Three-state jump model

Q and the Three-Time Correlation Function Two-State Jump Model Exact Solution... 

The Three-State Jump, Joint Conformation Model... 

The assumption of free rotation about each C-C bond in an alkyl chain can give conformations of molecules that are precluded on grounds of excluded-volume effects. Following Tsutsumi, a jump model was employed [8.11] to describe trans-gauche isomerisms in the chain of liquid crystals by allowing jumps about one bond at any one time. To evaluate internal correlation functions gi t), not only the equilibrium probabilities of occupation given by Eq. (8.4) are needed, but also the conditional probability P(7, t 7o,0), where 7 and 70 denote one of the three equilibrium states (1, 2, 3) at times t and zero, respectively,... 

Using real data, we are trying to find the suitable stochastic model. The collected dataset consists of the daily closing prices for 13 equity indexes from different countries. Starting from 1th January 1993 until 11th January 2013, the corresponding data series for each index forms 5000 daily points. In a preliminary study we found that the probabiUty distribution of the log-returns follows a combined density function of Normal and Laplace distribution, which is consistent with the previously mentioned proprieties of real data. In section 2, the model that we propose to use for the description of the dynamic of equity indexes is presented. First the data evolution is represented and briefly descried in order to clarify the chosen model motivation. Afterwards the two essential parts of the proposed model are represented the economic environmental is divided into three states (calm, normal and agitated) controlled by an external covariate that follows a Markov Chain, and the price evolution of different index at each state is considered to follow a log-normal diffusion, log-uniform jump... 

In general, jump models have been developed that permit instantaneous jumps between two or three nonequivalent molecular configurations. A more general formulation permitting jumps between several configurations is discussed in terms of lattice models. Jump models are particularly useful, in comparison to difiusion models, in that fluctuations in the intemuclear distance that may occur with the molecular motions can be accomodated easily. With the difiusion models, an avers e intemuclear distance r is used to calculate the dipolar contribution to relaxation parameters via Eq. (8). With jump models, the intemuclear distance can be explicitly specified for each jump state in this case the is removed from Eq. (8), and the distance... 

L.133 Using two sets of backbone RDC data, collected in bacteriophage Pfl and bicelle media, they obtained order tensor parameters using a set of crystallographic coordinates for the structural model. This allowed the refinement of C -C bond orientations, which then provided the basis for their quantitative interpretation of C -H RDCs for 38 out of a possible 49 residues in the context of three different models. The three models were (A) a static xi rotameric state (B) gaussian fluctuations about a mean xi torsion and (C) the population of multiple rotameric states. They found that nearly 75% of xi torsions examined could be adequately accounted for by a static model. By contrast, the data for 11 residues were much better fit when jumps between rotamers were permitted (model C). The authors note that relatively small harmonic fluctuations (model B) about the mean rotameric state produces only small effects on measured RDCs. This is supported by their observation that, except for one case, the static model reproduced the data as well as the gaussian fluctuation model. 

In this model (Table 3), substrate, A, is transformed to product, B, by an enzyme, E. The supply of A is large, ensuring far-from-equilibrium conditions. An intermediate, X, is produced autocatalytically, and degraded by the enzyme. (This feature of the model makes it unrealistic, as few autocatalytic processes arise this way.) The steady-state equation for X is cubic, and has three roots, or solutions for certain values of the parameters. One of the solutions is unstable a real system cannot maintain a steady-state concentration, [X]ss, with a value corresponding to this solution. Therefore, before [X]ss approaches such a value too closely, it jumps to a different value, corresponding to one of the stable solutions. This behavior leads, to hysteresis, as shown in Fig. 1. 

Figure 9-33a shows the predicted shear stress as a function of strain for the initial foam orientation depicted in Fig. 9-32. The stress grows continuously until at y = 1.15 a T1 reorganization occurs which brings the cell structure back to its starting state, and the stress jumps back to zero. Thereafter, the stress history repeats itself. Similar periodic stress patterns and stress jumps have been predicted for the three-dimensional tetrakaidecahedron foam model (Reinelt 1993). If the initial orientation is rotated through an angle of r/12 with respect to that shown in Fig. 9-32, the stress history also has jumps, but is aperiodic (see Fig. 9-33b). Aperiodic behavior is the norm, and periodic stress histories occur only for special initial orientations (Kraynik and Hansen 1986). These unsteady, discontinuous stress...

The stator of rotary Fi motor is composed of six proteins. Three of them catalyze the hydrolysis of ATP, which drives the rotation of a shaft. The shaft of this Fi complex is glued to a proton turbine called Fq, which is located in the internal membrane of mitochondria. The whole FoFi-ATPase synthesizes ATP using the proton flow across the inner membrane. The Fi protein complex can function in reverse and serve as a motor performing mechanical work. These motors are modeled as stochastic systems with random jumps between the chemical states. If the rotation follows discrete steps and substeps, then the shaft has motions between well-defined orientations corresponding to the chemical states of the motor leading to a stochastic system based on discrete states. The result still will be the transition rates of the random jumps between the discrete states. These transition rates depend on the mass action law of chemical kinetics. 

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