Time scale, effective

M.F. Horstemeyer et al Length scale and time scale effects on the plastic flow of fee metals. Acta Mateialia 49, 4363 1-374 (2001)... 

Electronic structure calculations of the type described above, provide the energy and related properties of the system at the absolute zero of temperature and do not account for any time-dependent effect. In some cases, temperature and/or time scale effects may be important and must be included. The appropriate theoretical approach is then molecular dynamics (MD) either in the classical or ab initio implementations. In the first approach, Newton s motion equations are solved in the field of a potential provided externally, which constitutes the main limitation of this approach. To overcome this problem, ab initio Molecular Dynamics (AIMD)94,95 solves Newton s motion equations using the ab initio potential energy surface or propagating nuclei and electrons simultaneously as in the Car-Parrinello simulation.96 The use of AIMD simulations will increase considerably in the future. In a way they furnish all the information as in classical MD, but there are no assumptions in the way the system interacts since the potential energy surface is obtained in a rather crude manner. 

Multiple regulation, see Model based on two instability mechanisms Multiple time scales effect on birhythmicity, 108 effect on bursting, 146 effect on oscillations, 66-8,73 see also Quasi-steady-state hypothesis Muscle, glycolytic oscillations, 37,344 Mutants of circadian rhythm, see frq gene per gene tim... 

The most accurate method of calculating the dynamical behaviour of surfactants is to integrate the equations of motion of all of the atoms in the system. It is obvious that the molecular dynamics calculations described in this chapter give only a rough estimate of the real situation. Such MD techniques require computer processor speeds and memory capacities that currently limit their applicability to a few nanoseconds of molecular motion. This is inadequate for many chemical processes of surfactants which occur on the microsecond (or longer) time-scales. Effects which are dependent on molecular diffusion cannot be investigated due to the... 

For PPY, in general when the anion is small and then mobile, the anion transfer will be dominant, and when the anion is very large (immobile), the cation transfer will be dominant on the time scale of most electrochemical measurements. When PPY is exposed to aqueous tosylate solutions, the authors explored the time scale effects on the competing ion transfers closely associated with solvent transfer. By using the scheme of cubes approach, they showed that on short time scales during reduction, cation entry competes effectively with anion ejection as a means of satisfying film electroneutrality. On longer time scales, the thermodynamically favoured anion mechanism prevails. ... 

In many cases faults will only restrict fluid flow, or they may be open i.e. non-sealing. Despite considerable efforts to predict the probability of fault sealing potential, a reliable method to do so has not yet emerged. Fault seal modelling is further complicated by the fact that some faults may leak fluids or pressures at a very small rate, thus effectively acting as seal on a production time scale of only a couple of years. As a result, the simulation of reservoir behaviour in densely faulted fields is difficult and predictions should be regarded as crude approximations only. 

The existence of the polyad number as a bottleneck to energy flow on short time scales is potentially important for efforts to control molecnlar reactivity rising advanced laser techniqnes, discussed below in section Al.2.20. Efforts at control seek to intervene in the molecnlar dynamics to prevent the effects of widespread vibrational energy flow, the presence of which is one of the key assumptions of Rice-Ramsperger-Kassel-Marcns (RRKM) and other theories of reaction dynamics [6]. 

General first-order kinetics also play an important role for the so-called local eigenvalue analysis of more complicated reaction mechanisms, which are usually described by nonlinear systems of differential equations. Linearization leads to effective general first-order kinetics whose analysis reveals infomiation on the time scales of chemical reactions, species in steady states (quasi-stationarity), or partial equilibria (quasi-equilibrium) [M, and ]. 

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Wliile the earliest TR-CIDNP work focused on radical pairs, biradicals soon became a focus of study. Biradicals are of interest because the exchange interaction between the unpaired electrons is present tliroiighoiit the biradical lifetime and, consequently, the spin physics and chemical reactivity of biradicals are markedly different from radical pairs. Work by Morozova et al [28] on polymethylene biradicals is a fiirther example of how this method can be used to separate net and multiplet effects based on time scale [28]. Figure Bl.16.11 shows how the cyclic precursor, 2,12-dihydroxy-2,12-dimethylcyclododecanone, cleaves upon 308 mn irradiation to fonn an acyl-ketyl biradical, which will be referred to as the primary biradical since it is fonned directly from the cyclic precursor. The acyl-ketyl primary biradical decarbonylates rapidly k Q > 5 x... 

Pump-probe absorption experiments on the femtosecond time scale generally fall into two effective types, depending on the duration and spectral width of the pump pulse. If tlie pump spectrum is significantly narrower in width than the electronic absorption line shape, transient hole-burning spectroscopy [101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112 and 113] can be perfomied. The second type of experiment, dynamic absorption spectroscopy [57, 114. 115. 116. 117. 118. 119. 120. 121 and 122], can be perfomied if the pump and probe pulses are short compared to tlie period of the vibrational modes that are coupled to the electronic transition. 

With M = He, experimeuts were carried out between 255 K aud 273 K with a few millibar NO2 at total pressures between 300 mbar aud 200 bar. Temperature jumps on the order of 1 K were effected by pulsed irradiation (< 1 pS) with a CO2 laser at 9.2- 9.6pm aud with SiF or perfluorocyclobutaue as primary IR absorbers (< 1 mbar). Under these conditions, the dissociation of N2O4 occurs within the irradiated volume on a time scale of a few hundred microseconds. NO2 aud N2O4 were monitored simultaneously by recording the time-dependent UV absorption signal at 420 run aud 253 run, respectively. The recombination rate constant can be obtained from the effective first-order relaxation time, A derivation analogous to (equation (B2.5.9). equation (B2.5.10). equation (B2.5.11) and equation (B2.5.12)) yield... 

One limitation of clique detection is that it needs to be run repeatedly with differei reference conformations and the run-time scales with the number of conformations pt molecule. The maximum likelihood method [Bamum et al. 1996] eliminates the need for reference conformation, effectively enabling every conformation of every molecule to a< as the reference. Despite this, the algorithm scales linearly with the number of conformatior per molecule, so enabling a larger number of conformations (up to a few hundred) to b handled. In addition, the method scores each of the possible pharmacophores based upo the extent to which it fits the set of input molecules and an estimate of its rarity. It is nc required that every molecule has to be able to match every feature for the pharmacophor to be considered. 

When the friction coefficient is set to zero, HyperChem performs regular molecular dynamics, and one should use a time step that is appropriate for a molecular dynamics run. With larger values of the friction coefficient, larger time steps can be used. This is because the solution to the Langevin equation in effect separates the motions of the atoms into two time scales the short-time (fast) motions, like bond stretches, which are approximated, and longtime (slow) motions, such as torsional motions, which are accurately evaluated. As one increases the friction coefficient, the short-time motions become more approximate, and thus it is less important to have a small timestep. 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

Replotting the data on a lorgarithmic time scale as shown in Fig. 4.8b has an interesting effect. Figure 4.8b shows that this modification produces a far more uniform set of S curves. As a matter of fact, if the various curves are shifted along the horizontal axis, they may be superimposed over a wide portion of the transformation. The arrows in Fig. 4.8b show this displacement of the data at 126 and 130°C to correspond to the data at 128°C. This superpositioning is examined in the example below. 

From the lengths of the arrows drawn in Fig. 4.8b, estimate the change in time scale which will produce the same effect on the rate of crystallization as changing the temperature from 130 to 128°C. Do the same for a temperature change from 126 to 128°C. 

The significance of these numbers is seen as follows.The average values of A log t are to be added to the log t values at 126 or 130°C to superimpose the latter curves on the one measured at 128°C. Since these values are added to log t values, the effect is equivalent to multiplying the individual t values at 126 and 130°C by the appropriate antilogs to change the time scale in the individual runs to a common time scale. Using the case of 6 = 0.5 as an illustration, we see the following times are required to reach this level of crystallinity ... 

For T > Tq, ay < 1, which corresponds to log a < 0. These values are used when the curves are shifted to the right. The effect on the mechanical properties is equivalent to expanding the time scale, since we express time as t/ay. 

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