Two dynamic

Figure 4 DynDom [67] analysis of the first two normal modes of human lysozyme. Dark grey and white indicate the two dynamic domains, separated by the black hinge bending region. The vertical line represents a hinge axis that produces a closure motion in the first normal mode. The horizontal line represents a hinge axis that produces a twisting motion in the second normal mode. (Adapted from Ref. 68.) The DynDom program is available from the Internet at http //md. chem.rug.nl/ steve/dyndom.html.

The coefficients of the above equations are the partial differentials of the two dynamic balance equations and are given by... 

A model of blending aqueous salt buffers for chromatography has been developed.1 The model assumed full miscibility, low mixing enthalpy and low volume change. It reproduced experimental S-curves of buffer strength produced by a Pharmacia P3500 dual piston system equipped with a model 24 V dynamic mixer with 0.6 mL internal volume as well as those produced by a BioSepra ProSys 4-piston system equipped with two dynamic mixers of 1.2 mL internal volume. 

This equation describes the Thomas precession of a classical spin (Thomas, 1927), which is driven by the underlying Hamiltonian dynamics in phase space. In combination the two types of dynamics, Hamiltonian on phase space and driven precession on the sphere, yield the following picture There is a combined phase space It3 x It3 x S2 with two dynamical systems,... 

According to Eq. (2.70), one has in this case two dynamic symmetry chains... 

A strong test of this theory is presented by a blend of two dynamically different components (but of identical local chemistry) such that the volume fraction of both is large. Two cases of especial interest suggest themselves blends of linear with star polymers [42,55] and blends of star polymers with widely separated molecular weights [56]. Recent work on both these systems has shed further light on the nature of co-operative constraint release and the remarkable power of the theoretical tools we now have at hand. 

The important feature in the SL method is that there is always a buffer of dormant SL region separating any two dynamically active regions, which eliminates the difficulty associated with synchronizing events and resolving conflicts at the boundaries between processors. For a finite cycle time, the SL method is not exact, but if the cycle time is comparable to or shorter than a typical reaction time, it is extremely accurate. A detailed discussion and demonstration of the requirements for accuracy in the case of KMC can be found in ref. 35. 

In the presence of both order-disorder and displacive, as in the KDP family, the two dynamic concepts have somehow to be merged. It could well be that the damping constant Zs becomes somewhat critical too (at least in the over-damped regime of the soft mode), because of the bihnear coupling of r/ and p. It would, however, lead too far to discuss this here in more detail. The corresponding theory of NMR spin-lattice relaxation for the phase transitions in the KDP family has been worked out by Blinc et al. [19]. Calculation of the spectral density is here based on a collective coordinate representation of the hydrogen bond fluctuations connected with a soft lattice mode. Excellent and comprehensive reviews of the theoretical concepts, as well as of the experimental verifications can be found in [20,21]. 

Two dynamic methods have been developed for measurement of the surface tensions, the method of ripples first employed by Rayleigh and the vibrating jet method developed by Bohr. 

Vq (dashed curve) are compared. F Tp) is about 0.9889 and 0.691, respectively. In (b), the population for each site at i = are compared between the two dynamics with (solid lines) and Vq (dashed fines). 

Solid tellurium is a bad conductor of heat and electricity 6 a maximum value for the electrical resistance has been observed and placed at 50° to 140° C. by different investigators.7 The occurrence of this maximum has also been attributed to the presence of two dynamic allotropic forms. At higher temperatures, above 360° C., the specific resistance decreases exponentially with rise in temperature.8... 

Two dynamic alternatives to the static approach have been used in HO calibration and measurement. In the CSTR (continuously stirred tank reactor) approach, air containing the tracer or tracers flows into the reactor to balance the bulk flow out to the HO measuring devices, and the contents are stirred by a fan or other means. The HO chemical tracer is measured in the inlet flow to obtain [T]() and in the outlet flow to obtain [T], Mass balance requires... 

Time-dependent correlation functions have been familiar for a long time in the theory of noise and stochastic processes. In recent years they have become very useful in many areas of statistical physics and spectroscopy. Correlation functions provide a concise method for expressing the degree to which two dynamical properties are correlated over a period of time. 

The correlation function C t) for two dynamical properties a and (5 is defined mathematically as... 

Two dynamic experiments with the extractant mixture of 0.06 M DB21C7 with 0.08 M DCH18C6 in the mixed diluent THDFH/synthanol (87 13 v v) were performed. The technological flowsheet (see Figure 6.4) includes eight stages of extraction, two... 

The only exception to a single population of sorbent in a glassy polymer was observed in the water-cellulose acetate system (5 1, 52). In this system two resonance frequencies and two relaxation rates for water were observed. However, the two dynamic states of the water in this system are due to specific hydrogen bonding interactions rather than sorption in Langmuir type holes. 

The Dirac bracket of two dynamical variables j and k which we write as [j,k] is defined using this inverse matrix as... 

As a conclusion, it appears clear that measures must be taken to avoid omitting the charging of compound (A) the omission of (B) is not as critical, and requires no special measure. Thus, based on two dynamic DSC thermograms, important conclusions for the safety of the studied process can be drawn. 

With the larger Ms(calix) crown (3.127),65 two dynamic processes are observed. The intermolecular association/disassociation equilibrium in which the complex equilibrates with the uncomplexed ligand and free metal cation is slow on the NMR time scale. The complex also exhibits a faster intramolecular vibration of the metal cation from one binding site to another (Scheme 3.26). Compound 3.127 is also interesting because the mechanism of this fast, intramolecular cation shuttling process may have important implications on the analogous movement of metal cations through transmembrane ion channels (Section 2.2). 

The spirobis[2,4]-benzodithiepine (90) has been prepared from l,2-bis(chloromethyl)-4,5-dimethylbenzene and sodium trithiocarbonate prepared in situ and a conformational analysis has been carried out using H- and l3C-NMR, X-ray analysis and semi-empirical calculations <95JOC6335). In the solid state it exists in a chair-twisted boat conformations whereas in solution it undergoes two dynamic processes, namely pseudorotation at lower temperatures and ring inversion at higher temperatures. 

The interaction of these two processes can be described by a simple isothermal model, which is based on balances of mass and charge. The model describes the extent of the reforming and oxidation reactions along the anode channel. The essential simulation results can easily be displayed in a conversion diagram which is a phase diagram of the two dynamic state variables, namely the extents of two reactions. 

With simultaneous phase and reaction equilibrium the system has only two dynamic degrees of freedom (five solutes - three chemical equilibria) and therefore corresponds again to a nonreactive system with two solutes. If the dimers are taken as reference components the following definition of the transformed concentration variables is found from Eq. (6)... 

Hwang, P.M., Bishop, R.E., Kay, L.E. The integral membrane enzyme PagP alternates between two dynamically distinct states. Proc Natl Acad Sci USA 101 (2004) 9618-9623. 

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