Stepwise perturbation

Czerlinski, G.H. (1966). Chemical Relaxation An Introduction to Theory and Application of Stepwise Perturbation. Marcel Dekker Inc., New York... 

Czerlinski, (1966). Chemical relaxation. An introduction to the theory and application of stepwise perturbation. Edward Arnold, London Dekker, New York. 

K z) has a characteristic shape, allowing an evaluation which leads directly to the main parameters of the stack structure. In order to explain the procedure, we first establish the shape of K z) for a strictly periodic two-phase system and then proceed by a consideration of the modifications introduced by a stepwise perturbation of the system. Figure A.2 provides an illustration and sketches all the steps. 

Since the splitting patterns calculated by the above mentioned procedure are based on pre-defined fixed coupling constant values, there may be some deviations between calculated and observed patterns. Therefore a stepwise perturbation procedure is employed for comparing these two patterns as follows ... 

The change of external parameter that induces the relaxation of the system can be of different types stepwise, rectangular, or harmonic. Consider the simplest case, that of a stepwise perturbation as in temperature-jiunp (T-jump), pressure-jump (p-jump), or electrical field-jump (E-jump) studies. Figure 2.1A shows the time-dependence of the perturbation, that is, the imposed variation, here the tempera-tme T(t) and the response of the system, P(t). The response is in fact the variation with time of a property P of the system measured as the system shifts toward its new state of equilibrium. The property P is selected as to be proportional to... 

It is necessary to analyze the responses of the plant against stepwise perturbations in the components used for plant control. In BWRs, these components are the control rods, the recirculation pumps, the feedwater pumps and the turbine control valves. 

Figure 3 The collapse of the peptide Ace-Nle30-Nme under deeply quenched poor solvent conditions monitored by both radius of gyration (Panel A) and energy relaxation (Panel B). MC simulations were performed in dihedral space 81% of moves attempted to change angles, 9% sampled the w angles, and 10% the side chains. For the randomized case (solid line), all angles were uniformly sampled from the interval —180° to 180° each time. For the stepwise case (dashed line), dihedral angles were perturbed uniformly by a maximum of 10° for 4>/ / moves, 2° for w moves, and 30° for side-chain moves. In the mixed case (dash-dotted line), the stepwise protocol was modified to include nonlocal moves with fractions of 20% for 4>/ J/ moves, 10% for to moves, and 30% for side-chain moves. For each of the three cases, data from 20 independent runs were combined to yield the traces shown. CPU times are approximate, since stochastic variations in runtime were observed for the independent runs. Each run comprised of 3 x 107 steps. Error estimates are not shown in the interest of clarity, but indicated the results to be robust.

More complex temperature programmes are sometimes useful. These might combine periods of variable heating and cooling rates with isothermal periods. For example, stepwise heating can be used to detect the onset of melting under quasi-isothermal conditions (Laye, 2002). Modulated temperature DSC (MTDSC), in which the linear temperature scan is perturbed by a sinusoidal, square or saw-tooth wave, or other modulation of temperature, has a number of potential advantages over the conventional linear scan. These include increased sensitivity and resolution, and the ability to separate multiple thermal events (Laye, 2002). 

Diffusion time (diffusion time constant) — This parameter appears in numerous problems of - diffusion, diffusion-migration, or convective diffusion (- diffusion, subentry -> convective diffusion) of an electroactive species inside solution or a solid phase and means a characteristic time interval for the process to approach an equilibrium or a steady state after a perturbation, e.g., a stepwise change of the electrode potential. For onedimensional transport across a uniform layer of thickness L the diffusion time constant, iq, is of the order of L2/D (D, -> diffusion coefficient of the rate-determining species). For spherical diffusion (inside a spherical volume or in the solution to the surface of a spherical electrode) r spherical diffusion). The same expression is valid for hemispherical diffusion in a half-space (occupied by a solution or another conducting medium) to the surface of a disk electrode, R being the disk radius (-> diffusion, subentry -> hemispherical diffusion). For the relaxation of the concentration profile after an electrical perturbation (e.g., a potential step) Tj = L /D LD being - diffusion layer thickness in steady-state conditions. All these expressions can be derived from the qualitative estimate of the thickness of the nonstationary layer... 

The evidence for the mechanisms of the mass-spectrometric and photochemical reactions leading to the eliminations of an olefin from a ketone [equation (120)] have been summarized (Section VIIDl). If it is accepted that the structure of the fragment ion from this process has an enolic structure, it is possible to discuss the mechanism of the reaction theoretically. The reaction appears to consist of two parts, first the transfer of hydrogen and second, the elimination of olefin. There has been considerable conjecture as to whether these parts of the mass-spectrometric McLafferty rearrangement are stepwise or concerted. Prom their self-consistent field calculations, Boer et al. (1968) have concluded the reaction is step-wise. From perturbation and valence-electron molecular orbital calculations, Dougherty (1968b) has concluded the reaction is concerted. The above results depend on the adjustable parameters fed into the equations one set of parameters may eventually prove to be better. 

Perturbation theory, which largely corrected the errors of the HF and CASSCF methods for the concerted pathway, fails to properly estimate the energy of 6 relative to 4. MP2 suggests that the stepwise barrier is 22 kcal mol" above the concerted TS, while CASSCF-MP2 suggests a separation of less than 2 kcal mol . However, the MR-AQCC method predicts that 6 lies about 6 kcal mol" above 4, ° in accord with experimental evidence. The Cl methods also largely fail, predicting that the stepwise path is disfavored by about 10 kcal mol". ... 

Thirty years of research with bacteriorhodopsin has provided answers to many questions about how protons are transported by transmembrane pumps. In this small seven-transmembrane protein, absorption of light by the retinal chromophore Initiates a reaction cycle in which the initial state recovers through multiple conformational changes of the retinal and the protein, and a proton Is translocated stepwise from one side of the membrane to the other. Spectroscopy, extensive use of site-specific mutations, and crystallography have defined the photocycle reactions in atomic detail and provide a step-by-step description of the proton transfers, the transient local and global perturbations in the protein and how they arise, and the energy flow through the system, which add up to the mechanism of the pump. 

The protein systems were equilibrated by a 20 ps stepwise heating scheme and thereafter 50 ps simulation at a constant temperature of 300 K. The water systems were equilibrated by directly simulating them for 50 ps at 300 K. The MD trajectories were run using a time step of 1 fs and energy data were collected every fifth step. The free energy perturbations were sampled using 47-83. -points and 5 ps simulation for each value of X,. Data from the first 2 ps of each step were discarded for equilibration. 

Pyridine adsorption on a self-supported wafer or on the solid deposited on a silicon slide, are compared. Results are similar and Fig. 4 summarized the spectra obtained by stepwise desorption of pyridine from cloverite deposited on silicon. At room temperature, pyridine interacts with hydro ls at 3673 and 3700 cm L The 944 cm band is also perturbed confirming that it is a vibrational band due to hydroxyl groups. The pyridine species formed are characterized as pyridinium species (1545 cm band) and coordinated species (1450 and 1610 cm bands). 

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