Spatial Density Fluctuations Research Articles

Medium-range structure in glasses and low-Q structure in neutron and X-ray scattering data

Attempts to understand the medium-range structure of glasses and other amorphous materials from X-ray and neutron scattering data necessarily focus on the low-Q region, where Q is the modulus of the scattering vector. Data for Q in the range 8–20nm−1 reveal real-space detail on a scale 2π/Q. This corresponds to the region often denoted as ‘medium-range structure’, 0.5–1.5nm. An attempt is made to describe the origin of low-Q structure in terms of spatial correlation of atomic density fluctuations and to delineate the inter-atomic distances involved. Amorphous silicon and silica are considered in detail showing that real-space data extending to about 1.1 and 1.6nm, respectively, are required to specify accurately the detail in the first peaks of the structure factor. The degree of order associated with spatial atomic density fluctuations then becomes a key question. Completely random fluctuations seem unlikely to offer an explanation. Aperiodic, non-crystallographic packing offers some promise, but remains inadequately tested. The most satisfactory results for simple oxide glasses, at least, come from medium-range organization based on the principles underlying compositionally and thermodynamically equivalent crystalline structures. Low-Q structures in neutron scattering data for lithium, sodium and lithium/potassium disilicate glasses are treated as examples.

Environmental uncertainty in modeling of shallow-water reverberation

Simulated monostatic shallow-water reverberation is produced by a broadband model that accounts for propagation and scattering in a waveguide that is horizontally stratified on average, but subject to slightly rough interfaces and small, random spatial fluctuations in density and sound speed. This model has been used to infer parameters characterizing these inhomogeneities (scattering parameters) from experimental data, assuming a specific background geoacoustic profile. In realistic situations, however, the background environment may either not be known with precision or may be too variable to admit a range-independent characterization. It is even possible that several geoacoustically distinct alternative sets of environmental parameters are plausible. This may occur, for instance, when geoacoustic inversion is used to determine a background profile. In this presentation, the effects of environmental uncertainties, including the existence of alternative geoacoustic profiles, on scattering parameters inferred from reverberation data are examined. [Work supported by ONR.]

Angular Momentum Transport by Magnetohydrodynamic Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability

The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard α disk model. From our numerical experiments we find that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength and is unaffected by ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly isothermal calculations, where pressure varies little with time. Over the entire region of parameter space explored, turbulence driven by the MRI has many characteristic ratios such as that of the Maxwell stress to the magnetic pressure. We also find that the amplitudes of the spatial fluctuations in density and the time variability in the stress are characterized by the ratio of magnetic pressure to gas pressure in the nonlinear regime. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of nonsteady magnetic reconnection.

Wavelike structures in the Martian topside ionosphere observed by Mars Global Surveyor

Seven hundred and forty three Martian ionospheric electron density altitude profiles, obtained by the radio occultation experiment onboard Mars Global Surveyor, have been analyzed for the purpose of determining possible spatial density fluctuations. In about 80% of these profiles the high altitude region, above ∼145 km, displays significant wavelike structures with spatial scales of tens kilometers. These structures appear as spatial wave activity superposed on background electron density distributions that decrease exponentially with altitude. The amplitudes of the density variations are mostly limited to be less than ±50% of the background densities. Spectrum analysis is applied to the ionospheric profiles above 145 km, and it is found that a “spatial wavelength” of ∼40 km is prevailing in the observations. It is demonstrated that the observed fluctuations are consistent with the occurrence of local density fluctuations. The prevailing scale of the wavelike structure agrees very well with the wavelength of hydrodynamic waves predicted by Wang and Nielsen [2002a, 2002b, 2003b]. If hydrodynamic waves is indeed the cause of these electron density fluctuations, then the ∼145 km altitude should be considered the lowest altitude at which the effects of external dynamic disturbances of the Martian ionosphere can reach, and should therefore be considered the lower boundary of the topside ionosphere.

Nonlocal k-space interaction and the rare existence of coherent structures in the tokamak edge plasma

The relation between turbulent density fluctuations occurring at two wave numbers is investigated at the plasma edge of the Tore Supra tokamak [G. Antar et al., Plasma Phys. Controlled Fusion 41, 947 (1998)]. To achieve this goal, light scattering is used with two laser beams performing a Fourier transform about two given wave vectors. Consequently a band-pass filter is applied to the spatial turbulent density fluctuations about each wave vector. When the separation is small between the analyzing wave numbers, it is found that the cross correlation between the two channels is dominated by the autocorrelation caused by the diagnostic resolution in the wave number space. For large separations, the instrumental resolution contribution is negligible but a cross correlation amplitude of about 1% to 2% is still detected. It reflects nonlocal coupling in the k space caused by eddy organization rarely taking place. In agreement with this behavior, a rather small deviation of the probability distribution from a Gaussian is reported.

Optimal exploitation of spatially distributed trophic resources and population stability

The relationships between optimal foraging of individuals and population stability are addressed by testing, with a spatially explicit model, the effect of patch departure behaviour on individual energetics and population stability. A factorial experimental design was used to analyse the relevance of the behavioural factor in relation to three factors that are known to affect individual energetics; i.e. resource growth rate (RGR), assimilation efficiency (AE), and body size of individuals. The factorial combination of these factors produced 432 cases, and 1000 replicate simulations were run for each case. Net energy intake rates of the modelled consumers increased with increasing RGR, consumer AE, and consumer body size, as expected. Moreover, through their patch departure behaviour, by selecting the resource level at which they departed from the patch, individuals managed to substantially increase their net energy intake rates. Population stability was also affected by the behavioural factors and by the other factors, but with highly non-linear responses. Whenever resources were limiting for the consumers because of low RGR, large individual body size or low AE, population density at the equilibrium was directly related to the patch departure behaviour; on the other hand, optimal patch departure behaviour, which maximised the net energy intake at the individual level, had a negative influence on population stability whenever resource availability was high for the consumers. The consumer growth rate ( r) and numerical dynamics, as well as the spatial and temporal fluctuations of resource density, which were the proximate causes of population stability or instability, were affected by the behavioural factor as strongly or even more strongly than by the others factors considered here. Therefore, patch departure behaviour can act as a feedback control of individual energetics, allowing consumers to optimise a potential trade-off between short-term individual fitness and long-term population stability.

Relativistic Conic Beams and Spatial Distribution of Gamma‐Ray Bursts

We study the statistics of gamma-ray bursts, assuming that gamma-ray bursts are cosmological and they are beamed in the form of a conical jet with a large bulk Lorentz factor $\sim 100$. In such a conic beam, the relativistic ejecta may have a spatial variation in the bulk Lorentz factor and the density distribution of gamma-ray emitting jet material. An apparent luminosity function arises because the axis of the cone is randomly oriented with respect to the observer's line of sight. The width and the shape of the luminosity function are determined by the ratio of the beam opening angle of the conical jet to the inverse of the bulk Lorentz factor, when the bulk Lorentz factor and the jet material density is uniform on the photon emitting jet surface. We calculate effects of spatial variation of the Lorentz factor and the spatial density fluctuations within the cone on the luminosity function and the statistics of gamma-ray bursts. In particular, we focus on the redshift distribution of the observed gamma-ray bursts. The maximum distance to and the average redshift of the gamma-ray bursts are strongly affected by the beaming-induced luminosity function. The bursts with the angle-dependent Lorentz factor which peaks at the center of the cone have substantially higher average gamma-ray burst redshifts. When both the jet material density and the Lorentz factor are inhomogeneous in the conical beam, the average redshift of the bursts could be 5 times higher than that of the case in which relativistic jet is completely homogeneous and structureless. Even the simplest models for the gamma-ray burst jets and their apparent luminosity distributions have a significant effect on the redshift distribution of the gamma-ray bursts.

Nonlocal dielectric functions of molecular liquids from computer simulations

The longitudinal dielectric function, χ( k)=1−1/ ε L( k), of both polar and nonpolar liquid environments is a key ingredient to modern theories of solvent effects upon charge transfer reactions in solution and solvation dynamics processes in general. In this work, we present a molecular dynamics simulation study of the dielectric function of several molecular liquids ranging from associating (H 2O, CH 3OH) and nonassociating ((CH 3) 2SO, CH 3CN) polar liquids to nondipolar ones (C 6H 6, CCl 4 and CO 2) aiming to better understand the relationships between the structure of the χ( k) functions to the charge–charge spatial correlations in each liquid. We show that the characteristic main peak of χ( k), located at some wave vector k ∗ , whose value depends on the liquid, arises from spatial charge density fluctuations of wavelength 2 π/k ∗ for all liquids considered, with the exception of CO 2. Further details about the shape of the χ( k) functions for the simulated liquids are discussed in terms of intra and intermolecular charge–charge correlations.

N-Particle-Simulations of Dust Growth: I. Growth Driven by Brownian Motion

In this paper we investigate the Brownian stage of dust growth in the cold part of a protoplanetary disc around a young stellar object. The growth due to diffusive particle motion is simulated numerically by a new N-particle method. In contrast to earlier studies the dust growth was investigated at astrophysically relevant small number densities. We found that the friction time of the grains scales with the fifth root of the particle radius although the average fractal dimension of the growing grains is smaller than two. The distribution of fractal dimension is very broad and about 10% of the dust grains have fractal dimensions larger than two. Nevertheless, the determined time scales of the pure Brownian dust growth are much too large for explaining the formation of planets within the lifetime of a protoplanetary disc. Our numerical results indicate that at very low number densities the Smoluchowski theory is not applicable for the description of the growth process. The reason might be that at low number densities spatial density fluctuations of the dust grains start to strongly influence the growth process.

Spatial energy and density fluctuations and the entropy of glass

Non-zero spatial energy fluctuations, , are characteristic of an amorphous material, and can be uniquely expressed in terms of molecular distributions and interaction potentials. An approximation relating to the density fluctuations, , enables us to express the former in terms of pair distribution, g(r) (or scattering function, S(k)), data and given pair potentials. A modelling of g(r) in a form g(r) = g(r; L, D), where L is an optimal virtual lattice characterizing the local configurations of atoms and D is a `structural diffusion' parameter specifying the degree of spatial decay of coherence between local structures in the amorphous system, provides expressions for the energy E and for in terms of L and D. This enables us to obtain the entropy function by integrating along a (virtual) path defined in parameter space {L, D}, connecting the amorphous state to an ordered state (L, D = 0). The method is illustrated on a model system of ions immersed in a uniform background of opposite charge (a model `metal'), by calculating its entropy as a function of D in a range corresponding to typical liquid and glass structures.

Orientational relaxation in a random dipolar lattice: Role of spatial density fluctuations in supercooled liquids.

We have carried out a computer experiment of orientational relaxation in a spatially random and orientationally disordered dipolar lattice (RDL), generated by quenching only the translational motion of a dense liquid. In the high polarity limit, the orientational relaxation of the RDL is dramatically different from that of the parent liquid, the former exhibits a very slow, nonexponential long time decay of the orientational correlation functions and markedly non-Debye dielectric relaxation. These results clearly demonstrate the importance of spatial density fluctuations in orientational relaxation.

The W1+∞ effective theory of the Calogero-Sutherland model and Luttinger systems

We construct the effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles N. It is given by a W 1+∞ conformal field theory (with central charge c = 1) that describes exactly the spatial density fluctuations arising from the low-energy excitations about the Fermi surface. Our approach does not rely on the integrable character of the model, and indicates how to extend previous results to any order in powers of 1 N . Moreover, the same effective theory can also be used to describe an entire universality class of (1 + 1)-dimensional fermionic systems beyond the Calogero-Sutherland model, which we identify with the class of chiral Luttinger systems. We also explain how a systematic bosonization procedure can be performed using the W 1+∞ generators, and propose this algebraic approach to classify low-dimensional non-relativistic fermionic systems, given that all representations of W 1+∞ are known. This approach has the appeal of being mathematically complete and physically intuitive, encoding the picture suggested by Luttinger's theorem.

Acoustic scattering by marine sediments with irregularities of different types

There are two different types of irregularities giving the main contributions to bottom scattering: volume inhomogeneities of the sediment and roughness of its surface and interfaces. The problem of distinguishing and/or separating these contributions is considered using differences in frequency-angular dependencies of the scattering coefficient and analysis of the spatial autocorrelation function of the scattered field. The volume inhomogeneities of the sediment in turn can be considered as one of two types: spatial fluctuations of density and fluctuations of sound velocity. For water-saturated sediments (without gas), density fluctuations are usually stronger and their contribution to the total volume scattering is much more than that due to sound velocity fluctuations. But even low concentrations of gas bubbles can alter acoustic properties of sediments considerably, reducing the effective (average) sound velocity and enhancing fluctuations of sound velocity, with virtually no effect on the density. As a result, some specific features appear in sound scattering, and these can be used for remote acoustic characterization of sediments and determination of the type of bottom irregularities. [Work partially supported by ONR.]

Quantitative analysis of the lens cell microstructure in selenite cataract using a two-dimensional Fourier analysis

Using two-dimensional (2-D) Fourier methods, we analysed the cellular microstructure of three rat lenses: normal transparent, selenite-induced cataractous and selenite-treated plus a phase separation inhibitor (PSI) to prevent cataract. 2-D Fourier analysis of electron micrographs of the lens cells quantified the dimensions of the spatial fluctuations in electron density of the lens cell microstructure. The 2-D Fourier spectra of the transparent normal and PSI-treated lens cells were remarkably similar while those of the opaque selenite-treated lens cells were dramatically different. In the opaque cells the contributions of large Fourier components (larger than half the wavelength of light) in the 2-D Fourier spectra were much greater than in the transparent cells. The results of the 2-D Fourier analysis of electron micrographs are consistent with the theory of transparency of the eye.

DISTRIBUTION AND PRODUCTION OF MICRODEUTOPUS GRYLLOTALPA (AMPHIPODA: AORIDAE) IN A SHALLOW COASTAL LAGOON IN THE BAY OF CADIZ, SPAIN

ABSTRACT The spatial and temporal fluctuations of density, life cycle, and production of Microdeutopus gryllotalpa in a seminatural lagoon system were studied by taking monthly samples at 3 sites during 1991 and 1992. Its numerical abundance and biomass, which showed considerable spatial and temporal variation, were positively related to the biomass of benthic macroalgae and water salinity (stepwise multiple regression analysis, P 17°C) than for the rest of the year (0.026 mm d-1; T < 17°C). The population studied was multivoltine, with overlapping cohorts and a possible maximum of 5 generations per year. Using the size-frequency method, the mean annual production and production/biomass ratio for the system were estimated to be 22.42 g DW (13.49 g AFDW) m-2 yr-1 and 12.8 (11.7), respectively. These results indicated that in warm temperate lagoons secondary production for species such as M. gryllotalpa may be high, despite its moderate mean biomass.

Random driving of a nonlinear oscillator.

The evolution equations for the density distribution and its two phase-space point correlation for nonlinear oscillators under the influence of an external random driving force are derived. We found that the correlation function obeys a Fokker-Planck-like evolution equation with decoherence, diffusion, and source terms. An asymptotic steady state solution is discussed, where the small-amplitude and short-wavelength spatial fluctuations of density ( microstructure'') are found to be the special effect of the coherent random driving, distinguishing it from incoherent noise.

The influence of spatial fluctuations in simple reaction-diffusion systems

In this paper we study the kinetics of the irreversible diffusion-controlled reactions A+ A→ inert and A+ B→ inert, respectively. By means of van Kampen's “method of compounding moments” we derive a modified rate equation describing the time evolution of the average particle density, which includes the influence of spatial density fluctuations. We show that below an upper critical spatial dimension d 0=2( d 0=4) the particle density of the A+ A system ( A+ B system with equal initial densities of A- and B-particles) decays at t − α with α=2/(4− d) ( α= d/4), which is slower than the t −1 decay predicted by the usual rate equation.

Chaotic behaviour of ionospheric turbulence from scintillation measurements

Ionospheric amplitude and phase scintillation data have been analysed to estimate the ‘information dimension’ associated with the attractor of the system. For weak scintillations, both amplitude and phase data yield identical results which demonstrate that spatial fluctuations of electron density in the ionosphere may be characterized by a few degrees of freedom. Stronger scintillations are attributed to steepened density irregularities which cause ‘focusing’ of the incident radio wave. This results in the amplitude scintillations exhibiting higher dimensional chaos but spatial fluctuations in ionospheric density still involve low dimensional chaos.

Fluctuation-induced kinetics of reversible reactions

The influence of spatial density fluctuations on the kinetics of a reversible reaction A+B to or from C involving charged particles is investigated. New explicit expressions for the long-time approach of mean A and B densities to equilibrium are obtained.

Small-angle X-ray scattering from block copolymers in disordered state: 2. Effect of molecular weight distribution

Spatial segmental density fluctuations occurring in a polystyrene-polyisoprene diblock copolymer in bulk and in disordered state were investigated by small-angle X-ray scattering. The observed wavelength of the dominant mode of the fluctuations was found to be larger than that predicted by the random phase approximation by a factor up to 50%. This discrepancy was found to be essentially removed by taking into account the distributions of molecular weight and composition of the block copolymer.