Initial Fluctuation Spectrum Research Articles

Effects of Fluctuating Magnetic Field on the Growth of the Kelvin‐Helmholtz Instability at the Earth's Magnetopause

AbstractAt the Earth's magnetopause, the Kelvin‐Helmholtz (KH) instability, driven by the persistent velocity shear between the magnetosheath and the magnetosphere, has been frequently observed during northward interplanetary magnetic field periods and considered as one of the most important candidates for transporting and mixing plasmas across the magnetopause. However, how this process interacts with magnetic field fluctuations, which persistently exist near the magnetopause, has been less discussed. Here we perform a series of 2‐D fully kinetic simulations of the KH instability at the magnetopause considering a power law spectrum of initial fluctuations in the magnetic field. The simulations demonstrate that when the amplitude level of the initial fluctuations is sufficiently large, the KH instability evolves faster, leading to a more efficient plasma mixing within the vortex layer. In addition, when the spectral index of the initial fluctuations is sufficiently small, the modes whose wavelength is longer than the theoretical fastest growing mode grow dominantly. The fluctuating magnetic field also results in the formation of the well‐matured turbulent spectrum with a −5/3 index within the vortex layer even in the early nonlinear growth phase of the KH instability. The obtained spectral features in the simulations are in reasonable agreement with the features in KH waves events at the magnetopause observed by the Magnetospheric Multiscale mission and conjunctively by the Geotail and Cluster spacecraft. These results indicate that the magnetic field fluctuations may really contribute to enhancing the wave activities especially for longer wavelength modes and the associated mixing at the magnetopause.

Generation of Suprathermal Electrons by Collective Processes in Collisional Plasma

Abstract The ubiquity of high-energy tails in the charged particle velocity distribution functions (VDFs) observed in space plasmas suggests the existence of an underlying process responsible for taking a fraction of the charged particle population out of thermal equilibrium and redistributing it to suprathermal velocity and energy ranges. The present Letter focuses on a new and fundamental physical explanation for the origin of suprathermal electron velocity distribution function (EVDF) in a collisional plasma. This process involves a newly discovered electrostatic bremsstrahlung (EB) emission that is effective in a plasma in which binary collisions are present. The steady-state EVDF dictated by such a process corresponds to a Maxwellian core plus a quasi-inverse power-law tail, which is a feature commonly observed in many space plasma environments. In order to demonstrate this, the system of self-consistent particle- and wave-kinetic equations are numerically solved with an initially Maxwellian EVDF and Langmuir wave spectral intensity, which is a state that does not reflect the presence of EB process, and hence not in force balance. The EB term subsequently drives the system to a new force-balanced steady state. After a long integration period it is demonstrated that the initial Langmuir fluctuation spectrum is modified, which in turn distorts the initial Maxwellian EVDF into a VDF that resembles the said core-suprathermal VDF. Such a mechanism may thus be operative at the coronal source region, which is characterized by high collisionality.

Mode-coupling effects in anisotropic flow in heavy-ion collisions

Higher-order anisotropic flows in heavy-ion collisions are affected by nonlinear mode coupling effects. It has been suggested that the associated nonlinear hydrodynamic response coefficients probe the transport properties and are largely insensitive to the spectrum of initial density fluctuations of the medium created in these collisions. To test this suggestion, we explore nonlinear mode coupling effects in event-by-event viscous fluid dynamics, using two different models for the fluctuating initial density profiles, and compare the nonlinear coupling coefficients between the initial eccentricity vectors before hydrodynamic expansion and the final flow vectors after the expansion. For several mode coupling coefficients we find significant sensitivity to the initial fluctuation spectrum. They all exhibit strong sensitivity to the specific shear viscosity at freeze-out, but only weak dependence on the shear viscosity during hydrodynamic evolution.

Shape and flow fluctuations in ultracentral Pb + Pb collisions at the energies available at the CERN Large Hadron Collider

In ultracentral heavy-ion collisions, anisotropic hydrodynamic flow is generated by density fluctuations in the initial state rather than by geometric overlap effects. For a given centrality class, the initial fluctuation spectrum is sensitive to the method chosen for binning the events into centrality classes. We show that sorting events by total initial entropy or by total final multiplicity yields event classes with equivalent statistical fluctuation properties, in spite of viscous entropy production during the fireball evolution. With this initial entropy-based centrality definition we generate several classes of ultracentral Pb + Pb collisions at Cern Large Hadron Collider energies and evolve the events using viscous hydrodynamics with nonzero shear but vanishing bulk viscosity. Comparing the predicted anisotropic flow coefficients for charged hadrons with CMS data we find that both the Monte Carlo Glauber (MC-Glb) and Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) models produce initial fluctuation spectra that are incompatible with the measured final anisotropic flow power spectrum, for any choice of the specific shear viscosity. In spite of this failure, we show that the hydrodynamic model can qualitatively explain, in terms of event-by-event fluctuations of the anisotropic flow coefficients and flow angles, the breaking of flow factorization for elliptic, triangular, and quadrangular flow measured by the CMS experiment. For elliptic flow, this factorization breaking is large in ultracentral collisions. We conclude that the bulk of the experimentally observed flow factorization breaking effects are qualitatively explained by hydrodynamic evolution of initial-state fluctuations, but that their quantitative description requires a better understanding of the initial fluctuation spectrum.

Scaling Laws for Dark Matter Halos in Late-Type and Dwarf Spheroidal Galaxies

AbstractDark matter (DM) halos of Sc–Im galaxies satisfy structural scaling laws analogous to the fundamental plane relations for elliptical galaxies. Halos in less luminous galaxies have smaller core radii rc, higher central densities ρ^, and smaller central velocity dispersions σ. If dwarf spheroidal (dSph) and dwarf Magellanic irregular (dIm) galaxies lie on the extrapolations of these correlations, then we can estimate their baryon loss relative to that of Sc–Im galaxies. We find that, if there had been no enhanced baryon loss relative to Sc–Im galaxies, typical dSph and dIm galaxies would be brighter by ΔMB ≃ -4.0 mag and ΔMB ≃ -3.5 mag, respectively. Instead, the galaxies lost or retained as gas (in dIm galaxies) baryons that could have formed stars. Also, dSph and dIm galaxies have DM halos that are more massive than we thought, with σ ~ 30 km s−1 or circular-orbit rotation velocities Vcirc ~ 42 km s−1. Comparison of DM and visible matter parameter correlations confirms that, at MV ≳ -18, dSph and dIm galaxies form a sequence of decreasing baryon-to-DM mass ratios in smaller dwarfs. We show explicitly that galaxy baryon content goes to (almost) zero at Vcirc ≲ 42 ± 4 km s−1, in agreement with Vcirc as found from our estimate of baryon depletion. Our results suggest that there may be a large population of DM halos that are dark and undiscovered. This helps to solve the problem that the initial fluctuation spectrum of cold dark matter predicts more dwarf galaxies than we observe.

Results from the Wilkinson Microwave Anisotropy Probe

The Wilkinson Microwave Anisotropy Probe (WMAP) mapped the distribution of temperature and polarization over the entire sky in five microwave frequency bands. These full-sky maps were used to obtain measurements of temperature and polarization anisotropy of the cosmic microwave background with unprecedented accuracy and precision. The analysis of two-point correlation functions of temperature and polarization data gives determinations of the fundamental cosmological parameters such as the age and composition of the universe, as well as the key parameters describing the physics of inflation, which is further constrained by three-point correlation functions. WMAP observations alone reduced the flat |$\Lambda $| cold dark matter (⁠|$\Lambda $|CDM) cosmological model (six) parameter volume by a factor of |$>$|68,000 compared with pre-WMAP measurements. The WMAP observations (sometimes in combination with other astrophysical probes) convincingly show the existence of non-baryonic dark matter, the cosmic neutrino background, the flatness of the spatial geometry of the universe, a deviation from a scale-invariant spectrum of initial scalar fluctuations, and that the current universe is undergoing an accelerated expansion. The WMAP observations provide the strongest ever support for inflation; namely, the structures we see in the universe originate from quantum fluctuations generated during inflation.

Quantum chaos in the quantum fluid: Spectrum of initial fluctuations in the little bang

Abstract We outline how unstable quantum fluctuations decohere classical fields in heavy ion collisions, leading to an equation of state and hydrodynamics. Explicit numerical realization of this frame-work in a scalar ϕ 4 theory demonstrates that anomalously low values of η / s can be generated.

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical integration. We use such models to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the 3D EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent \gamma depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter \kappa controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which \gamma depends strongly on both n and \kappa and where it agrees very well with a simple generalisation of the so-called stable clustering hypothesis in three dimensions, and (2) a region in which \gamma is more or less independent of both the spectrum and the expansion of the universe. We explain the observed location of the boundary in (n, \kappa) space dividing the "stable clustering" region from the "universal" region. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of "universality" of non-linear clustering in this context.

Cosmological fluctuation growth in bimetric MOND

I look at the growth of weak density inhomogeneities of nonrelativistic matter, in bimetric-MOND (BIMOND) cosmology. I concentrate on matter-twin-matter-symmetric versions of BIMOND, and assume that, on average, the universe is symmetrically populated in the two sectors. MOND effects are absent in an exactly symmetric universe, apart from the appearance of a cosmological constant, Lambda~(a0/c)^2. MOND effects-local and cosmological-do enter when density inhomogeneities that differ in the two sectors appear and develop. MOND later takes its standard form in systems that are islands dominated by pure matter. I derive the nonrelativistic equations governing small-scale fluctuation growth. The equations split into two uncoupled systems, one for the sum, the other for the difference, of the fluctuations in the two sectors. The former is governed strictly by Newtonian dynamics. The latter is governed by MOND dynamics, which entails stronger gravity, and nonlinearity even for the smallest of perturbations. These cause the difference to grow faster than the sum, conducing to matter-twin-matter segregation. The nonlinearity also causes interaction between nested perturbations on different scales. Because matter and twin matter (TM) repel each other in the MOND regime, matter inhomogeneities grow not only by their own self gravity, but also through shepherding by flanking TM overdensitie. The relative importance of gravity and pressure in the MOND system depends also on the strength of the perturbation. The development of structure in the universe, in either sector, thus depends crucially on two initial fluctuation spectra: that of matter alone and that of the matter-TM difference. I also discuss the back reaction on cosmology of BIMOND effects that appear as "phantom matter" resulting from inhomogeneity differences between the two sectors.

An Excursion Set Model of the Cosmic Web: The Abundance of Sheets, Filaments, and Halos

We discuss an analytic approach for modeling structure formation in sheets, filaments, and knots. This is accomplished by combining models of triaxial collapse with the excursion set approach: sheets are defined as objects that have collapsed along only one axis, filaments have collapsed along two axes, and halos are objects in which triaxial collapse is complete. In the simplest version of this approach, which we develop here, large-scale structure shows a clear hierarchy of morphologies: the mass in large-scale sheets is partitioned up among lower mass filaments, which themselves are made up of still lower mass halos. Our approach provides analytic estimates of the mass fraction in sheets, filaments, and halos and its evolution, for any background cosmological model and any initial fluctuation spectrum. In the currently popular ΛCDM model, our analysis suggests that more than 99% of the cosmic mass is in sheets, and 72% in filaments, with mass larger than 1010 M☉ at the present time. For halos, this number is only 46%. Our approach also provides analytic estimates of how halo abundances at any given time correlate with the morphology of the surrounding large-scale structure and how halo evolution correlates with the morphology of large-scale structure.

Bounds on cold dark matter and neutrino isocurvature perturbations from CMB and LSS data

Early universe models for the origin of structure typically produce a spectrum of initial fluctuations with a mixture of adiabatic and isocurvature perturbations. Using the observed anisotropies of the cosmic microwave backgound, the matter power spectra from large scale structure surveys and the luminosity distance vs. redshift relation from supernovae of type Ia, we obtain strong bounds on the possible cold dark matter/baryon as well as neutrino isocurvature contributions to the primordial fluctations in the Universe. Neglecting the possible effects of spatial curvature and tensor perturbations, we perform a Bayesian likelihood analysis with 13 free parameters, including independent spectral indexes for each of the modes and for their cross-correlation angle. We find that around a pivot wave number of $k=0.05h\text{ }\text{ }{\mathrm{M}\mathrm{p}\mathrm{c}}^{\ensuremath{-}1}$ the amplitude of the correlated isocurvature component cannot be larger than about 60% for the cold dark matter mode, 40% for the neutrino density mode, and 30% for the neutrino velocity mode, at two sigma. In the first case, our bound is larger than the WMAP first-year result, presumably because we prefer not to include any data from Lyman-$\ensuremath{\alpha}$ forests, but then obtain large blue spectral indexes for the nonadiabatic contributions. We also translate our bounds in terms of constraints on double inflation models with two uncoupled massive fields.

How big were the first cosmological objects?

We calculate the cooling times at constant density for haloes with virial temperatures from 100 K to 1 × 105 K that originate from a 3σfluctuation of a CDM power spectrum in three different cosmologies. Our intention is to determine the first objects that can cool to low temperatures, but not to follow their dynamical evolution. We identify two generations of haloes: those with low virial temperatures, Tvir ≲ 9000 K that remain largely neutral, and those with larger virial temperatures that become ionized. The lower temperature, lower mass haloes are the first to cool to 75 per cent of their virial temperature. The precise temperature and mass of the first objects are dependent upon the molecular hydrogen (H2) cooling function and the cosmological model. The higher mass haloes collapse later but, in this paradigm, cool much more efficiently once they have done so, first via electronic transitions and then via molecular cooling: in fact, a greater residual ionization once the haloes cool below 9000 K results in an enhanced H2 production and hence a higher cooling rate at low temperatures than for the lower mass haloes, so that within our constant-density model it is the former that are the first to cool to really low temperatures. We discuss the possible significance of this result in the context of CDM models in which the shallow slope of the initial fluctuation spectrum on small scales leads to a wide range of halo masses (of differing overdensities) collapsing over a small redshift interval. This ‘crosstalk’ is sufficiently important that both high- and low-mass haloes collapse during the lifetimes of the massive stars which may be formed at these epochs. Further investigation is thus required to determine which generation of haloes plays the dominant role in early structure formation.

On the Abundance of Collapsed Objects

The redshift dependence of the abundance of collapsed objects places strong constraints on cosmological models of structure formation. We apply a recently proposed model describing the anisotropic collapse of inhomogeneous spatial domains. Compared with the spherical top-hat model, this generic model leads to significantly more collapsed objects at high redshifts: at redshift one and on the scale of rich clusters a factor of 65. Furthermore, for a fixed normalization of the initial fluctuation spectrum (\sigma_8=1), we predict four times as much presently collapsed objects on the mass-scale of rich clusters within the standard CDM cosmogony, compared to the spherical collapse.

Standard Cosmology and Alternatives: A Critical Appraisal

▪ Abstract This review takes a critical look at the cosmological scenario at the turn of the century by examining the available cosmological models in the light of the present observational evidence. The center stage is held by the big bang models, which are collectively referred to here as standard cosmology (SC) and its extensions. SC itself is characterized by a seven parameter set of models based on Einstein's general theory of relativity. The seven parameters are H0, ΩB, ΩDM, ΩΛ, ΩR (describing the background universe, and A, n (specifying the amplitude and power law index of initial fluctuation spectrum). The extended SC includes extrapolations of the SC to earlier epochs when the mean energies of the particles were greater than about 100 GeV. The strength of the SC is seen to lie in its successful prediction of the expansion of the universe, the abundance of light nuclei, and the spectrum and anisotropies of the cosmic microwave background (CMBR). The SC has led to a whole class of theories of structure formation, which are, in principle, testable observationally. The subject of twentieth century cosmology gained considerably from occasional ideas different from the SC; some of these are briefly outlined and placed in historical perspective. Currently there is only one alternative cosmology, the quasi steady state cosmology (QSSC), that has been developed to a stage where it can be compared with observations and also with the SC. Although the SC does appear quite successful, there are still many unresolved issues that keep the cosmological scene fairly open.

Modelling galaxy clustering at high redshift

We discuss the theoretical interpretation of observational data concerning the clustering of galaxies at high redshifts. Building on the theoretical machinery developed by Matarrese et al. (1997), we make detailed quantitative predictions of galaxy clustering statistics for a variety of cosmological models, taking into account differences in spatial geometry and initial fluctuation spectra and exploring the role of bias as a complicating factor in these calculations. We demonstrate that the usual description of evolution (in terms of the parameters $\epsilon$ and $r_0$) is not useful for realistic galaxy clustering models. We compare the detailed predictions of the variation of correlation functions with redshift against current observational data to constrain available models of structure formation. Theories that fit the present-day abundance of rich clusters are generally compatible with the observed redshift evolution of galaxy clustering if galaxies are no more than slightly biased at $z\sim 1$. We also discuss the interpretation of a concentration of Lyman-break galaxies found by Steidel et al. (1998), coming to the conclusion that such concentrations are not unexpected in `standard' models of structure formation.

Properties of galaxy clusters in different cosmological scenarios – I. Intrinsic properties

We study the influence of the various parameters of scenarios of large-scale structure formation on properties of galaxy clusters, and investigate which cluster properties are most sensitive to these parameters. We present a set of large N-body simulations and derive the intrinsic properties of galaxy clusters in these simulations, which represent a volume of $256^3 h^{-3}$ Mpc^3. The cosmological scenarios studied differ in either the shape of the power spectrum of initial fluctuations, its normalization, the density parameter $\Omega_{0}$, or the Hubble parameter $H_{0}$. Between each of the simulations, only one parameter is set differently, so that we can study the influence of that parameter on the cluster properties. The cluster properties that are studied are the mass, line-of-sight velocity dispersion, peculiar velocity, intrinsic shape, and orientation with respect to its surroundings. $\sigma_{8}$ has a large impact on the cluster properties. The latter, viz. the cluster number density, mass, line-of-sight velocity dispersion and peculiar velocity, are also determined by $\Omega_{0}$, though somewhat less. Other parameters, such as $H_{0}$, the tilt of the initial fluctuation spectrum, and the exact shape of this spectrum, are generally less important. Unlike the other cluster properties studied, the peculiar velocity is found to depend on all parameters of the formation scenario. Using scaling relations between the average properties of the cluster sample and the parameters of the formation scenario, one may try and interpolate between the scenarios studied here in order to find the parameters of the scenario that is most consistent with the data.

Dark halo mergers and the formation of a universal profile

We argue that a universal density profile for dark matter haloes arises as a natural consequence of hierarchical structure formation: it is a fixed point in the process of repeated mergers. We present analytic and numerical arguments for the emergence of a particular form of the central cusp profile. At small radii, the density should vary as r−α, with α determined by the way in which the characteristic density of haloes scales with their mass. If small haloes are dense, then α is large. The mass–density relation can be related to the power spectrum of initial fluctuations, P(k), through ‘formation time’ arguments. Early structure formation leads to steep cusps. For P(k) ∼ kn we find α ≃ 3(3 + n)/(5 + n). The universal profile is generated by tidal stripping of small haloes as they merge with larger objects.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in -space are consistent with a DeltaT flat in frequency and broadly follow inflation-based expectations. That the levels are approximately (10(-5))2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Lambda cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 +/- 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 +/- 0.08 for DMR plus the SK95 experiment; 1.00 +/- 0.04 for DMR plus all smaller angle experiments; 1.00 +/- 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Lambda and moderate constraints on Omegatot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

The correlation function of clusters of galaxies and the amplitude of mass fluctuations in the Universe

We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by the spectrum of linear density fluctuations. Thus if the shape of the initial fluctuation spectrum is known, its amplitude $\sigma_8$ can be estimated directly from the correlation length of a cluster sample in a way which is independent of the value of $\Omega_0$. If the cluster mass corresponding to the sample threshold is also known, it provides an independent estimate of the quantity $\sigma_8\Omega_0^{0.6}$. Thus cluster data should allow both $\sigma_8$ and $\Omega_0$ to be determined observationally. We explore these questions using N-body simulations together with a simple but accurate analytical model based on extensions of Press-Schechter theory. Applying our results to currently available data we find that if the linear fluctuation spectrum has a shape similar to that suggested by the APM galaxy survey, then a correlation length $r_0$ in excess of $20\mpch$ for Abell clusters would require $\sigma_8>1$, while $r_0<15\mpch$ would require $\sigma_8<0.5$. With conventional estimates of the relevant mass threshold these imply $\Omega_0\la 0.3$ and $\Omega_0\ga 1$ respectively.

The zero-point of the cluster-cluster correlation function: A key test of cosmological power spectra

view Abstract Citations (37) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Zero-Point of the Cluster-Cluster Correlation Function: A Key Test of Cosmological Power Spectra Klypin, Anatoly ; Rhee, Geroge Abstract We propose the zero-point of the cluster-cluster correlation function r_0_ as a sensitive test for the shape of the power spectrum of initial fluctuations. With a wealth of new available redshifts for rich clusters the correlation function is measured to higher accuracy than has previously been done. It is now possible to go beyond the power law description to measure the point at which the correlation function becomes zero. A number of measurements of the zero-point of the rich galaxy cluster correlation function indicate that the zero-point should be in the range (40-60) h^-1^ Mpc. We discuss different effects, which could affect the zero-point and conclude that it is reasonably stable. The large value of r_0_ at which the zero-point occurs rules out conventional CDM models independently of the assumed amplitude. The most severe constraints are imposed on the CDM models with the cosmological constant. Models with {OMEGA} < 0.25 should he rejected because they predict too large r_0_. If the age of the universe is assumed to be larger than 15 Gyr, models with either {OMEGA} < 0.5 or h > 0.55 are rejected. We present the results of numerical simulations of clusters in the mixed model (the cold-plus-hot-dark-matter or CHDM). The correlation function of clusters in the model has a zero-point, r_0_ = 55 h^-1^ Mpc that matches the zero-point of the observed function and is very close to the zero-point predicted by the linear theory. The shape of the function on all available scales (up to 100 h^-1^ Mpc) is reproduced for both the Abell and the APM clusters. The CHDM model predicts the mass function for the clusters, which is higher than that given by Bahcall & Cen (1993) (masses are larger by a factor 1.5), but is compatible with the results of Biviano et al. (1993). Publication: The Astrophysical Journal Pub Date: June 1994 DOI: 10.1086/174252 arXiv: arXiv:astro-ph/9309034 Bibcode: 1994ApJ...428..399K Keywords: Cosmology; Dark Matter; Distribution Functions; Galactic Clusters; Power Spectra; Stellar Models; Variations; Computerized Simulation; Density (Number/Volume); Numerical Analysis; Red Shift; Stellar Mass; Astronomy; COSMOLOGY: THEORY; GALAXIES: CLUSTERING; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; METHODS: NUMERICAL; Astrophysics E-Print: 16 pages, tex, UNLV/93/32 full text sources arXiv | ADS |