Osculation

Marcu V, Tenne R (1988) Photocurrent oscUlations in the CdTe electrolyte systems. J Phys Chem 92 7089-7092... 

When q = 0, the Hugoniot curve represents an adiabatic shock. Point 1 (Pi, p ) is then on the curve and Y and J are 1. Then [(l/pt) - (Ilp2) = 0, and the classical result of the shock theory is found that is, the shock Hugoniot curve osculates the adiabat at the point representing the conditions before the shock. 

The image of the A-level Hilbert space is the subspace of the A-oscUlator Hilbert space with a single quantum excitation. Again, this (physical) subspace is invariant under the action of any operator which results by the mapping (80a) from an arbitrary A-level system operator. As a consequence we obtain the propagator identity... 

Through many examples, it has been demonstrated that VCD arises essentially from two rather distinct mechanisms. The first is the coupling of achiral oscillators that are chirally disposed in their spatial relationship to one another. The mechanism is embodied in its purest form in the simple coupled oscUlator... 

There are three modes of free and forced oscillatory deformations which are commonly used experimentally, torsional oscillations, uniaxial extensional oscUlations and flexural oscillations. 

In the limiting cases (6) and (7), simple first order kinetics is expected. In the intermediate case (5), the kinetics is complex as seen in Fig. 4. At low contact time and conversion, r2 is negligible and the slope of the conversion curve represents k- at high conversion, the slope reflects k2. In this regime it is not admissible to do a single experiment and from the observed conversion calculate a rate constant by assuming first order kinetics. Apparent "rate constants osculated in this way yield variable values that depend on the arbitrarily chosen conversion (slope of dashed lines, Fig. 4). 

For the particular case of an axisymmetric surface r(z), the curvature is the sum of the radius of the osculating circle (in the plane shared by the surface normal) and the curvature of r(z) in two dimensions ... 

The solution to the damped forced oscUlator differential equation proceeds as follows. Begin with (Braun, 1978) ... 

Synthesized oscUlator An instrument that digitally synthesizes a controlled-amplitude, controlled-frequency signal. The source is typically computer controllable, allowing a sweep (in discrete steps) of frequency. 

As a result of equation (9), the Mims ENDOR signal is minimal ( blind ) at t = (n/Aiso), n = 0 (which is experimentally meaningless), 1,2,..., and is maximum at T = [(In -F l)/2Aiso]. Mims ENDOR spectra of a broad H pattern can clearly show the oscUlating blind spot pattern... 

We believe that the arguments above should convince the reader that the interesting phenomenon detected by Carmeli and Nitzan is another manifestation of the decoupling effect, well understood at least since 1976 (see ref. 86). The only physical systems, the dissipative properties of which are completely independent of whether or not an external field is present, are the purely ideal Markovian ones. Non-Markovian systems in the presence of a strong external field provoking them to exhibit fast oscUlations are characterized by field-dependent dissipation properties. These decoupling effects have also been found in the field of molecular dynamics in the liquid state studied via computer simulation (see Evans, Chapter V in this volume). 

Schuster S, Marhl M, Hofer T. ModeUing of simple and complex calcium oscUlations - From single-cell responses to intercellular signalUng. Eur. J. Biochem. 2002 269 1333-1355. 

An alternative but not so general selection rule (it is restricted to the harmonic oscUlator approximation) is that dr is zero if... 

Fig. 14.1 Scheme and plots illustrating the dependence of nanoscale-confinement parameters T and/on the radius 6 of the osculating sphere at the protein-water interface. First-order contacts with a polar or nonpolar patch on the protein surface are treated individually. Values were determined at equilibrium obtained by integrating Newton s equations of motion in an NPT ensemble with box size 103 nm3, starting with the PDB structure embedded in a pre-equilibrated cell of water molecules. The box size was calibrated so that the solvation shell extended at least 10 A from the protein surface at all times. Simulations were performed as described in Chap. 4... 

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