Time scales overview

A variety of techniques have been introduced to increase the time step in molecular dynamics simulations in an attempt to surmount the strict time step limits in MD simulations so that long time scale simulations can be routinely undertaken. One such technique is to solve the equations of motion in the internal degree of freedom, so that bond stretching and angle bending can be treated as rigid. This technique is discussed in Chapter 6 of this book. Herein, a brief overview is presented of two approaches, constrained dynamics and multiple time step dynamics. 

For the quantitative description of the metabolic state of a cell, and likewise which is of particular interest within this review as input for metabolic models, experimental information about the level of metabolites is pivotal. Over the last decades, a variety of experimental methods for metabolite quantification have been developed, each with specific scopes and limits. While some methods aim at an exact quantification of single metabolites, other methods aim to capture relative levels of as many metabolites as possible. However, before providing an overview about the different methods for metabolite measurements, it is essential to recall that the time scales of metabolism are very fast Accordingly, for invasive methods samples have to be taken quickly and metabolism has to be stopped, usually by quick-freezing, for example, in liquid nitrogen. Subsequently, all further processing has to be performed in a way that prevents enzymatic reactions to proceed, either by separating enzymes and metabolites or by suspension in a nonpolar solvent. 

As reported by Romano (1996), surfactant films may be more common than previously assumed. In the Indian Ocean he found such films in 30% of coastal and 11% of open sea water. At wind speeds w10 > 6 m s-1 these films seem to be destroyed by turbulence, but they are able to form again on a time scale of a few hours. Frost and Upstill-Goddard (1999) give an overview of available information on the composition of surfactant films. 

I had the honor to review the field, as described by the title of this chapter. I would like to take this opportunity here to focus on some concepts that were essential in the development of femtochemistry reaction dynamics and control on the femtosecond time scale. The following is not an extensive review, as many books and articles have already been published [1-12] on the subject, but instead is a summary of our own involvement with the development of femtochemistry and the concept of coherence. Most of the original articles are given in a recent two-volume book that overviews the work at Caltech [5], up to 1994. 

The aim of this book is to provide a concise introductory overview of the various light-induced processes in physics, chemistry, biology, as well as, in medicine and industry. It is largely based on the course of photophysics and photochemistry given at the University of Fribourg, and every effort has been made to keep it up to date with the latest developments in this field, in particular the probing of the fastest light-induced reactions on picosecond and femtosecond time scales. 

The paper is organized as follows. Section 1 gives an overview of the physical situations studied, in terns of reaction mechanisms and time scales. The various models developed to deal with such situations are also briefly discussed. Section 2 provides a survey of the theoretical tools used in our calculations. Section 3 is devoted to a discussion of typical excitation processes by ion collisions or laser irradiations. Conclusions arid perspectives are given in section 4. 

Adequate extrapolation of results from standard laboratory toxicity tests to other time scales of exposure and response requires observations on the time course of toxic effects. These observations can then be used to construct time-to-event models, such as the DEBtox model mentioned above. These models explicitly address both intensity and duration of exposure to hazardous chemicals, and better use is made of the data gathered from toxicity experiments. Diverse endpoints in time can be addressed, and individual organism characteristics and/or environmental circumstances (e.g., temperature) can be incorporated as covariables. An overview of time-to-event models and approaches and their use in the risk assessment of chemicals is provided by Crane et al. (2002). 

Time-scale decomposition and model reduction methods for multiply singularly perturbed systems typically involve the nested application of the procedures discussed so far. For the interested reader, an overview of existing research results concerning the dynamic behavior of multiply singularly perturbed systems is presented in Appendix B. 

Different scales presented in Figure 3-1 are related to different approximation levels. For an overview of conventional molecular modelling methods, (see e.g.1-3). Bridging the above mentioned disparate time scales for the description of biologically relevant collective motions requires hierarchical, multi-scale approaches. In practice, to describe real complex (bio)molecular or material systems and processes various models have to be coupled to each other. Selected coupling mechanisms will be briefly reviewed. 

Several recent reviews have presented broad overviews of ultrafast time-resolved spectroscopy [3-6], We shall concentrate instead on a selected, rather small subset of femtosecond time-resolved experiments carried out (and to a very limited extent, proposed) to date. In particular, we shall review experiments in which phase-coherent electronic or, more often, nuclear motion is induced and monitored with time resolution of less than 100 fs. The main reason for selectivity on this basis is the rather ubiquitous appearance of phase-coherent effects (especially vibrational phase coherence) in femtosecond spectroscopy. As will be discussed, nearly any spectroscopy experiment on molecular or condensed-phase systems is likely to involve phase-coherent vibrational motion if the time scale becomes short enough. Since the coherent spectral bandwidth of a femtosecond pulse often exceeds collective or molecular vibrational frequencies, such a pulse may perturb and be perturbed by a medium in a qualitatively different manner than a longer pulse of comparable peak power. The resulting spectroscopic possibilities are of special interest to these reviewers. 

Chemical d5mamics and mechanisms of reactions in the ocean-atmosphere system on time scales equal to and less than that of ocean circulation are evaluated by stud5nng the distribution of chemical compounds within the sea. In order to understand the processes controlling the chemical distributions and their rates, one must know something about how the ocean circulates. The following brief descriptive overview describes the main wind-driven and thermohaline current distributions. 

Fig. 15 An overview of the properties of Cy ( ) (solid lines ) for the same values for and y as in Fig. 14 from [86]. The dotted lines show the leading asymptotes for the corresponding time scales the critical decay ( / o) (a), the von Schweidler law — (t/to) (b), the arrest on the plateau value /(l-A) (c) and the shear-induced linear asymptote -tjlj (d). The dashed line shows a generalization of the latter law evaluated to higher order with a fitted parameter ai (at = 0)...

As the focus of this chapter is on the synthetic utility of the rDA reaction, an overview of mechanism is beyond the scope of this review however, the subject has been reviewed previously. Structural and medium effects on the rate of the rDA reaction are of prime importance to their synthetic utility, and therefore warrant discussion here. A study of steric effects on the rate of cycloreversion was the focus of early work by Bachmann and later by Vaughan. The effect of both diene and dienophile substitution on the rate of the rDA reaction in anthracene cycloadducts has been reported in a study employing 45 different adducts. If both cycloaddition and cycloreversion processes are fast on the time scale of a given experiment, reversibility in the DA reaction is observed. Reversible cycloaddition reactions involving anthracenes, - furans, " fulvenes and cyclopentadienes are known. Herndon has shown that the well-known exception to the endo rule in die DA reaction of furan with maleic anhydride (equation 2) occurs not because exo addition is faster than endo addition (it is not), but because cycloreversion of the endo adduct is about 10 000 times faster than that of the exo adduct. ... 

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