Intrinsic time-scale

To separate the non-bonded forces into near, medium, and far zones, pair distance separations are used for the van der Waals forces, and box separations are used for the electrostatic forces in the Fast Multipole Method,[24] since the box separation is a more convenient breakup in the Fast Multipole Method (FMM). Using these subdivisions of the force, the propagator can be factorized according to the different intrinsic time scales of the various components of the force. This approach can be used for other complex systems involving long range forces. 

In addition to the intrinsic time scales of the system xf, xs, and xelec, one... 

FIG. 3 Cation surface species on the basal planes of 2 1 layer type clay minerals. Inset indicates the spectroscopic methods used to quantify counterion surface species, their intrinsic time scales over which molecular structure is probed, and the residence time of surface species. 

One aspect of Mossbauer spectroscopy that has not been widely exploited in phase transformation studies is time resolution. Studies with conventional techniques are possible over a wide range of time scales, starting from the intrinsic time scale of the Te Mossbauer effect (t <= 10 s) to investigate processes such as electron transfer, to time scales of t 10 s to measure diffusion, to longer timescales of t > 10 s to study phase transitions, oxidation and other chemical reactions. 

A key characteristic of microscopic instabilities is their time scale. Other important intrinsic time scales that need to be determined when analyzing a... 

Most of the research on CR was focused on the case of white noise. White noise is a good approximation as long a.s the intrinsic time scale.s of the deterministic system are much larger than the correlation time of the external fiuctnatioiis. This is the case for example in neuronal dynamics where a neuron can be exteniallj forced by another randomly bursting neuron. In general, when deterministic and stochastic time scales are not well separated from each other, not only the amplitude but also the temporal correlation is expected to influence iioise-induced phenomena as CR. In... 

If the kinetic matrix is constant, eq. (12.127) can be solved either analytically by using the Sylvester theorem of the Laplace transformation, or numerically. Finally, the relation between the intrinsic time scale and the laboratory time scale t can be determined from t = u ( )] A constant kinetic matrix is sufficient for... 

On the other hand the isomer shift in a Mossbauer experiment on an intermediate-valent system is considered to be slow relative to the intrinsic time scale of the valence fluctuations. The hyperfine interaction of the nucleus with mainly the 5s character electronic charge at the nucleus is an electric monopole interaction (only s electrons can interact with the nucleus, but the 5s electrons being outside the 4f shell are quite sensitive to the occupation of the 4f shell because of different screening of the nuclear... 

Lion A, Kardelky C (2004) The Payne effect in finite viscoelasticity constitutive modelling based on Iractional derivatives and intrinsic time scales. Int J Plast 20 1313-1345... 

Intrinsic time scale vs. strain at fixed frequency... 

The fractional exponent a gives a nonlinear variation of the intrinsic time scale with frequency (at constant strain). 

---