Relaxation constant

If the coupling parameter (the Bath relaxation constant in HyperChem), t, is too tight (<0.1 ps), an isokinetic energy ensemble results rather than an isothermal (microcanonical) ensemble. The trajectory is then neither canonical or microcanon-ical. You cannot calculate true time-dependent properties or ensemble averages for this trajectory. You can use small values of T for these simulations ... 

If the Bath relaxation constant, t, is greater than O.I ps, you should be able to calculate dynamic properties, like time correlation functions and diffusion constants, from data in the SNP and/or CSV files (see Collecting Averages from Simulations on page 85). 

For a stable trajectory, use a Bath relaxation constant greater than 0.1 ps. A constant of 0.01 ps is too small and causes disturbances in a simulation... 

For a constant temperature simulation, a molecular system is coupled to a heat bath via a Bath relaxation constant (see Temperature Control on page 72). When setting this constant, remember that a small number results in tight coupling and holds the temperature closer to the chosen temperature. A larger number corresponds to weaker coupling, allowing more fluctuation in temper-... 

Berendsen et al. [H. I. C. Berendsen, I. P. M. Postma, W. F. van Gun-steren, A. di Nola, and I. R. Haak, J. Chem. Phys. 81, 3684 (1984)] have described a simple scheme for constant temperature simulations that is implemented in HyperChem. You can use this constant temperature scheme by checking the constant temperature check box and specifying a bath relaxation constant t. This relaxation constant must be equal to or bigger than the dynamics step size D/. If it is equal to the step size, the temperature will be kept as close to constant as possible. This occurs, essentially, by rescaling the velocities used to update positions to correspond exactly to the specified initial temperature. For larger values of the relaxation constant, the temperature is kept approximately constant by superimposing a first-order relaxation process on the simulation. That is ... 

If the relaxation constant is large there is little effect on a trajectory apart from the long term drift towards fluctuation about T, and... 

For constant temperature dynamics where the constant temperature check box in the Molecular Dynamics Options dialog box is checked, the energy will not remain constant but will fluctuate as energy is exchanged with the bath. The temperature, depending on the value set for the relaxation constant, will approach con-stan cy. 

The T) and T2 dependence is described by Eqs. (3.4.3) and (3.4.4) [34] where Qi and q2 are spin-lattice and spin-spin surface relaxivity constants, and S/ Vis the surface-to-volume ratio of the pore. These equations provide the basis of a methodology for crack detection in cement paste specimens [13]. 

H longitudinal and transverse relaxation constants are the most measured parameters in investigating small molecules/polymer interactions, as the high natural abundance of the proton nuclei ensures a rapid measurement and excellent signal to noise. 

In fact, since the relaxation constant is t = C/G and C is linear in the higher temperature range, while G a T2-5, r scales as T h5. Hence, at higher temperatures, the number of useful data points, obtained in a single thermal discharge measurement, vanishes and the error in the determination of r increases. For example, at the highest temperatures, t was as low as 2 3 seconds. 

A kinetic technique for determining a fluorophore s excited state lifetime by using a light source whose intensity is modulated sinusoidally at a certain frequency, such that the intensity of the fluorescence emission likewise varies sinusoidally but with an added delay from the finite relaxation constant for fluorescence decay. The period of the sinusoidal modulation is chosen to be in the neighborhood of the magnitude of the fluorescence lifetime. 

Figure 3.11 Catalytic efficiency, (fcca,/K ,)app ( ), of salt-activated subtilisin Carlsberg in hexane, THF, and acetone in comparison with T2 (transverse relaxation constant) (O) of mobile deuterons as a function of dielectric constant of solvent [103].

In the absence of noise, the system [179] describes the generation of a singlemode laser field interacting with a homogeneously broadened two-level medium [180]. The variables and parameters of the Lorenz system can be interpreted in terms of a laser system as q is the normalized electric field amplitude, the normalized polarization, q3 the normalized inversion, a = fe/y1 r = A+l, b = 72/71, with k the decay rate of the field in the cavity, yj and y2 the relaxation constants of the inversion and polarization, and A the pump parameter. Far-infrared lasers have been proposed as an example of a realization of the Lorenz system [162]. A detailed comparison of the dynamics of the system (42) and a far-infrared laser, plus a discussing the validity of the Lorenz system as laser model, can be found in Ref. 163. 

The behaviour of the polarized reflectivity and optical conductivity spectra of new quasi-two-dimensional organic conductor p -(BEDO-TTF)5[CsHg(SCN)4]2 versus temperature for E L and E1. L are quite different. For E . L, the temperature changes of R(ro) and ct(co) are due to the decrease of the optical relaxation constant of the free carriers as expected for a metal. For E L at temperatures below 200 K, the energy gaps in the ct(co) spectra at about 4000 cm 1 and at frequencies below 700 cm 1 appear simultaneously with the two new bands of ag vibrations of the BEDO-TTF molecule activated by EMV coupling. This suggests a dimerization of the BEDO-TTF molecules in the stacks, which leads to a metal-semiconductor transition.. In the direction perpendicular to L, the studied salt shows metallic properties due to a very favourable overlap of the BEDO-TTF molecular orbitals. 

Relaxation constant, defined by CTh Horizontal normal stress... 

It is the super operator for the time-dependent relaxation constants. Notice that... 

However, the alignment relaxation constant 72 may be measured separately by means of the method of laser-interrogated dichroism, as discussed in the preceding Section (Section 3.5]. Let us assume that in the scheme shown in Fig. 3.17 the strong field Eg is interrupted at time ... 

If we assume the lower level Lande factor as known, then the fit of non-linear Hanle signals permits us to determine the relaxation constants 7K = 7, as well as the effective cross-sections light field, which mixes the multipole moments aPq with different k, does not permit us to determine the values for definite k separately. Nevertheless (Section 3.3), the discrepancies between the 7K values are negligible in many cases, and the information obtained is sufficiently reliable. 

As can be seen, for any isotropic relaxation process different rank polarization moments change independently. The question arises can the relaxation constants 7 and Tk be arbitrary The following simple example [135] shows that this is not the case. Let us assume that the angular momentum J = 1 and the initial state are such that only level M = 1... 

One must understand that the limitations obtained are less strict than inequalities (5.98) and (5.99). They do not characterize the shape of the allowed region of relaxation constants on the full scale. The restrictions define the multidimensional parallelepiped in (2J — l)-dimensional space which is encircled around the allowed region of Tk/ Ii satisfying the restrictions obtained. Nevertheless, the restrictions obtained are much more obvious and they give a good idea of the limitations imposed by inequalities (5.98) and (5.99). 

Tables 5.4 and 5.5 and formulae for the minimal values and the maximal values of Tk/ i seem to be very useful in the case where not all the relaxation constants with 0 < K < 2J are taken into consideration. In this situation it is impossible to use inequalities (5.98) and (5.99) directly, but limitations obtained in [42] for t K/f i are still valid. This is especially important in the case of molecules where the angular momentum values are, as a rule, large and not all the possible polarization moments are taken into account in the description of the physical process.

Auzinsh, M.P. (1992). General restrictions for the relaxation constants of the polarization moments of the density matrix, Chem. Phys. Lett., 198, 305-310. 

Dyakonov, M.I. and Perel, V.I. (1972). General inequalities for the relaxation constants of a spin density matrix, Phys. Lett., 41 A, 451-452. 

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