Multiple time scale

Tuckerman M, Berne B J and Martyna G J 1992 Reversible multiple time scale molecular-dynamics J. Chem. Phys. 97 1990-2001... 

Procacci P, March M and Martyna G J 1998 Electrostatic calculations and multiple time scales in molecular dynamics simulation of flexible molecular systems J. Chem. Phys. 108 8799-803... 

Tuckerman, M.E., Berne, B.J., Rossi, A. Molecular dynamics algorithm for multiple time scales systems with long range forces. J. Chem. Phys. 94 (1991) 6811-6815. 

Mark E. Tuckerman, Glenn J. Martyna, and Bruce J. Berne. Molecular dynamics algorithm for condensed systems with multiple time scales. J. Chem. Phys., 93(2) 1287-1291, Jul. 1990. 

M. E. Tuckerman and B. J. Berne. Molecular dynamics in systems with multiple time scales Systems with stiff and soft degrees of freedom and with short and long range forces. J. Comp. Chem., 95 8362-8364, 1992. 

Molecular Dynamics in Systems with Multiple Time Scales Reference System Propagator Algorithms... 

Methods for Dealing with the Intrinsic Multiple Time Scale Problem in Molecular Dynamics... 

By now it should be clear that this kind of operator algebra can be a useful method for generating integrators. We show, in the following, how it can be applied to generate a wide variety of methods for treating the multiple time scale problem. 

New Sampling Methods for the Extrinsic Multiple Time Scale Problem... 

Since many systems of interest in chemistry have intrinsic multiple time scales it is important to use integrators that deal efficiently with the multiple time scale problem. Since our multiple time step algorithm, the so-called reversible Reference System Propagator Algorithm (r-RESPA) [17, 24, 18, 26] is time reversible and symplectic, they are very useful in combination with HMC for constant temperature simulations of large protein systems. 

Wisdom, J. The Origin of the Kirkwood Gaps A Mapping for Asteroidal Motion Near the 3/1 Commensurability. Astron. J. 87 (1982) 577-593 Tuckerman, M., Martyna, G. J., Berne, J. Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys. 97 (1992) 1990-2001 Tuckerman, M., Berne, J. Vibrational Relaxation in Simple Fluids Comparison of Theory and Simulation. J. Chem. Phys. 98 (1993) 7301-7318 Humphreys, D. D., Friesner, R. A., Berne, B. J. A Multiple-Time Step Molecular Dynamics Algorithm for Macromolecules. J. Chem. Phys. 98 (1994) 6885-6892... 

Tuckerman, M., Martyna, G. J., Berne, J. Molecular Dynamics Algorithm for Condensed Systems with Multiple Time Scales. J. Chem. Phys. 93 (1990) 1287-1291... 

M. Tuckerman, B.J. Berne, and G. Martyna. Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys., 97 1990-2001, 1992. 

BJ Berne. Multiple Time Scales. New York Academic Press, 1985, pp 419-436. 

Tuckerman M, Berne BJ, Martyna GJ (1993) Reversible multiple time-scale molecular-dynamics — reply. J Chem Phys 99(3) 2278-2279... 

In such cases, the MEHMC method could be employed in combination with an enhanced sampling method that deforms the effective energy surface (but preserves the location of the potential minima), such as that in [29, 97]. Likewise, it may be worthwhile to explore the use of a reversible multiple-time-scale molecular dynamics propagator [103] with MEHMC to accelerate the dynamical propagation. 

Schiestel, R. (1987). Multiple-time-scale modeling of turbulent flows in one-point closures. 

O. V. Boyarkin, T. R. Rizzo, and D. S. Perry, Intramolecular energy transfer in highly vibrationally excited methanol. II. Multiple time scales of energy redistribution. J. Chem. Phys. 110, 11346 11358 (1999). 

In computational science and engineering, researchers frequently speak of multiple time-scale problems. These are problems ivhere the characteristic times for events span many orders of magnitude. More often than not, the full range of desired time-scales is not experimentally accessible. The combined experimental and numerical approach must settle for analysis of a narrow ivindoiv of time-scales. For most of our purposes, the half-life of an event w ill prove to be a useful definition of characteristic time-scale... 

Miron, R.A., Fichthorn, K.A. Multiple-time scale accelerated molecular dynamics addressing the small-barrier problem. Phys. Rev. Lett. 2004, 93, 128301-1—1. 

A special version of UV-vis spectroscopy is the detection of the sample light emission after irradiative molecular excitation. This phenomenon is called luminescence and specified as fluorescence in case of relatively fast electron relaxation processes without changing spin multiplicity (time scale of microseconds and below). 

Errors and confusion in modelling arise because the complex set of coupled, nonlinear, partial differential equations are not usually an exact representation of the physical system. As examples, first consider the input parameters, such as chemical rate constants or diffusion coefficients. These input quantities, used as submodels in the detailed model, must be derived from more fundamental theories, models or experiments. They are usually not known to any appreciable accuracy and often their values are simply guesses. Or consider the geometry used in a calculation. It is often one or two dimensions less than needed to completely describe the real system. Multidimensional effects which may be important are either crudely approximated or ignored. This lack of exact correspondence between the model adopted and the actual physical system constitutes the basic problem of detailed modelling. This problem, which must be overcome in order to accurately model transient combustion systems, can be analyzed in terms of the multiple time scales, multiple space scales, geometric complexity, and physical complexity of the systems to be modelled. 

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