Function Of Time Lag Research Articles

Efficient solution of non-Markovian covariance evolution equations in fluid turbulence

A method is described for efficient treatment of the time-history effects that arise in closure models constructed by truncation of renormalized perturbation expansions. The scheme is based on rational polynomial (Pade) approximations for the time-lagged functions, combined with Gaussian quadrature applied to a coarse-time evolution equation for equal-time covariances. Power series coefficients required for the Pade approximants are generated by recursion relations resulting from successive differentiation of the slow-varying form of the dynamic equations for time-lagged functions. This strategy is illustrated by applications to equations of the direct interaction approximation for fluid turbulence. Several benefits accrue from such an approach. Computational efficiency comparable to that of Markovian closures is obtained without introduction of arbitrary constants orad hoc Markovianization assumptions: (1) Scaling of the leading operations count is reduced fromO(n T 3 ) toO(n g n t ), wheren T is the number of steps in coarse time, and ng≈ 4–8. For typical problems in fluid turbulence, this results in savings of afactor∼40 in computing time. (2) Scaling of working array size is reduced fromO(n T 2 ) toO(p), wherep is the order of Pade approximant; this reduces in-core storage requirements for dynamical quantities by afactor ∼20. These and other advantages depend on the order of Pade approximant required to give acceptable accuracy. Test cases from several problems in fluid turbulence indicate very substantial savings, such that certain CPU-intensive problems with spatial inhomogeneities become computationally feasible.

Income Inequality, Regime Repressiveness, and Political Violence

Death rate from political violence is postulated to vary cross-nationally as a positively accelerated time-lagged function of income inequality and as a nonmonotonic inverted U function of regime repressiveness. The former hypothesis is consistent with approaches to the explanation of collective political violence that emphasize the general concept of discontent or, more specifically, relative deprivation; the latter hypothesis is consistent with a political-process version of the resource mobilization approach. In the context of a multivariate model estimated across two decades, 1958-67 and 1968-77, support is found for the inequality hypothesis. Support also is foundfor the regime repressiveness hypothesis in the decade (1968-77) for which the index of regime repressiveness is available. The U-curve effect of regime repressiveness appears to have stronger impact on variation in rates of deadly political violence than the positively accelerated effect of income inequality.

Some Correlations between the Large-Scale Meridional Eddy Momentum Transport and Zonal Mean Quantities

Abstract An empirical study has been made which compares the large-scale meridional eddy momentum transport with some selected zonal mean quantities by calculating correlations between them as a function of time lag and latitude. The basic dataset was the daily 200 mb geopotential and temperature grid analysis fields of the German Weather Service over an eight-year period. The results gave generally only small correlation values but show that a meridional covergence of the eddy transport leads to an increasing zonal mean wind or meridional curvature of the zonal wind component. The correlation maxima are reached at a time lag of +2 days. The same tendency can be recognized from an examination of the relation which Green found between the convergence of momentum transport and the transport of sensible heat and potential vorticity. An introductory discussion of two-dimensional models is given which focuses on the methods of parameterizing the eddy transports.

Statistical Properties of the Atmospheric Pressure Field Over the Arctic Ocean

Many useful statistical properties can be derived for isotropic, stationary, homogeneous, Gaussian random fields. The field of surface pressure in the region north of 70°N is shown to approximately satisfy these conditions. Under these conditions, all properties of the field are related to the autocovariance, which is a function of time and space lag. In particular, the following quantities are derived: the time and space covariance functions for the geostrophic wind; the covariance functions for the vorticity of the geostrophic wind; the average number of highs, lows and saddles per unit area; the average number of highs, lows and saddles at which the vorticity exceeds a specified threshold; and the probability density function for the Gaussian curvature of the pressure surface. The horizontal shear in the geostrophic wind is also investigated, as is the number of umbilic points per unit area. Estimates for all these quantities are constructed using observations of surface pressure from the Arctic Basin during 1979 and 1980. The comparison between theory and observation is favorable. At least when these several quantities are considered, the isotropic, stationary, homogeneous, Gaussian random process is a good model of the actual pressure field.

Effect of immobilizing adsorption on mass transport through polymer films

The Freundlich isotherm used in place of the Langmuir isotherm to describe the adsorption mode in the dual sorption theory of glassy polymer—gas systems. Time-lag expressions have been derived and compared with the available corresponding results for the Langmuir case. In the case of large and moderate values of the upstream boundary activity a 0, the value of the time-lag function L a )(l) calculated with the proposed model is close to that calculated by Paul for the Langmuir isotherm. In the case of small values of a 0, the L a (l) values predicted by Paul and the proposed model are different and the difference increases when the value of a 0 decreases. The ability of the present model to represent systems exhibiting positive deviations from Henry's law is also described.

Simple stochastic models for the sources and sinks of two aerosol types

The statistical properties of two time-dependent and steady-state aerosol concentration distributions are derived from simple stochastic models of the particle sources and sinks. The analysis is applied to statistics of area averaged aerosol concentrations in two examples: (a) anthropogenic sulfate particles, for which the source is assumed constant in time, and removal is by precipitation at random times, and (b) windblown dust) for which we assume the sources are a constant background plus randomly occurring dust storms, and the sinks are time independent advection and dry deposition. The models are solved both analytically and by numerical simulation. For both models the time-lagged autocorrelation function of the pollutant is a simple exponential, and the ratio of the steady-state variance to the squared mean concentration varies inversely with the effective lifetime. Application of data from the World Meteorological Organization to model (a) shows that the expected lifetimes for sulfates are between SO and 175 h, and the deposition distances are between 800 and 2000 km. DOI: 10.1111/j.2153-3490.1979.tb00880.x

Measurement of rain parameters by optical scintillation

We describe a technique for measuring path-averaged rain parameters by analyzing the rainfall-induced scintillations of a laser beam. From the time-lagged covariance function of two vertically spaced line detectors, we determine the average rainfall rate and drop-size distribution along the optical path. This technique requires no prior assumption of the form of the drop-size distribution. Sample measurements on a 140-m path confirm that the path-averaged drop-size distribution of a steady rain follows a Marshall-Palmer distribution. The optically measured path-averaged rain rate also shows good agreement with conventional tipping-bucket rain-gauge data.

Time lag of ion exchange in the gel layer of hydrogenion-selective glass electrodes

The loose external part of the gel layer of a hydrogen-ion-selective glass electrode acts as a cation exchanger with fixed anion sites. In the last period of a complete ion exchange the rate of the process is governed by the ion present in deficit in the exchanger. Estimates of self-diffusion coefficient ratios for interdiffusing ions have been made by using the result obtained from e.m.f. measurements and by applying the time lag function. The e.m.f. measurements were performed during the apparently complete ion-exchange process in the gel layer of the glass electrode.

Time lag of ion exchange in the gel layer of hydrogen-ion-selective glass electrodes

Summary The loose external part of the gel layer of a hydrogen-ion-selective glass electrode acts as a cation exchanger with fixed anion sites. In the last period of a complete ion exchange the rate of the process is governed by the ion present in deficit in the exchanger. Estimates of self-diffusion coefficient ratios for interdiffusing ions have been made by using the result obtained from e.m.f. measurements and by applying the time lag function. The e.m.f. measurements were performed during the apparently complete ion-exchange process in the gel layer of the glass electrode.

Weak scattering in random media, with applications to remote probing

A simple phase-screen technique has been used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical, or beamed) propagating through a random medium. The method is essentially physical rather than mathematical; its application is limited only by the weak-scattering approximation, a limitation which is important only for long optical or acoustical paths. No other wavelength restriction is imposed. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, anisotropic or lossy media, and polarization effects. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving phase and amplitude fluctuations, angle-of-arrival covariances, frequency covariance, and other higher order quantities.

Time-Lag Analysis of the Townsend Discharge in Argon with Activated Caesium Electrodes

A study of the time-lag in a photoelectric, gas amplified discharge for parallel electrodes as a function of gas pressure, plate separation, and amplification has demonstrated that diffusion of metastable argon atoms is the source of the lag and that these atoms striking the activated caesium cathode are highly efficient in liberating secondary electrons. The Townsend ionization coefficients, $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$, have been determined in the usual manner over an extended range of values of $\frac{E}{{p}_{0}}$. Analysis of the time-lag function has made possible the separation of the number of secondary electrons released at the cathode into those due to positive ions and those produced by metastable argon atoms. A factor representing the fraction of electron energy gained in the field which is used to excite atoms to the metastable level has been determined as a function of $\frac{E}{{p}_{0}}$. The coefficient of diffusion of metastable argon atoms in argon has been computed and shown to be that expected for a metastable atom having a diameter effectively 1.74 that of the normal atom.