Energy time series

Figure 3.2.4 shows the calculated results of the time series of temperafure distribution with the total spark energy of 0.7mj and the ratio of capacity spark of 100%. The hot kernel is initially an ellipsoid and the maximum temperature region is located in the center of the spark gap. Afterwards, the hot kernel develops into a torus and the highest temperature region moves into the ring... 

Calculated time series of temperature distribution. Spark energy O.ZOmJ spark gap width 1.0mm spark electrode diameter 0.50mm ratio of capacity spark energy 100%. Left time = 1 ps, central time = 10 ps, right time = 100 ps. 

From the wavelet coefficients Ttl,[x](a, b) one can calculate the energy density Ethree-dimensional surface E(l,[x](a, t). Sections of this surface at fixed time moments t = b define the local energy spectrum Ev[x](f, t) with / = a 1. Finally, in order to obtain the mean spectral distribution of the time series x t) we may consider a so-called scalogram, i.e., the time-averaged energy spectrum. This is analogous to the classic Fourier spectrum. 

As soon as a decision has been made on the type of renewable energy technology to be introduced in the overall system, the third step is to find data on the natural resource (wind speed data, solar irradiance data, biomass data, etc.). Meteorological data recorded onsite is the first priority, but if such a solution is not possible, the designer should use time series of meteorological data, which can be drawn from various databases such as NASA (2005) and the National Observatory of Athens (2007). 

Fig. 4.2. Time series of potential energy of the C-peptide system from the multi-canonical MD production run (a) and the average potential energy as a function of temperature (b). The latter was obtained from the trajectory of the multicanonical MD production run by the single-histogram reweighting techniques...

Fig. 4.4. Time series of potential energy E from (a) the conventional isobaric-isothermal MD simulation at To = 240 K and Vo = 0.1 MPa (b) the conventional isobaric-isothermal MD simulation at To = 298 K and Vo = 0.1 MPa (c) the conventional isobaric-isothermal MD simulation at To = 298 K and Vo = 300 MPa and (d) the multibaric-multithermal MD simulation...

Liquids and proteins are complex systems for which the smdy of dynamical systems has wide applicability. In the conference, relaxation in liquids (s-entropy by Douglas at the National Institute of Standards and Technology, nonlinear optics by Saito, and energy bottlenecks by Shudo and Saito), energy redistribution in proteins (Leitner and Straub et al.), structural changes in proteins (Kidera at Yokohama City University), and a new formulation of the Nose-Hoover chain (Ezra at Cornell University) were discussed. Kidera s talk discussed time series analyses in molecular dynamics, and it is closely related to the problem of data mining. In the second part of the volume, we collect the contributions by Leitner and by Straub s group, and the one by Shudo and Saito in the third part. 

P. Bienfang, J. Szyper and others Biogeochemistry time-series at two Hawaii Ocean Thermal Energy Conversion (OTEC) program sites (20°N, 156°W and 21°N, 158°W)... 

Fig. 4.8. A time series plot of the numerically estimated total potential energy Et of the spring-block system for...

Fig. 7. Calculated time series for an isothermal coverage-dependent activation energy model showing both sinusoidal (left) and relaxation (right) behaviors. (From Ref. 285.)...

Figure 17 Time series of AOT (top) and Angstrom exponent (bottom) at the Department of Energy Atmospheric Radiation Measurement site in North Central Oklahoma over the period 1993-1999. Measurements are by sun-photometry. The points represent daily averages the curves are smooth fits of the data to guide the eye (Michalsky et aL, 2001) (reproduced by permission of American Geophysical Union from /. Geophys. Res. 2001,106, 12099-12107).

Figure 4. The time series of at three typical energy regions. (a) — 15.505e (solid-like phase), (h) -13.505e (coexistence region), and (c) —11.505e (liquid-like phase). (Reproduced from Ref. 19 with permission.)...

Figure 11. Time series of the short-time average of the total kinetic energy, (a) Ar7, (b) Ar, and (c) Arn, due to Beck at al. (Reproduced from Ref. 34 with permission.)...

In the following sections, we present our recent studies on multibasin protein folding dynamics on minimalistic protein landscapes. Here, we focus on the question of how the time series of scalar quantities can shed light on the underlying configurational energy landscapes and geometry of the state space [41]. 

Figure 6 shows the so-called Allan variance [61-63] of time series of the potential energies V(t) for these models at several temperatures. The Allan variance c> (N) is defined by... 

The Allan variance analyses of energy fluctuations can tell us about the nature of the configurational energy landscapes and the existence of (multidimensional) cooperativity among individual DOFs, enhanced for an intermediate time scale at the transition temperature. However, what can we learn or deduce from an (observed) scalar time series about the geometrical aspects of the underlying multidimensional state (or phase) space buried in the observations The so-called embedding theorems attributed to Whitney [75] and Takens [76] provide us with a clue to the answer of such a question (see also Section VI.A and Refs. 77-80). 

---