The principle of corresponding states and the dynamic properties of simple liquids

We present a corresponding states analysis of existing data on sound velocity, transport coefficients and intermolecular interaction times of a number of simple fluids. With appropriate choices of parameters for the intermolecular pair potential, such properties as the adiabatic sound velocity, the shear and bulk viscosities, the thermal conductivity and the intermolecular interaction time can be reduced along the liquid-vapor equilibrium curve. Deviations from the simple law of corresponding states are most pronounced for the transport properties, indicating a stronger sensitivity of the dynamical properties to the interaction potential and the molecular structure.     

A kinetic theory of dense fluids

A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.     

A collisional approach to the calculation of time correlation functions. Transport coefficients of gases

A method of successive approximations is proposed for the evaluation of the time-correlation functions such as those that give the thermal transport coefficients of gases. The method is based on a calculation of the changes in correlations of appropriate functions of the molecular velocity which are a result of collisions in the gas. The decaying rates of the correlations are expressed as integrals of the differential collision cross section. When the first approximation is introduced in the expressions for thermal transport coefficients, results are obtained for the coefficient of binary diffusion and the viscosity and thermal conductivity of single-component systems which are identical with those of the first Chapman-Enskog solutions of the Boltzmann and Enskog equations. For the coefficients of viscosity and thermal conductivity in multicomponent systems, it is shown that the first approximation leads to expressions of the form of the Sutherland and Wassiljewa relations, respectively.     

Equilibrium molecular dynamics simulation of shear viscosity of two-dimensional complex (dusty) plasmas

Shear viscosity is examined throughout the entire range of strongly coupled states of two-dimensional complex (dusty) plasma liquids (CDPLs). We have employed equilibrium molecular dynamics (EMD) simulation to compute the shear viscosity coefficients of CDPLs. In the strongly coupled liquid region, the values of valid viscosity coefficient can be estimated only in order of magnitude. The variations in the valid viscosity coefficients with screening strength (κ) and Coulomb coupling strengths (Γ) are observed. A systematic dependence of shear viscosity on κ is observed for an intermediate and higher Γ. The investigations showed that the position of the minimum viscosity coefficient shifts towards higher Γ as κ increases. The computational results for the entire range of liquid states of the strongly coupled dusty plasma obtained using the shear autocorrelation functions are in good agreement with the available simulation results and experimental data. It is shown that new simulations extended the range of plasma states (Γ, κ) used in our earlier simulation results for the existence of a finite minimum possible viscosity coefficient and it is also dependent on plasma states.     

Microscopic transport theory of heavy-ion collisions

Drift and diffusion coefficients for the variables of mass fragmentation and excitation energy are studied for deeply inelastic collisions. The transport coefficients are obtained in closed form as functions of the parameters of the interaction matrix elements between nucleonic states and as functions of the binding energy of the intermediate rotating quasimolecular configuration. Drift and diffusion coefficients for excitation and mass transfer are related (dissipation fluctuation theorem). In good approximation these relations take the simple form of Einstein's relation between the mobility and the diffusion coefficient of a particle in a medium. For the total mass numbers 100, 250 and 500 the results are discussed in detail. The transport coefficients are compared with experimental results. Within the uncertainties of determination from experimental data, the drift and diffusion coefficients are well described by two previously adjusted parameters of the mean interaction matrix elements. Consequences for the production of superheavy elements in deeply inelastic collisions of U on U or Cf are discussed.     

Kubo formulas for relativistic fluids in strong magnetic fields

Magnetohydrodynamics of strongly magnetized relativistic fluids is derived in the ideal and dissipative cases, taking into account the breaking of spatial symmetries by a quantizing magnetic field. A complete set of transport coefficients, consistent with the Curie and Onsager principles, is derived for thermal conduction, as well as shear and bulk viscosities. It is shown that in the most general case the dissipative function contains five shear viscosities, two bulk viscosities, and three thermal conductivity coefficients. We use Zubarev’s non-equilibrium statistical operator method to relate these transport coefficients to correlation functions of the equilibrium theory. The desired relations emerge at linear order in the expansion of the non-equilibrium statistical operator with respect to the gradients of relevant statistical parameters (temperature, chemical potential, and velocity.) The transport coefficients are cast in a form that can be conveniently computed using equilibrium (imaginary-time) infrared Green’s functions defined with respect to the equilibrium statistical operator.     

Transport Coefficients for Inelastic Maxwell Mixtures

The Boltzmann equation for inelastic Maxwell models (IMM) is used to determine the Navier–Stokes transport coefficients of a granular binary mixture in d-dimensions. The Chapman–Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transport coefficients: the mutual diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient, the pressure energy coefficient, and the thermal conductivity. All these coefficients are exactly obtained in terms of the coefficients of restitution and the ratios of mass, concentration, and particle sizes. The results are compared with known transport coefficients of inelastic hard spheres (IHS) obtained analytically in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows a reasonably good agreement between both interaction models for not too strong dissipation, especially in the case of the transport coefficients associated with the mass flux     

Transport coefficients of a massive pion gas

We review our main results concerning the transport coefficients of a light meson gas,in particular we focus on the case of a massive pion gas.Leading order results according to the chiral power-counting are presented for the DC electrical conductivity,thermal conductivity,shear viscosity,and bulk viscosity.We also comment on the possible correlation between the bulk viscosity and the trace anomaly in QCD,as well as the relation between unitarity and a minimum of the quotient η/s near the phase transition.     

A theoretical study of transport coefficients in benzene vapour

The shear and bulk viscosities, and thermal conductivity, of benzene vapour have been calculated using a realistic interaction potential. Results are reported for the Taxman and Wang Chang-Uhlenbeck theories under the assumptions that internal vibrational states do not contribute to the transport coefficients and that the rotational motion of the molecules can be treated using classical mechanics. Apart from these assumptions the calculations are rigorous, and in particular the solution to the two-particle trajectory problem has not been simplified either by neglecting out-of-plane scattering or by holding the relative orientations of the molecules fixed during a collision. A small, but systematic, difference between results from the Taxman and Wang Chang-Uhlenbeck theories was found and it is suggested that the former theory is more accurate. Good agreement between theory and experiment is readily obtained for the shear viscosity but the corresponding results for the thermal conductivity are in poor agreement. After a correction term is included to allow for energy transfer between rotational and translational states, and the internal vibrational states, the thermal conductivity is also in good agreement with experiment. The results are used to develop an effective pair potential for benzene that is in agreement with experimental values of the shear viscosity, thermal conductivity, and second virial coefficient of the vapour and with the static lattice energy and structure of the solid.     

Molecular simulation study of the glass transition in a soft primitive model for ionic liquids

In this paper, we present a molecular dynamics study of the glass transition for a soft-core primitive model for ionic liquids, in which cations are fully flexible chains of tangent soft spherical monomers, being the positively charged monomer at one of the ends of the chain, and anions as charged soft spheres. We have monitored transport coefficients such as the self-diffusion coefficients and the shear viscosity, as well as correlation functions such as the mean-square displacement, the self-intermediate scattering function, and probes of heterogeneous dynamics such as the van Hove distribution function and the four-points susceptibility. The analysis of these properties indicates that, for a given pressure, the glass transition shows a weak temperature dependence on the cation length, occurring first for short-chain than for long-chain ionic liquids.     

The interacting quasiparticle–phonon picture and odd–even nuclei. Overview and perspectives

The role of the nucleon correlations in the ground states of even–even nuclei on the properties of low-lying states in odd–even spherical and transitional nuclei is studied. We reason about this subject using the language of the quasiparticle–phonon model which we extend to take account of the existence of quasiparticle?phonon configurations in the wave functions of the ground states of the even–even cores. Of paramount importance to the structure of the low-lying states happens to be the quasiparticle–phonon interaction in the ground states which we evaluated using both the standard and the extended random phase approximations. Numerical calculations for nuclei in the barium and cadmium regions are performed using pairing and quadrupole–quadrupole interaction modes which have the dominant impact on the lowest-lying states’ structure. It is found that states with same angular momentum and parity become closer in energy as compared to the predictions of models disregarding the backward amplitudes, which turns out to be in accord with the experimental data. In addition we found that the interaction between the last quasiparticle and the ground-state phonon admixtures produces configurations which contribute significantly to the magnetic dipolemoment of odd-A nuclei. It also reveals a potential for reproducing their experimental values which proves impossible if this interaction is neglected.     

Calculation of the eigenvalues of pure quadrupole interaction in Mössbauer effect studies

Summary Two approximate formulae to calculate the eigenvalues of pure quadrupole interaction in M?ssbauer effect studies have been proposed and the eigenvalue coefficients in the formulae have been given for various excited states and ground states of the nucleus with different spin. All the eigenvalues of pure quadrupole interaction between both excited state and ground state of nucleus with spinI=3/2÷9/2 and the electric-field gradient with different asymmetry parameter (η=0÷1.0) have been calculated by these formulae. The results show that the accuracies in all the calculations are more satisfactory or same in comparison with those obtained by the formula of Shenoy and Dunlap, especially when the asymmetry parameter of electric-field gradient is larger than 0.8 for the nucleus with spinI=5/2.     

Shear viscosity of strongly coupled Yukawa systems on finite length scales

The Yukawa shear viscosity has been calculated using nonequilibrium molecular dynamics. Near the viscosity minimum, we find exponential decay consistent with the Navier-Stokes equation, with significant deviations on finite length scales for larger viscosity values. The viscosity is determined to be nonlocal on a scale length consistent with the correlation length, revealing the length scales necessary for obtaining transport coefficients in the hydrodynamic limit by nonequilibrium molecular dynamics methods. Our results are quasiuniversal with respect to excess entropy for excess entropies well below unity.     

On relativistic kinetic gas theory: XIV. Transport coefficients of a binary mixture. General expressions

A relativistic method to calculate transport coefficients is developed for a binary mixture with arbitrary particle interaction. The heat conductivity, the diffusion coefficient, the thermal-diffusion coefficient, the shear viscosity and the volume viscosity are expressed in terms of relativistic omega integrals.     

Analysis of E1 and E2 radiative α-capture and giant multipole resonances

Experimental data on E1 and E2 radiative α-capture are analyzed by taking account of direct and semidirect processes as well as the compound process. Observed excitation functions for these reactions are reasonably well reproduced assuming the reactions take place mainly through giant multipole resonances. It is shown that the compound process dominates in the lower energy region especially for E1 capture whereas in the higher energy region direct and semidirect captures are the major processes especially for E2 capture. Several interesting results are obtained on α-particle spectroscopic factors of target ground states and on spreading widths and isospin-mixing coefficients of the giant multipole resonance states. The data are shown to be consistent with the existence of the isoscalar giant quadrupole resonances. The applicability of direct and semidirect capture theories to α-capture is examined.     

Bulk viscosity,interaction and the viability of phantom solutions

We study the dynamics of a bulk viscosity model in the Eckart approach for a spatially flat Friedmann–Robertson–Walker (FRW) Universe. We have included radiation and dark energy, assumed as perfect fluids, and dark matter treated as an imperfect fluid having bulk viscosity. We also introduce an interaction term between the dark matter and dark energy components. Considering that the bulk viscosity is proportional to the dark matter energy density and imposing a complete cosmological dynamics, we find bounds on the bulk viscosity in order to reproduce a matter-dominated era (MDE). This constraint is independent of the interaction term. Some late time phantom solutions are mathematically possible. However, the constraint imposed by a MDE restricts the interaction parameter, in the phantom solutions, to a region consistent with a null value, eliminating the possibility of late time stable solutions with \(w<-1\). From the different cases that we study, the only possible scenario, with bulk viscosity and interaction term, belongs to the quintessence region. In the latter case, we find bounds on the interaction parameter compatible with latest observational data.     

Histogram reweighting method for dynamic properties

The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from molecular dynamics simulations. The theory presented here is based on the fact that the correlation functions in systems in thermodynamic equilibrium are averages over initial conditions of trajectory functions, the latter depending on the volume of the system, the total number of particles, and the classical Hamiltonian. Thus, the well-known histogram reweighting method can be almost straightforwardly applied to reconstruct the probability distribution of initial states at different thermodynamic conditions, without extra computational effort. Correlation functions and transport coefficients are obtained with this method from few simulation data sets.