Stochastic difference equation in length

A. Stochastic Difference in Time Definition A Stochastic Model for a Trajectory Weights of Trajectories and Sampling Procedures Mean Field Approach, Fast Equilibration, and Molecular Labeling Stochastic Difference Equation in Length Fractal Refinement of Trajectories Parameterized by Length... 

The stochastic difference equation in length is conceptually similar to the stochastic difference in time. We therefore do not repeat all of the arguments and... 

We are using a similar approach to define the analogous action for the stochastic difference equation in length, Ssdel [Sr is defined in Eq. (10)] ... 

In this review a variant of the SDET algorithm is summarized. In this more recent formulation called SDEL (for stochastic difference equation in length) the trajectory is parameterized as a function of its arc length and a unique path is obtained connecting the two boundary conformations [45,54,55]. In the next section, we will describe the algorithm and details of its numerical implementation to obtain conformational changes of peptides and folding mechanisms of protein systems. 

Apb is the scattering length density difference, Q is Porod s invariant, and Y the mean chord length. For the calculation of Yo(r) we approximated I(q) hy a cubic spline. The equations used for the calculation of " pore and " soUd are to be found in [8,30,39-41,47]. Analytical expressions for the descriptors of RES were published in [10,11,13,42,43]. In its most simple variant, the stochastic optimization procedure evolves the two-point probability S2 (r) of a binary representation of the sample towards S2(r) by randomly excWiging binary ceUs of different phases, starting from a random configuration which meets the preset volume fractions. After each exchange the objective function... 

From the above equation it follows that the surface salinity of the Baltic Sea is controlled by the ratio between the freshwater surplus and the sum of the stochastic salt fluxes normalized by the salinity difference between the Kattegat and the Arkona Sea surface water, see Fig. 2.6. The turbulent salt diffusivity k is a function of the geometry of the Belt Sea in terms of the length of the channel and the sill depth as well as of the spectrum of wind fluctuations determining the sea level difference between the Kattegat and the Arkona Sea and subsequently the barotropic current fluctuations in the Belt Sea. 

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