Dynamical general

Luckhaus D 2000 6D vibrational quantum dynamics generalized coordinate discrete variable representation and (a)diabatic contraction J. Chem. Phys. 113 1329—47... 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

Quantum Cellular Automata (QCA) in order to address the possibly very fundamental role CA-like dynamics may play in the microphysical domain, some form of quantum dynamical generalization to the basic rule structure must be considered. One way to do this is to replace the usual time evolution of what may now be called classical site values ct, by unitary transitions between fe-component complex probability- amplitude states, ct > - defined in sncli a way as to permit superposition of states. As is standard in quantum mechanics, the absolute square of these amplitudes is then interpreted to give the probability of observing the corresponding classical value. Two indepcuidently defined models - both of which exhibit much of the typically quantum behavior observed in real systems are discussed in chapter 8.2,... 

For classical evolutions, we merely substitute crj for p. Looking at plots of N fi, p vs. v/N, it is clear that although the quantum dynamics generally appears to preserve the characteristic structure of the classical spectrum, particular structural details tend to be washed-away [ilachSSbj. If high or low frequency components are heavily favored in the classical evolution, for example, they will similarly be favored in the quantum model discrete peaks, however, will usually disappear. White-noise spectra, of course, will remain so in the quantum model. 

Chernyak, V. Chertkov, M. Jarzynski, C., Dynamical generalization of nonequilibrium work relation, Phys. Rev. E 2005, 71, 025102... 

Thermofield dynamics Generalized bogoliubov transormations and applications to Casimir effect... 

T. Gross, Population Dynamics General Results from Local Analysis, Der Andere Verlag Tonning, Germany (2004). 

Fluid Dynamics General Relativity Number Theory Numerical Analysis Particle Physics Plasma Physics Solid-State Physics Structural Mechanics Thermodynamics... 

Morrow et al. measured the spin-lattice relaxation time Ti and quadrupole echo decay times T ) of headgroup deuterated d4-DMPC as a function of temperature and pressure to yield additional information about changes in the headgroup dynamics. Generally, motions in a LC phospholipid bilayer can... 

Keywords stochastic dynamics, generalized Langevin equation, nonstationary and colored friction... 

Although not dealt with in this chapter, AC impedance measurements (sometimes called electrochemical impedance spectroscopy) are important in studying electrode dynamics. Generally in this method, a sinusoidal voltage (10 2 to 105 Hz) is applied to the cell, the phase angle and the amplitude of the response current are measured as a function of... 

Rept. GA-7598, General Dynamics, General Atomic Division (Jan. 1967). 

As quoted in Sect. 1.2, different theoretical models for chain dynamics generally lead to different analytical expression for the OACF, which can be compared with the experimental anisotropy. The knowledge of the statistical distribution of errors on each channel is an essential tool for this comparison. It provides objective criteria to decide whether a discrepancy between a model and a set of data is significant or not, and to compare different models. Among these criteria, the most well known one is the reduced which should be 1 for purely statistical deviations, and increases... 

In this paper we gave a dynamic extension of the DFT, by deriving a L-D equation (11) with the fluctuation-dissipation theorem (9). We showed that the stochastic equation correctly samples the density field according to the probability exp —jflf [n], (17), based on the second H-theorem (16). At this point we note however that our TO-DFT is phenomenological md it is desirable to have a first-principle dynamics generalization of DFT. 

Molecular Dynamics simulation is one of many methods to study the macroscopic behavior of systems by following the evolution at the molecular scale. One way of categorizing these methods is by the degree of determinism used in generating molecular positions [134], On the scale from the completely stochastic method of Metropolis Monte Carlo to the pure deterministic method of Molecular Dynamics, we find a multitude and increasingly diverse number of methods to name just a few examples Force-Biased Monte Carlo, Brownian Dynamics, General Langevin Dynamics [135], Dissipative Particle Dynamics [136,137], Colli-sional Dynamics [138] and Reduced Variable Molecular Dynamics [139]. 

M. E. Tuckerman, Y. Liu, G. Ciccotti, and G. J. Martyna (2001) Non-Hamiltonian molecular dynamics Generalizing Hamiltonian phase space principles to non-Hamiltonian systems. J. Chem. Phys. 115, p. 1678... 

However, in analogy to the breakdown of classical thermodynamics due to fluctuations (see Eq. [A.7]) Onsager s eqs. (A.38) and (A.40) must also break down. Namely, motions of the unconstrained A s do not cease after the state Tp is reached. Rather, as a dynamical generalization of Eq. (A.7), these parameters fluctuate about A, executing random motions with microscopic amplitudes. 

Nordliaus, VV. D., and Yang, Z. (1996). A regional dynamic general equilibrium model (rf alternative climate-change strategies. Am. Earn. Rev. 86, 741-765. 

D. K. Hoffman, Y. Huang, W. Zhu, and D. J. Kouri, Further analysis of solutions to the time-independent wave packet equations for quantum dynamics general initial wave packets, J. Chem. Phys. 101 1242 (1994). 

Such a system generally does not have analytically integrable equations of motion. However, we may apply Hamilton s equations of motion, solve them numerically, and thus generate a unique trajectory for each set of initial conditions we choose. The resulting dynamics generally exhibits a variety of interesting phenomena. First, the frequency of motion in each mode is no longer a constant [as would be the case if we had f(q, qi) = 0] but depends on the instantaneous values of the canonical coordinates ( p, ) ... 

Dynamics. General Aspects and Application to Chain Molecules. 

To deseribe the dynamie interaction of bubble with polymeric solution it is necessary to invoke equations of liquid motion, heat transfer and gas dynamics. General approach to description of bubble growth or collapse in a non-Newtonian liquid was formulated and de-veloped. The radial flow of incompressible liquid around growing or collapsing bubble is described by equations, following from [7.2.21], [7.2.22] ... 

Lumped mechanical models have been used to analyze impact dynamics. Generally, muscle is represented by a combination of a spring and a dashpot, whereas a ligament is modeled by a spring. Human body vibrations can be analyzed by similar models (Fritton et al., 1997). 

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