Linear Autocorrelation Research Articles

Surface charge induced modifications of the structure and dynamics of mixed dipolar liquids at solid–liquid interfaces: A molecular dynamics simulation study

Molecular dynamics simulations are carried out to investigate the structural and dynamical properties of binary Stockmayer liquids near charged solid surfaces at varying surface charge density. The two solvent components differ widely in their polarity. The dipolar mixtures are formed at varying composition and the properties of the interfacial molecules are calculated in terms of several equilibrium and dynamical quantities such as the number density and polarization profiles, electrostriction at surfaces, linear and angular velocity autocorrelation functions, perpendicular (z) and parallel (x,y) components of translational diffusion tensors and rotational diffusion coefficients. The extent of selective adsorption of one species against the other at the surfaces is investigated as a function of surface charge density and composition and its effects on translational and rotational diffusion of interfacial molecules are discussed. The dynamical properties of the interfaces are also compared with those of the bulk.

Surface effects in order–disorder transformations in molecular clusters

The effect of a surface on structural phase transitions in clusters is examined by means of velocity autocorrelation functions for TeF6 clusters. Isothermal molecular dynamics via quaternion-based equations of motion reveals two successive phase transitions in this plastic substance. The lower-temperature transition is continuous, associated with rotational ordering. The other transition involves translation–rotation coupling in which the growth of correlations causes a crossover from a displacive to an order–disorder regime. Both the linear and angular autocorrelation functions show negative regions at low temperatures. The negative portion of the linear velocity autocorrelation function arises from the system’s memory in the rebound of a molecule against its shell of neighbors. The negative part of the angular velocity autocorrelation function is ascribed to librations of the molecules in their close-packed cages. At still lower temperatures, the negative part exhibits two minima, which are best resolved when linear velocity autocorrelation functions are plotted separately for the surface and the volume molecules. This indicates different memories for surface and volume molecules.

Non-linear analysis of intracranial human EEG in temporal lobe epilepsy

Objective: Intracranial EEG recordings from patients suffering from medically intractable temporal lobe epilepsy were analyzed with the aim of characterizing the dynamics of EEG epochs recorded before and during a seizure and comparing the classification of the EEG epochs on the basis of visual inspection to the results of the numerical analysis.Methods: The stationarity of the selected EEGs was assessed qualitatively. The coarse-grained correlation dimension and coarse-grained correlation entropy were used for the non-linear characterization of the EEG epochs.Results: High-pass filtering was necessary in order to make the majority of the epochs appear stationarity beyond a time scale of about 2 s. It was found that the dimension of the ictal EEGs decreased with respect to the epochs containing ongoing (interictal) activity. The entropy of the ictal recordings however increased. A scaling of the entropy was applied and it was found that the scaled entropy of the ictal EEG decreased, consistent with the increased regularity of the ictal EEG. The coarse-grained quantities discriminated well between EEG epochs recorded prior to and during seizures at locations displaying ictal activity and classification improved by including the linear autocorrelation time in the analysis.Conclusions: It is concluded that ictal and non-ictal EEG can be well distinguished on the basis of non-linear analysis. The results are in good agreement with the visual analysis.

Fourier Analysis of Textural Variations in Human Normal and Cataractous Lens Nuclear Fiber Cell Cytoplasm

Variations in cytoplasmic texture of human normal and cataractous lenses were investigated with Fourier analysis. Fixed Vibratome sections of six normal transparent human lenses (age range 55–72 years) and six nuclear cataractous lenses (age range 66–89 years) were examined using transmission electron microscopy. Images were taken of the fiber cell cytoplasm and examined using linear optical density scans, Fourier transforms and autocorrelation analysis. The cytoplasm of normal human lenses was found to be smooth and homogeneous. Radially-averaged plots of Fourier transforms revealed a broad band of intensity over the range of 15–50 nm. Four of the six cataracts also had homogeneous cytoplasm without substantial density variations. Fourier transforms and radially-averaged plots were similar to those of the normal, although slightly lower in intensity for components⩽20 nm. Two of the six cataracts had a slightly granular or textured cytoplasm that showed significant density variations. Fourier transforms and radially-averaged plots revealed significant intensity in the range⩾200 nm. Autocorrelation analysis supported the data obtained by Fourier transforms. Radially-averaged plots of the autocorrelation resultant displays detected only small structural units in the normal and non-textured cataractous cytoplasm, whereas larger structural units were detected in the textured cataractous cytoplasm. The appearance of the textured cataractous cytoplasm suggests that redistribution or loss of protein may be the cause of density variations in these types of cataracts. Importantly, these results indicate that some nuclear cataracts do not contain spatial fluctuations in the cytoplasm large enough to cause significant light scattering. The data suggest that nuclear cataractogenesis is a multi-factorial process involving minor alterations in cellular structure.

Uncertainty of One-Dimensional Ground-Water Flow in Strongly Heterogeneous Formations

The writers have formulated quasi-analytical nonlinear solutions to investigate the uncertainty of one-dimensional ground water flow in heterogeneous formulations in which the standard deviation of the log hydraulic conductivity σ\Dln(\iK)\N > 1. The writers have studied three cases for fixed boundary conditions: a semibounded domain, a free domain, and a both-side-bounded domain. The writers have also studied the random boundary conditions for the bounded domain. The writers have obtained variances and covariances of head for semibounded and free domains, and have calculated variances of head for the both-side-bounded domain. Monte Carlo simulations are generated to obtain the head variances and are used to verify the quasi-analytical solutions. The ergodicity assumption is proven to be rigorously correct in a semibounded or a free domain but not correct in a both-side-bounded domain by using a linear autocorrelation function.

On the Ergodicity Hypothesis in Heterogeneous Formations

Application of the ergodicity hypothesis to the stochastic subsurface hydrology has been checked by investigating the hydraulic conductivity field. The relative variance of the spatial average of conductivity, which is denoted as R, and the error index E.I. = \(\sqrt R \), were employed to justify the uncertainties and errors of using the ergodicity hypothesis. Six factors influence R: autocorrelation function; variance of logconductivity; spatial correlation scales of logconductivity; domain sizes; anisotropy; and dimensionality of the problem. Closed-form analytical solutions of R for the linear autocorrelation function were derived and the numerical integration of R for the exponential autocorrelation function for one-, two-, and three-dimensional problems calculated. It is easy to fulfill the ergodicity hypothesis under these conditions: weak heterogeneity and large ratio of domain size vs. correlation length (L/I). The uncertainties and errors of using this hypothesis increase rapidly when the variances of logconductivity increase and/or the ratios of L/I decrease. The ergodicity hypothesis has less error when applied to a problem with higher dimensionality.

On cyclotomic generator of order r

In this paper the cyclotomic generator of order r is studied in detail. Their linear complexity, minimal polynomial, and autocorrelation function of its output sequences are calculated. The decimation property of those sequences, the implementation and some applications are also considered.

Q-ary cascaded GMW sequences

Cascaded GMW sequences over GF(q) of arbitrary characteristic are investigated. Their periods are derived. As compared with the existing results on such sequences, substantially extended and improved theorems concerning their linear spans and autocorrelation functions are obtained. A criterion and an algorithm for constructing cascaded GMW sequences that have much larger linear spans than GMW sequences with the same periods are given. These provide a new class of complex-valued sequences which have larger linear spans and two-valued autocorrelation functions.

A nonlinear correlation function for selecting the delay time in dynamical reconstructions

Numerical results discussed in this paper suggest that a function which detects nonlinear correlations in time series usually indicates shorter correlation times than the linear autocorrelation function which is often used for this purpose. The nonlinear correlation function can also detect changes in the data which cannot be distinguished by the linear counterpart. This affects a number of approaches for the selection of the delay time used in the reconstruction of nonlinear dynamics from a single time series based on time delay coordinates.

Nonlinear sequence-dependent structure of nigral dopamine neuron interspike interval firing patterns

Firing patterns of 15 dopamine neurons in the rat substantia nigra were studied. These cells alternated between two firing modes, single-spike and bursting, which interwove to produce irregular, aperiodic interspike interval (ISI) patterns. When examined by linear autocorrelation analysis, these patterns appeared to reflect a primarily stochastic or random process. However, dynamical analysis revealed that the sequential behavior of a majority of these cells expressed "higher-dimensional" nonlinear deterministic structure. Dimensionality refers to the number of degrees of freedom or complexity of a time series. Bursting was statistically associated with some aspects of nonlinear ISI sequence dependence. Controlling for the effects of nonstationarity substantially increased overall predictability of ISI sequences. We hypothesize that the nonlinear deterministic structure of ISI firing patterns reflects the neuron's response to coordinated synaptic inputs emerging from neural circuit interactions.

Don't bleach chaotic data.

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is "bleached"), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.

Spectral Slope of Vowels Produced by Tracheoesophageal Speakers

Spectra of vowels were analyzed to determine whether differences exist between the spectral slope of vowels produced by tracheoesophageal (TE) speakers and normal speakers and, if so, to quantify such differences. The linear predictive autocorrelation method was used to calculate smoothed spectra and the spectra were normalized with respect to a low frequency component. Comparisons between normalized spectral energy within a selected high frequency range revealed that energy within this frequency range for vowels produced by TE speakers was significantly higher than that produced by normal speakers. A least-square distance matching procedure was used to quantify speaker group differences in the spectral slope of vowels. Average spectra of vowels produced by the normal speakers could be matched to average spectra of vowels produced by the TE speakers by decreasing the spectral slope of their vowels by 2-3 dB/octave.

Analysis of signals from superposed relaxation processes

System functions of many linear physical systems or autocorrelation functions of their output signals are often a sum of relaxator terms with different relaxation times and amplitudes. In the time domain a superposition of exponential decays e−γt is observed, while in the frequency domain a sum of relaxator terms of structure 1/(γ+iω) is measured. Thus, the response is either the Laplace transform of the system function or its Stieltjes transform, respectively. In both cases it is the task of an analyst to gain the relaxation times and weights from the measured signal. An exact reconstruction of the system function is limited by the noise, measuring time, and number of points measured. In this paper procedures for the approximate reconstruction of the system function are introduced. The equivalence of most of them is shown and their properties are discussed. An expression for the limit of resolution is derived for a given signal-to-noise ratio. The results are applicable to experimental data from various physical systems. For illustration the autocorrelation function of the light scattered from polymer solutions and the response of photoconductors are used.

Finite sample power of linear regression autocorrelation tests

We consider autocorrelation tests in the linear regression model which can be expressed as ratios of quadratic forms in the true disturbances. Given a particular such test (as e.g., the Durbin-Watson test and many others), we show that there exist design matrices such that the power of the test drops to zero as autocorrelation among the disturbances increases. We also show how to compute this limiting power for arbitrary design matrices.

Cross correlation functions in protein dynamics and function.

The role of time cross correlation functions induced in liquid water by protein function and dynamics is discussed in the context of recent computer simulations of the gramicidin channel by Swamy and Clementi. On the basis of time autocorrelation functions already computed for this system, such as the orientational and linear velocity auto-correlation functions of the water molecules arranged around the gramicidin channel, it is concluded that cross correlation functions can play a determining role in protein function by controlling the aqueous solvation dynamics at a fundamental, single molecule level. In the manner of Careri, to whom this article is dedicated, this shows how details of molecular dynamics at fundamental level can be used to synthesize macroscopic protein function by using the global approach to computer simulation.

A computer simulation study of the effect of molecular mass distribution on mass and momentum transport in molecular liquids

Molecular dynamics computer simulation has been used to determine diffusion coefficients and viscosities for four thermodynamical ly identical one component model liquids composed of rigid triatomic molecules of the type XY2 at the same temperature and density. Exactly the same intermolecular potential was used throughout. The molecules comprising these liquids all had the same total mass but the molecular mass distributions were different for each liquid. Differences in the viscosities and the diffusion coefficients clearly show that the molecular mass distribution is a factor which in itself influences transport properties, a point seldom considered in the past. The viscosities were determined by nonequilibrium molecular dynamics and a new method is described for implementing isokinetic shear flow in molecular liquid simulations which employ quaternion algorithms. To obtain satisfactory diffusion coefficients for the equilibrium liquids it was necessary to use simulations extending up to 300 ps. The results are particularly relevant to the phenomenon of rotation–translation coupling and, together with the linear and angular velocity autocorrelation functions, are discussed in this context.

Behaviour of ambient temperature on daily basis in Italian climate

The authors analyse the daily ambient temperature time series in five Italian stations for twenty years (1958-1977). It is shown that these time series are well described mathematically as composite series of two periodic components (one in the mean and the other in the standard deviation) and one stochastic component. Furthermore the stochastic component is stationary and follows the first order linear autocorrelation model of dependence. The only significant harmonic of the periodic components is the one relative to the basic period (365 days). Performance of the model is tested by comparing the statistics of generated and experimental data.

A molecular dynamics simulation study of the plastic crystalline phase of sulphur hexafluoride

A molecular dynamics simulation study of the plastic crystalline phase of SF6 is reported. Various equilibrium properties have been measured and, where possible, compared with corresponding experimental measurements. The form of the molecular orientational distribution function has been obtained and is found to be in good agreement with that determined in a recent neutron scattering study. Information concerning the single-molecule dynamics has been obtained from calculations of linear and angular velocity autocorrelation functions, and it has been shown that the SF6 molecules undergo hindered rotation. The existence of coupling between the translational and rotational motions has been demonstrated, and it is shown how the behaviour of the plastic crystal is related to the form of the intermolecular potential. In addition, a transition to a trigonal low-temperature crystal phase at 80K has been observed, and the structure of this phase has been identified and found to be in good agree with experimental results. The calculations have been performed using a large parallel-array processor, and features of the simulation algorithms that reflect the architecture of such a computer are discussed.

Chaos in a continuous stirred tank reactor

A model is derived for a nonisothermal, continuous, stirred tank reactor in which two, exothermic, first order, irreversible, reactions are occuring in parallel. A numerical examination of this model reveals that complex periodic and chaotic oscillations are possible. This behavior is studied using linear stability analysis, autocorrelation analysis, and next-amplitude plots. The next-amplitude plots are found to be fractal curves. An examination of the system trajectories shows that in some circumstances the trajectories follow a Möbius-band attractor in state space.

Représentation statistique des alternances pluie-non pluie à partir des séries pluviographiques Applications à Montpellier-Bel Air (1920-1971) et Paris-Montsouris (1949-1978)

This is an attempt at the statistical portrayal of a succession of showers at a station using the shortest possible time interval. Two long numerised rainfall series are used: Montpellier - Bel Air, provided by the Ministry of Agriculture and Paris Montsouris, supplied by the national meterorological agency. The discrete units used are a thousandth of a day for time and a tenth of a millimeter for water heights. Successive precipitations are given schematically by an alternating series of dry spells (Ds) and rainy spells (Dh); the latter are also characterised by a continuous rainfall height H. The statistical properties of this process are studied separately for each month of the year. The marginal distribution of continuous rainfall heights H is characterised by a high frequency of heights lower than or equal to a threshold Ho (0.4 mm at Montpellier - 0.2 mm in Paris). The frequency distribution of these low heights is well described by an exponential law whose parameter is associated with the frequency of H ≤ Ho. The distribution of values H' higher than the Ho [H' = H - (Ho + 0.05)] is either protrayed by an exponential law after a parabolic transformation of the variable (Montpellier) or by a Weibull law (Paris). The couples (Ds - H) are log-linearly dependent. The value of the correlation coefficient is between 0.6 and 0.8 according to the season. Residual precipitation has a somewhat symmetrical distribution around the regression line, with a constant variance. The frequency distribution of dry spells is bimodal. The first mode corresponds to short dry spells between successive showers, and the second to much longer spells of true good weather. This distribution is described by combining the two lognormal lanes in a proportion p. The successive variables: spells and heights are all but independent. The tests carried out always lead to a slightly higher number of rejections than acceptances of the hypotheses of independence, for parametrical testing using the linear auto-correlation coefficient pl, for non-parametrical testing, distinguishing between two states on either side of a numerical value, and for scrutiny of the average duration of chronological sequences which are lower or higher than a given quantile. However, when comparing the rejections under various tests of each hall' of a series, the same seasons are never systematically found. Independence has thus been accepted, subject to it providing accurate results during simulation tests. Simulation offers no particular difficulty in the conditions stated above. To make a judgement of the results, rainfall heights have been added over 24 consecutive hours to obtain a series similar to a rainfall series in which successive rainy days have been cumulated. The observed and simulated series can then be compared at the level of the first two moments of the variables characterising a daily rainfall model: length in days of dry and rainy spells and the corresponding height of the latter. The comparison can also be made using monthly totals. The first simulation shows reasonably satisfactory results, except for the standard deviations of length of dry spells (overestimated) and heights during rainy spells (under estimated). The first anomaly is easily corrected by setting the maximum value observed as boundary to the dry spells (Ds). This touches on the problem of statistical portrayal of a physically bounded variable by a non-bounded law. The second anomaly is linked to a typology of daily spells : some corresponding to cyclonic disturbances involve only light showers; by contrast, others associated with convective phenomena, involve only heavy showers. It is found that a simulation distinguishing type of spell arbitrarily by drawing only from a small part of the law governing H (but preserving the law governing H over ail the spells) improves the results. The portrayal of a succession of showers at a station remains to be perfected by a typological study of spells and completed by a study of the succession of rain intensity within continuous spells of rainfall.