Dominant Time Scales Research Articles

Time scale of thermally activated diffusion in random systems: A new law of thermal activation.

Exact time scales are obtained for a class of stochastic models of thermally activated diffusion in random systems with a one-dimensional quantum reaction coordinate. The results are valid at any temperature. At low temperatures various forms of the thermal activation law of Arrhenius emerge, the dominant time scale of the diffusion depending on the temperature T according to ${T}^{p}$ exp(A/${k}_{B}$T), where A is the activation energy and p an exponent depending on the details of the models. These correspond to different bounded energy spectra for the randomly selected energy levels along the reaction coordinate. As an example we consider the Wigner semicircular distribution of eigenvalues of large random matrices. Another example considered is a Gaussian distribution of energy levels, and in this case a new thermal-activation law is obtained, having the form exp[${B}^{2}$/(${k}_{B}$T${)}^{2}$], where B is proportional to the width of the distribution. This form has recently been found in Monte Carlo experiments on large Ising-spin-glass models by Young.

Eigenanalysis of recent United States sea levels

Spatial and temporal patterns of recent sea-level rise along the United States coastline have been examined to ascertain rates of rise, and possible causes for high-frequency fluctuations in sea level. Eigenanalysis identified several distinct coastal compartments within each of which sea-level behavior is consistent. The United States east coast has three of these compartments: one north of Cape Cod, where sea-level rise increases with distance to the north; one between Cape Cod and Cape Hatteras where sea-level rise increases to the south; and the third from Cape Hatteras south to Pensacola, where sea-level rise decreases to the south. The western gulf coast represents another compartment (poorly sampled in this study), where subsidence is partly due to compaction. The final compartment is along the United States west coast, where poor spatial sampling produces a highly spatially variable sea-level record that has some temporal uniformity. Spectral analysis shows a dominant time scale of six years for sea-level variability, with different coastal compartments responding relatively in or out of phase. No evidence for increased rates of sea-level rise over the past 10 years was found. This objective statistical technique is a valuable tool for identifying spatial and temporal sea-level trends in the United States. It may later prove useful for identifying elusive world-wide trends of sea level, related to glacial melting, glacial rebound, tectonism, and volcanic activity.

A Suggestion for the Presentation of Correlations and Their Significance Levels

Abstract It is suggested that the results of correlation calculations between concurrent time series be presented in the form of normalized correlations, the normalization factor being the estimated large-lag standard error. This factor is easily estimated from the data using the Bartlett formula and reflects the interplay of the dominant time scales of the input processes and the finite record length. It is shown that significance levels are inherent in the normalized correlations and the procedure used to obtain them is mathematically equivalent to that now widely used in oceanography.

Design of an Oceanographic Network in the Midlatitude North Pacific

Reported here are the statistical results leading to the design of an optimum oceanographic network in the interior midlatitude North Pacific from 30 to 50°N, the primary function of which is to detect the generation and evolution of large-scale temperature anomalies in both the surface and subsurface layers of the upper 50 m of ocean. The method used in this optimum network design is based on linear least-squares estimation developed by Gandin (1963), wherein it is necessary to determine the first and second statistical moments (i.e., mean and covariance distribution, respectively) of the variable field, leading to the estimation of the dominant space and time scales of variability, as well as the signal-to-noise ratio. Having determined this information on the statistical structure of the thermal field in the interior midlatitude North Pacific (i.e., Lx = 1500 km, Ly = 1000 km, T = 10 months, S/N = 0.5), the minimum sampling density (i.e., 1 station per 200 km square per month) and maximum instrument error (a lσ accuracy of 0.2°C) are defined, necessary to detect the large-scale thermal variability. This latter information is then used in the actual construction of an oceanographic network, where since January 1976 XBT systems (having a lσ accuracy of 0.07°C) have been placed aboard 22 ships of opportunity that ply the trade routes between the west coast of North America and Japan. Examples of temperature anomaly maps, constructed monthly from 300 XBT's taken randomly over the region 30–50°N, 140–150°E, are presented. As a check on map reliability, the surface and subsurface temperature maps produced by this XBT network are compared with surface maps constructed by ship-injection temperature and subsurface maps constructed from research vessel XBT data.

Temporal and Spatial Scales of the Wind Field over the North Pacific and North Atlantic

Abstract Quasi-geostrophic wind fields over the northern parts of the Pacific and Atlantic Oceans are calculated from synoptic surface pressure data for the four-year period 1973–76. Maps of mean and rms wind stress and of mean wind stress curl are given. Spectral and cross-spectral analysis reveals the dominant space and time scales of atmospheric disturbances. At periods shorter than 10 days, eastward traveling cyclones dominate the atmospheric variability. At longer time scales the atmospheric spectra are white in frequency and symmetric with respect to wavenumber, and there is no preferred direction of propagation. Differences between the spectra of pressure, wind and wind stress are discussed. To estimate the amount of fluctuations at high wavenumbers which are not present in smoothed synoptic maps, direct wind observations from two weather stations in the North Atlantic are analyzed and compared to synoptic data. It is found that the smoothing is severe for fluctuations with a period shorter than 10...

Laser Studies of Gas Phase Chemical Reaction Dynamics

This perspective is addressed primarily to active reaction dynamicists (i.e. chemical kineticists working on a reactant state to product state level of inquiry) to outline current capabilities of coherent light sources for the detailed study of chemical rate processes, to record past successes, and to identify future areas of important and likely progress. We assert that the following axioms, already well known to time­ independent spectroscopists, also apply to time-dependent measurements of evolving reactant-product systems: (a) any matter-radiation interaction can be studied better with a coherent, rather than an incoherent, light source, and (b) coherent light sources of nearly ultimate (i.e. uncertainty principle limited) frequency and time resolution are currently available or will soon be developed for the entire energy spectrum appropriate to chemical interactions. It is now timely and meaningful for every dynamicist to inquire whether existing experiments can be improved via laser devices and, indeed, whether totally new and highly refined experiments are feasible. We emphasize the state-to-state (i.e. microscopic) approach to chemical reaction dynamics; we wish to scrutinize chemical reactions on a global detailed level (1): at a given total system energy E, many reactant and product channels are open and many transition probabilities [i.e. the rich person's P-matrix (I)J must be con­ sidered. Of practical interest (2) to dynamicists (and others) are questions of energy requirements and energy disposal (1): e.g. (a) what is the optimal reactant internal state which promotes reaction at energy E? and (b) what is the distribution of product internal states for a particular reactant internal state at energy E?; as well as questions of energy redistribution: e.g. (c) are unimolecular reactants ergodic on the time scale of their fragmentation? and (d) what are the dominant collisional relaxation processes and time scales which degrade an initial nonequilibrium distribution? Laser methods aid the dynamicist in many ways: reactants can be selectively excited to particular internal states, product state distributions can be 1 Literature search completed in December 1974. 2 Camille and Henry Drcyfus Foundation Teacher-Scholar, Alfred P. Sloan Foundation Research Fellow. 3 Our own laser studies are supported by the Directorate of Chemical Sciences, US Air Force Office of Scientific Research under Grants AFOSR-73-2423 and AFOSR-74-2666.

On the Development of Blocking Ridge Activity Over the Central North Pacific

Monthly mean atmospheric data taken over the North Pacific during the period 1950–70 are used to investigate blocking ridge activity over the central ocean. The blocking ridge is observed to be a finite-amplitude, quasi-stationary long wave, most often centered over the North Pacific at 170W, superimposed upon the quasi-zonal mid-latitude westerlies. The dominant length scale is 7000 km, the same dimensions as the width of the mid-latitude ocean. The growth time scale is 1–2 weeks, with the duration of blocking activity rarely exceeding 2 months in any given year. The blocking activity is confined almost exclusively to the autumn/winter months, where block development is closely coupled with the sensible heat transfer from the underlying ocean (anomalously small beat transfer under the ridge and anomalously large heat transfer under the associated troughs). Year-to-year variability in blocking ridge activity is found to have a dominant time scale of approximately 5 years from 1950–70 and to be inversely correlated (−0.79) with the strength of the autumn/winter mean mid-latitude westerlies (the mean formed using months not containing blocking activity). Further analysis shows that both blocking ridge activity and the strength of the westerly winds fluctuate together with the Southern Oscillation over this time period. These space/time scale considerations suggest that this regional blocking activity owes its existence to the marine environment. To test this idea, appeal is made to some theoretical work by Haltiner, where the baroclinic instability process was modified by sensible heat transfer from the ocean to the atmosphere. Haltiner found that for normal winter values of the background flow, the otherwise stable stationary long wave became unstable when sensible heat transfer was allowed. The wavelength for the unstable stationary wave was 7000–8000 km with a growth time scale of approximately 2 weeks. The scales are similar to that of blocking ridge activity over the North Pacific. In addition to good scale agreement with observations, Haltiner's theory is able to explain both the seasonal and year-to-year variability in blocking activity in terms of corresponding fluctuations in sensible heat transfer and the strength of the mean westerly winds.