Time regime

By a variation of chemistry and/or chain length the different time regimes can be shifted. From a simulation point of view we are again faced by the decision what kind of information we want to get out of the simulation. If one wants to look at very local properties, depending on the local chemistry of the individual monomers, there is no way around a simulation with all chemical details. However, one should keep in mind that by such a technique it is impossible to equilibrate the system near the glass transition temperature. 

Perez-Galvez, A., Homero-Mendez, D., and Mmguez-Mosquera, M.I., Dependence of carotenoid content and temperature-time regimes during the traditional slow drying of red pepper for paprika production at La Vera County, Eur. Food Res. Technol., 221, 645, 2005. 

The laser we use in these experiments is an exclmer laser with a pulse width of approximately 20 nsec. In this time regime the laser heating can be treated using the differential equation for heat flow with a well defined value for the thermal diffusivity (k) and the thermal conductivity (K) (4). 

The effect on the current-time behavior of varying Kg while keeping the kinetics of the interfacial process high and nonlimiting is shown in Fig. 11, for a typical tip-interface distance log(T) = —0.5. The general trends in Fig. 11 can be explained as follows. At short times, the diffusion field at the UME tip is not of sufficient size to intercept the interface, and there is thus no perturbation of the interfacial equilibrium. In this time regime,... 

Since modern FTIR spectrometers can operate in a rapid scan mode with approximately 50 ms time resolution, TRIR experiments in the millisecond time regime are readily available. Recent advances in ultra-rapid scanning FTIR spectroscopy have improved the obtainable time resolution to 5 ms. Alternatively, experiments can be performed at time resolutions on the order of 1-10 ms with the planar array IR technique, which utilizes a spectrograph for wavelength dispersion and an IR focal plane detector for simultaneous detection of multiple wavelengths. ... 

This ansatz is only expected to be valid for large enough x such that the two intervals may be regarded as independent. This restricts the following results to the intermediate time regime. 

That the terminal acceleration should most likely vanish is true almost by definition of the steady state the system returns to equilibrium with a constant velocity that is proportional to the initial displacement, and hence the acceleration must be zero. It is stressed that this result only holds in the intermediate regime, for x not too large. Hence and in particular, this constant velocity (linear decrease in displacement with time) is not inconsistent with the exponential return to equilibrium that is conventionally predicted by the Langevin equation, since the present analysis cannot be extrapolated directly beyond the small time regime where the exponential can be approximated by a linear function. 

The first three terms arise from the expansion of A2(x3. x2 x) about x3, which accounts for the appearance of the daggers, and the second three terms arise from the expansion of S1 2 1 (x2, xj x) about xj. This ansatz is only expected to be valid for large enough x such that the two intervals may be regarded as independent. This restricts the following results to the intermediate time regime. 

This relates the time-independent part of the natural nonlinear force to the thermodynamic force for a system of general parity in the intermediate time regime. 

Second is the application of a wide range of experimental designs and techniques. DNA CT is observed in a diverse array of systems over different distance and time regimes. Consequently, a versatile approach which draws upon complementary methods is required to explore different facets of this chemistry and develop a complete picture. We interrogate a variety of nucleic acid assemblies using spectroscopic, biochemical and electrochemical tools to define mechanistic features, exploit biological applications, and explore biological consequences of DNA CT. 

Figure 6 shows the measured dynamic structure factors for different momentum transfers. The solid lines display a fit with the dynamic structure factor of the Rouse model, where the time regime of the fit was restricted to the initial part. At short times the data are well represented by the solid lines, while at longer times deviations towards slower relaxations are obvious. As it will be pointed out later, this retardation results from the presence of entanglement constraints. Here, we focus on the initial decay of S(Q,t). The quality of the Rouse description of the initial decay is demonstrated in Fig. 7 where the Q-dependence of the characteristic decay rate R is displayed in a double logarithmic plot. The solid line displays the R Q4 law as given by Eq. (29). 

Local reptation regime For times t > xe we have to consider curvilinear Rouse motion along the spatially fixed tube. The segment displacement described by Eq. (18) (n = m) must now take the curvilinear coordinates s along the tube into consideration. We have to distinguish two different time regimes. For (t < xR), the second part of Eq. (19) dominates - when the Rouse modes... 

Fig. 19a-c. Schematic representation of a reptating chain in different time regimes a Short-time unrestricted Rouse motion b equilibration of density fluctuations along tha chain c creep motion of a chain out of its tube. 

The theoretical approach described before dealt with the short-time dynamic response of the star molecules. However, in the case of completely labelled stars [148] it was found that the line shape of the Zimm model provides a good description of the NSE spectra not only in the short-time regime (t < 5 ns), but also on longer time scales. 

For short times, the correlation function (7(f) depends on the microscopic details of the dynamics as the system crosses from to 38. These motions take place on a molecular time scale rmoi essentially equal to the time required to move through the transition region. For times f larger than rmoi but still very small compared to the reaction time rrxn (if the crossing event is rare rrxn L> rmoi such that such an intermediate time regime exists), C(f) can be replaced by an approximation linear in time. Using the detailed balance condition k jk = h )/ h ) [33] one then obtains... 

The slope of (7(f) in the time regime rmoi < f forward reaction rate constant. Thus, for the calculation of reaction rate constants it is sufficient to determine the time correlation function (7(f). In the following paragraphs we will show how to do that in the transition path sampling formalism. 

In practice, five different time regimes are loosely discerned as defined in Table 10.1. We are already familiar with the two extreme cases for a small molecule in aqueous solution at ambient temperatures xc 10-12 s, that is, the extremely fast regime illustrated by the 363 K spectrum in Figure 10.4. For a frozen solution at cryogenic temperatures xc 10-3 s, that is, the rigid regime illustrated by the 176 K spectrum in Figure 10.4. Now let us look at the three intermediate cases. 

Finally, in the very slow time regime, tumbling has become too slow to affect the regular powder spectrum under nonsaturating conditions, however, when, during a regular scan in which the external magnetic field is slowly scanned, an intermediate imposition of the powder pattern is partly saturated, then this saturation can be transferred... 

Kosch U., Klimant I., Werner T., Wolfbeis O.S., Strategies To Design pH Optodes With Luminescence Decay Times In The Microsecond Time Regime, Anal. Chem. 1998 70 3892-3897. 

Fig. 6 Correlation curve showing the various processes that occur in different time regimes. Supramolecular dynamics can be measured in any of the time regimes between the antibunching and diffusion phenomena.

Figure 12.16 shows the rising fire plume (or falling salt plume) of Tanaka, Fujita and Yamaguchi [24] from Chapter 10 compared to the saltwater data of Strege [25]. The saltwater data correspond to the long-time regime, and follow the combustion data from Tanaka. 

We can analyze this intervening time regime as we did for the beadspring model by fitting it with an extended von Schweidler law... 

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