Time-series

The idea of using mathematical modeling for describing materials behavior under loads is well known. Some physical phenomena, which can be observed in materials during testing, have time dependent quantitative characteristics. It gives a possibility to consider them as time series and use well developed models for their analysis [1, 2]. Usually applied... 

Forecasting of time series behavior using lead time data (data obtained during current experiment) for prediction of the material response to the similar actions and loads in future or of testing results for twin material specimens during lead time . 

Figure A3.14.7. Example oscillatory time series for CO + O2 reaction in a flow reactor corresponding to different P-T locations in figure A3,14,6 (a) period-1 (b) period-2 (c) period-4 (d) aperiodic (chaotic) trace (e) period-5 (1) period-3.

The trajectory description problem of chemical reactions is resolved by using phase-space reconstmction from a single time series [8] this method uses delayed data at times t, t+ip t+X2,.. ., for an -dimensional attractor,... 

Figure C3.6.4(a) shows an experimental chaotic attractor reconstmcted from tire Br electrode potential, i.e. tire logaritlim of tire Br ion concentration, in tlie BZ reaction [F7]. Such reconstmction is defined, in principle, for continuous time t. However, in practice, data are recorded as a discrete time series of measurements (A (tj) / = 1,...

Molecular dynamics simulations can produce trajectories (a time series of structural snapshots) which correspond to different statistical ensembles. In the simplest case, when the number of particles N (atoms in the system), the volume V,... 

G. E. P. Box and G. M. Jenkins, Time Series Analysis Forecasting and Control, Holden-Day, San Francisco, Calif., 1970. 

Time series plots give a useful overview of the processes studied. However, in order to compare different simulations to one another or to compare the simulation to experimental results it is necessary to calculate average values and measure fluctuations. The most common average is the root-mean-square (rms) average, which is given by the second moment of the distribution. 

An important property of the time autocorrelation function CaU) is that by taking its Fourier transform, F CA(t) a, one gets a spectral decomposition of all the frequencies that contribute to the motion. For example, consider the motion of a single particle in a hannonic potential (harmonic oscillator). The time series describing the position of the... 

Figure 3 (a) A time series describing the position as a function of time of a particle moving... 

In time series of measurements of air quality and estimates of atmospheric concentration made by a model, residuals d can be computed for each location. The residual d is the difference between values paired timewise. 

Wiener, N. (1949) The Extrapolation, Interpolation and Smoothing of Stationary Time Series, John Wiley, New York. 

Detailed sampling can include, but is not limited to, the installation of monitoring well networks. After the wells have been installed, aquifer tests are typically performed. Once the aquifer tests are performed and the aquifer characteristics are determined, time series sampling for a given contaminant, or a surrogate, is undertaken. The combined results of these efforts provide the basis for development of a treatment strategy. Modeling can be used as part of this effort to help determine the best technical and most cost-effective techniques to be used at a site. 

Katsouyanni, K., Touloumi, G., Spix, C., Schwartz, J., Balducci, F., Medina, S., Rossi, G Woj tyiiiak, B., Sunyep Bacharova, L., Schouten, J. P., Ponka, A., and Anderson, H. R. (1997). Short term effects of ambient sulphur dioxide and particulate matter on mortality in 12 Eiiiopean cities Results from time series data from the APHEA project. Brit. Med. J. 314, 1658-1663. 

Algorithm A method of calculation that produces a control output by operating on an error signal or a time series of error signals. 

Walls, L. A. and A. Bendell. Time Series Methods in Reliability. Proceedings of the 9th Advances in Reliability Technology Symposium. Bradford, C2/3, 1986, pp. 1-18. 

One of the most common ways of characterizing complexity is by taking Fourier transforms. The spatial power spectrum of a time series of [Pg.394]

Among its many useful features is the ability to simulate both discrete and continuous CA, run in autorandoinize and screensaver modes, display ID CAs as color spacetime diagrams or as changing graphs, display 2D CAs either as flat color displays or as 3D surfaces in a virtual reality interface, file I/O, interactive seeding, a graph-view mode in which the user can select a sample point in a 1-D CA and track the point as a time-series, and automated evolution of CA behaviors. 

Nonlinear Dynamics and Topological Time Series Analysis Archive http //t13.lanl.gov/ nxt/intro.html... 

N. Wiener, Cybernetics, The Technology Press and John Wiley A Sons, Inc., New York, 1948 Extrapolation, Interpolation, and Smoothing of Stationary Time Series, The Technology Press and John Wiley A Sons, Inc., New York, 1948. 

Karl, D. M. and Michaels, A. F. (eds) (1996). Ocean Time-Series Results from the Hawaii and Bermuda Research Programs. Deep-Sea Res. II43,127-685. 

Zinsmeister, A. R. and Redman, T. C. (1980). A time series analysis of aerosol composition measurements, Atmos. Environ. 14,201-215. 

Much of the variation in these time series for the past 700 kyr can be described by a combination of a 100 kyr cycle plus additional cycles with periods of 20 and 40 kyr. This result immediately suggests that the ice-age cycles are caused by variations in the amount and seasonality of solar radiation reaching the Earth (insolation), because the 20, 40, and 100 kyr periods of climate history match the periods of cyclic variations in Earth s orbit and axial tilt, line hypothesis that these factors control climate was proposed by Milutin Milankovitch in the early part of the 20th century and is widely known as "Milankovitch Theory." It is now generally accepted that the Milankovitch variations are the root cause of the important 20 and 40 kyr climate cycles. The 100 kyr cycle, however, proves to be a puzzle. The magnitude of the insolation variation at this periodicity is relatively trivial, but the 100 kyr cycle dominates the climate history of the last 700 kyr. Further,... 

Fig. 2 Time-series of annual mean water temperature in the San Reservoir (Spain) and air temperature in the Ter River watershed. The series start in 1964, after the first filling of the reservoir. Annual means are based on monthly measures of the volume weighted mean temperature. Only years with at least 10 temperature profiles were included in the figure. The air temperatures are annual means for the whole Ter River watershed, calculated from data collected in several meteorological stations in the basin, and weighted according to their area of influence...

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