with clearly different accuracy and some attractions to construct series equations of state (EOSs) for real fluids, and then we discussed the saturated properties at liquid–gas equilibrium. We found that the answer to the question aforementioned is not definitely standing.

scholarly journals Landau's statistical mechanics for quasi-particle models

2014 ◽  
Vol 29 (10) ◽  
pp. 1450056 ◽  
Author(s):  
Vishnu M. Bannur
Keyword(s):  
Energy Density ◽  
Statistical Mechanics ◽  
Quark Gluon Plasma ◽  
Statistical Physics ◽  
Particle System ◽  
Gluon Plasma ◽  
Particle Model ◽  
Quasi Particle ◽  
Thermodynamics And Statistical Mechanics

Landau's formalism of statistical mechanics [following L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, Oxford, 1980)] is applied to the quasi-particle model of quark–gluon plasma. Here, one starts from the expression for pressure and develop all thermodynamics. It is a general formalism and consistent with our earlier studies [V. M. Bannur, Phys. Lett. B647, 271 (2007)] based on Pathria's formalism [following R. K. Pathria, Statistical Mechanics (Butterworth-Heinemann, Oxford, 1977)]. In Pathria's formalism, one starts from the expression for energy density and develop thermodynamics. Both the formalisms are consistent with thermodynamics and statistical mechanics. Under certain conditions, which are wrongly called thermodynamic consistent relation, we recover other formalism of quasi-particle system, like in M. I. Gorenstein and S. N. Yang, Phys. Rev. D52, 5206 (1995), widely studied in quark–gluon plasma.

scholarly journals Nakedly singular counterpart of Schwarzschild’s incompressible star. A barotropic continuity condition in the center

2019 ◽  
Vol 51 (11) ◽  
Author(s):  
Łukasz Bratek ◽  
Joanna Jałocha ◽  
Andrzej Woszczyna
Keyword(s):  
Energy Density ◽  
Incompressible Fluid ◽  
Equations Of State ◽  
Continuity Condition ◽  
Interior Solution ◽  
Regularity Conditions ◽  
Initial Condition ◽  
Static Sphere ◽  
Proper Energy

Abstract A static sphere of incompressible fluid with uniform proper energy density is considered as an example of exact star-like solution with weakened central regularity conditions characteristic of a nakedly singular spherical vaccuum solution. The solution is a singular counterpart of the Schwarzschild’s interior solution. The initial condition in the center for general barotropic equations of state is established.

scholarly journals Cohesive Energy Densities Versus Internal Pressures of Near and Supercritical Fluids

Molecules ◽  
2019 ◽  
Vol 24 (5) ◽  
pp. 961 ◽  
Author(s):  
Michal Roth
Keyword(s):  
Energy Density ◽  
Internal Pressure ◽  
Molar Volume ◽  
Intermolecular Interactions ◽  
Supercritical Fluids ◽  
Cohesive Energy ◽  
Equations Of State ◽  
Reduced Pressure ◽  
Cohesive Energy Density ◽  
Internal Pressures

Over half a century ago, Wiehe and Bagley suggested that a product of the internal pressure and molar volume of a liquid measures the energy of nonspecific intermolecular interactions whereas the cohesive energy reflects the total energy of intermolecular interactions in the liquid. This conjecture, however, has never been considered in connection with near and supercritical fluids. In this contribution, the cohesive energy density, internal pressure and their ratios are calculated from high precision equations of state for eight important fluids including water. To secure conformity to the principle of corresponding states when comparing different fluids, the calculations are carried out along the line defined by equality between the reduced temperature and the reduced pressure of the fluid (Tr = Pr). The results provide additional illustration of the tunability of the solvent properties of water that stands apart from those of other near and supercritical fluids in common use. In addition, an overview is also presented of the derivatives of cohesive energy density, solubility parameter and internal pressure with respect to temperature, pressure and molar volume.

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