Dust in the Local Interstellar Wind

The gas-to-dust mass ratios found for interstellar dust within the Solar System, versus values determined astronomically for the cloud around the Solar System, suggest that large and small interstellar grains have separate histories, and that large interstellar grains preferentially detected by spacecraft are not formed exclusively by mass exchange with nearby interstellar gas. Observations by the Ulysses and Galileo satellites of the mass spectrum and flux rate of interstellar dust within the heliosphere are combined with information about the density, composition, and relative flow speed and direction of interstellar gas in the cloud surrounding the solar system to derive an in situ value for the gas-to-dust mass ratio, $R_{g/d} = 94^{+46}_{-38}$. Hubble observations of the cloud surrounding the solar system yield a gas-to-dust mass ratio of Rg/d=551+61-251 when B-star reference abundances are assumed. The exclusion of small dust grains from the heliosheath and heliosphere regions are modeled, increasing the discrepancy between interstellar and in situ observations. The shock destruction of interstellar grains is considered, and comparisons are made with interplanetary and presolar dust grains.Comment: 87 pages, 9 figures, 6 tables, accepted for publication in Astrophysical Journal. Uses AASTe

Interface Roughening in a Hydrodynamic Lattice-Gas Model with Surfactant

Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form for large surfactant concentrations. To assist in determining the stability limits of the interface, we calculate the change in the roughness and growth exponents $\alpha$ and $\beta$ as a function of surfactant concentration along the interface.Comment: 4 pages with 4 embedded ps figures. Requires psfig.tex. Will appear in PRL 14 Oct 199

Speculations on Primordial Magnetic Helicity

We speculate that above or just below the electroweak phase transition magnetic fields are generated which have a net helicity (otherwise said, a Chern-Simons term) of order of magnitude $N_B + N_L$, where $N_{B,L}$ is the baryon or lepton number today. (To be more precise requires much more knowledge of B,L-generating mechanisms than we currently have.) Electromagnetic helicity generation is associated (indirectly) with the generation of electroweak Chern-Simons number through B+L anomalies. This helicity, which in the early universe is some 30 orders of magnitude greater than what would be expected from fluctuations alone in the absence of B+L violation, should be reasonably well-conserved through the evolution of the universe to around the times of matter dominance and decoupling, because the early universe is an excellent conductor. Possible consequences include early structure formation; macroscopic manifestations of CP violation in the cosmic magnetic field (measurable at least in principle, if not in practice); and an inverse-cascade dynamo mechanism in which magnetic fields and helicity are unstable to transfer to larger and larger spatial scales. We give a quasi-linear treatment of the general-relativistic MHD inverse cascade instability, finding substantial growth for helicity of the assumed magnitude out to scales $\sim l_M\epsilon^{-1}$, where $\epsilon$ is roughly the B+L to photon ratio and $l_M$ is the magnetic correlation length. We also elaborate further on an earlier proposal of the author for generation of magnetic fields above the EW phase transition.Comment: Latex, 23 page

Analysis of Velocity Fluctuation in Turbulence based on Generalized Statistics

The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity fluctuations. These formulae are derived by the present authors with the multifractal aspect based on the statistics that are constructed on the generalized measures of entropy, i.e., the extensive R\'{e}nyi's or the non-extensive Tsallis' entropy. It is revealed that there exist two scaling regions separated by a crossover length, i.e., a definite length approximately of the order of the Taylor microscale. It indicates that the multifractal distribution of singularities in velocity gradient in turbulent flow is robust enough to produce scaling behaviors even for the phenomena out side the inertial range.Comment: 10 Pages, 5 figure

Multifractality and percolation in the coupling space of perceptrons

The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated analytically using the replica formalism. The storage capacity and the generalization behaviour of the perceptron are shown to be related to properties of $f(\alpha)$ which are correctly described within the replica symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a transition from percolating to non-percolating cells. The existence of empty cells gives rise to singularities in the multifractal spectrum. The analytical results for binary couplings are corroborated by numerical studies.Comment: 13 pages, revtex, 4 eps figures, version accepted for publication in Phys. Rev.

Kolmogorov Spectrum of Quantum Turbulence

There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.Comment: 14pages, 24 figures and 1 table. Appeared in Journal of the Physical Society of Japan, Vol.74, No.12, p.3248-325

Depolarization regions of nonzero volume in bianisotropic homogenized composites

In conventional approaches to the homogenization of random particulate composites, the component phase particles are often treated mathematically as vanishingly small, point-like entities. The electromagnetic responses of these component phase particles are provided by depolarization dyadics which derive from the singularity of the corresponding dyadic Green functions. Through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. We present an extension to the strong-property-fluctuation theory in which depolarization regions of nonzero volume and ellipsoidal geometry are accommodated. Therein, both the size and spatial distribution of the component phase particles are taken into account. The analysis is developed within the most general linear setting of bianisotropic homogenized composite mediums (HCMs). Numerical studies of the constitutive parameters are presented for representative examples of HCM; both Lorentz-reciprocal and Lorentz-nonreciprocal HCMs are considered. These studies reveal that estimates of the HCM constitutive parameters in relation to volume fraction, particle eccentricity, particle orientation and correlation length are all significantly influenced by the size of the component phase particles

Anharmonic transitions in nearly dry L-cysteine I

Two special dynamical transitions of universal character have been recently observed in macromolecules at $T_{D}\sim 180 - 220$ K and $T^{*}\sim 100$ K. Despite their relevance, a complete understanding of the nature of these transitions and their consequences for the bio-activity of the macromolecule is still lacking. Our results and analysis concerning the temperature dependence of structural, vibrational and thermodynamical properties of the orthorhombic polymorph of the amino acid L-cysteine (at a hydration level of 3.5%) indicated that the two referred temperatures define the triggering of very simple and specific events that govern all the biochemical interactions of the biomolecule: activation of rigid rotors ($T<T^{*}$), phonon-phonon interactions with phonons of water dimer ($T^{*}<T<T_{D}$), and water rotational barriers surpassing ($T>T_{D}$).Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Universality of the Wigner time delay distribution for one-dimensional random potentials

We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out on samples whose sizes are large compared to the localisation length (localised regime). The case of small samples is also discussed (ballistic regime). We provide a physical argument which explains in a quantitative way the origin of the exponential divergence of the moments. The occurence of a log-normal tail for finite size systems is analysed. Finally, we present exact results in the low energy limit which clearly show a departure from the universal behaviour.Comment: 4 pages, 3 PostScript figure

Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks

Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum $f(\alpha)$ can be calculated analytically using the replica trick. Phase transition in the multifractal spectrum correspond to the crossover from percolating to non-percolating cell sizes. Instabilities of negative moments are related to the VC-dimension.Comment: 10 pages, Latex, submitted to PR