Showing papers on "Correlation function (statistical mechanics) published in 2011"
TL;DR: In this article, the angle-averaged correlation function of transmitted flux (F = exp(-tau)) is securely detected out to comoving separations of 60 Mpc/h, the first detection of flux correlations across widely separated sightlines.
Abstract: Using a sample of approximately 14,000 z>2.1 quasars observed in the first year of the Baryon Oscillation Spectroscopic Survey (BOSS), we measure the three-dimensional correlation function of absorption in the Lyman-alpha forest. The angle-averaged correlation function of transmitted flux (F = exp(-tau)) is securely detected out to comoving separations of 60 Mpc/h, the first detection of flux correlations across widely separated sightlines. A quadrupole distortion of the redshift-space correlation function by peculiar velocities, the signature of the gravitational instability origin of structure in the Lyman-alpha forest, is also detected at high significance. We obtain a good fit to the data assuming linear theory redshift-space distortion and linear bias of the transmitted flux, relative to the matter fluctuations of a standard LCDM cosmological model (inflationary cold dark matter with a cosmological constant). At 95% confidence, we find a linear bias parameter 0.16
139 citations
TL;DR: The comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter, and in cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula.
Abstract: We present three formulas for calculating intersystem crossing rates in the Condon approximation to the golden rule by means of a time-dependent approach: an expression using the full time correlation function which is exact for harmonic oscillators, a second-order cumulant expansion, and a short-time approximation of this expression. While the exact expression and the cumulant expansion require numerical integration of the time correlation function, the integration of the short-time expansion can be performed analytically. To ensure convergence in the presence of large oscillations of the correlation function, we use a Gaussian damping function. The strengths and weaknesses of these approaches as well as the dependence of the results on the choice of the technical parameters of the time integration are assessed on four test examples, i.e., the nonradiative S1 ⇝ T1 transitions in thymine, phenalenone, flavone, and porphyrin. The obtained rate constants are compared with previous results of a time-independent approach. Very good agreement between the literature values and the integrals over the full time correlation functions are observed. Furthermore, the comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter. In cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula. A great advantage of the time-dependent approach over the time-independent approach is its excellent computational efficiency making it the method of choice in cases of large energy gaps, large numbers of normal modes, and high densities of final vibrational states.
131 citations
TL;DR: In this paper, the authors show that a significant fraction of the observed LRG ellipticity can be explained by alignment with the background tidal field on scales 10 \hMpc.
Abstract: Weak gravitational lensing has become a powerful probe of large-scale structure and cosmological parameters. Precision weak lensing measurements require an understanding of the intrinsic alignment of galaxy ellipticities, which can in turn inform models of galaxy formation. It is hypothesized that elliptical galaxies align with the background tidal field and that this alignment mechanism dominates the correlation between ellipticities on cosmological scales (in the absence of lensing). We use recent large-scale structure measurements from the Sloan Digital Sky Survey to test this picture with several statistics: (1) the correlation between ellipticity and galaxy overdensity, wg+; (2) the intrinsic alignment auto-correlation functions; (3) the correlation functions of curl-free, E, and divergence-free, B, modes, the latter of which is zero in the linear tidal alignment theory; (4) the alignment correlation function, wg(rp,θ), a recently developed statistic that generalizes the galaxy correlation function to account for the angle between the galaxy separation vector and the principle axis of ellipticity. We show that recent measurements are largely consistent with the tidal alignment model and discuss dependence on galaxy luminosity. In addition, we show that at linear order the tidal alignment model predicts that the angular dependence of wg(rp,θ) is simply wg+(rp)cos (2θ) and that this dependence is consistent with recent measurements. We also study how stochastic nonlinear contributions to galaxy ellipticity impact these statistics. We find that a significant fraction of the observed LRG ellipticity can be explained by alignment with the tidal field on scales 10 \hMpc. These considerations are relevant to galaxy formation and evolution.
107 citations
TL;DR: An analytical method is presented that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one, and derives an approximation scheme that satisfies the linearly realized ones.
Abstract: We present an analytical method, rooted in the nonperturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one We analyze the symmetries of the KPZ problem and derive an approximation scheme that satisfies the linearly realized ones We implement this scheme at the minimal order in the response field, and show that it yields a complete, qualitatively correct phase diagram in all dimensions, with reasonable values for the critical exponents in physical dimensions We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling function We find a very satisfactory quantitative agreement with the exact result from Prahofer and Spohn [J Stat Phys 115, 255 (2004)] In particular, we obtain for the universal amplitude ratio g_{0}≃1149(18), to be compared with the exact value g_{0}=11504 (the Baik and Rain [J Stat Phys 100, 523 (2000)] constant) We emphasize that all these results, which can be systematically improved, are obtained with sole input the bare action and its symmetries, without further assumptions on the existence of scaling or on the form of the scaling function
97 citations
TL;DR: There are only small spatial correlations between local density and structural fluctuations, suggesting that features in density-density correlations (such as measured by the structure factor) are not straightforwardly related to spatial correlations of structure in liquid water.
Abstract: We use large-scale classical simulations employing different force fields to study spatial correlations between local density and structural order for water in the liquid temperature range. All force fields investigated reproduce the main features of the experimental SAXS structure factor S(q), including the minimum at small q, and the recent TIP4P/2005 parametrization yields almost quantitative agreement. As local structural order parameters we consider the tetrahedrality and the number of hydrogen bonds and calculate all pure and mixed spatial two-point correlation functions. Except for the density-density correlation function, there are only weak features present in all other correlation functions, showing that the tendency to form structural clusters is much weaker than the well-known tendency of water to form density clusters (i.e., spatially correlated regions where the density deviates from the mean). In particular, there are only small spatial correlations between local density and structural fluctuations, suggesting that features in density-density correlations (such as measured by the structure factor) are not straightforwardly related to spatial correlations of structure in liquid water.
90 citations
TL;DR: In this paper, the authors show that a significant fraction of the observed LRG ellipticity can be explained by alignment with the tidal field on scales >~10 h^-1 Mpc.
Abstract: Weak gravitational lensing has become a powerful probe of large-scale structure and cosmological parameters. Precision weak lensing measurements require an understanding of the intrinsic alignment of galaxy ellipticities, which can in turn inform models of galaxy formation. It is hypothesized that elliptical galaxies align with the background tidal field and that this alignment mechanism dominates the correlation between ellipticities on cosmological scales (in the absence of lensing). We use recent large-scale structure measurements from the Sloan Digital Sky Survey to test this picture with several statistics: (1) the correlation between ellipticity and galaxy overdensity, w_{g+}; (2) the intrinsic alignment auto-correlation functions; (3) the correlation functions of curl-free, E, and divergence-free, B, modes (the latter of which is zero in the linear tidal alignment theory); (4) the alignment correlation function, w_g(r_p,theta), a recently developed statistic that generalizes the galaxy correlation function to account for the angle between the galaxy separation vector and the principle axis of ellipticity. We show that recent measurements are largely consistent with the tidal alignment model and discuss dependence on galaxy luminosity. In addition, we show that at linear order the tidal alignment model predicts that the angular dependence of w_g(r_p,theta) is simply w_{g+}*cos(2*theta) and that this dependence is consistent with recent measurements. We also study how stochastic nonlinear contributions to galaxy ellipticity impact these statistics. We find that a significant fraction of the observed LRG ellipticity can be explained by alignment with the tidal field on scales >~10 h^-1 Mpc. These considerations are relevant to galaxy formation and evolution.
89 citations
TL;DR: In this paper, the authors investigate how to most effectively measure the anisotropic correlation function as a function of both line-of-sight (radial) and transverse separations, using analytic techniques and mock catalogues.
Abstract: The baryonic acoustic feature in galaxy clustering is a promising tool for constraining the nature of the cosmic acceleration, through measurements of expansion rates H and angular diameter distances D_A. Angle-averaged measurements of clustering yield constraints on the quantity D_A^2/H. However, to break the degeneracy between these two parameters one must measure the anisotropic correlation function as a function of both line-of-sight (radial) and transverse separations. Here we investigate how to most effectively do so, using analytic techniques and mock catalogues. In particular, we examine multipole expansions of the correlation function as well as "clustering wedges" xi(Delta mu, s), where mu = s_||/s and s_|| is the radial component of separation s. Both techniques allow strong constraints on H and D_A, as expected. The radial wedges strongly depend on H and the transverse wedges are sensitive to D_A. Analyses around the region of the acoustic peak constrain H ~20% better when using the wedge statistics than when using the monopole-quadrupole combination. However, we show that the hexadecapole allows substantially stronger constraints than the monopole and quadrupole alone. Our findings here demonstrate that wedge statistics provide a practical alternative technique to multipoles, that should be useful to test systematics and will provide comparable or better constraints. Finally, we predict the constraints from galaxy clustering that will be possible with a completed version of the ongoing Baryonic Oscillation Spectroscopic Survey.
87 citations
TL;DR: In this paper, the authors study correlation functions in (0, + 1)-dimensional maximally supersymmetric U(N ) Yang-Mills theory, which was proposed by Banks et al. as a nonperturbative definition of 11-dimensional M-theory in the infinite-momentum frame.
Abstract: We study correlation functions in (0 + 1)-dimensional maximally supersym-metric U(N ) Yang-Mills theory, which was proposed by Banks et al. as a non-perturbative definition of 11-dimensional M-theory in the infinite-momentum frame. We perform first-principle calculations using Monte Carlo simulations, and compare the results against the predictions obtained previously based on the gauge-gravity correspondence from 10 dimensions. After providing a self-contained review on these predictions, we present clear evidence that the predictions in the large-N limit actually hold even at small N such as N =2 and 3. The predicted behavior seems to continue to the far infrared regime, which goes beyond the naive range of validity of the 10D supergravity analysis. This suggests that the correlation functions also contain important information on the M-theory limit.
73 citations
TL;DR: In this paper, a new method was presented for the quantitative measurement of charge separation about the reaction plane, where a correlation function was obtained whose shape is concave when there is a net separation of positive and negative charges.
Abstract: A new method is presented for the quantitative measurement of charge separation about the reaction plane. A correlation function is obtained whose shape is concave when there is a net separation of positive and negative charges. Correlations not specifically associated with charge, from flow, jets, and momentum conservation, do not influence the shape or magnitude of the correlation function. Detailed simulations are used to demonstrate the effectiveness of the method for the quantitative measurement of charge separation. Such measurements are a prerequisite to the investigation of topological charge effects in the quark-gluon plasma as derived from the ``strong $\mathcal{CP}$ problem.''
72 citations
TL;DR: In this article, the morphological evolution of laboratory snow under isothermal conditions at −3,− 9a nd−19 ◦ C, using X-ray tomography was investigated, and a two-point density correlation function was employed to measure spatial fluctuations of the density of the bicontinuous ice/vapor system at different length scales.
Abstract: We investigated the morphological evolution of laboratory snow under isothermal conditions at −3,− 9a nd−19 ◦ C, using X-ray tomography. We employed a two-point density correlation function to measure spatial fluctuations of the density of the bicontinuous ice/vapor system at different length scales. Length scales were derived from the correlation function to distinguish between interfacial coarsening due to the minimization of surface energy on the smallest scales and anisotropic structural re- arrangements due to gravity on larger scales. On the smallest scales our data suggest a crossover between T = − 9a nd−19 ◦ ◦ C from evaporation/condensation to surface diffusion as the dominant transport mechanism. Anomalous growth was found for the slope of the correlation function at the origin, and it was similar to those reported for the coarsening of fractal clusters. This is consistent with the observed persistence of dendritic structures throughout an entire year. The dynamics of large-scale morphology was characterized by the first zero-crossing of the correlation function which displays a nonmonotonic evolution with a pronounced anisotropy between the direction of gravity and horizontal directions. Since the correlation function naturally emerges in problems of scattering of radiation in snow, our results appear to be important for optical and remote-sensing methods.
59 citations
TL;DR: In this paper, the authors consider the low-temperature limit of the long-distance asymptotic behavior of the finite temperature density-density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe ansatz framework.
Abstract: We consider the low-temperature limit of the long-distance asymptotic behavior of the finite-temperature density–density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe ansatz framework. Our results confirm the predictions based on the Luttinger liquid and conformal field theory approaches. We also demonstrate that the amplitudes arising in this asymptotic expansion at low temperature coincide with the amplitudes associated with the so-called critical form factors.
TL;DR: In this paper, the authors apply a wavelet transform based on the superposition of azimuthally adjacent complex Morlet wavelets, in a manner similar to the fan wavelet developed in the plane.
Abstract: [1] The spectral relations (admittance and correlation) between gravity and topography are often used to obtain information on the density structure, flexural support, and heat flow of planetary lithospheres. Mapping spatial variations in these quantities requires spatiospectral analysis techniques. Here we describe the application of a directional, continuous spherical wavelet transform using a wavelet basis constructed from the superposition of azimuthally adjacent complex Morlet wavelets, in a manner similar to the “fan” wavelet developed in the plane. The method is applied to gravity and topography of the Earth, Venus, Mars, and the Moon. The wavelet coefficients are used to compute isotropic and directional wavelet autospectra and cross spectra, which are then combined to form the admittance and correlation functions. The resulting maps offer insights into lithospheric structure of the terrestrial planets. In particular we show that the Earth and Venus have uniformly low positive admittance and high correlation, whereas Mars and the Moon display hemispherical contrasts with large negative and anisotropic coefficients coinciding with lowlands. As has long been known, the two largest impact basins in the inner solar system, the South Pole–Aitken basin on the Moon and the Hellas basin on Mars, display low positive admittance and high correlation, indicating isostatic compensation. In contrast, most other impact basins, particularly the Martian and lunar mascons, show negative coefficients at low wavelet degrees suggesting flexural support by a strong lithosphere. These results imply that, although simple isotropic flexural models can account for most observations, future models may need to incorporate anisotropy as an additional parameter.
TL;DR: In this paper, the effect of size distribution within a seed material on measured relaxation time is examined, with polydisperse particles of the same median diameter shown to possess a significantly higher relaxation time than their monodisperse counterparts when measured via a particle image velocimetry algorithm.
Abstract: A study of some aspects of tracer particle responses to step changes in fluid velocity is presented. The effect of size distribution within a seed material on measured relaxation time is examined, with polydisperse particles of the same median diameter shown to possess a significantly higher relaxation time than their monodisperse counterparts when measured via a particle image velocimetry algorithm. The influence of a shock wave–induced velocity gradient within a PIV interrogation window on the correlation function is also examined using the noiseless cross-correlation function of Soria (Turbulence and coherent structures in fluids, plasmas and nonlinear media. World Scientific, Singapore, 2006). The presence of a shock is shown to introduce an artificial fluctuation into the measurement of velocity. This fluctuation is a function of the shock position, shock strength, spatial ratio and particle distribution. When the shock is located at the middle of the window, the magnitude of the fluctuation increases monotonically with increasing spatial ratio, increases asymptotically with shock strength, and decreases for increasing particle polydispersity. When the shock is located at the left-hand edge of the window, the magnitude of the artificial fluctuation is highest for intermediate spatial ratios, going to zero at infinitely high and low values. In this instance, particle polydispersity acts to increase the magnitude of fluctuations in measured velocity. In both cases, particle polydispersity serves to broaden the PDF of measured velocity. For the cases presented herein, with a shock located within the interrogation window, the root mean square of the artificial velocity fluctuations reaches values in excess of 30% of the freestream velocity.
TL;DR: In this article, a full analytical treatment of signal functions in time-domain NMR of entangled polymer melts is presented, based on the segmental orientation autocorrelation function for entangled chains previously determined experimentally via field cycling NMR, and via analyzing the initial rise of normalized doublequantum buildup curves, which yield consistent data over about 10 decades in time based on time−temperature superposition.
Abstract: We present a full analytical treatment of signal functions in time-domain NMR of entangled polymer melts. Our approach is based on the segmental orientation autocorrelation function for entangled chains previously determined experimentally via field cycling NMR, on the one hand, and via analyzing the initial rise of normalized double-quantum buildup curves, on the other hand, which yield consistent data over about 10 decades in time based on time−temperature superposition. The correlation function is similar to but deviates in a few aspects from the predictions of the tube model. We use the Anderson−Weiss approximation to derive formulas for different signal functions for simple transverse relaxation experiments and specifically for the signal functions from multiple-quantum NMR. We demonstrate that our treatment is, for moderate NMR evolution times, in good agreement with proton NMR data of entangled poly(butadiene) samples over large temperature and molecular weight ranges. Our results represent a showc...
TL;DR: In this paper, the authors consider the low-temperature limit of the long-distance asymptotic behavior of the finite temperature density-density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe ansatz framework.
Abstract: We consider the low-temperature limit of the long-distance asymptotic behavior of the finite temperature density-density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe ansatz framework. Our results confirm the predictions based on the Luttinger liquid and conformal field theory approaches. We also demonstrate that the amplitudes arising in this asymptotic expansion at low-temperature coincide with the amplitudes associated with the so-called critical form factors.
TL;DR: This work derives a simple formula for the fluctuations of the time average x(t) around the thermal mean for overdamped brownian motion in a binding potential U(x) using a backward Fokker-Planck equation.
Abstract: xðtÞ around the thermal mean hxieq for overdamped Brownian motion in a binding potential UðxÞ. Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.
TL;DR: In this article, the authors compared the effects of variations in the between-earthquake correlation and in the site-to-site correlation on seismic loss and damage estimations for the extended objects (hypothetical portfolio) and critical elements (e.g. bridges) of a network.
Abstract: In addition to the mean values of possible loss during an earthquake, parameters of the probability distribution function for the loss to a portfolio (e.g. fractiles and standard deviation) are very important. Recent studies have shown that the proper treatment of ground-motion variability and, particularly, the correlation of ground motion are essential for the estimation of the seismic hazard, damage and loss for distributed portfolios. In this study, we compared the effects of variations in the between-earthquake correlation and in the site-to-site correlation on seismic loss and damage estimations for the extended objects (hypothetical portfolio) and critical elements (e.g. bridges) of a network. A scenario earthquake approach and a portfolio containing a set of hypothetical building and bridges were used for the purpose. We showed that the relative influences of the types of correlation on characteristics of loss distribution and the probability of damage are not equal. In some cases, when the median values of loss distribution or the probability that at least one critical element of a lifeline will be damaged are considered and when the spatial correlation of ground motion is used, the possible variations in the between-earthquake correlation may be neglected. The shape of the site-to-site correlation function (i.e. the rate of decrease of the coefficient of spatial correlation with separation distance) seems also to be important when modelling spatially correlated ground-motion fields.
TL;DR: The freezing densities of particle monolayers at the oil/water interface are studied and compared with Monte Carlo simulation results reported by H. Löwen and it was found that, upon increasing the surface coverage, a freezing transition occurs, that leads to the formation of a 2D crystalline structure.
Abstract: The structure and the interaction potential of monolayers of charged polystyrene microparticles at fluid interfaces have been studied by optical microscopy. Microparticles of different sizes have been studied over a broad range of surface particle densities. The structural characterization is based on the analysis of images obtained by digital optical microscopy. From the experimental images, radial distribution functions, hexagonal bond order correlation functions, and temporal orientational correlation functions have been calculated for different monolayer states at both the air/water and oil/water interfaces. The interaction potential has been calculated from the structure factor using integral equations within the hypernetted chain closure relationship. For particles trapped at the oil−water interface, it was found that, upon increasing the surface coverage, a freezing transition occurs, that leads to the formation of a 2D crystalline structure. We have studied the freezing densities of particle monol...
TL;DR: A dual competition hypothesis of city development is proposed to explain the value intervals and the special value, 1, of the power exponent of Zipf's law and this theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.
Abstract: Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively Based on the Pareto distribution, a frequency correlation function can be constructed By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (05, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2) Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity) Because of struggle of the two effects, the scaling exponent varies from 05 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1 A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences
TL;DR: In this article, a Bethe ansatz-based method was proposed to derive the long-distance asymptotic behavior at finite temperature of the density-density correlation function in the interacting one-dimensional Bose gas.
Abstract: We describe a Bethe ansatz-based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density–density correlation function in the interacting one-dimensional Bose gas. We compute the correlation lengths in terms of solutions of non-linear integral equations of the thermodynamic Bethe ansatz type. Finally, we establish a connection between the results obtained in our approach and the correlation lengths stemming from the quantum transfer matrix method.
TL;DR: In this paper, the power spectral density (PSD) is computed using a common stretched exponential correlation function with three parameters (standard deviation, correlation length, and roughness exponent) for one, two, and three dimensions.
Abstract: Analytical expressions for the power spectral density (PSD) are often useful in stochastic lithography simulation and the metrology of roughness. Using a common stretched exponential correlation function with three parameters (standard deviation, correlation length, and roughness exponent), the PSD can be computed as the Fourier transform of the autocorrelation function. For the special cases of roughness exponent equal to 0.5 and 1, the PSD can be computed analytically for one, two, and three dimensions. In this paper, the analytical results of these calculations are given. The resulting equations can be used when modeling rough lines, surfaces, or volumes.
TL;DR: In this article, the authors revisited the aquisition of angular momentum of galaxies by tidal shearing and computed the angular momentum variance sigma l 2 as well as angular momentum correlation function C_L(r) from a peak-restricted Gaussian random process.
Abstract: In this paper, we revisit the aquisition of angular momentum of galaxies by tidal shearing and compute the angular momentum variance sigma_L^2 as well as the angular momentum correlation function C_L(r) from a peak-restricted Gaussian random process. This stochastic process describing the initial conditions treats both the tidal shear as well as the inertia as dynamical fields and explicitly accounts for the discreteness of the inertia field. We describe the way in which the correlations in angular momentum result from an interplay of long-ranged correlations in the tidal shear, and short ranged correlations in the inertia field and which reflects the correlation between the eigensystems of these two symmetric tensors. We propose a new form of the angular momentum correlation function which is able to distinguish between parallel and antiparallel alignment of angular momentum vectors, and comment on implications of intrinsic alignments for weak lensing measurements. We confirm the scaling L/M propto. M^{2/3} and find the angular momentum distribution of Milky Way-sized haloes to be correlated on scales of ~1 Mpc/h. The correlation function can be well fitted by an empirical relation of the form C_L(r) propto. exp(-[r/r_0]^beta).
TL;DR: A detailed relaxation theory of PDSD in rotating solids appears to provide an accurate, parameter-free alternative and predictions of this theory agreed well with the full quantum mechanical simulations of the R(2) dynamics in the few simple model systems the authors considered.
Abstract: Proton-driven spin diffusion (PDSD) experiments in rotating solids have received a great deal of attention as a potential source of distance constraints in large biomolecules. However, the quantitative relationship between the molecular structure and observed spin diffusion has remained obscure due to the lack of an accurate theoretical description of the spin dynamics in these experiments. We start with presenting a detailed relaxation theory of PDSD in rotating solids that provides such a description. The theory applies to both conventional and radio-frequency-assisted PDSD experiments and extends to the non-Markovian regime to include such phenomena as rotational resonance (R(2)). The basic kinetic equation of the theory in the non-Markovian regime has the form of a memory function equation, with the role of the memory function played by the correlation function. The key assumption used in the derivation of this equation expresses the intuitive notion of the irreversible dissipation of coherences in macroscopic systems. Accurate expressions for the correlation functions and for the spin diffusion constants are given. The theory predicts that the spin diffusion constants governing the multi-site PDSD can be approximated by the constants observed in the two-site diffusion. Direct numerical simulations of PDSD dynamics via reversible Liouville-von Neumann equation are presented to support and compliment the theory. Remarkably, an exponential decay of the difference magnetization can be observed in such simulations in systems consisting of only 12 spins. This is a unique example of a real physical system whose typically macroscopic and apparently irreversible behavior can be traced via reversible microscopic dynamics. An accurate value for the spin diffusion constant can be usually obtained through direct simulations of PDSD in systems consisting of two (13)C nuclei and about ten (1)H nuclei from their nearest environment. Spin diffusion constants computed by this method are in excellent agreement with the spin diffusion constants obtained through equations given by the relaxation theory of PDSD. The constants resulting from these two approaches were also in excellent agreement with the results of 2D rotary resonance recoupling proton-driven spin diffusion (R(3)-PDSD) experiments performed in three model compounds, where magnetization exchange occurred over distances up to 4.9 A. With the methodology presented, highly accurate internuclear distances can be extracted from such data. Relayed transfer of magnetization between distant nuclei appears to be the main (and apparently resolvable) source of uncertainty in such measurements. The non-Markovian kinetic equation was applied to the analysis of the R(2) spin dynamics. The conventional semi-phenomenological treatment of relxation in R(2) has been shown to be equivalent to the assumption of the Lorentzian spectral density function in the relaxatoin theory of PDSD. As this assumption is a poor approximation in real physical systems, the conventional R(2) treatment is likely to carry a significant model error that has not been recognized previously. The relaxation theory of PDSD appears to provide an accurate, parameter-free alternative. Predictions of this theory agreed well with the full quantum mechanical simulations of the R(2) dynamics in the few simple model systems we considered.
TL;DR: In this article, the 2-D spatial correlation function of the number density and magnetic field in magnetosheath turbulence was derived using the Cluster four-spacecraft measurements of the fluctuations with respect to a temporally and spatially varying background magnetic field.
Abstract: [1] Knowledge of multidimensional correlation functions is crucial for understanding the anisotropy of turbulence. The two-dimensional (2-D) spatial correlation functions (SCFs) obtained in previous studies of space plasma turbulence were restricted to large-length scales and covered a limited angular domain of the two-point separation vector with respect to the mean magnetic field. Here we aim to derive 2-D SCFs with smaller-length scale and nearly full angular distribution for the fluctuations of the number density and magnetic field in magnetosheath turbulence. We use the Cluster four-spacecraft measurements of the fluctuations with respect to a temporally and spatially varying background magnetic field to construct the 2-D SCFs. We find that the correlation function of the density fluctuations shows a pattern similar to that of the magnetic field fluctuations, both of which appear to be composed of two populations, whereby the major population extends along the coordinate parallel to mean magnetic field (S∥) and the minor one deviates toward the perpendicular coordinate (S⊥). This pattern of 2-D SCFs implies that the energy of magnetosheath turbulence seems to cascade, in the inertial range close to the ion scale, mostly transverse to the background magnetic field and meanwhile partly along the field (i.e., k⊥ ≫ k∥).
TL;DR: In this article, the epitaxial growth of pyramidal patterns in stochastic systems with interacting adsorbate within the framework of the phase-field approach based on the Burton?Cabrera?Frank model was studied.
Abstract: We study the epitaxial growth of pyramidal patterns in stochastic systems with interacting adsorbate within the framework of the phase-field approach based on the Burton?Cabrera?Frank model. Considering the statistical criteria of pattern formation, it is shown that the system dynamics is governed by the interaction strength of adatoms and the noise intensity of the total flux fluctuations. We have shown that the noise action can crucially change the processes of pyramidal pattern formation. The scaling behavior of the height?height correlation function is discussed.
TL;DR: In this paper, instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for a stochastic optimization method, which is tested on a few digitized binary and greyscale images.
Abstract: A multi-scale approach to the inverse reconstruction of a pattern’s microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for a stochastic optimization method. The first of them measures a spatial inhomogeneity, for a binary pattern, or compositional one, for a greyscale image. The second one quantifies a spatial or compositional statistical complexity. The EDs reveal structural information that is dissimilar, at least in part, to that given by correlation functions at almost all discrete length scales. The method is tested on a few digitized binary and greyscale images. In each of the cases, the persuasive reconstruction of the microstructure is found.
TL;DR: In this paper, the authors extended the study by Glauber of the time-dependent statistics of the Ising chain to the case where each spin is influenced unequally by its nearest neighbours.
Abstract: The study by Glauber of the time-dependent statistics of the Ising chain is extended to the case where each spin is influenced unequally by its nearest neighbours. The asymmetry of the dynamics implies the failure of the detailed balance condition. The functional form of the rate at which an individual spin changes its state is constrained by the global balance condition with respect to the equilibrium measure of the Ising chain. The local magnetization, the equal-time and two-time correlation functions and the linear response to an external magnetic field obey linear equations which are solved explicitly. The behaviour of these quantities and the relation between the correlation and response functions are analysed both in the stationary state and in the zero-temperature scaling regime. In the stationary state, a transition between two behaviours of the correlation function occurs when the amplitude of the asymmetry crosses a critical value, with the consequence that the limit fluctuation-dissipation ratio decays continuously from the value 1, for the equilibrium state in the absence of asymmetry, to 0 for this critical value. At zero temperature, under asymmetric dynamics, the system loses its critical character, yet keeping many of the characteristic features of a coarsening system.
TL;DR: The results in terms of density correlation function reveal that the decay rate is linear in wavenumber, which is consistent with a narrow Lorentzian distribution of cargo velocity.
Abstract: We studied the active transport of intracellular components along neuron processes using a new method developed in our laboratory: dispersion-relation phase spectroscopy. This method is able to quantitatively map spatially the heterogeneous dynamics of the concentration field of the cargos at submicron resolution without the need for tracking individual components. The results in terms of density correlation function reveal that the decay rate is linear in wavenumber, which is consistent with a narrow Lorentzian distribution of cargo velocity.
05 Jun 2011
TL;DR: In this paper, the authors focus on the theoretical and experimental investigations of five different integral length scales evaluation methodologies, namely i) two-point space correlation based method, ii) single point power-spectrum based approach, iii) the most energy containing eddy dependent method, iv) auto correlation via Taylor's hypothesis and, v) correlation function curve fitting method.
Abstract: Accurate evaluation of the turbulence integral correlation length scales is important for a large group of numerical flow-induced noise prediction methods. Due to the complex mathematical interrelationships of the two-point space-time velocity statistics, a direct evaluation of the integral length scale is a challenging task from the standard CFD methods. The present paper focuses on the theoretical and experimental investigations of five different integral length scales evaluation methodologies, namely i) two-point space correlation based method, ii) single point power-spectrum based approach, iii) wavenumber of the most energy containing eddy dependent method, iv) auto correlation via Taylor’s hypothesis and, v) correlation function curve fitting method. All these methods are analyzed based on the previously performed two-point turbulent boundary-layer (BL) correlation measurement data. A detail comparison study has been performed with discussions on the limitations and drawbacks of each method. Other length scales found in turbulence theory such as pseudo length scale, dissipation length scale, Prandtl mixing length, Taylor microscale and Kolmogorov scale have been also discussed elaborately. A theoretical relationship for the derivation of integral length scales based on standard RANS simulation is derived by employing Kolmogorov local isotropy hypothesis. The enhanced method allows modelling of the isotropic length scale and dissipation from the anisotropic experimental spectral data. This outcome is applied further for the RANS turbulence model validation purpose in the framework of a turbulent boundary-layer trailingedge interaction (TBL-TE) noise prediction model. Results are extensively validated with the wind tunnel measurement of high Reynolds number airfoil BL flows.