Cross-correlation Contributions Research Articles

Terahertz Spectroscopy of Aqueous Solutions of Sodium Halides (NaX): Self- and Cross-Correlation Contributions of Ions and Hydration Shell Water for X- = F-, Cl-, Br-, and I.

We investigated the terahertz (THz) absorption spectra of aqueous sodium halide solutions through molecular dynamics simulations using polarizable models of both water and ions. Specifically, we have considered aqueous solutions (∼1 M) of NaF, NaCl, NaBr, and NaI and calculated the difference THz spectrum of these solutions by subtracting the corresponding pure water contribution from the total THz spectrum of an ionic solution. The difference absorption spectrum of a given solution is then dissected into contributions from ion and ion-water correlations and also modifications of water-water correlations in the presence of the ions. The different components are further decomposed into induced dipole and permanent charge/dipole components and also into self- and cross-correlation components. The ion-water cross-correlation components are subsequently decomposed into contributions coming from different solvation shells through radially resolved calculations of such ion-water cross-correlations. Through all of these dissections, we could investigate the origin of different parts of the difference THz spectra of the sodium halide solutions studied here. It is found that while features below or around 100 cm-1 and also around 200 cm-1 arise mainly from ion and ion-water motion, that at the librational region above 600 cm-1 primarily originates from changes in water librational motion influenced by the ions. The variations of intensities of different components are also linked to the size and charge density of the anions in the solutions.

Generic Structural Relaxation in Supercooled Liquids.

One of the unsolved problems of dynamics in supercooled liquids are the differences in spectral shape of the structural relaxation observed among different methods and substances, and a possible generic line shape has long been debated. We show that the light scattering spectra of very different systems, e.g., hydrogen bonding, van der Waals liquids, and ionic systems, almost perfectly superimpose and show a generic line shape of the structural relaxation, following ∝ ω-1/2 at high frequencies. In dielectric spectra the generic behavior is recovered only for systems with low dipole moment, while in strongly dipolar liquids additional cross-correlation contributions mask the generic structural relaxation.

A probabilistic model for on-line estimation of the GNSS carrier-to-noise ratio

This article is dedicated to the estimation of the GNSS signal carrier-to-noise ratio using the in-phase component of the signals as observations. In a GNSS receiver, it is the statistic of the correlation provided by the code tracking loop that is used to estimate the carrier-to-noise ratio. In fact, carrier-to-noise estimation is used to monitor the performance of GNSS receivers and the quality of the received signals. In this article, we aim at high rate carrier-to-noise estimation, namely the code repetition rate (e.g. 1ms for GPS C/A), in order to maximize the time resolution of carrier-to-noise observations. We show that in a 1-bit quantization receiver, the in-phase component of the signal can provide a direct observation of the signal amplitude, and therefore of the carrier-to-noise ratio. However, the model that links the 1ms rate observations of the in-phase component with the signal amplitude is non-linear. The non-linear expression that links the maximum value of the in-phase correlation component to the signal amplitude is derived. In order to estimate the time varying amplitudes of the signals, we propose an Extended Kalman Filter to reverse the non-linear expression with the noisy observations of correlation provided by the tracking loop. The proposed model and filter inversion method are assessed on synthetic and real data, while investigating the effect of the cross-correlation contribution of the visible satellites on the estimations. We show using real data that, for a 1-bit quantization receiver, the proposed estimator can achieve the same accuracy as a widely known commercial GNSS receiver with a much higher data rate. We also show that the proposed approach can cope with abrupt changes in the observations compared to a classical C/N0 estimate.

Local dielectric response in 1-propanol: α-relaxation versus relaxation of mesoscale structures.

The dielectric Debye relaxation in monohydroxy alcohols has been subject of long-standing scientific interest and is presently believed to arise from the relaxation of transiently H-bonded supramolecular structures. Therefore, its manifestation in a measurement with a local dielectric probe might be expected to be different from the standard macroscopic dielectric experiment. In this work we present such local dielectric measurements obtained by triplet state solvation dynamics (TSD) and compare the results with macroscopic dielectric and light scattering data. In particular, with data from an improved TSD setup, a detailed quantitative comparison reveals that the Debye process does not significantly contribute to the local Stokes shift response function, while α- and β-relaxations are clearly resolved. Furthermore, this comparison reveals that the structural relaxation has almost identical time constants and shape parameters in all three measurement techniques. Altogether our findings support the notion that the transiently bound chain structures lead to a strong cross-correlation contribution in macroscopic dielectric experiments, to which both light scattering and TSD are insensitive, the latter due to its local character and the former due to the molecular optical anisotropy being largely independent of the OH bonded suprastructures.

Temperature Dependence of the Air/Water Interface Revealed by Polarization Sensitive Sum-Frequency Generation Spectroscopy.

The temperature dependence of the vibrational sum-frequency generation (vSFG) spectra of the air/water interface is investigated using many-body molecular dynamics (MB-MD) simulations performed with the MB-pol potential energy function. The vSFG spectra calculated for different polarization combinations are then analyzed in terms of molecular autocorrelation and cross-correlation contributions. To provide molecular-level insights into interfacial hydrogen-bonding topologies, which give rise to specific spectroscopic features, the vSFG spectra are further investigated by separating contributions associated with water molecules donating zero, one, or two hydrogen bonds to neighboring water molecules. This analysis suggests that the low frequency shoulder of the free OH peak which appears at ∼3600 cm-1 is primarily due to intermolecular couplings between both singly and doubly hydrogen-bonded molecules.

Dissecting ion-specific dielectric spectra of sodium-halide solutions into solvation water and ionic contributions.

Using extensive equilibrium molecular dynamics simulations we determine the dielectric spectra of aqueous solutions of NaF, NaCl, NaBr, and NaI. The ion-specific and concentration-dependent shifts of the static dielectric constants and the dielectric relaxation times match experimental results very well, which serves as a validation of the classical and non-polarizable ionic force fields used. The purely ionic contribution to the dielectric response is negligible, but determines the conductivity of the salt solutions. The ion-water cross correlation contribution is negative and reduces the total dielectric response by about 5%-10% for 1 M solutions. The dominating water dielectric response is decomposed into different water solvation shells and ion-pair configurations, by this the spectral blue shift and the dielectric decrement of salt solutions with increasing salt concentration is demonstrated to be primarily caused by first-solvation shell water. With rising salt concentration the simulated spectra show more pronounced deviations from a single-Debye form and can be well described by a Cole-Cole fit, in quantitative agreement with experiments. Our spectral decomposition into ionic and different water solvation shell contributions does not render the individual contributions more Debye-like, this suggests the non-Debye-like character of the dielectric spectra of salt solutions not to be due to the superposition of different elementary relaxation processes with different relaxation times. Rather, the non-Debye-like character is likely to be an inherent spectral signature of solvation water around ions.

Cross-Correlation Contributions to Orientational Relaxations in Primitive Chain Network Simulations

Models for entangled polymer dynamics can be conveniently thought of as belonging to two major categories - multichain models, such as the Kremer-Grest model simulated using molecular dynamics and single chain models, such as the tube and sliplink models. The single chain models typically assume that each polymer chain moves essentially independently of the other chains in the system. Hence they also assume that the cross-correlations between the different chains make negligible contribution to the various physical quantities (for e.g., the time-dependent relaxation modulus). However, Cao and Likhtman [Phys Rev Lett 104, 207801 (2010)] using molecular dynamics simulations have shown that there exist significant cross-correlation contributions to the time-dependent orientational relaxation function. In this study, the effect of cross-correlation was investigated using the primitive chain network model, a multi-chain sliplink model. Orientational relaxation functions for both the subchain vectors between entanglements and also for the end-to-end vector of whole chain were evaluated. In the case of the subchain relaxation function (and which corresponds to the time-dependent relaxation modulus by the stress-optical rule), the cross-correlation contribution to the total relaxation function appears to progressively increase with time. Further, the ratio of the cross-correlation function to the total relaxation function reaches a maximum value of approximately 40 % in the terminal region. Besides indicating that the cross-correlation contributions to the total relaxation function are non-negligible, this also demonstrates that the relaxation spectrum itself is modified if the cross-correlation contribution is neglected from the total relaxation. Specifically, the cross-correlation contribution affects the relaxation spectrum in the time range where the effect of the constraint release process is expected to be important. On the other hand, the results indicate that effect of cross-correlations on the shape of the relaxation curve is not significant at long times around the terminal region and that the autocorrelation and the total correlation functions can be superimposed by rescaling the unit of modulus. In contrast, the contribution from cross-correlation to the end-to-end relaxation (that corresponds to the dielectric relaxation of type-A polymers) is less significant than that for the subchain relaxation. In fact, no significant difference was found in the prediction of dielectric relaxation between the end-to-end relaxation functions with and without the contribution of the cross-correlations.

Contribution of cross-correlations to the 21-cm angular power spectrum in the epoch of re-ionization

Measurement of the 21cm hyperfine transition of neutral hydrogen provides a unique probe of the epoch of reionization and the Dark Ages. Three major mechanisms are believed to dominate the radiation process: emission from neutral hydrogen surrounding the ionized bubbles of first galaxies and/or quasars, emission from neutral hydrogen inside minihalos, and absorption of diffuse neutral hydrogen against the cosmic microwave background. In the present work, by simply combining the existing analytic models for the three mechanisms, we investigate the contribution of cross-correlation between these three components to the total 21cm angular power spectrum, in the sense that neutral hydrogen associated with different radiation processes traces the large-scale structures of underlying density perturbations. While the overall 21cm power spectrum remains almost unchanged with the inclusion of the cross-correlations, the cross-correlation may play a key role in the determination of the 21cm power spectrum during the transition of 21cm radiation from emission-dominated phase to absorption-dominated phase at redshift z~20. A significant suppression in the 21cm angular power spectrum during this transition is anticipated as the result of negative contribution of the cross-correlation between the absorption of diffuse neutral hydrogen and the emission components. Therefore, an accurate prediction of the cosmic 21cm power spectrum should take the cross-correlation into account especially at the transition phase.

Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole–dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA × DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/ r 6 distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSA × DSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.

Cross-correlations and predictability of stock returns

Studies have shown that small stock returns can be partially predicted by the past returns of large stocks (cross-correlations), while a larger body of literature has shown that macroeconomic variables can predict future stock returns. This paper assesses the marginal contribution of cross-correlations after controlling for predictability inherent in lagged macroeconomic variables. Macroeconomic forecasting models generate trading rule profits of up to 0.431% per month, while the inclusion of cross-correlations increases returns to 0.516% per month. Such results suggest that cross-correlations may serve as a proxy for omitted macroeconomic variables in studies of stock market predictability. Macroeconomic variables are more important than cross-correlations in forecasting small stock returns and encompassing tests suggest that the small marginal contribution of cross-correlations is not statistically significant. Copyright © 2001 by John Wiley & Sons, Ltd.

Cross correlations in the longitudinal relaxation of strongly coupled spins

A generalized set of magnetization modes for quantifying cross-correlation contributions to longitudinal relaxation in strongly coupled spin systems is described in this paper. Such a set of modes (called longitudinal multiple-quantum modes) is used to unravel cross-correlation information in strongly coupled systems, where the strength of the J coupling tends to obscure such effects. The applicability of such methods is demonstrated for a small molecule which exhibits some strong coupling effects even at high magnetic field strengths. The contribution of "remote" cross correlations to the longitudinal relaxation of strongly coupled spins is detailed. Copyright 2000 Academic Press.

Dynamic mechanical and dielectric relaxations of poly(difluorobenzyl methacrylates)

This work reports the mechanical and dielectric relaxation spectra of three difluorinated phenyl isomers of poly(benzyl methacrylate), specifically, poly(2,4-difluorobenzyl methacrylate), poly(2,5-difluorobenzyl methacrylate) and poly(2,6-difluorobenzyl methacrylate). The strength of the dielectric glass-rubber relaxation of the 2,6 difluorinated phenyl isomer is, respectively, nearly three and two times larger than the strengths of the 2,5 and 2,4 isomers. The 2,4 isomer presents a mechanical a peak the intensity of which is nearly two times that of the other two isomers. Both the mechanical and dielectric relaxation spectra display a subglass process, called γ relaxation, centered in the vicinity of -50 °C at 1 Hz and, in some cases, a subglass β absorption is detected at higher temperature partially masked by the glass-rubber relaxation. The mean-square dipole moments per repeating unit, /x, measured at 25 °C in benzene solutions, are 2.5 D 2 , 1.9 D 2 , and 5.0 D 2 for poly(2,4-difluorobenzyl methacrylate), poly(2,5-difluorobenzyl methacrylate) and poly(2,6-difluorobenzyl methacrylate), respectively. These results, in conjunction with Onsager type equations, permit to conclude that auto and cross-correlation contributions to the dipolar correlation coefficient may have the same time-dependence. On the other hand, dipole intermolecular interactions, rather than differences in the flexibility of the chains, seem to be responsible for the relatively high calorimetric glass-transition temperature of the 2,6 diphenyl isomer, which is, respectively, nearly 36 °C and 32 °C above the T g 's of the 2,4 and 2,5 isomers. Molecular Mechanics calculations give a good account of the differences observed in the polarity of the polymers.

Measurement of Homonuclear Cross-Correlation Cross-Relaxation Rates along an Effective Field: Application to Dipole–Dipole Cross-Correlation

We describe three new schemes to explore homonuclear cross-correlation contributions to relaxation along an effective field tilted by an angle θ from the static magnetic field direction. Their key feature is to detect, during the evolution timet1, multiquantum transverse coherences whose frequencies are characteristic of the multispin order produced by cross-correlation processes. This makes it possible to obtain in-phase magnetization in both dimensions. The three schemes correspond to the combination of two evolutions due either to staticJcoupling in the transverse plane or to cross-correlation cross-relaxation along an effective field. This combination allows the conversion of one-spin order into multispin order and the reverse. If only cross-correlation cross-relaxation transfers are involved, there is no restriction on the coupling network. The quantitative exploitation of the results to obtain structural information from cross-correlation-induced relaxation rates requires a normalization coefficient which is provided by the simultaneous monitoring of one-spin coherence. These ideas have been tested experimentally in the case of dipole–dipole cross-correlation on a sample of cyclosporin. Buildup curves at various angles θ are described which yield information on the internal dynamics.

On the interpretation of virtual geomagnetic pole (VGP) scatter curves

The present paper aims at assessing the information contained in the so-called virtual geomagnetic pole (VGP) scatter curves which are commonly used in palaeosecular variation studies. As the corresponding curve derived for the last 5 Myr has been compared to a very similar “equivalent” VGP scatter curve derived from the present geomagnetic field (McFadden et al., 1988), we also address the meaning of these “equivalent” curves. We especially investigate the way the two types of curve are related to each other within the statistical formalism first introduced by Constable and Parker (1988). A number of simple and useful (but approximate) properties are derived for that purpose. In particular, a close formal link is established between the two quantities. This allows us to first study the behaviour of the equivalent VGP scatter curve (this curve is shown to be highly time dependent and mainly controlled by the degree and order (1, 1), (2, 1), (3, 1) and (4, 1) terms) and then proceed with some suggestions regarding the interpretation of palaeomagnetic scatter curves. These curves are shown to be (albeit approximately) the quadratic sum of a mean field contribution and of a variance and cross-correlation contribution, which cannot be distinguished from one another unless additional information is being used. In the case of the VGP scatter of the last 5 Myr, available mean field models show that the mean field contribution is very weak. But assuming an isotropic-with-no-correlations statistical model of the field cannot account for the corresponding VGP scatter curve, whatever the spectrum of the non-dipole field. Anisotropy and/or cross-correlations are thus required. We show examples of statistical models incorporating such ingredients. It appears that the separation into dipole and quadrupole (antisymmetric and symmetric) families along the line suggested by McFadden et al. (1988) is not the most appropriate. Rather, it is likely that the pre-eminence of the order 1 terms suggested by the observation of the historical field is responsible for the VGP scatter curve of the past 5 Myr. This study somewhat follows and completes the very recent work of Kono and Tanaka (1995).

Mutual diffusion in binary Ar-Kr mixtures and empirical diffusion models.

Molecular dynamics simulations of four binary Ar-Kr mixtures are used to compute self- and mutual-diffusion coefficients. Results using mean squared displacements and using velocity correlation functions are presented. The diffusivity coefficients are also presented in the time and frequency domains where a comparatively low frequency structure is evident in some simulations. The computed diffusivities are dependent on the maximum time over which the velocity correlation functions are integrated and the time at which the Einstein relationships are evaluated. This dependence explains in part the small systematic differences between our results (20--80 ps) and earlier molecular dynamics results (4 ps) in the system Ar-Kr. We compare the computed mutual diffusion coefficients to two empirical models, Darken's model and the common force model. Darken's model is consistent with our results over the entire frequency range we resolve. At frequencies lower than about 5 ${\mathrm{ps}}^{\mathrm{\ensuremath{-}}1}$ Darken's model and the common force model converge and we cannot discriminate between them. At higher frequencies the common force model prediction is significantly different from the computed mutual diffusion coefficient. Assumptions regarding the contribution of cross correlations that are implicit in the empirical models are discussed and tested against our simulation results. The net contribution of velocity cross correlations is found to be negligible, as is often assumed in deriving Darken's model, but the individual cross-correlation terms are substantial and negative---a finding contrary to common assumptions. \textcopyright{} 1996 The American Physical Society.

Magnetic relaxation of xenon-131 dissolved in benzene. A study by molecular dynamics and Monte Carlo simulations

Molecular dynamics and Monte Carlo simulations were carried out for xenon atoms dissolved in liquid benzene in order to study the quadrupolar relaxation mechanism of the xenon-131 nucleus. We confirm that a proper description of the relaxation is obtained by taking into account the quadrupole moment of benzene molecules. In contrast to the Xe–water system, the cross-correlation contribution to the electric field gradient (experienced by the Xe nucleus) is negligible in benzene, and the time correlation function of the total electric field gradient shows a relatively smooth decay. Several molecular motions take part in this decay, but not with the same efficiency. The major contribution can be attributed to the rotation of the benzene molecules around their C2 axes. The adequacy of the Sternheimer model for quadrupolar interactions is confirmed with ab initio calculations. Some methodological aspects of simulations are also discussed, such as the use of a termination function to treat the electrostatic interactions and the effect of the xenon interaction parameters on the simulated relaxation rate.

Generation-recombination noise of hot carriers in semiconductors

We present an original Monte Carlo procedure to account for generation-recombination noise through impurity centers in semiconductors. An exact decomposition procedure of the current spectral density evidences the importance of a cross-correlation contribution coming from velocity and number fluctuations.