Family-Vicsek scaling of detachment fronts in granular Rayleigh-Taylor instabilities during sedimentating granular/fluid flows

When submillimetric particles are confined in a fluid such that a compact cluster of particles lie above the clear fluid, particles will detach from the lower boundary of the cluster and form an unstable separation front giving rise to growing fingers of falling particles. We study this problem using both experiments and hybrid granular/fluid mechanics models. In the case of particles from 50 to 500 microns in diameter falling in air, we study the horizontal density fluctuations at early times: the amplitude of the density difference between two points at a certain horizontal distance grows as a power law of time. This happens up to a saturation corresponding to a power law of the distance. The way in which the correlation length builds up to this saturation also follows a power law of time. We show that these decompaction fronts in sedimentation problems follow a Family-Vicsek scaling, characterize the dynamic and Hurst exponent of the lateral density fluctuations, respectively z ∼ 1 and ζ ∼ 0.75, and show how the prefactors depend on the grain diameter. We also show from similar simulations with a more viscous and incompressible fluid, that this feature is independent of the fluid compressibility or viscosity, ranging from air to water/glycerol mixtures.     

Robust statistical tests of Dragon-Kings beyond power law distributions

We ask the question whether it is possible to diagnose the existence of “Dragon-Kings” (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent characterizing the null hypothesis, which can use an exponential or power law distribution. We demonstrate how to apply these two tests on the distributions of cities and of agglomerations in a number of countries. We find the following evidence for Dragon-Kings: London in the distribution of city sizes of Great Britain; Moscow and St-Petersburg in the distribution of city sizes in the Russian Federation; and Paris in the distribution of agglomeration sizes in France. True negatives are also reported, for instance the absence of Dragon-Kings in the distribution of cities in Germany.     

Feasibility of an optical experimental method for the sizing of primary spherules in sub-micron agglomerates by polarized light scattering

The possibility of inferring by a non-invasive experimental method the size of primary particles (spherules), which constitute the agglomerated soot generated in an ethylene–air diffusion flame, is investigated. In contrast to the predictions from the Mie theory for isolated spheres, experimental evidence is provided here about the fact that the size of spherules (some tens of nanometers), which stick together to form agglomerates (some hundreds of nanometers), can be recognized from polarization ratio measurements. Validation of the proposed scattering technique is obtained by first performing standard measurements of the primary particle size by SEM analysis of soot samples taken on quartz inserted directly in the flame along the burner axis. Then, the polarization ratio P(θ)≡σ_HH/σ_VV of scattered light is measured at the same locations and for the same flame conditions for different polar scattering angles θ. As major result, evidence is provided of a linear relationship existing between the primary sizes, obtained independently by SEM analysis, and the measurements of the polarization ratio P(90°). Finally, a procedure is reported and applied to retrieve the absolute spherule size from the direct observation of the transition between the power-law and Porod’s scattering regimes, which correspond to the domains of long-range (fractal) and short-range (not fractal) interactions between primary particles, respectively. Received: 24 February 1999 / Final version: 6 December 1999 / Published online: 1 March 2000     

Antivortices due to competing orbital and paramagnetic pair-breaking effects

Thermodynamically stable vortex—antivortex structures in a quasi-twodimensional superconductor in a tilted magnetic field are predicted. For this geometry, both orbital and spin pair-breaking effects exist, with their relative strength depending on the tilt angle θ. The spectrum of possible states contains the ordinary vortex state (for large θ) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state (for θ = 0) as limits. The quasi-classical equations are solved nearH _c2 for arbitrary θ and it is shown that stable states with co-existing vortices and antivortices exist in a small interval close to θ= 0. The results are compared with recent predictions of antivortices in mesoscopic samples.     

Dielectric behaviour and AC conductivity of LiCF3SO3 doped H-chitosan polymer films

H-chitosan that exhibited solubility in THF was prepared by acyl modification of chitosan. Films of H-chitosan containing LiCF₃SO₃ were prepared by the solution cast technique. The effect of salt concentration on the frequency-dependent dielectric properties of H-chitosan: LiCF₃SO₃ complexes were investigated by impedance spectroscopy, in the temperature range from 243 to 373 K. The dielectric properties and ac conductivity of the samples prepared have been analyzed. The dielectric constant increases sharply with temperature in the low frequency region. At higher frequencies, the effect of temperature on the dielectric constant is negligible. The values of dielectric constant were also found to increase with increasing conductivity of the samples. The imaginary part, M_i of electrical modulus shows the formation of dispersion peak. Relaxation times for the ionic charge carriers were extracted from the loss tangent maximum peak at various temperatures. The plot of relaxation times as a function of temperature shows Arrhenius type behaviour. The ac conductivity was found to obey the universal power law and as the temperature increases, the feature of σ(θ) α θⁿ is more predominant. The temperature dependence of the power law exponent n is reasonably interpreted by the overlapping large polaron tunneling (OLPT) model.     

Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems

We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Lévy regime α < 2, the power law decay with large exponent ( α > 2), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement. Received 29 July 2000 and Received in final form 25 September 2000     

Large Deviations for a Stochastic Model of Heat Flow

We investigate a one-dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ₋ and τ₊. Kipnis et al. (J. Statist. Phys., 27:65–74 (1982).) proved that this model satisfies Fourier’s law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has a linear energy density profile , u ∈[−1,1]. We derive the large deviation function S(θ(u)) for the probability of finding, in the stationary state, a profile θ(u) different from . The function S(θ) has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general models and find the features common in these two and other models whose S(θ) is known.     

Two inverse problems induced by multifractal phenomena

In frame of the phenomena revealing multifractality, two inverse problems are formulated and their solution is outlined; namley, (i) to what extent the indices characterizing scaling properties of dynamical fluctuations (specified by factorial moments) are determined by means of power law indicesτ(q) which characterize scaling properties of the associated frequency moments, the later moments representing asymptotics (for sufficiently large multiplicities) of the former ones, and (ii) to what extent the scaling indicesτ(q) are determined by their asymptotic properties (at large absolute value of the orderq ascribed to the associated frequency moments and taken at a finite and fixed energy).     

Rapid growth of ternary eutectic under high undercooling conditions

~~Rapid growth of ternary eutectic un der high undercooling conditions1.Offerman, S.E., Dijk, N.H., Sietsma, J.et al., Grain nucleation and growth during phase transformations, Science, 2002, 298: 1003-1005. 2.Warren, J.A., Langer, J.S., Prediction of dendritic spacings in a directional-solidification experiment, Phys.Rev.E, 1993, 47: 2702-2712. 3.Cao, C.D., Wang, N., Wei, B., Containerless rapid solidification of undercooled Cu-Co peritectic alloys, Science in China, Ser.A, …     

Persistence in financial markets

Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain either above or below their 'starting' values. As a result, we estimate a persistence exponent for the underlying financial market to be θ_f∼0.5.     

A glimpse at ten years of microwaves and IR spectroscopy on high temperature superconductors

The different technical approaches are considered mostly to compare the accuracy attainable in microwaves to Far IR where new resonant tchniques have been developped. It is possible to use the fringes of the observed spectra to get directly the London penetration length. However in the present state of the Art there is more accuracy to use a two-fluid model with at least one Mid-IR oscillator, and a strategy is possible to fit separately the different parameters. The different results are reviewed and compared to the microwaves data. There is a good accordance, except perhaps for the power law-giving the concentration of quasiparticles in the superconductive phase. For a thin film of YBCO devoid of grain-boundaries (no twins), a θ⁴ law is found instead of a θ^1.5 law for an ordinary film. It should be highly valuable that both microwaves and Far-IR data should be taken on the same sample. presented at the 22nd International Conference on Infrared and Millimeter Waves, July 20–25, 1997, Wintergreen, Virginia 22958 USA.     

Residual strain measurements in InGaAs metamorphic buffer layers on GaAs

This work deals with the strain relaxation mechanism in InGaAs metamorphic buffers (MBs) grown on GaAs substrates and overgrown by InAs quantum dots (QD). The residual strain is measured by using Raman scattering and X-ray diffraction, both in Reciprocal Space Map and in single ω-2θ scan modes (ω and θ being the incidence angles on the sample surface and on the scattering planes, respectively). By relating the GaAs-like longitudinal optical phonon frequency ω^LO of InGaAs MBs to the in-plane residual strain ε measured by means of photoreflectance (PR), the linear ε-vs.-ω^LO working curve is obtained. The results of Raman and XRD measurements, as well as those obtained by PR, are in a very satisfactory agreement. The respective advantages of the techniques are discussed. The measurements confirm that strain relaxation depends on the thickness t of the buffer layer following a ~t^-1/2 power law, that can be explained by an energy-balance model.     

Deviation from tri-bimaximal mixings through flavour twisters in inverted and normal hierarchical neutrino mass models

We explore a novel possibility for lowering the solar mixing angle (θ ₁₂) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle (θ ₂₃ = 45°) and zero reactor angle (θ ₁₃ = 0°) in the inverted and normal hierarchical neutrino mass models having 2–3 symmetry. This can be done through the identification of a flavour twister term in the texture of neutrino mass matrix and the variation of such term leads to lowering of solar mixing angle. For the observed ranges of Δm ₂₁² and Δm ₂₃², we calculate the predictions on tan² θ ₁₂ = 0.5, 0.45, 0.35 for different input values of the parameters in the neutrino mass matrix. We also observe a possible transition from inverted hierarchical model having even CP parity (Type-IHA) to inverted hierarchical model having odd CP parity (Type-IHB) in the first two mass eigenvalues, when there is a change in input values of parameters in the same mass matrix. The present work differs from the conventional approaches for the deviations from tri-bimaximal mixing, where the 2–3 symmetry is broken, leading to θ ₂₃ ≠ 45° and θ ₁₃ ≠ 0°.      

C2GT: intercepting CERN neutrinos to Gran Sasso in the Gulf of Taranto to measure θ13

Today’s greatest challenge in accelerator-based neutrino physics is to measure the mixing angle θ₁₃ which is known to be much smaller than the solar mixing angle θ₁₂ and the atmospheric mixing angle θ₂₃. A non-zero value of the angle θ₁₃ is a prerequisite for observing CP violation in neutrino mixing. In this paper, we discuss a deep-sea neutrino experiment with 1.5 Mt fiducial target mass in the Gulf of Taranto with the prime objective of measuring θ₁₃. The detector is exposed to the CERN neutrino beam to Gran Sasso in off-axis geometry. Monochromatic muon neutrinos of ≈ 800 MeV energy are the dominant beam component. Neutrinos are detected through quasi-elastic, charged-current reactions in sea water; electrons and muons are detected in a large-surface, ring-imaging Cherenkov detector. The profile of the seabed in the Gulf of Taranto allows for a moveable experiment at variable distances from CERN, starting at 1100 km. From the oscillatory pattern of the disappearance of muon neutrinos, the experiment will measure sin²θ₂₃ and especially Δm² ₂₃ with high precision. The appearance of electron neutrinos will be observed with a sensitivity to P(ν_μ→ν_e) as small as 0.0035 (90% CL) and sin²θ₁₃ as small as 0.0019 (90% CL; for a CP phase angle δ=0° and for normal neutrino mass hierarchy).     

Lateral dispersion in light-wind stable conditions

Summary At downwind distances of 400 m or less, the angular standard deviation, σ_θc, of the lateral distribution of pollutants released from a point source over a given time period is shown to equal the standard deviation, σ_θ, of the wind direction fluctuations observed over the same time period. Data taken during light wind, stable conditions at two field sites (Idaho Falls, ID, and Oak Ridge, TN) are used in this analysis. This relation is most reliable if the pollutant concentration distribution is observed on a circle at constant distance from the source (i.e., on a polar coordinate system). Paper presented at the GNFAO/EURASAP Meeting, Turin, September 1989. To speed up publication, proofs were not sent to the author and were supervised by the Scientific Committee.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

Determination of optical properties and thickness of nanolayers from the angular dependences of reflectance

The possibility of multiparametric determination of properties of structures from the data on the dependence of reflectances R _p and R _s for polarized radiation and ratio R _p /R _s on the angle of incidence θ and from the angular dependence 1/R _p (ΔR/Δθ) is investigated. The results of natural and computer experiments revealed a high sensitivity of the angular dependence R _p (θ) of the reflectance to the values of optical constants and thickness of layered structures. Quantitative results of multiparametric measurements are verified by the independent method of spectral ellipsometry. The possibility of multiparametric determination of the properties and thickness of nanometer dielectric, metallic, and semiconducting layers on various substrates and the properties of substrates in such structures is established.     

Detecting vorticity filaments using wavelet analysis: About the statistical contribution of vorticity filaments to intermittency in swirling turbulent flows

Swirling turbulent flows display intermittent pressure drops associated with intense vorticity filaments. Using the wavelet transform modulus maxima representation of pressure fluctuations, we propose a method of characterizing these pressure drop events from their time-scale properties. This method allows us to discriminate fluctuations induced by just formed (young) as well as by burst (old) filaments from background pressure fluctuations. The statistical characteristics of these filaments (core size, waiting time) are analyzed in details and compared with previously reported experimental and numerical findings. Their intermittent occurrence is found to be governed by a pure Poisson's law, the hallmark of independent events. Then we apply the wavelet transform modulus maxima (WTMM) method to the background pressure fluctuations. This study reveals that, once removed all the filaments, the “multifractal” nature of pressure fluctuations still persists. This is a clear indication that the statistical contribution of the filaments is not important enough to account for the intermittency phenomenon in turbulents flows. Received 27 July 1998 and Received in final form 23 November 1998     

Low frequency fluctuations of laser beam intensity run through the system of cavitation water clusters

Experiments on water cavitation in ultrasonic field have been carried out. Low frequency fluctuations of the intensity of laser beam run through the cavitation area have been studied. Experiments have proved presence of low-frequency random fluctuations with frequency dependence of power spectra, S ∼ 1/f ^α where the exponent α ranged within 0.8 ≤ α ≤ 1.2. From experimental realizations, large-scale low frequency pulsations characterized by scale invariance, which duration is distributed according to the power law, have been distinguished. The results are explained on the basis of mathematical model for the rise of scale invariant fluctuations with 1/f ^α power spectrum in the system of two nonlinear stochastic differential equations describing interaction of heterogeneous phase transitions. Distribution of extreme low frequency emissions obtained from numerical solutions to stochastic equations takes the power series form. Correlations of dynamic scaling between critical indicators determining frequency dependence of pulsations power spectra α and distribution functions of extreme low frequency pulsation amplitudes β have been determined. It is shown that both in the experiments on acoustic cavitation of water and in the theoretical model of interacting phase transitions critical indicators are bound with the correlation α + β = 2. Spectra of fluctuation power are determined in the experiments simpler and more accurately than the function of extreme amplitudes distribution. In case when only one frequency dependence of fluctuation capacity spectra is known correlations between indicators serve to obtain information on the distribution of large scale emissions and to estimate critical amplitudes.     

Application of optical pyrometry for on-line monitoring in laser-cutting technologies

The results of measurement of fluctuations of brightness temperature T in the region of exposure to laser radiation of a 3 mm-thick steel plate are presented. The local luminosity along the cut-front was measured using two-color multichannel pyrometer. Cutting trials were carried out with CO₂ laser (10.6 μm, 1200 W) and fiber laser (1.07 μm, 1800 W). Special attention was given to the frequency range of temperature fluctuations above frequency of melt overflight, aiming on on-line monitoring applications. It is shown that local fluctuations of T are related to local melt’s surface deformations due to unequal radiation absorption; thus the noise spectrum of T fluctuations reflects turbulent surface deformation, caused by gas jet and capillary waves. It is also shown that the thermo-capillary effect with capillary-wave turbulence generation can be observed in case of exposure to 10.6 μm radiation with a laser intensity of about 1 MW/cm². The power law of “−7/6” describes the spectrum of the T fluctuation variance in this case of anomalous absorption of radiation, and the standard deviation of T is in excess of 10 K for a frequency of 14 kHz. There is no such effect in case of fiber-laser radiation applying, and the source of the capillary waves is only forced low-frequency deformations of the melt surface. The standard deviation of T does not exceed 3 K on the frequency of 14 kHz, and above, and a power law of the spectrum fluctuation is described by about “−3” in that range.