Movement time scale

Sediment model Water movement time scale K 10.0... 

Molecular dynamics simulations ([McCammon and Harvey 1987]) propagate an atomistic system by iteratively solving Newton s equation of motion for each atomic particle. Due to computational constraints, simulations can only be extended to a typical time scale of 1 ns currently, and conformational transitions such as protein domains movements are unlikely to be observed. 

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

While these calculations provide information about the ultimate equilibrium conditions, redox reactions are often slow on human time scales, and sometimes even on geological time scales. Furthermore, the reactions in natural systems are complex and may be catalyzed or inhibited by the solids or trace constituents present. There is a dearth of information on the kinetics of redox reactions in such systems, but it is clear that many chemical species commonly found in environmental samples would not be present if equilibrium were attained. Furthermore, the conditions at equilibrium depend on the concentration of other species in the system, many of which are difficult or impossible to determine analytically. Morgan and Stone (1985) reviewed the kinetics of many environmentally important reactions and pointed out that determination of whether an equilibrium model is appropriate in a given situation depends on the relative time constants of the chemical reactions of interest and the physical processes governing the movement of material through the system. This point is discussed in some detail in Section 15.3.8. In the absence of detailed information with which to evaluate these time constants, chemical analysis for metals in each of their oxidation states, rather than equilibrium calculations, must be conducted to evaluate the current state of a system and the biological or geochemical importance of the metals it contains. 

Turner SP, George RMM, Evans PJ, Hawkesworth CJ, Zelhner GF (2000b) Time-scales of magma formation, ascent and storage beneath subdnction-zone volcanoes. Phil Trans R Soc 358 1443-1464 Turner SP, Evans P, Hawkesworth CJ (2001) Ultrafast source-to-snrface movement of melt at island arcs from Ra- °Th systematics. Science 292 1363-1366... 

Perhaps the most Important effect of conformational variations In electron transfer reactions would be to alter the distances and the relative orientations of donors and acceptors. In photosynthetic RC s, where the primary donors and acceptors lie within 4-5A of each other ( ), small structural displacements (, 5A) may significantly affect rates of back reactions. If they occur rapidly (24), (Conformational movements on a picosecond time scale are not Inconsistent with resonance Raman data on photo-dlssoclated heme-CO complexes (25)), On a longer time scale, protein rearrangements triggered by and propagating from the chromophores may also help subsequent reactions such as the transport of protons that Is Initiated by the primary photochemical event In the R,C, (26),... 

Since the water movement will be very slow compared with the rate at which the wastes dissolve, we are concerned first and foremost with equilibrium solubility. Also, if only to relate behaviour on the geological time scale to that on the laboratory time scale, we will need to know about the mechanisms and kinetics of dissolution and leaching. The waste forms envisaged at present are glass blocks containing separated fission products and residual actinides fused into the glass and, alternatively, the uranium dioxide matrix of the used fuel containing unseparated fission products and plutonium. In the... 

The values of /labs were determined from the experimentally measured absorption anisotropy with Eq. 6. In viscous polyTHF, the rotational movement of dye molecules on a lOOps time scale is assumed to be negligible, and thus, does not reduce the limiting value of anisotropy. For the concentrated fluorene solutions (5 x 10 M, 1 mm cuvette), the anisotropy Tabs was not affected by FOrster depolarization mechanisms [13] due to the short time delay, tD, between probe and pump pulses when td/ti 1 [35]. 

Mechanical properties of PNCs can also be estimated by using computer modeling and simulation methods at a wide range of length and time scales. Seamless movement from one scale to another, for example, from the molecular scale (e.g., MD) and microscale (e.g., Halphin-Tsai) to macroscale (e.g., finite element method, FEM), and the combination of scales (or the so-called multiscale methods) is the most important prerequisite for the efficient transfer and extrapolation of calculated parameters, properties, and numerical information across length scales. 

Another technique, single particle tracking, allows one to follow the movement of a single lipid molecule in the plasma membrane on a much shorter time scale. Results from these studies confirm the rapid lateral diffusion within small, discrete regions of the cell sur-... 

There are a number of alternatives and variations to the reduced mechanism method. The intrinsic low dimensional manifold (ILDM) approach [253] and similar methods [399] seek to decouple the fastest time scales in the chemistry. There is a wide range of time scales for chemical reactions in most high-temperature processes, from 10-9 second to seconds. Fast reactions, or reactions with small time scales, quickly bring composition points down to attracting manifolds in the composition space. Then composition points move along on manifolds. In the ILDM approach it is assumed that any movement of the... 

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