Space-time Correlation Function Research Articles

Solvent Motions and Solvation Processes in a Short-Time Regime: Effects on Excited-State Intramolecular Processes in Solution

We propose a method for treating equation of motions for atoms taking into account the inertial term with an interaction site model for capturing solvent dynamics attributed to solvent motions in a short-time regime, t < 100 fs. We show a prescription for solving the equation which governs the development of the fluctuation of solvent number density with the inertial term, and the results of the van Hove space-time correlation function of water are compared with those by a molecular dynamics simulation. Also, the procedure is applied to the study of solvation dynamics of the simplest betaine dye molecule pyridinium N-phenoxide in water in the excited state. It is shown that the coupling between solvation and a fast intramolecular reaction such as charge transfer is likely to play an important role in solvation dynamics of the simplest betaine, and the importance of tracking solvation process associated with electronic reorganization in the solute molecule in the short-time region is indicated.

Noncolliding Jacobi processes as limits of Markov chains on the Gelfand–Tsetlin graph

We introduce a stochastic dynamics related to the measures that arise in harmonic analysis on the infinite–dimensional unitary group. Our dynamics is obtained as a limit of a sequence of natural Markov chains on the Gelfand–Tsetlin graph. We compute the finite-dimensional distributions of the limit Markov process, the generator and eigenfunctions of the semigroup related to this process. The limit process can be identified with the Doob h-transform of a family of independent diffusions. The space-time correlation functions of the limit process have a determinantal form. Bibliography: 21 titles.

Dynamics of counterions in dendrimer polyelectrolyte solutions

Molecular dynamics simulations were employed in models of peripherally charged dendrimers in solutions of explicit solvent and monovalent counterions in order to explore aspects of the dynamic behavior of counterions. The present study explores the effects of varying strength of electrostatic interactions for models of two dendrimer generations, in explicit solvent solutions below the dendrimer overlap concentration. Counterion diffusional motion as well as residence lifetimes of pairs formed by charged dendrimer beads and condensed counterions is monitored in the different electrostatic regimes. Spatiotemporal characteristics of self- and collective counterion motion are explored by means of space-time Van Hove correlation functions. A characteristic scaling law is found to describe the counterion diffusion coefficient as a function of Bjerrum length in the strong electrostatic regime, independent of the size of the dendrimer molecules at the examined volume fractions. The change noted in the diffusional motion of counterions in the range of strong Coulombic interactions is also reflected to their relevant residence times. Development of dynamic heterogeneities in counterion self-motion is observed during the gradual increase in the strength of electrostatic interactions, characterized by the emergence of distinct counterion populations in terms of their mobility. The time scale for the development of such a mobility contrast in the self-motion of the counterions can be correlated with that describing their collective motion as well. The latter increases with Bjerrum length but remains shorter compared to the time scale at which free diffusional motion sets in. Findings from the present study provide further insight on the mechanisms pertinent to ion migration in macroion dispersions and may serve as a basis for the interpretation of ionic motion in a broader range of polyelectrolyte systems.

Distributions of products of the quasifree knocking-out reaction (p, p′n) on halo nuclei in the intermediate-energy region

Expressions for the distribution functions of products of the reaction (p, p′n) of valence neutron knocking-out from halo nuclei were derived using space-time correlation functions. The possibility of using this reaction to study the neutron halo structure was analyzed.

Space-time description of scalar particle creation by a homogeneous isotropic gravitational field

We give the generalization of the method of the space-time description of particle creation by a gravitational field for a scalar field with nonconformal coupling to the curvature. The space-time correlation function is obtained for a created pair of the quasi-particles, corresponding to a diagonal form of the instantaneous Hamiltonian. The case of an adiabatic change of the metric of homogeneous isotropic space is analyzed. We show that the created pairs of quasi-particles in de Sitter space should be interpreted as pairs of virtual particles.

Three-Dimensional Modeling, Simulation, and Capacity Analysis of Space–Time Correlated Mobile-to-Mobile Channels

A 3-D reference model is proposed for multiple-input multiple-output (MIMO) mobile-to-mobile (M-to-M) multipath-fading channels. From this model, a closed-form joint space-time correlation function is derived for a 3-D nonisotropic scattering environment. Two sum-of-sinusoids-based 3-D simulation models for MIMO M-to-M multipath-fading channels are proposed. The statistics of the simulation models are verified by simulation. Finally, these simulation models are used to evaluate the effect of the space-time correlation on the outage capacity of uniform linear antenna arrays and to compare the capacities of linear, circular, and spherical antenna arrays.

Space-Time Correlated Mobile-to-Mobile Channels: Modelling and Simulation

A single- and double-bounced two-ring parametric reference model is proposed for multiple-input multiple-output (MIMO) mobile-to-mobile (M-to-M) Ricean fading channels. From this model, a closed-form joint space-time correlation function and a space-Doppler power spectrum are derived for a two-dimensional (2D) non-isotropic scattering environment. Also, space-time correlation functions for the in-phase and quadrature components of the complex faded envelope are derived, assuming a 2D isotropic scattering environment. Finally, two new sum-of-sinusoids based simulation models for MIMO M-to-M Ricean fading channels are proposed. The statistics of the simulation models are verified by simulation. The results show that the simulation models are a good approximation of the reference model and that they outperform existing simulation models.

The space-time operator product expansion in string theory duals of field theories

We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting (single-trace) terms in the OPE of the field theory arise in this limit from the OPE of the worldsheet theory of the string dual, using a dominant saddle point which appears in computations of worldsheet correlation functions in the space-time OPE limit. The worldsheet OPE generically contains only non-physical operators, but all the non-physical contributions are resummed by the saddle point to a contribution similar to that of a physical operator, which exactly matches the field theory expectations. We verify that the OPE limit of the worldsheet theory does not have any other contributions to the OPE limit of space-time correlation functions. Our discussion is completely general and applies to any local field theory (conformal at high energies) that has a weakly coupled string theory dual (with arbitrary curvature). As a first application, we compare our results to a proposal of R. Gopakumar for the string theory dual of free gauge theories.

Statistical properties of dynamic speckles formed by a deflecting laser beam

We analyze statistical properties of dynamic speckles formed when an optically rough surface is illuminated by a fast-deflecting laser beam. The modified space-time correlation function of the light-intensity fluctuations has been introduced to estimate the correlation parameters of a dynamic speckle pattern. Dynamic speckles are considered in their application to range sensing using evaluation of the light-power-modulation frequency of a signal obtained from the integrating photodetector after spatial filtering of the scattered light. Multichannel configuration is suggested to improve the system accuracy. Conditions that should be fulfilled to get uncorrelated responses of photodiode are found. Proper averaging of the multichannel data allows designing a non-interferometric range sensor capable for measuring distance with accuracy of 1 microm during as short time as 1 ms.

A sensitivity analysis of the point reference global correlation (PRGC) technique for spatio-temporal correlations in turbulent flows

The point reference global correlation (PRGC) technique which combines single and global measurements as proposed by Chatellier and Fitzpatrick (Exp Fluids 38(5):563–757, 2005) is of significant interest for the analysis of the turbulent statistics for noise source modeling in jet flows as it allows the 2D spatio-temporal correlation functions to be obtained over a region of the flow. This enables the statistical characteristics including inhomogeneous and anisotropic features to be determined. The sensitivity of the technique is examined in some detail for the specific case of laser doppler velocimetry (LDV) and particle image velocimetry (PIV). Simulated data are used to enable a parametric study of the accuracy of the PRGC technique to be determined as a function of the various measurement parameters. The sample frequencies and the number of samples of both the LDV and PIV signals are shown to be critical to errors associated with the estimated spatio-temporal correlations and that low data rates can lead to significant errors in the estimates. Measurements performed in single stream and co-axial jet flows at Mach 0.24 using PIV and LDV systems are reported and the 2D space–time correlation functions for these flows are determined using the PRGC technique. The results are discussed in the context of noise source modeling for jet flows.

Modeling and Applications of Space–Time Correlation for MIMO Fading Signals

In this paper, the space-time correlation (STC) functions of multiple-input multiple-output (MIMO) fading signals are derived for both frequency-flat and frequency-selective channels in macrocell and microcell environments. To avoid large computation load in calculating the exact STC, we recommend the concept of effective scatterers and provide simplified expressions of STC functions. The STC functions are used to calculate the coefficient matrices that are necessary for generating MIMO channels, when the vector autoregressive method is used. The analytical results are verified by Monte Carlo simulations. Finally, we use the generated channels to investigate MIMO capacities under various channel parameters and to evaluate the bit-error-rate performance of downlink wideband code-division-multiple-access system with transmit and receive diversity.

Statistical analysis of fluctuations and noise-driven transport in particle-in-cell simulations of plasma turbulence

The problem of discrete particle noise has been studied based on direct fluctuation measurements from gyrokinetic particle-in-cell simulations of stable plasmas. From the statistical analysis of electrostatic potential time evolution, the space-time correlation function has been measured. Fluctuation spectra have been constructed and analyzed in detail. Noise-driven transport is calculated using the quasilinear expression for the diffusion coefficient and the obtained noise spectrum. The theoretical value of electron heat conductivity shows good agreement with that measured in the simulation. It has been shown that for the realistic parameters in actual turbulence simulations, the noise-driven transport depends linearly on the entropy of the system. This study makes it possible to estimate and subtract the noise contribution to the total transport during turbulence simulations.

Symmetry-based determination of space-time functions in nonequilibrium growth processes

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space- and time-dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.

Dynamics of fluctuation-dominated phase ordering: Hard-core passive sliders on a fluctuating surface

We study the dynamics of a system of hard-core particles sliding downwards on a one-dimensional fluctuating interface, which in a special case can be mapped to the problem of a passive scalar advected by a Burgers fluid. Driven by the surface fluctuations, the particles show a tendency to cluster, but the hard-core interaction prevents collapse. We use numerical simulations to measure the autocorrelation function in steady state and in the aging regime, and space-time correlation functions in steady state. We have also calculated these quantities analytically in a related surface model. The steady-state autocorrelation is a scaling function of t/L(z), where L is the system size and z is the dynamic exponent. Starting from a finite intercept, the scaling function decays with a cusp, in the small argument limit. The finite value of the intercept indicates the existence of long-range order in the system. The space-time correlation, which is a function of r/L and t/L(z), is nonmonotonic in t for fixed r. The aging autocorrelation is a scaling function of t(1) and t(2) where t(1) is the waiting time and t(2) is the time difference. This scaling function decays as a power law for t(2)>>t(1); for t(1)>>t(2), it decays with a cusp as in steady state. To reconcile the occurrence of strong fluctuations in the steady state with the fact of an ordered state, we measured the distribution function of the length of the largest cluster. This shows that fluctuations never destroy ordering, but rather the system meanders from one ordered configuration to another on a relatively rapid time scale.

Fine-Scale Turbulence Noise from Hot Jets

Experimental measurements indicate that the noise radiated from a jet depends not just on the jet-exit velocity alone, but is significantly affected by the jet temperature. Now, there is evidence to support the proposition that jet mixing noise consists of two principal components. These are the noise from the large turbulence structures of the jet flow and the fine-scale turbulence. The prediction of fine-scale turbulence noise from hot jets is considered. Earlier Tam and Auriault developed a semi-empirical theory capable of predicting the fine-scale turbulence noise from cold to moderate temperature jets. In this work, their semi-empirical theory is extended to high-temperature jets, up to a temperature ratio above that of present day commercial engines. The density gradient present in hot jets promotes the growth of Kelvin-Helmholtz instability in the jet mixing layer. This causes a higher level of turbulent mixing and stronger turbulence fluctuations. In addition, recent experiments reveal that the two-point space-time correlation function of turbulent mixing for hot jets is substantially different from that for cold jets. The eddy decay time is shorter, and the eddy size is slightly reduced. These changes have an appreciable impact on the noise radiated. In the present extended fine-scale turbulence theory, both effects are taken into account

Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells.

We introduce a new extension of image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS) that relies on complete analysis of both the temporal and spatial correlation lags for intensity fluctuations from a laser-scanning microscopy image series. This new approach allows measurement of both diffusion coefficients and velocity vectors (magnitude and direction) for fluorescently labeled membrane proteins in living cells through monitoring of the time evolution of the full space-time correlation function. By using filtering in Fourier space to remove frequencies associated with immobile components, we are able to measure the protein transport even in the presence of a large fraction (>90%) of immobile species. We present the background theory, computer simulations, and analysis of measurements on fluorescent microspheres to demonstrate proof of principle, capabilities, and limitations of the method. We demonstrate mapping of flow vectors for mixed samples containing fluorescent microspheres with different emission wavelengths using space time image cross-correlation. We also present results from two-photon laser-scanning microscopy studies of alpha-actinin/enhanced green fluorescent protein fusion constructs at the basal membrane of living CHO cells. Using space-time image correlation spectroscopy (STICS), we are able to measure protein fluxes with magnitudes of mum/min from retracting lamellar regions and protrusions for adherent cells. We also demonstrate the measurement of correlated directed flows (magnitudes of mum/min) and diffusion of interacting alpha5 integrin/enhanced cyan fluorescent protein and alpha-actinin/enhanced yellow fluorescent protein within living CHO cells. The STICS method permits us to generate complete transport maps of proteins within subregions of the basal membrane even if the protein concentration is too high to perform single particle tracking measurements.

Extracting coherent wave fronts from acoustic ambient noise in the ocean

A method to obtain coherent acoustic wave fronts by measuring the space–time correlation function of ocean noise between two hydrophones is experimentally demonstrated. Though the sources of ocean noise are uncorrelated, the time-averaged noise correlation function exhibits deterministic waveguide arrival structure embedded in the time-domain Green’s function. A theoretical approach is derived for both volume and surface noise sources. Shipping noise is also investigated and simulated results are presented in deep or shallow water configurations. The data of opportunity used to demonstrate the extraction of wave fronts from ocean noise were taken from the synchronized vertical receive arrays used in the frame of the North Pacific Laboratory (NPAL) during time intervals when no source was transmitting.

Aging dynamics of the Heisenberg spin glass

We numerically study the non-equilibrium dynamics of the three dimensional Heisenberg Edwards-Anderson spin glass following a sudden quench to its low temperature phase. The subsequent aging behavior of the system is analyzed in detail, and the scaling behavior of various space-time correlation functions is investigated for both spin and chiral degrees of freedom. We carefully compare our results with those obtained from simulations of the more studied Ising version of the model, and with experiments on real spin glasses in which the spins have vectorial character. Finally, the present dynamical study offers new perspectives into the possibility of spin-chirality decoupling at low temperature in vectorial spin glasses.

Measurement of the space-time correlation function of thermal acoustic radiation

The space-time correlation function of thermal acoustic radiation pressure is measured for a stationary heated source (a narrow plasticine plate). The correlation dependence is obtained by the multiplication of two signals shifted in time with respect to each other and measured by two receivers. The dependence exhibits an oscillating behavior and changes sign when the source is displaced by half the spatial period of the correlation function.

Nanoparticle velocity relaxation in a condensed carrying medium

The interaction of a nanoparticle occurring in a carrying condensed medium with fluctuations of the medium momentum caused by the particle motion have been studied. The space-time velocity correlation functions of the nanoparticle and surrounding molecules were determined by the molecular dynamics method. These functions exhibit one or two maxima, depending on the system parameters. The first maximum is related to an acoustic wave propagating in the medium, and the second, to multiple collisions between the nanoparticle and nearest neighbor molecules. It is established that collective effects significantly influence both the velocity autocorrelation function and the diffusion coefficient of the nanoparticle.