Space distribution and energy straggling of charged particles via Fokker-Planck equation

Summary The Fokker-Planck equation describing a beam of charged particles entering a homogeneous medium is solved here for a stationary case. Interactions are taken into account through Coulomb cross-section. Starting from the charged-particle distribution as a function of velocity and penetration depth, some important kinetic quantities are calculated, like mean velocity, range and the loss of energy per unit space. In such quantities the energy straggling is taken into account. This phenomenon is not considered in the continuous slowing-down approximation that is commonly used to obtain the range and the stopping power. Finally the well-known Bohr or Bethe formula is found as a first-order approximation of the Fokker-Planck equation. The authors of this paper have agreed to not receive the proofs for correction.     

Collision-induced absorption in dense mixtures of simple fluids

Summary Collision-induced absorption (CIA) spectroscopy is a probe of the dynamical properties of dense systems. Two simple cases of CIA spectra are here discussed: the translational band observed in solutions of a noble gas in liquid Ar and the rotational lines of H₂ observed in solutions of H₂ in Ar. In the first case, the analysis of the translational band allows one to derive the characteristic frequency ω₀, associated with the rattling component of the motion of the impurity in the Ar medium. In the second case, the analysis of the rotational lines allows one to derive the parameter δ, that characterizes the density narrowing effect. In the high-density region, the parameter δ is directly related to the diffusive motion of the Ar atoms around the impurity. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

From macroscopic to atomic motions in liquid metals

Summary In the present review of liquid dynamics studies on liquid metals are reported. Particularly the case of liquid lead is reviewed because this case was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities. In addition extensive supplementary MD simulations were made using a 16 384-particle system. The simulations ranged from a determination of an effective pair potential for lead to simulation of the density correlation functionsF(Q,t) andF _s(Q,t), as well as the longitudinal and transversal current correlation functionsJ ₁(Q,t) andJ _T(Q,t). The MD simulation ?calibrated? via the experimentalS(Q) andS(Q,ω) was used to prolong the range of neutron data to draw conclusions regarding such quantities as dispersion relations for the current correlationsJ ₁(Q,t) andJ _T(Q,t), the generalized viscosity functions ν₁(Q,t), ν₁(Q) and ν_s(Q). Information regarding bulk viscosity ν_B(Q) is also gained. Conclusions are drawn regarding the relative importance of the derived pair potential form by comparison to corresponding hard-sphere data. The general framework of linearized hydrodynamic equations for the macroscopic situation transforming to visco-elastic equations of motion for finite wave-length and high frequency works well also for the case of a continuous potential. The region of transition from simple visco-elastic to hydrodynamic behaviour is occurring at wavelengths in the range (12÷20) ? for the cases studied. The spatial properties of the viscosity functions ν₁(r), ν_s(r) and ν_B(r) are found to correlate well with the range of the radial distribution function for the liquid. The general results for liquid lead probably have wide range of applicability to other simple liquids with similarS(Q) andg(r) properties. The authors have agreed not to receive proofs for correction.     

Stationary extended kinetic theory for a gas of hard spheres

Summary Analytical and numerical results for the stationary, spatially homogeneous distribution function of a gas of ?hard-sphere? particles are reported. Both removal and scattering effects are accounted for. In the case of only removal, comparison is also made with results obtained in the frame of alternative models proposed for approximating the exact ?hard-sphere? model.     

Neutron brillouin scattering and liquid metal-molten salt mixtures

Summary The dispersion of collective density fluctuations (extended sound modes) has been measured in mixtures of liquid alkali metals and the corresponding molten alkali-halide salts. Mixtures with salt concentrations from 10 to 40% were investigated for momentum transfersQ between 4 and 14 nm⁻¹. ForQ-values larger than 11 nm⁻¹ the collective modes could even in the most favourable case no longer be separated from the quasi-elastic peak, the width of which increases roughly ∼Q ² in this region of momentum transfers. At a concentration of 10% RbCl in Rb we find a dispersion which would correspond to expanded liquid Rb at the temperature of the mixture (∼1000 K), demonstrating the dominant metallic character of the mixture (screening by nearly free electrons) at this salt concentration. At higher concentrations of salt, where influences from different partial dynamic structure factors interplay, the dispersions deviate from this simple structured dispersion curve, most likely due to the influence of an early onset of some ionic type of screening in the liquid. The proofs of this paper have been supervised by the Scientific Committee.     

Diffusion near an interface via onsager-type equations

Summary Onsager-type transport equations, as were derived in a previous paper by the authors, are applied to the diffusion of test particles near the interface of a scattering medium with a perfect absorber. Temperature and density profiles are obtained for different types of scattering cross-section.     

Melting properties of group-V elements and InSb

Summary In this paper, we study the structural properties of liquid group-V elements (and a compound InSb) and we analyse the differences with their room temperature crystalline phases. Neutron diffraction experiments are performed using short-wavelength neutrons (0.7 ?). We show different melting behaviours of a light element (As) and a heavy element (Sb) under study. Whereas As keeps its coordination three upon melting, Sb is six-coordinated in the melt. Similarly, InSb has a coordination number increasing from 4 to about 6 upon melting. Large entropies of melting are related to important structural variations. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Exact solutions for a semilinear hyperbolic system with general quadratic interactions

Summary The approximate conservation laws for a binary gas mixture with quadratic interactions can be written as a system of two semilinear hyperbolic equations. By using the method of characteristics the study of this system is reduced to the study of a system of nonlinear ordinary differential equations, for which we find several classes of exact solutions. Exact integrability conditions are found for ODE systems of generalized Lotka-Volterra type. Some situations are also considered, in which the characteristic method cannot be applied and exact solutions are obtained via an operator method.     

A multigroup approach to the non-linear extended boltzmann equation

Summary Following a procedure which is typical of linear (neutron) transport theory, a multigroup approach is proposed for the non-linear extended Boltzmann equation in the presence of removal, a background medium, an external source and an external force field. The relevant multigroup equations, corresponding to a discretization of the speed variable only, are derived and discussed, especially in connection with the so-called semi-discrete models recently introduced in kinetic theory.     

Electronic fluctuation,the nature of interactions and the structure of liquid metals

Summary Interactions controlling ionic motion and structure in liquid metals can be systematically developed beginning with the ultimate view of such systems as neutral assemblies of nuclei and electrons, and proceeding to standard reduced Hamiltonians reflecting assemblies ofions and electrons. The assumption of electronically rigid ion leads via response methods and pseudopotentials to statically screened ion-ion potentials and beyond. Fluctuations are introduced into this otherwise common viewpoint by relaxing the assumption of electronically rigid ion cores and also by treating electronic response beyond linear order. It is argued that both effects can lead to more attractive pair interactions and possibly to effects much larger than, for example, Friedel oscillations. These contributions are state (i.e. density) dependent and their presence might be expected on the basis of clustering behavior seen for some systems in theirvapour phases. This leads to two limiting viewpoints on the liquid-state structure of such systems, the first as an entirely monoatomic phase but with a pair interaction that is unusual, the second as a system supporting transient clusters whose presence reflects the complexities argued on the basis of a more extended treatment of the electron problem. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1– May, 1989.     

On a 3×3 semilinear hyperbolic system arising in extended kinetic theory

Summary A 3×3 semi-linear hyperbolic system arising in extended kinetic theory is studied. Direct solutions to such system are discussed in a systematic way, and for various physical situations.     

Transport coefficients of liquid N2 computed by molecular dynamics

Summary With three potential functions including quadrupole interaction, we computed the shear and the bulk viscosity coefficients as well as the thermal conductivity by molecular dynamics for a number of states of liquid nitrogen. The results indicated that the transport coefficients are determinable with a statistical error of about 10 per cent, even for the angledependent molecular potentials in the rigid-rotor approximation. An exception represents the bulk viscosity, for which systems of large particle numbers are necessary to reach the few perent accuracy for states near the triple point. The quadrupole interaction affects weakly the time correlation functions and thus the transport coefficients. In several cases, it improves, however, the agreement with experimental data. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Statistical mechanical models for liquid and amorphous structure in covalently bonded systems

Summary Considerable effort has been given for some years to developing models of interatomic forces aimed at accounting for bond directionality in liquid and amorphous state calculations. Models involving three-body potentials have been especially useful for computer simulation studies of liquid and amorphous states in elemental semiconductors and binary chalcogenides of group-IV elements, starting with the work of Stillinger and Weber on silicon. However, pair potential models that may still account for the main effects of angular dependences of the effective interatomic forces, though at a primitive level, are desirable from the viewpoint of liquid structure theory. Developments in this direction are briefly reviewed, with particular emphasis on bond particle models for the structure of liquid and amorphous germanium. We also discuss the relation between liquid structure in a bond-particle model and crystallization accompanied by electron localization and volume expansion, as observed in elemental and III-V polar semiconductors. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Neutron scattering studies of simple fluids

Summary Neutron scattering may be used in a variety of ways to study simple fluids, and four examples will be given. In the first the nature of the forces causing the structure of noble-gas fluids will be examined. Secondly the structure of homonuclear diatomic liquids will be considered including studies of molecular bonding. Thirdly, the structure of a relatively complicated atomic fluid, sulphur, will be reviewed. And in the fourth the properties of a model Lorentz gas—a dilute mixture of hydrogen in fluid argon—will be described. These examples show both the power and diversity of neutron results, especially when they are combined with accurate computer simulations of these fluids. Proposals for future experiments in this field will be discussed. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Translational light scattering in simple liquids

Summary A short review of translational light scattering of simple liquids is reported. The microscopic cross-section is compared with the equivalent expression for neutron scattering experiments (Van Hove, 1954). A survey of the fundamental experiments is reported and the possible application to the study of the dynamics of simple dense systems is analysed. The relevant approximations are critically discussed and the limits of the technique are established. The review mainly deals with classical or almost classical liquids, but also some extensions to quantum systems are considered. paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May 1989.     

Aggregation phenomena and dynamics in II-I and III-I hydrated molten salts

Summary We present results from EXAFS and Raman scattering on aqueous solutions on II-I and III-I salts. As II-I salt the system investigated was the ZnCl₂ and its mixture with LiCl, CaCl₂ and SrCl₂. It was shown that ZnCl₂ evidences a tetrahedral arrangement around the Zn²⁺ ion whereas Li⁺, Ca⁺ and Sr²⁺ ions prefer an inner-shell water complexation. In particular it was shown that the tetrahedral units become less and less interacting when the ratio Cl⁻/Zn²⁺ is increasing. Such structural results are confirmed by the Raman probe that shows the vibrational bands becoming more and more localized for Cl⁻/Zn²⁺ values higher than 2. For what III-I salts are concerned we report results on SbCl₃/H₂O mixture. EXAFS evidenciates an Sb−Cl and Sb...Cl coordination very close to that of pure SbCl₃. The water molecule appears linked to the chlorine giving rise to a cross-link between SbCl₃ chains. Raman confirms such a result showing that the C_3v symmetry of SbCl₃ molecule is lowered in the presence of water and shows a new chlorine-water contribution plus a phononlike contribution in the very lowfrequency region. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Recent developments in the theory of ionic melts

Summary A brief review is given of the present state of the art in the theory and numerical simulation of ionic melts, and in particular of molten alkali halides. Some recent developments concerning the theoretical evaluation of the static pair structure, the phase diagram and the microscopic dynamics in these melts are discussed. The importance of ionic polarizabilities is stressed. Some perspectives for future work are pointed out in the conclusion. Unité de Recherche Associée 1325 du CNRS.     

Segregation by thermal diffusion in moderately dense granular mixtures

A theory based on a solution of the inelastic Enskog equation that goes beyond the weak dissipation limit is used to determine the thermal diffusion factor of a binary granular mixture under gravity. The Enskog equation that aims to describe moderate densities neglects velocity correlations but retains spatial correlations arising from volume exclusion effects. As expected, the thermal diffusion factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, composition, density and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail in the tracer limit case, showing that the phase diagrams depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: i) absence of gravity, and ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis, which is based on a preliminary short report of the author (Phys. Rev. E 78, 020301(R) (2008)), extends previous theoretical results derived in the dilute limit case.     

Diffusion in ordinary and supercooled liquids

Summary We discuss a simplified approach for the recollision part of the memory function for self-motion in ordinary and supercooled liquids. This part accounts for the substantial decrease of the diffusion coefficient with respect to the binary prediction, an effect which becomes larger and larger on cooling the system. The quantitative results compare satisfactorily with previous and new simulation data obtained for a liquid rubidium model both near the triple point and in moderately supercooled states. Paper presented at the workshop ?Highlights on Simple Liquids”, held in Turin at ISI on 1–3 May, 1989.     

Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised. Received 17 April 2000 and Received in final form 7 June 2000