Markoff process

It may be shown [31] that, if the fluctuations are described by a stationary Markoff process, the diagonal elements of matrix W are determined by the off-diagonal elements Wij according to ... 

Fig. 36 shows experimental results in a single logarithmic graph. They are compared with the theoretical prediction of a stochastic Markoffs process. For details see [61]. 

Markoff processes, I should like to stress the fact that many of the ideas developed below are already weU known to specialists in the theory of stochastic processes [5]. By definition, the stochastic case is the case that P is a so-caUed stochastic matrix satisfying = 1 (whence Q satisfies... 

If one keeps this special case in mind, it should not be too hard to interpret the abstract arguments to be sketched below. Moreover, the fact that similar techniques have already been found appropriate for Markoff processes [5], ergodic theory, and even in the theory of radiation transfer [12], gives... 

Lax, M. (1966a). Classical noise. III Nonlinear Markoff processes. Rev. Mod. Phys., 38, 359-79. 

What has gone wrong in the analysis Why doesn t Eq. 4.21 work for the hypothetical mixture of polystyrene spheres in water The answer is that particle motions in a bidisperse system are not a Markoff process, because each particle has a memory. Each particle remembers its own size and diffusion coefficient. In fact, (, t)... 

Berne and Pecora s demonstration is a special case of Doob s theorem(5), which shows for random processes that are also Markoff processes, such as the processes generated by the Langevin equation, that P(Ax,t) must be a Gaussian having uncorrelated sequential steps, that Eq. 9.5 is correct, and that g q, t) must be a single exponential in t. A contrapositive to Doob s theorem shows that if g q, t) is not a simple exponential then 8x is not described by a Gaussian Markoff process, and Eq. 9.5 is not applicable. An explicit calculation has been given that correctly... 

In general D q,t) has a nontrivial q -dependence, so it is equally generally incorrect to replace D q,t)t with a -independent F t), hence the closing inequality in the above equation. In a viscoelastic fluid, such as most polymer solutions, the elastic moduli are frequency-dependent. The fluctuation-dissipation theorem then substantially guarantees that the random thermal forces on probe particles have nonzero correlation times, so probe motions in polymer solutions are not described by Markoff processes. The mathematically correct discussion in Berne and Pecora on Brownian particles, including Eq. 9.5, therefore does not apply to probes in polymer solutions. 

At elevated concentrations, light-scattering spectra of solutions of colloidal spheres become multimodal. Correspondingly, as required by Doob s theorem, particle motions cease to be described by a Gaussian random Markoff process. Segre, et al. report t), as obtained using a two-color, two-detector homo-... 

In this chapter we have shown that the dynamics and spectroscopy of the initial events taking place in bacterial photosynthetic RCs can be described by the model shown in Table I and Fig. 19. Using these physical constants we can calculate the absorption spectra, ET rate constants, and fs time-resolved spectra. It should be noted that for processes taking place in sub-ps range, it is more reasonable not to use rate constant because the concept of rate constant requires the validity of the Markoff approximation [82,88]. Instead the... 

Ear less is known about the process of flavivirus assembly. Electron microscopy has shown that immature virions can be found in the lumen of the endoplasmic reticulum (Murphy, 1980). The nucleocapsid core is not assembled free in the cytoplasm rather, its assembly appears to take place on the cytoplasmic face of membranes with which prM and E proteins are associated (Khromykh et al., 2001). The carboxy-terminal signal sequence of the precursor to the capsid protein is thought to anchor that protein to the membrane (Amberg et al., 1994). This should allow interactions to occur between the capsid protein and the envelope proteins, which are also anchored to the membrane but reside in the lumen of the endoplasmic reticulum or vesicles. The capsid protein also contains a conserved stretch of hydrophobic residues located roughly in the middle of the protein that has been suggested to serve as an additional or alternative membrane anchor (Markoff et al., 1997). 

M. Green,/. Chem. Phys., 22, 398 (1954). Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. 

Green MS. Markoff random processes and the statistical mechanics of time-dependent phenomena. J Chem Phys 1952 20 1281-1295. 

The sequence distribution followed by copolymers produced by the conventional free radical processes at low conversions is the first-order Markoff distribution, which possesses an associated P-matrix. This model predicts ° "... 

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