Short timescale regime

The plan of Section IV is as follows In section IV.A, we qualitatively outline the general picture of reaction dynamics that emerges from fast variable physics. Next, in section IV.B, we examine liquid phase-activated barrier crossing in the short time regime of Section II.C. In Section IV.C we note that the fast variable/slow bath timescale separation also applies to liquid phase vibrational energy relaxation and then discuss that process from the fast variable standpoint. Finally, in Section IV.D, we discuss some related work of others. 

At present, bioremediation is receiving a lot of interest as it appears sustainable, low cost, and low energy and therefore meets the needs of a remediation solution that will both benefit the environment directly and also have a relatively low carbon footprint. In practice, it often needs to be combined with other approaches to achieve an effective solution. This requirement is frequently driven by the need to remediate over a short timescale, in the case of ex situ bioremediation, or the need to promote long-term effectiveness under a regime such as monitored natural attenuation or permeable reactive barriers. The engineering of bioremediation to enhance its effectiveness has been studied for the last few decades with considerable success. It has become a mainstream part of the toolbox for contaminated sites. 

At short timescales (t < 500 ps) the MSD exhibits a quadratic time dependence. This is known as the ballistic regime, where particle collisions are infrequent. In nanoporous materials, an intermediate regime starts when particles are colliding but only with a subset of the other particles due to the confinement. When particles are able to escape the local environment and explore the full macroscopic network, the diffusive regime is reached. In the diffusive regime, the MSD becomes linear with time, exhibiting a slope of one on a log-log scale. 

Dynamic melting models produce all correlated excesses at the bottom of the melting regime and require melt transport rates sufficient to transport radium from the bottom of the melting regime on timescales short compared to the half-life of radium (1,600 yr). 

There are two interesting regimes of time evolution in the probing/detection of dynamical nonequilibrium structures. In the regime of dynamics, the time evolution of atomic positions is detected on its intrinsic timescale, i.e., femtoseconds. Short X-ray pulses - on the timescale of atomic motion - are required in order to follow the dynamics of the chemical bond. In the regime of kinetics, which has to do with the time evolution of populations - and in the context of time-resolved X-ray diffraction -the time evolution in an ensemble average of different interatomic distances or the structural determination of short-lived chemical species is considered. 

Equation (6) shows that the current response following a potential step contains both time-independent and time-dependent terms. The differences in the electrochemical responses observed at macroscopic and microscopic electrodes arise because of the relative importance of these terms at conventional electrochemical timescales. It is possible to distinguish two limiting regimes depending on whether the experimental timescale is short or long. 

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. 

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