Dynamical timescale

If we take the total observed mass in the Universe as 2 x 109MSun and divide this by the dynamic timescale for a GMC, this suggests that star formation is occurring at a rate of 500 MSun yr-1, which is 100 times the currently observed formation rate. This calculation is riddled with assumptions and approximations, including the efficiency of star formation. 

Typical timescales 1/v range from as little as 108 years (roughly the dynamical timescale) for a starburst galaxy to maybe 2 x 109 years in an early-type spiral to... 

The neutron star formed after the merger may be supported by rapid and differential rotation even if its mass exceeds 60% of the maximum mass of a single non-rotating neutron star, and the GWs are emitted due to non-axisymmetric andquasiradial oscillations of the remnant for longer than the dynamical timescale [30], If these oscillations persist for a longer time, the integrated GW may be... 

Figure 1 Widely varying timescales in n-butane. Even the simple butane molecule (upper left) exhibits a wide variety of dynamical timescales, as exhibited in the three time traces. Even in the fast motions of the C-C-C bond angle, a slow undulation can be detected visually.

The decline from the peak is relatively rapid, since the opacity of the core is determined by electron scattering. As the heavy elements recombine, this declines precipitately and the diffusion timescale rapidly becomes shorter than the dynamical timescale (see, for example, Shaeffer, Cassd and Cahen). In the radioactive tail, the luminosity can be set equal to the rate of energy generation in radioactivity (Weaver, Axelrod and Woosley, 1980) ... 

Halley et al. employed a MD method for the simulation of metal/water interfaces.72 They found that the occupancy of on-top binding sites for water in this model as applied to a (1 0 0) surface of copper was very sensitive to potential. They suggested that this may provide an explanation for some previously unexplained features of X-ray data on water structure and noble metal/water interfaces. They also noticed that the strong bonding of water on a metal surface may result in metastable charging of the interface in molecular dynamics timescales. 

Cluster studies provide a unique window on the Universe. Although clusters are the most massive collapsed systems in the Universe, with dynamical timescales of order 109 yrs in their cores, they are relatively young and remember the conditions from which they formed. Also, clusters form from rare overdensities. Therefore, cluster properties and numbers are sensitive to cosmological parameters. 

Evidently, Lyman break galaxies span a wide range of ages. One fifth of the sample considered by Shapley et al. (2001) consists of objects which apparently have just collapsed and are forming stars on a dynamical timescale ( 35Myr). As we have seen,... 

Conditions for explosive burning can only occur if the core collapses at a speed vs, the local sound speed. In a star with an iron core, vs 107ms 1, which implies a collapse timescale < 3 s - essentially a dynamical timescale. Any slower and the star can reorganize itself without an explosion, so a lot of energy ( 1014 Jkg-1) must be removed rapidly. 

Fig. 24. The likelihood of a DYR r-process for given combinations of the electron fraction Ye and the entropy per baryon s. A SoS-like r-process is expected for a suitable superposition of conditions between the black lines. The results inferred from an initial NSE phase at low s are smoothly connected to those of various nuclear network calculations for high s values. In the latter cases, the assumed expansion timescales imply that the freeze-out of the charged-particle induced reactions is reached after dynamical timescales Tdyn in excess of about 50 - 100 ms. The two dotted lines represent the contours of successful r-processing for Tdyn = 50 ms (left line) and 100 ms (right line) (see [59] for details)...

It has been considered that protein dynamics are too slow to affect electron transfer. However, the different kinetic constants measured for the electron transfer for proteins indicates that the electron transfer can occur within the range of the protein dynamics timescale. For example, the highest kinetic constant for the electron transfer between Zn porphyrin to Ruthenium both bound to myoglobin is found equal to 7.2 x 10 s (Casimiro et al. 1993.) This means a time equal to 14 ns. This time is in the same range of the protein rotation and even slower from the time of the local rotation which averages 1 ns or less. 

Translational and rotahonal diffusion coefficient of a molecule in a liquid provides a quantitahve measure of the dynamic timescales in the liquid. These coefficients are related to viscosity by the Stokes-Einstein [2] and the Debye-Stokes-Einstein relation [3], respectively. Using the definihon of diffusion coefficient in terms of mean-square displacement [2] and the Stokes-Einstein relahon, we can estimate the time needed by a water molecule to translate a distance equal to its molecular diameter a... 

Capturing adequate dynamic timescales for the rearrangement of solvent particles around atoms undergoing dissolution... 

Note that the Markovian dissipative dynamical process is governed by a frequency -independent Il-dissipator in eqn (13.48) that also implies an 5-in-dependent /C-tensor here, while the Markovian kinetic rate process is governed by the constant rate matrix, Al(j) = iC(0). Equation (13.52) would indicate non-Markovian rates in general, even with Markovian dissipative dynamics. However, kinetic rates are physically concerned with post-coherence events, in which the coherence-to-coherence dynamics timescale, the magnitude of l ccl is short compared with the relevant of interest. Therefore, the kinetic rate matrix of eqn (13.52) in the kinetics regime is often of K s) K K 0) = - /Cpp -I- /Cpc cc cp, where /Cpp = 0 in the absence of level relaxations. 

Molecular Dynamics Timescales with Milestoning Example of Complex Kinetics in a Solvated Peptide. 

The data reduction and analysis of a typical XPCS data of an equilibrium dynamic system is well documented [87, 124, 125]. The quantification of the equilibrium dynamic timescale is assisted by the normalized second-order intensity correlation function g2(q,r), which is defined by... 

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