Algebraic decay of velocity fluctuations near a wall

Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the long-time tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Amplitude envelope synchronization in coupled chaotic oscillators.

A peculiar type of synchronization has been found when two Van der PolDuffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.

Capacity of MIMO Channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-inputmultiple-output channels with fading correlation at either thetransmitter or the receiver. We consider the asymptotic situation,where the number of inputs and outputs increase without boundat the same rate. A simple uniparametric model for the fadingcorrelation function is proposed and the asymptotic capacity perantenna is derived in closed form. Although the proposed correlationmodel is introduced only for mathematical convenience, itis shown that its shape is very close to an exponentially decayingcorrelation function. The asymptotic expression obtained providesa simple and yet useful way of relating the actual fadingcorrelation to the asymptotic capacity per antenna from a purelyanalytical point of view. For example, the asymptotic expressionsindicate that fading correlation is more harmful when arising atthe side with less antennas. Moreover, fading correlation does notinfluence the rate of growth of the asymptotic capacity per receiveantenna with high Eb /N0.

PREDICTING DIFFUSIVITIES IN DENSE FLUIDS

In this work the Weeks-Chandler-Andersen (WCA) perturbation theory coupled with the Enskog’s solution of the Boltzmann equation for dense hard-sphere fluids is employed for estimating diffusion coefficients in compressed pure liquids and fluids and dense fluid mixtures. The effect of density correction on the estimation of diffusivities is analyzed using the Carnahan-Starling pair correlation function and the correlation of Speedy and Harris which have been proposed as models of self-diffusion coefficient of hard-sphere fluids. The approach presented here is based on the smooth hard-sphere theory without any binary adjustable parameters and can be readily used for estimating diffusivities in multicomponent fluid mixtures. It is shown that the correlated and the predicted diffusivities are in good agreement with the experimental data and much better than estimates of Wilke-Chang equation.

Low frequency Raman scattering in amorphous materials: fused quartz, "pyrex" boro-silicate glass and soda-lime silicate glass

Raman scattering in the region 20 to 100 cm -1 for fused quartz, "pyrex" boro-silicate glass, and soft soda-lime silicate glass was investigated. The Raman spectra for the fused quartz and the pyrex glass were obtained at room temperature using the 488 nm exciting line of a Coherent Radiation argon-ion laser at powers up to 550 mW. For the soft soda-lime glass the 514.5 nm exciting line at powers up to 660 mW was used because of a weak fluorescence which masked the Stokes Raman spectrum. In addition it is demonstrated that the low-frequency Raman coupling constant can be described by a model proposed by Martin and Brenig (MB). By fitting the predicted spectra based on the model with a Gaussian, Poisson, and Lorentzian forms of the correlation function, the structural correlation radius (SCR) was determined for each glass. It was found that to achieve the best possible fit· from each of the three correlation functions a value of the SCR between 0.80 and 0.90 nm was required for both quartz and pyrex glass but for the soft soda-lime silicate glass the required value of the SCR. was between 0.50 and 0.60 nm .. Our results support the claim of Malinovsky and Sokolov (1986) that the MB model based on a Poisson correlation function provides a universal fit to the experimental VH (vertical and horizontal polarizations) spectrum for any glass regardless of its chemical composition. The only deficiency of the MB model is its failure to fit the experimental depolarization spectra.

Statistics of avalanches in martensitic transformations, II. Modelling

Using a scaling assumption, we propose a phenomenological model aimed to describe the joint probability distribution of two magnitudes A and T characterizing the spatial and temporal scales of a set of avalanches. The model also describes the correlation function of a sequence of such avalanches. As an example we study the joint distribution of amplitudes and durations of the acoustic emission signals observed in martensitic transformations [Vives et al., preceding paper, Phys. Rev. B 52, 12 644 (1995)].

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.

Structure of AuCN determined from total neutron diffraction

The structure of gold cyanide, AuCN, has been determined at 10 and 300 K using total neutron diffraction. The structure consists of infinite -Au-(CN)-Au-(CN)-Au-(CN)- linear chains, hexagonally packed, with the gold atoms in sheets. The Au-C and Au-N bond lengths are found to be identical, with d(Au-C/N) = 1.9703(5) Angstrom at 300 K. This work supersedes a previous study, by others, which used Rietveld analysis of neutron Bragg diffraction in isolation, and found these bonds to have significantly different lengths (Deltad = 0.24 Angstrom) at 300 K. The total correlation function, T(r), at 10 and 300 K, has been modeled using information derived from total diffraction. The broadening of inter- and intrachain correlations differs markedly due to random displacements of the chains in the direction of the chain axes. This is a consequence of the relatively weak bonding between the chains. An explanation for the negative thermal expansion in the c-direction, which occurs between 10 and 300 K, is presented.

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Local and average structure in zinc cyanide: towards an understanding of the atomistic origin of negative thermal expansion

Neutron diffraction at 11.4 and 295 K and solid-state 67Zn NMR are used to determine both the local and average structures in the disordered, negative thermal expansion (NTE) material, Zn(CN)2. Solid-state NMR not only confirms that there is head-to-tail disorder of the C≡N groups present in the solid, but yields information about the relative abundances of the different Zn(CN)4-n(NC)n tetrahedral species, which do not follow a simple binomial distribution. The Zn(CN)4 and Zn(NC)4 species occur with much lower probabilities than are predicted by binomial theory, supporting the conclusion that they are of higher energy than the other local arrangements. The lowest energy arrangement is Zn(CN)2(NC)2. The use of total neutron diffraction at 11.4 K, with analysis of both the Bragg diffraction and the derived total correlation function, yields the first experimental determination of the individual Zn−N and Zn−C bond lengths as 1.969(2) and 2.030(2) Å, respectively. The very small difference in bond lengths, of ~0.06 Å, means that it is impossible to obtain these bond lengths using Bragg diffraction in isolation. Total neutron diffraction also provides information on both the average and local atomic displacements responsible for NTE in Zn(CN)2. The principal motions giving rise to NTE are shown to be those in which the carbon and nitrogen atoms within individual Zn−C≡N−Zn linkages are displaced to the same side of the Zn···Zn axis. Displacements of the carbon and nitrogen atoms to opposite sides of the Zn···Zn axis, suggested previously in X-ray studies as being responsible for NTE behavior, in fact make negligible contribution at temperatures up to 295 K.

THE VORONOI TESSELLATION CLUSTER FINDER IN 2+1 DIMENSIONS

We present a detailed description of the Voronoi Tessellation (VT) cluster finder algorithm in 2+1 dimensions, which improves on past implementations of this technique. The need for cluster finder algorithms able to produce reliable cluster catalogs up to redshift 1 or beyond and down to 10(13.5) solar masses is paramount especially in light of upcoming surveys aiming at cosmological constraints from galaxy cluster number counts. We build the VT in photometric redshift shells and use the two-point correlation function of the galaxies in the field to both determine the density threshold for detection of cluster candidates and to establish their significance. This allows us to detect clusters in a self-consistent way without any assumptions about their astrophysical properties. We apply the VT to mock catalogs which extend to redshift 1.4 reproducing the ACDM cosmology and the clustering properties observed in the Sloan Digital Sky Survey data. An objective estimate of the cluster selection function in terms of the completeness and purity as a function of mass and redshift is as important as having a reliable cluster finder. We measure these quantities by matching the VT cluster catalog with the mock truth table. We show that the VT can produce a cluster catalog with completeness and purity > 80% for the redshift range up to similar to 1 and mass range down to similar to 10(13.5) solar masses.

Gamma transition intensity determination using multidetector coincidence data

This work describes two similar methods for calculating gamma transition intensities from multidetector coincidence measurements. In the first one, applicable to experiments where the angular correlation function is explicitly fitted, the normalization parameter from this fit is used to determine the gamma transition intensities. In the second, that can be used both in angular correlation or DCO measurements, the spectra obtained for all the detector pairs are summed up, in order to get the best detection statistics possible, and the analysis of the resulting bidimensional spectrum is used to calculate the transition intensities; in this method, the summation of data corresponding to different angles minimizes the influence of the angular correlation coefficient. Both methods are then tested in the calculation of intensities for well-known transitions from a (152)Eu standard source, as well as in the calculation of intensities obtained in beta-decay experiments with (193)Os and (155)Sm sources, yielding excellent results in all these cases. (C) 2009 Elsevier B.V. All rights reserved.

The stochastic nature of predator-prey cycles

We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.

Magnetic-field asymmetry of nonlinear transport in a small ring

We have investigated the magnetic-field asymmetry of the conductance in the nonlinear regime in a small Aharonov-Bohm ring. We have found that the odd-in B and linear in V (the DC bias) correlation function of the differential conductance exhibits periodical oscillations with the Aharonov-Bohm flux. We have deduced the electron interaction constant and analyzed the phase rigidity of the Aharonov-Bohm oscillations in the nonlinear regime. Copyright (C) EPLA, 2009