Specificity relaxed

The existence of characteristic time D"1 must lead to the appearance of specific relaxation effects. This relaxation mechanism has nothing in common with visco-... 

A possible approach to interpretation of a low-frequency region of the G ( ) dependence of filled polymers is to compare it with a specific relaxation mechanism, which appears due to the presence of a filler in the melt. We have already spoken about two possible mechanisms — the first, associated with adsorption phenomena on a filler s surface and the second, determined by the possibility of rotational diffusion of anisodiametrical particles with characteristic time D 1. But even if these effects are not taken into account, the presence of a filler can be related with the appearance of a new characteristic time, Xf, common for any systems. It is expressed in the following way... 

It can be noticed that the maximum NOE factor (2 when A is a carbon-13 and B a proton) is reached under extreme narrowing (see Section 6) conditions and if RA arises exclusively from the A-B dipolar interaction. On the other hand, the cross-relaxation rate gab is easily deduced from the NOE factor and from the A specific relaxation rate... 

As a consequence of the two above points, there is presently no satisfactory theory able to incorporate the specific relaxation of the fast mode and of the bending modes in a model working beyond both the adiabatic and exchange approximations. 

Kinetic schemes involving sequential and coupled reactions, where the reactions are either first-order or pseudo-first order, lead to expressions for concentration changes with time that can be modeled as a sum of exponential functions where each of the exponential functions has a specific relaxation time. More complex equations have to be derived for bimolecular reactions where the concentrations of reactants are similar.19,20 However, the rate law is always related to the association and dissociation processes, and these processes cannot be uncoupled when measuring a relaxation process. 

NMR imaging Images (one-, two-, or three-dimensional array of voxel intensities) pixel-specific relaxation curves maps, and movies (i.e., density, 7), T2, or D weighted) Hills (1998) McCarthy (1994) Price (1998b)... 

Automated relaxation already is an integrated feature of newest version of optimization tools that a manually programmed relaxation concept would not be necessary. However, a problem-specific relaxation concept can control, which constraints are subject to relaxation that are suitable to be relaxed from a planners perspective. Therefore, a manually programmed relaxation concept still will be an important element even if optimization tools provide relaxation as standard feature. 

This section intends to provide the reader with some examples of how the high relaxivity challenge has been tackled for Gd(III) complexes so far. For the sake of clarity, this section has been divided in three sub-sections in relation to the specific relaxation parameter considered for relaxivity enhancement, namely the hydration state of the metal centre, the tumbling rate of the CA, and the exchange rate of the mobile protons coordinated to the paramagnetic center. 

After the partial exchange of the Na counter cations for Gd " ", the specific relaxivity (here defined as the measured water relaxation rate per gram of material) was measured at Larmor frequencies ranging from 0.01 to 30 MHz. The NMRD profiles obtained were compared with that obtained after complexing the encapsulated Gd(III) with DTPA. After correction for the differences in the Gd(III) content of the samples, the NMRD curves appeared to be superimposable. Based on this result, a... 

Models for solvation in water that allow for a structured solvent do indeed predict a multiexponential response. For instance, the dynamical mean spherical approximation (MSA) for water solvation predicts that solvation of an ion in water is well represented by two characteristic times [38]. Nonetheless, the specific relaxation times differ substantially from the observed behavior [33],... 

For a comparison of theoretical predictions with experimental data, the isolation of specific relaxation channels is necessary. Standard techniques for this purpose developed by Raman spectroscopists and adopted for CARS studies are the variation of concentration (e.g., isotopic dilution), temperature, and pressure (40,53). 

By monitoring excitation spectra with a time-resolved detection of the emission, briefly called time-resolved excitation spectroscopy , it is possible, to identify specific relaxation paths. Although, these occur on a ps time scale, only measurements with a ps time resolution are required. It is shown that the relaxation from an excited vibrational state of an individual triplet sublevel takes place by a fast process of intra-system relaxation (on the order of 1 ps) within the same potential surface to its zero-point vibrational level. Only subsequently, a relatively slow crossing to a different sublevel is possible. This latter process is determined by the slow spin-lattice relaxation. A crossing at the energy of an excited vibrational/phonon level from this potential hypersurface to the one of a different substate does not occur (Fig. 24, Ref. [60]). This method of time-resolved excitation spectroscopy, applied for the first time to transition metal complexes, can also be utilized to resolve spectrally overlapping excited state vibrational satellites and to assign these to their triplet substates. 

Equation 14K sets the lower limit of the pulse time, for a given solution resistance. The upper limit is set by the requirement that it very short with respect to the specific relaxation time for the ietction being studied. We may choose this limit as... 

Two specific relaxation approaches are discussed the first approach involves measurement of the NMR longitudinal and transverse relaxation times (Ti and T2) wheareas the second approach involves measurement of transferred NOE intensities. In the relaxation time measurement approach, the distance information is assumed known and the focus is on dynamic information. In the transferred NOESY approach, the motion is considered constant and the focus is on the structural information. These are discussed in terms of two different biological systems. 

An ATP-independent DNA topoisomerase activity has also been described in crude extracts of archaebacteria lacking reverse gyrase activity [91] (Fig. 7) and has been partially purified from T. acidophilum [90]. This enzyme specifically relaxes negatively supercoiled DNA and could be phylogenetically related either to reverse gyrase and/or to the DNA topoisomerase III of D. amylolyticus. 

We will present the topic by introducing the nuclear spins as probes of molecular information. Some basic formal NMR theory is given and connected to MD simulations via time correlation functions. A large number of examples are chosen to demonstrate different possible ways to combine MD simulations and experimental NMR relaxation studies. For a conceptual clarity, the examples of MD simulations presented and discussed in different sections, are arranged according to the specific relaxation mechanisms. At the end of each section, we will also specify some requirements of theoretical models for the different relaxation mechanisms in the light of the simulation results and in terms of which properties these models should be parameterized for conceptual simplicity and fruitful interpretation of experimental data. 

Dicycloverine, in the doses generally used (up to 450 mg/ day), is of disputed value. It may have a non-specific relaxant action on the gastrointestinal muscle. The evidence of its effects is meager and it seems to be an anticholinergic drug that which has been promoted in doses that are often too low to result in either a useful therapeutic effect or in adverse effects. 

The treatment presented thus far applies to systems where only one independent variable is subject to relaxation. Frequently, however, m > 1) such variables are needed to describe the relaxation properties of interest. Under these circumstances, a set of m relaxation equations of the type given in Eq. [4] can be established. Accordingly, m relaxation times are determined and in a specific relaxation process each relaxation time will contribute its share to the overall effect in proportion to a corresponding amplitude. The ensemble of relaxation times and amplitudes is called the relaxation spectrum of the process under consideration. It reflects the underlying molecular rate mechanism. Thus, in principle, experimental relaxation spectrometry offers a way to elucidate kinetic mechanisms. 

Ermakov, G. V. (2002) Thermodynamic Properties and Boiling-Up Kinetics of Superheated Liquids, UrO RAN, (Ekaterinburg,), in Russian. Skripov, P. V. and Puchinskis, S. E. (1996) Spontaneous Boiling-Up as a Specific Relaxation Process in Polymer-Solvent Systems, J. Appl. Polym. Sci. 59, 1659-1665. 

To demonstrate the "overlapping" conditions between chemical reactions and surface processes controlled by "specific" relaxation times we can compare processes in both areas. Such areas are diffusion of components, formation of new phases, e.g. crystallisation, evaporation, freezing, the transformation from an aggregate to a monomer state or vice versa. For example the component A produces the component B in dependence of temperature, pressure or other forces, such as outer electric fields. 

The objective function value of an optimal solution to a relaxation bounds the optimed objective function value of the main problem. Specifically, relaxation optima provide lower bounds for minimize problems and upper bounds for maximize problems. 

The more direct identification of the molecular character of a secondary relaxation or information regarding the processes that are involved in the a-relaxation requires more information of a kinetic nature. This is accomplished by complementary experiments under different frequencies of probing to observe a temperature shift of the specific relaxation or by conducting stress-relaxation experiments at different temperatures and noting related shifts in the relaxation time of the specific transition. We explore these shifts in the following sections. 

In contrast, if the local solvent density fluctuates only very slowly, such that the solute remains in the same, initial local environment for the duration of the decay of the force correlation function, then the full eq. 9 must be maintained. Indeed, in this limit one finds a distribution of initial-local-density(p o)-dependent force correlation functions. Additionally, if the initial local density is maintained for times much longer than the local-density-specific relaxation times local solvent... 

We shall now consider the state in which actual fluctuation characteristics initially differ from those for either the real or fictitious homogeneous state. Obviously, these characteristics must relax to the values pertaining to this homogeneous state. To develop a simple model of such a relaxation, we must first briefly discuss specific relaxation times. 

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