Dynamics long-time

Long time dynamic load involves behaviors such as creep, fatigue, and impact. T vo of the most important types of long-term material behavior are more specifically viscoelastic creep and stress relaxation. Whereas stress-strain behavior usually occurs in less than one or two hours, creep and stress relaxation may continue over the entire life of the structure such as 100,000 hours or more. 

Elber, R. Ghosh, A. Cardenas, A., Long time dynamics of complex systems, Acc. Chem. Res. 2002, 35, 396-403... 

Rostov, K.S. Freed, K.F., Mode coupling theory for calculating the memory functions of flexible chain molecules influence on the long time dynamics of oligoglycines, J. Chem. Phys. 1997,106, 771-783... 

G. Gerber At moderate laser intensities we do see in femtosecond pump-probe experiments a very similar slow time and long time dynamics in all cluster sizes n > 5 up to n = 50 (largest size investigated up to now) irrespective of the charge state of the particular Hg cluster. From single-pulse TOF mass spectrometry we infer that the... 

A. Proper Marriage Between the Short- and the Long-Time Dynamics... 

The situation is far more complex for reactions in high viscous liquids. The frequency-dependent friction, (z) [in the case of Fourier frequency-dependent friction C(cu)], is clearly bimodal in nature. The high-frequency response describes the short time, primarily binary dynamics, while the low-frequency part comes from the collective that is, the long-time dynamics. There are some activated reactions, where the barrier is very sharp (i.e., the barrier frequency co is > 100 cm-1). In these reactions, the dynamics is governed only through the ultrafast component of the total solvent response and the reaction rate is completely decoupled from the solvent viscosity. This gives rise to the well-known TST result. On the other hand, soft barriers... 

As discussed in Section IX, there are several approximate schemes to stitch together the short- and long-time dynamic behavior. While the initial decay is determined by the short-time expansion, the long-time decay is determined... 

The mode coupling theory of molecular liquids could be a rich area of research because there are a large number of experimental results that are still unexplained. For example, there is still no fully self-consistent theory of orientational relaxation in dense dipolar liquids. Preliminary work in this area indicated that the long-time dynamics of the orientational time correlation functions can show highly non-exponential dynamics as a result of strong in-termolecular correlations [189, 190]. The formulation of this problem, however, poses formidable difficulties. First, we need to derive an expression for the wavevector-dependent orientational correlation functions C >m(k, t), which are defined as... 

The development of reliable density functionals coupled to effective discrete/continuum solvent methods and suitable dynamical approaches is allowing researchers to achieve an accuracy comparable with experimental measurements for phenomena dominated by short time dynamics. The situation is different for long time dynamical effects, such as... 

Chang X-Y, Freed KF (1993) Test of theory for long time dynamics of floppy molecules in solution using Brownian dynamics simulation of octane. J Chem Phys 99(10) 8016—8030 Chompff A J, Duiser JA (1966) Viscoelasticity of networks consisting of crosslinked or entangled macromolecules. I Normal modes and mechanical spectra. J Chem Phys 45(5) 1505-1514... 

Guenza M, Freed KF (1996) Extended rotational isomeric model for describing the long time dynamics of polymers. J Chem Phys 105(9) 3823-3837 Hansen JP, McDonald JR (1986) Theory of simple liquids, 2nd edn. Academic Press, London... 

Shen M, Freed KF (2002) Long time dynamics of met-enkephalin comparison of explicit and implicit solvent models, Biophys J, 82 1791-1808... 

There are models for water in the literature which aim at building up an effective Hamiltonian from a description of structure V. These models must give the same results for long-time dynamics as those that will emerge straightforwardly from our statistical model, based on H-bond dynamics. This must be expected in the temperature range at which the structural features of the H-bond network are dominant, lliese literature models are limited to descaibing the short-time dynamics and some thermodynamic properties of water. 

W. E, W. Ren, and E. Vanden-Eijnden (2005) Finite Temperature String Method for the Study of Rare Events. J. Phys. Chem. B, 109, pp. 6688-6693 R. Fiber, A. Ghosh, A. Cardenas, and H. Stern (2004) Bridging the gap between reaction pathways, long time dynamics and calculation of rates. Adv. Chem. Phys., 126, pp. 93-129... 

R. Elber, A. Ghosh, and A. Cardenas (2002) Long time dynamics of complex systems. Account of Chemical Research 35, p. 396... 

R. Elber, A. Ghosh, A. Cardenas, and H. Stern (2003) Bridging the gap between reaction pathways, long time dynamics and calculation of rates. Advances in Chemical Physics 126, p. 93... 

A trajectory is obtained after specifying two initial conditions, the coordinate vector, X t = 0) = Xo, and the velocity vector, V(t = (V) = Vo- The size of the time step is restricted because steps larger than a few femtoseconds result in numerical instabilities. To obtain long time dynamics, many small time steps of size At are required (e.g., to reach a few nanoseconds, millions of steps are required). The necessity of using small time steps is the major obstacle in the computation of long time dynamics with the initial value formulation. 

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