Fluids of pseudo-hard bodies II. Reference models for water,methanol, and ammonia

Pseudo-hard body fluids resulting from extended primitive models of water, methanol, and ammonia have been investigated both by computer simulations and theory for a number of geometrical parameters. It is shown that none of the existing equations of state and integral equations for the site-site correlation functions is able to describe the properties of the pseudohard body fluids reasonably accurately. For the equation of state an accurate semi-empirical method is proposed and for the site-site correlation functions the reference average Mayer function perturbation theory has been found to perform at least qualitatively correctly, which is not the case with Ornstein-Zernike equation based theories.     

How unique are the Friedmann-Robertson-Walker models of the universe

By accepting the validity of certain conjectures in classical general relativity and kinetic theory, it is argued that, in a sense, the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) cosmological models are unique. This is accomplished in two steps. First, there is reason to believe that kinetic theory requires perfect fluids to be shear-free. Second, it seems that general relativity constrains expanding shear-free fluids to be irrotational. The uniqueness of the FRW models then follows, since it has already been established that they are the only space-times which represent an expanding shear-free irrotational perfect fluid that are physically reasonable on a global scale.This essay received an honorable mention (1986) from the Gravity Research Foundation—Ed.     

A new class of LRS Bianchi type-I cosmological models in Lyra geometry

LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe. The physical behaviour of the models is examined in vacuum and in the presence of perfect fluids.     

From realistic to simple models of associating fluids. II. Primitive models of ammonia,ethanol and models of water revisited

Recently developed methodology to construct primitive models of associating fluids directly from realistic intermolecular potential functions is applied to ammonia, ethanol and several models of water. Hard cores of the molecules are pictured as fused hard-sphere bodies defined by composite short-range repulsions, and the Coulombic repulsions and attractions are approximated by hard-sphere and square-well potentials, respectively. Hard-sphere diameters are determined directly from the parent potential using a theoretical route and the range of the square-well attraction is adjusted using constraints imposed on hydrogen bonding. It is shown that the developed primitive models, despite their simplicity and lack of any long-range interactions, are able to reproduce the structural properties (the set of the site–site correlation functions) of the parent realistic models and may thus serve well as a reference in the perturbation theory.     

From realistic to simple models of fluids. III. Primitive models of carbon dioxide,hydrogen sulphide and acetone,and their properties

Recently developed methodology to construct primitive models of associating fluids as direct descendants of complex realistic intermolecular potential functions [L. Vl?ek, I. Nezbeda. Molec. Phys., 102, 485 (2004).] is extended to polar fluids and applied to three substances of practical importance: quadrupolar carbon dioxide, and dipolar hydrogen sulphide and acetone. It is shown that the structural properties (in terms of the site–site correlation functions) of the primitive models of polar fluids reproduce very well those of their parent realistic models but, nonetheless, they perform worse than in the case of associating fluids. A number of thermodynamic properties of the developed models obtained by computer simulations is also reported (for their later use in theoretical investigation) and discussed.     

Towards a unified view of fluids

It has traditionally been believed that, unlike normal fluids whose structural properties are determined primarily by the intermolecular short-range repulsive interactions, the properties of polar and associating fluids are strongly affected by the long-range Coulombic interactions. In the course of investigations to determine the primary driving forces governing the behaviour of various (non-simple) fluids, and hence to gain a deeper understanding of the molecular mechanisms leading to the development of theoretically based simple models and theory, extensive and systematic computer simulations have been performed on typical quadrupolar (carbon dioxide), dipolar (acetone and acetonitrile), and associating (hydrogen fluoride, methanol, and water) fluids using the available realistic effective pair potentials and their variants involving forces of different ranges. In addition to the main structural characteristics (one- and two-dimensional site–site correlation functions, local g factors, and radial slices through the full pair correlation function), the dielectric constants and the thermodynamic properties (internal energy and pressure) of both the homogeneous liquid and supercritical fluid phases, and vapor–liquid equilibria have also been considered. Furthermore, in the case of water, the diffusion coefficient and viscosity have also been considered along with water at the interface. All the obtained results lead to the unambiguous conclusion that the structure, defined in terms of the complete set of site–site correlation functions, for both polar and associating pure fluids is governed by the same molecular mechanism as for normal fluids, i.e. by the short-range interactions (which, however, may be both repulsive and attractive), whereas the long-range part of the electrostatic forces, regardless of their strength, plays only a marginal role and may be treated as a perturbation only. The consequences of these findings for theory and applications are also discussed.     

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low- and high-confinement states in confined plasmas are analyzed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.     

On a conjecture of Alley and Alder for fluids and Lorentz models

We discuss a conjecture of Alley and Alder predicting a relation between the four-point and the two-point velocity autocorrelation functions for fluids and Lorentz models at sufficiently long times. If the conjecture is correct a modified Burnett coefficient can be defined, which has a finite value, contrary to the ordinary Burnett coefficient, which is divergent. The conjecture is tested for four classes of models with different methods: for three-dimensional fluids mode-coupling theory yields a negative result. The conjecture is confirmed for thed-dimensional deterministic Lorentz gas (d 2) and for a class ofd-dimensional stochastic Lorentz models (d 1) by low-density kinetic theory, as well as by rigorous results, available for one dimension. For yet another class of one-dimensional stochastic Lorentz models, which are exactly solvable in one dimension, the result is negative again. All four classes of models show long-time tails in the velocity autocorrelation function and have a finite diffusion coefficient.     

Topology of the momentum space,Wigner transformations,and a chiral anomaly in lattice models

Lattice models that can be used to discretize the quantum field theory with massless fermions have been discussed. These models can also be used to describe Dirac semimetals. It has been shown that the axial current for general lattice models should be redefined in order for the usual expression for the chiral anomaly to remain valid. In this case, in the presence of a time-independent potential of the external electromagnetic field, the formalism of Wigner transformations allows relating the divergence of the axial current to a topological invariant in the momentum space that is defined for a system in equilibrium and is responsible for the stability of the Fermi point. The evaluated expression is the axial anomaly for general lattice models. This expression has been illustrated for models with Wilson fermions.     

Direct correlation functions for three-site and four-site water models

ABSTRACT

Direct correlation functions (DCFs) play a pivotal role in modern liquid-state theories and are virtually indispensable for non-mean-field implementation of the classical density functional theory (cDFT). Whereas analytical expressions have been derived for the DCFs of simple fluids and electrolytes, DCFs for molecular systems are attainable only through numerical solution of the integral-equation theories in combination with molecular simulation or an approximate closure. Unlike radial distribution functions, DCFs reflect the variational of the local chemical potential of individual atoms/interaction sites with the density-profile fluctuations, which are difficult to be sampled from the simulation trajectory. This article presents an improved numerical procedure to calculate the DCFs of three-site (SPC/E and TIP3P) and four-site (TIP4P-Ew) water models based on the reference interaction site model and molecular dynamics simulations. In combination with the modified fundamental measure theory for the bridge functionals, the DCFs have been utilised to predict the hydration free energies of 504 small organic molecules. The theoretical predictions yield an average unsigned error of 0.66 kcal/mol in comparison with the simulation data, better than that (～1 kcal/mol) reported in previous cDFT calculations.     

Lanczos–Lovelock models of gravity

Lanczos–Lovelock models of gravity represent a natural and elegant generalization of Einstein’s theory of gravity to higher dimensions. They are characterized by the fact that the field equations only contain up to second derivatives of the metric even though the action functional can be a quadratic or higher degree polynomial in the curvature tensor. Because these models share several key properties of Einstein’s theory they serve as a useful set of candidate models for testing the emergent paradigm for gravity. This review highlights several geometrical and thermodynamical aspects of Lanczos–Lovelock models which have attracted recent attention.     

Macroscopic models of internal dynamics of electrical discharges

The existence of thresholds for electrical discharge onset suggests a functional relation between macroscopic resistivity and current. At low current, the resistivity should be inversely proportional to the magnitude of the current. Macroscopic models which employ this scaling predict many empirically observed properties of transient electrical discharges such as: (i) thresholds for the onset of current, (ii) the abrupt termination of current in active regions of a current channel, (iii) current restart in passive regions of current channels, (iv) leaders, and (v) residual charge, both in channels and at sources when current terminates. An overview of research with these models is presented and examples are used to illustrate the results that have been obtained. These models are shown to predict current channel formation and describe results of efforts to benchmark theory with experimental data     

Gibbs ensemble simulation of the vapour-liquid equilibrium of square well spherocylinders

Gibbs ensemble Monte Carlo simulations have been performed for systems of square-well spherocylinders of different length-to-breadth ratio. The results are used to test a recent perturbation theory proposed for this kind of system. In addition, the results are compared to similar simulations performed for a Kihara fluid of elongated molecules. An unexpected good agreement is found for the coexistence thermodynamic and structural properties of both model fluids, hence suggesting that the hard spherocylinder plus square-well interaction should be considered as a reference potential for a perturbative treatment of more complex fluid models.     

Critical assessment of mean field models based on effective interactions

Mean field schemes, from simple Hartree—Fock plus random phase approximation calculations of the ground and excited states to more sophisticated approaches which include pairing as well, have been popular for quite a long time. In these models, the input is an effective interaction. We still lack a precise link between this interaction and a more fundamental theory; however, there have been various new recent attempts to correlate empirical pieces of evidence about nuclear (and neutron) matter, or experimental results, with the properties of the effective interactions. In this contribution, we claim that, while we have indeed made some progress in our understanding of certain features of the interactions, we are still missing a clue about its proper density dependence and about its isovector properties. The text was submitted by the author in English.     

Comparative analysis of symmetries for the models of mechanics of nonuniform fluids

The symmetries for the main models of mechanics of binary fluids are calculated by the methods of the theory of continuous groups. The fundamental system of the differential form of the main conservation laws is characterized by the ten-parametric Galilean group. The Navier-Stokes set of equations possesses an extended set of symmetries with infinite dimensionality. Simplification of the model changes the order of the set of equations of motion, which leads to the impossibility to take into account the complete set of boundary conditions and formation of discontinuities in solutions for reduced models.     

Scaling properties of percolation models for multifragmentation

We have used scaling properties of nuclear multifragmentation, which have been observed with emulsion data, to investigate the properties of some approaches based on percolation. We have studied different percolation models on a cubic lattice and shown that they can rather well reproduce the data except for binary break up. We have described what the mean field approximation would give in this context and showed that it cannot reproduce the experimental results. Most of the paper is focused on the restructured aggregation model introduced earlier which allows to well reproduce the scaling properties observed experimentally. This model has been studied in details and extended to take account of bonds breaking. It is shown that, in some cases, a nucleus can break up in two pieces. This process cannot be obtained in conventional percolation or aggregation but is observed experimentally in the emulsion data. Other features like the dimensionality of the aggregation model, the restructuration of the clusters and a schematic constraint in momentum space have also been investigated.     

The classical fluid of associating hard rods in an external field

Two models of one-dimensional fluids of associating hard rods in an arbitrary external field are investigated. In the first model particles can only form dimers, while in the second model, which has been solved previously by Percus, aggregates of any size coexist. In both cases the grand canonical potential and the external potential are found exactly as functionals of the density. It is shown that Wertheim's thermodynamic perturbation theory of polymerization provides a straightforward route to the exact solution by expanding the functional space to include more density parameters. This suggests that Wertheim's theory should be used also for studying the structure (and not only the thermo-dynamics) of real associating fluids.     

Convergence of electron kinetic,two-temperature,and one-temperature models for laser short-pulse heating

The laser short-pulse heating of metallic workpieces initiates the non-equilibrium heating in the surface vicinity of the substrate. The material response to the non-equilibrium heating cannot be predicted accurately by the one-temperature model. Consequently, new models pertinent to laser short-pulse heating are needed. In the present study, laser short-pulse heating of gold, copper, and lead is considered. The material responses to the laser short-pulse due to the electron kinetic theory and the two-temperature and the one-temperature models are examined in detail. The differences between the collisional and diffusional heating mechanisms are presented. The conditions for the convergence of conduction mechanisms are discussed. The electron kinetic theory, the two-temperature, and the one-temperature predictions are compared for three substrates. It is found that the electron kinetic theory predictions differ from the predictions of the one-temperature model in the surface vicinity of the substrate during the early heating duration. As the heating progresses, both models predict similar temperature profiles. The electron kinetic theory and the two-temperature model predictions are in good agreement. PACS 44.10.+i; 42.62.-b