Phase shifts modeling

The relationship between mean squared phase shift and mean squared displacement can be modelled in a simple way as follows This motion is mediated by small, random jumps in position occurring with a mean interval ij. If the jump size in the gradient direction is e, then after n jumps at time the displacement of a spin is... 

We have derived time-reversible, symplectic, and second-order multiple-time-stepping methods for the finite-dimensional QCMD model. Theoretical results for general symplectic methods imply that the methods conserve energy over exponentially long periods of time up to small fluctuations. Furthermore, in the limit m —> 0, the adiabatic invariants corresponding to the underlying Born-Oppenheimer approximation will be preserved as well. Finally, the phase shift observed for symmetric methods with a single update of the classical momenta p per macro-time-step At should be avoided by... 

The summation for the coefficient of the P2 term likewise includes phase insensitive contributions where I m = Im, but also now one has terms for which I = I 2, which introduce a partial dependence on relative phase shifts— specifically on the cosine of the relative phase shift. Again, this conclusion has long been recognized for example, by an explicit factor cos(ri j — ri i) in one term of the Cooper-Zare formula for the photoelectron (3 parameter in a central potential model [43]. 

With some further assumptions, it is possible to use single frequency FLIM data to fit a two-component model, and calculate the relative concentration of each species, in each pixel [16], To simplify the analysis, we will assume that in each pixel of the sample we have a mixture of two components with single exponential decay kinetics. We assume that the unknown fluorescence lifetimes, iq and r2, are invariant in the sample. In each pixel, the relative concentrations of species may be different and are unknown. We first seek to estimate the two spatially invariant lifetimes, iq and t2. We make a transformation of the estimated phase-shifts and demodulations as follows ... 

Hellstrand That is what I am getting at. There are a lot of phase shifts in this system. One observation we have made is that under hypoxia we see a decrease in amplitude but an increase in frequency of the waves. We are trying to model a case where this would account for reduction of force simply on the basis of non-linearity of the [Ca2+] versus myosin phosphorylation versus force reactions. It seems intuitively that this could explain why there can be a reduction in force although there is no reduction in the overall level of global Ca2+. Is amplitude modulation something that people have seen ... 

The results obtained with the model for the mammalian circadian clock provide cues for circadian-rhythm-related sleep disorders in humans [117]. Thus permanent phase shifts in LD conditions could account for (a) the familial advanced sleep phase syndrome (FASPS) associated with PER hypopho-sphorylation [118, 119] and (b) the delayed sleep phase syndrome, which is also related to PER [120]. People affected by FASPS fall asleep around 7 30 p.m. and awake around 4 30 a.m. The duration of sleep is thus normal, but the phase is advanced by several hours. Moreover, the autonomous period measured for circadian rhythms in constant conditions is shorter [121]. The model shows that a decrease in the activity of the kinase responsible for PER phosphorylation is indeed accompanied by a reduction of the circadian period in continuous darkness and by a phase advance upon entrainment of the rhythm by the LD cycle [114]. 

All these methods exploit the fact that there is no need to recalculate the structure factors of the model each time it is rotated or translated it is sufficient to be able to sample the structure factors at the rotated Miller indices, with or without a phase shift coming from the translation, and this can be done quite effectively by interpolation in reciprocal space (see Protocol 7.4). 

This is a very fundamental hypothesis (very well verified indeed within the accuracy limits +0,02 A) of EXAFS and allows the analysis of an unknown system, say an interface between a transition metal and silicon, by using the amplitudes and phase shifts from a model compound of known crystallography, say a silicide. 

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