Particle Density Fluctuations Research Articles

The demixing and gas–liquid instability of a binary Yukawa fluid

For a binary mixture we relate the second order expansion of the grand canonical potential Ω to direct correlation functions and to thermodynamic expressions. The matrix of second functional derivatives of Ω with respect to the particle density fluctuations is diagonalized. The zero of the smallest eigenvalue indicates a phase instability vs particle density fluctuations. The related eigenvector characterizes the instability uniquely. Calculations of correlation functions via the reference hypernetted chain integral equations are performed for a binary mixture of hard core particles with attractive Yukawa interactions; the spinodals are established for different concentrations and different interaction potentials using the calculated correlation functions. Along the spinodal we find a continuous change from predominantly demixing to mainly condensation instabilities.

On zero-frequency magnetic fluctuations in plasmas

A plasma sustains fluctuations of electromagnetic fields and particle density even in thermal equilibrium and such fluctuations have a large zero-frequency peak. The level of fluctuations in the plasma for a given wavelength and frequency of electromagnetic fields is calculated through the fluctuation–dissipation theorem. The frequency spectrum shows that the energy contained in this peak is complementary to the energy ‘‘lost’’ by the plasma cutoff effect. The level of the zero (or nearly zero) frequency magnetic fields is computed as 〈B2〉0/8π = (1/2π3)T(ωp/c)3, where T and ωp are the temperature and plasma frequency. The relation between the nonradiative and radiative fluctuations is elucidated. Both a simple collision model and a kinetic theoretic treatment are presented with essentially the same results. The size of the fluctuations is λ ∼ (c/ωp)(η/ω)1/2, where η and ω are the collision frequency and the (nearly zero) frequency of magnetic fields oscillations. Perhaps the most dramatic application of the present theory, however, is to the cosmological plasma of early epoch (say t = 10−2–100 sec after the Big Bang). Implications of these magnetic fields in the early Universe are discussed.

On the origin of cosmological magnetic fields

view Abstract Citations (77) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Origin of Cosmological Magnetic Fields Tajima, T. ; Cable, S. ; Shibata, K. ; Kulsrud, R. M. Abstract The paper shows that a plasma with temperature T sustains fluctuations of electromagnetic fields and particle density even if it is assumed to be in a thermal equilibrium. The level of fluctuations in the plasma for a given wavelength and frequency of electromagnetic fields is rigorously computed by the fluctuation-dissipation theorem. A large zero-frequency peak of electromagnetic fluctuations is discovered. It is shown that the energy contained in this peak is complementary to the energy 'lost' by the plasma cutoff effect. The present computer particle simulation confirms the theory and exhibits a peaking of the magnetic energy spectrum at zero frequency. The level of magnetic fields is significant at the early radiation epoch of the universe. Such magnetic fluctuations provide seed fields for later evolution. Implications of these magnetic fields in the early universe are discussed. Publication: The Astrophysical Journal Pub Date: May 1992 DOI: 10.1086/171281 Bibcode: 1992ApJ...390..309T Keywords: Cosmology; Magnetic Fields; Magnetohydrodynamics; Space Plasmas; Universe; Computational Astrophysics; Computerized Simulation; Energy Spectra; Astrophysics; COSMOLOGY: EARLY UNIVERSE; COSMOLOGY: THEORY; ISM: MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS: MHD full text sources ADS |

The instability of a dispersion of sedimenting spheroids

It is shown that hydrodynamic interactions between non-Brownian, non-spherical, sedimenting particles give rise to an increase in the number of neighbouring particles in the vicinity of any given particle. This result suggests that the suspension is unstable to particle density fluctuations even in the absence of inertia; a linear stability analysis confirms this inference. It is argued that the instability will lead to convection on a lengthscale (nl)−½, where l is a characteristic particle length and n is the particle number density. Sedimenting suspensions of spherical particles are shown to be stable in the absence of inertial effects.

A search for non-statistical particle density fluctuations in 16O + Ag(Br) and 32S + Au interactions at 200 A GeV

Fluctuations in particle densities of non-statistical origin are studied in central 16O+Ag(Br) and 32S+Au interactions at 200 A GeV. Non-statistical fluctuations in the 32S-induced interactions seem to enhance the local particle densities, and suggest the presence of intermittancy. The fluctuations are found to be accompanied by a clustering tendency also in the azimuthal plane. A new method for the study of azimuthal correlations is proposed.

Temporally and spatially resolved wave fluctuations in helium positive columns

A method to detect fluctuations of charged particle density, electron temperature, electric field and plasma potential by Langmuir probes is proposed. The fluctuations are detected for ionisation wave packets excited in a helium positive column with a gas pressure of 0.4 Torr. The radical profile of the ionisation wave component is more concentrated near the centre of the tube as compared with that of the steady-state charged particle density. The wave front is slightly convex towards the cathode. The results suggest that the theory of ionisation waves needs some modifications.

Intermittency model for rapidity particle density fluctuations

Abstract The one-dimensional model of intermittency is applied to particle density fluctuations in rapidity. Intermittency may explain the “anomalous” events with large density of particles in small rapidity windows and the, approximately energy-independent, linear relation between the average maximum rapidity density and the multiplicity. The connection of “host-spots” in rapidity with large transverse energy jets and the formation of the quark-gluon plasma is briefly discussed.

Molecular dynamics simulation of hydrocarbon molecules in condensed phases. II. Benzene

Molecular dynamics simulations of liquid (305 K) and solid (10 K) benzene have been carried out to investigate the vibrational properties of benzene in the condensed phase. The benzene molecule is modeled as a fully flexible system of 12 atoms with intramolecular interactions based on ab initio harmonic potentials and intermolecular interactions given by semiempirical atom–atom potentials. Vibrational frequencies are analyzed in terms of the frequency spectrum of the velocity autocorrelation function and the results are found to correlate well with optical absorption and scattering data. Single particle density fluctuations are calculated over a range of wave numbers and results are obtained that can be directly compared to the intensity distributions of inelastically scattered thermal neutrons. The different comparisons indicate that the existing potential energy function provides an essentially quantitative description of molecular vibrations of benzene.

On plasma disturbances caused by the motion of the space shuttle and small satellites: A comparison of in situ observations

Recent results regarding the interactions between a body and its environmental space plasma, made by charged particle probes mounted in the bay of the space shuttle Orbiter Columbia (STS 3 mission), are compared with earlier results, obtained from small ionospheric satellites, in an attempt to widen our scope of knowledge and understanding regarding such interactions. The objective is to work toward a unified model of body‐space plasma interactions in the solar system covering a variety of plasma and body conditions. The comparisons focus mainly on (1) the (wake/ram) current ratio; (2) the generation of charged particle density fluctuations (indicative of plasma turbulence) around the body; and (3) the increase in electron temperature ahead and in the wake of the satellite. The main results of the comparison are that (1) the (wake/ram) current ratio (or current depletion in the wake) for the Orbiter is 1 to 2 orders of magnitude larger than the ratio for small ionospheric satellites; and (2) fluctuations in density (or turbulence) are observed for both “large body” (shuttle Orbiter) and “smaller body” (standard ionospheric satellites). However, the cause of the turbulence may not be the same for both cases; (3) the results for the electronic temperature enhancement due to the shuttle Orbiter are in contrast with measurements from smaller ionospheric satellites. We suggest a path to follow in future shuttle experiments and caution that care be taken in interpreting local particle and field measurements.

Theory of the spontaneous polarization of the adsorbed monolayer of polar molecules. The collective variables method

The theory of the spontaneous polarization of the adsorbed monolayer of polar molecules is developed using the collective variables method. The total potential of the system is represented as the sum of the one-body and two-body interaction potentials. The one-body potential depends on the orientation of the molecular dipoles in the external electric field and on the interactions between the molecules and the substrate. The two-body potential consists of the sum of intermolecular potentials which can be separated into the “short-range” part describing the orientation-independent interaction at distances, and the long-range part dependent on both the coordinates and the orientations of the interacting species. The variation of the configurational Helmholtz free energy of the system related to the long-range orientational interactions is shown to consist of three terms describing different modes of interactions of density fluctuations: (a) neglect of particle's density fluctuation or self-consistent mean field approximation (SCMF), (b) harmonic oscillations of the particle's density-the random phases approximation (RPA), and (c) various unharmonic interactions of the fluctuation waves. In the SCMF approximation using the assumption of the multiplicative separation of the high-order distribution function the singlet distribution function is calculated and the polarization vector of the adsorbed monolayer is determined. The corrections to the singlet distribution function arising from the terms (b) and (c) of the free energy are calculated. It is shown that the spontaneous polarization of the adsorbed monolayer of polar molecules may be regarded as the first-order phase transition.

Backscattering in the one-dimensional many-fermion system

The Sawada Hamiltonian model is generalized to include the backscattering interaction in a one-dimensional many-fermion system. The collective excitations of the particle-density fluctuations and the backscattering dielectric function are obtained. It is shown that the giant Kohn anomaly of the longitudinal phonon spectrum, observed in the quasi-one-dimensional conductors, is qualitatively reproduced within the present approach.

Binary mixture of hard spheres with attractive square-well interaction between unlike spheres

We report calculations of partial structure factors, concentration and particle density fluctuations for a binary mixture of equal-sized hard spheres at equimolar composition, where spheres of different species interact via an attractive square well. This model exhibits the qualitative features attributed to liquid binary alloys with compound-forming tendencies.

On the radial expansion of the solar wind plasma between 0.3 and 1.0 astronomical units

The radial expansion--within 1 AU heliocentric distance--of the extended solar corona is studied. The work was stimulated by the recent availability of solar wind measurements by the Helios 1 solar probe for the period 1974 December--1975 April covering (for the first time) the interplanetary medium between 1 and 0.3 AU. The first part of the work analyzes these data from a theoretical point of view. Thus, in order to classify the plasma states represented by the data, the particle fluxes Jequivalentnupsilonr/sup 2/ are calculated by using measured proton densities, n/sub p/(r), and streaming velocities, upsilonp (r), and are correlated with heliocentric distances as well as with density and streaming velocity fluctuations, ..delta..n/sub p/ and ..delta..upsilon/sub p/, respectively. The quantity J has been chosen as a classifying criterion. The results of these calculations indicated that (i) the normalized particle flux J-barequivalentJ/J/sub E/ (E indicates 1 AU heliocentric distance) varies by a factor of 10 (between approx.0.5 and 5) over the interplanetary range explored by Helios 1; (ii) the strong deviations from the value 1 are found only for states with streaming velocities below about 500 km s/sup -1/, while for the high-speed states J-barapprox. =1; (iii) the deviations /sup 0/J-bar foundmore » for low-speed states are strongly correlated with particle density fluctuations and moderately anticorrelated with streaming velocity fluctuations; and (iv) time-dependent and/or additional process could play a significant role.In the second part of the work we use all observational data representing high-speed flows (i.e., satisfying the condition upsilon> or =600 km s/sup -1/) in conjunction with the fluid equations for a two-component plasma (protons + electrons) in order to estimate unknown properties of the solar wind.« less

Polarization potentials and elementary excitations in liquid 3He

The results of a generalized polarization potential calculation of the particle and spin density fluctuation excitation spectra of 3He in the low-temperature limit are described and compared with the recent neutron scattering experiments of Skold and Pelizzari. The extent to which the range and shape of the effective repulsive interaction between particles of parallel and antiparallel spin may differ is explored, and it is shown that changes of only a few percent have experimentally observable consequences. Good agreement with experiment is found for the dispersion of zero sound; the wave vector dependence of the enhancement of the low-frequency part of the spin density fluctuation excitations, and the coherent and incoherent static structure factors, are examined and compared with experiment for identical and slightly different repulsive parallel and antiparallel spin interactions. Simple qualitative arguments are presented which suggest that for wave vectors 0.4⩽q⩽ 1.2»-1, the zero-sound mode will be little affected as the temperature is raised to 1.2K, while the low-frequency spin fluctuation excitation spectrum undergoes considerable broadening, again in accord with experiment. Changes in the zero-sound dispersion relation with pressure are shown to be sensitive to the range of the repulsive part of the effective quasiparticle interaction, and it is suggested that experiments at 20 atm will help determine the physical origin of the comparatively large range (∼3 ») required to explain the experimental results for 3He at SVP.

Kinetic theory of rough sphere fluids: Density fluctuations

We construct a kinetic equation for the phase space density correlation function (PSDCF) in a rough sphere fluid (at the generalized Enskog level) which is valid for arbitrary wave number and frequency. The kinetic equation yields the first two kinetic sum rules exactly; also the density–density correlation function implied by it has the correct first four sum rules exactly. We use the short time behavior of PSDCF and the generalized hydrodynamics approach to construct approximate interpolation formulas for a variety of space–time dependent correlation functions related to conserved variables in the fluid. The coupling of modes described by these correlation functions to the test particle density fluctuations is responsible for the known asymptotic power law decay in the linear and angular velocity correlation functions. As a by-product of this study, we also obtain expressions for various (bare) transport coefficients in a dense rough sphere fluid.

Kinetic theory of rough sphere fluids: Linear and angular velocity correlation functions

We present a renormalized kinetic theory for tagged particle motion in a rough sphere fluid which includes the effects of correlated collisions. The kinetic theory is a generalization of a recent theory for monatomic fluids by Mazenko. The correlated collisions create slowly decaying memory in the linear (ψv) and angular (ψω) velocity correlation functions on account of the coupling of the test particle density fluctuations to various moments of the full phase space density correlation function. (These moments are connected with the conserved variables in the system). We use the theory to study ψv and ψω and compare the results with recent molecular dynamics experiments of O’Dell and Berne. The kinetic theory yields the correct long time power law decay for both ψv and ψω without imposing any wave vector cutoff characteristic of the hydrodynamic theories. It also yields useful new insights into various mode couplings responsible for the behavior of ψv and ψω at small and intermediate times. The qualitative features of the computer experiments are reproduced by the theory.

Statistical mechanics of dense ionized matter. IV. Density and charge fluctuations in a simple molten salt

The results of a molecular-dynamics study of a simple model of a molten salt are reported. The interionic pair potential which is used consists of the Coulombic term an an inverse-power repulsion which is assumed to be the same for all ions. The structure of the liquid is found to be dominated by charge-ordering effects and the calculated equilibrium properties are in good agreement with the predictions of the hypernetted-chain approximation. The relation between the self-diffusion coefficient and the electrical conductivity is discussed, and the observed deviations from the Nernst-Einstein relation in real molten salts are shown to have a natural explanation in terms of short-lived cross correlations. Data on the spectra of charge and particle density fluctuations are presented. At small wave numbers there is a propagating optic-type mode which shows a strong negative dispersion, but no Brillouin peak is seen even at the lowest wave number which is accessible. The data are analyzed in terms of a single-relaxation-time model incorporating the low-order spectral moments, for which we give explicit formulas. The fit achieved is fair, but the low-frequency behavior of the charge fluctuations at small wave numbers is incorrectly reproduced, and there is evidence for the necessity of introducing a second relaxation time. Comparison is made with results previously obtained for the classical one-component plasma.

A theory for scattering by density fluctuations based on three-wave interaction

The theory of scattering by charged particle density fluctuations of a plasma is developed for the case of zero magnetic field. The source current is derived on the basis of, first, a three-wave interaction between the incident and scattered electromagnetic waves and one electrostatic plasma wave (either Langmuir or ion-acoustic), and secondly, a synchronous interaction between the same two electromagnetic waves and the discrete components of the charged particle fluctuations. Previous work is generalized by no longer making the assumption that the frequency of the electromagnetic waves is large compared to the plasma frequency. The general result is then applied to incoherent scatter, and to scatter by strongly driven plasma waves. An expansion is carried out for each of these cases to determine the lower order corrections to the usual high-frequency scattering formulae.

Ambipolar transport noise in a semiconductor in the presence of a magnetic field

The noise spectrum due to fluctuations in the electron-hole pair particle density in a semiconductor in the presence of a magnetic field is presented in this paper. This spectrum was obtained via the Green's function for the macroscopic differential equation which governs the behavior of the conditional average for fluctuations in the electron-hole pair particle density when ambipolar transport and generation-recombination are the important noise processes. The macroscopic differential equation is a generalization of van Roosbroeck's small-signal continuity equation to include the presence of a magnetic field. The resultant spectrum was evaluated numerically and a family of curves corresponding to different values of magnetic field strength generated. This was done for specified values of τ/τa and τ/τd, where τ is the mean volume lifetime of electron-hole pairs, τa is the characteristic ambipolar drift time, and τd is the characteristic ambipolar diffusion time. In the extreme situations when ambipolar drift is important and diffusion is negligible and vice versa, the obtained numerical results are consistent with those obtained previously by the author. For the case treated in this paper when both ambipolar drift and diffusion are equally important, the ``universal 3/2 power law'' still prevails in the high-frequency portion of the spectrum, thus indicating the dominance of ambipolar diffusion in that region of the spectrum.

Fluctuations in Plasma and Nonlinear Susceptibilities

The nonlinear electromagnetic properties of plasma are considered and it is shown, that the nonlinear plasma susceptibilities may be expressed in terms of higher order correlation functions for the charge density fluctuations of noninteracting particles. The generalization of the fluctuation-dissipation theorem for nonlinear electrodynamic systems is obtained.