Generalized two-level quantum dynamics. II. Non-Hamiltonian state evolution

A theorem is derived that enables a systematic enumeration of all the linear superoperators (associated with a two-level quantum system) that generate, via the law of motion = , mappings (0) (t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state (t ) that is in some cases independent of (0).     

Single star evolution I. Massive stars and early evolution of low and intermediate mass stars

We survey the results of those model calculations of the early evolution of single stars that have been obtained over approximately the last decade, and compare some of these results with the observations, concentrating particularly on the comparison between theoretical predictions regarding surface abundances of red giants and Cepheids and abundance estimates obtained by an analysis of spectral data.For massive stars, we discuss the ramifications of the fact that the time scale for mass loss (via stellar winds) during main sequence and red supergiant evolution can be comparable to the nuclear burning timescale, noting in particular the unusual distribution of stars in the Hertzsprung-Russell diagram, and the probability that significant mass loss is responsible for the chemically highly evolved spectra of Wolf-Rayet stars. finally, we sketch (1) recent progresses in following the evolution of massive stars to the presupernova stage, which is described by a configuration consisting of a core of near-Chandrasekhar mass made up of iron peak elements and a series of “onion”-skin layers of less highly thermonuclearly processed matter and (2) recent progress in understanding the nature of the type II supernova phenomenon.For low and intermediate mass stars, we discuss postulated “extramixing” (beyond convective) processes, which may occur on the main sequence and on the first red giant branch, and continue on to a discussion of asymptotic giant branch evolution, placing considerable emphasis on the character of the thermal pulses that occur in such stars and, in particular, on the nucleosynthesis that occurs in the helium burning convective shells during these pulses and on the dredge-up phenomenon that brings fresh carbon and neutron-rich isotopes to the surface following pulse peak.     

A theorem allowing the derivation of deterministic evolution equations from stochastic evolution equations. III The Markovian-non-Markovian mix

The proof of a theorem that allows one to construct deterministic evolution equations from a set, with two subsets, containing two types of discrete stochastic evolution equation is developed. One subset evolves Markovianly and the other non-Markovianly. As an illustrative example, the deterministic evolution equations of quantum electrodynamics are derived from two sets of Markovian and non-Markovian stochastic evolution equations, of different type, after an average over realization, using the theorem. This example shows that deterministic differential equations that contain both first-order and second-order time derivatives can be derived after a Taylor series expansion of the dynamical variables. It is shown that the derivation of such deterministic differential equations can be done by solving a set of linear equations. Two explicit examples, the first containing updating rules that depend on one previous time step and the second containing updating rules that depend on two previous time steps, are given in detail in order to show step by step the linear transformations that allow one to obtain the deterministic differential equations.     

Corpuscular diagnostics of a hollow-cathode discharge-III. The metal-ions-regime evolution

The variations in time of mass spectra of ions, extracted from the hollow-cathode discharge in the regime of the intensive sputtering of the cathode material were measured. The mass spectrum changes in time conspicuously. From the results of measurements a distinct anisotropy of ion beam is inferred. The discharge turns into a metal-ions regime.The helpful discussions with Dr. J. Musil are gratefully acknowledged.     

Band structure and packet-martensite structure. Comparison of evolution paths

We consider the similarities and differences between the band substructure and the packet-martensite structure in Ni₃Fe alloyed with 38KhN3MFA steel. The variation of their quantitative characteristics with strain and with initial polycrystal grain size is analyzed. The main factors governing the morphological features and the behavior of the considered structures are found to be the laws governing the evolution of the dislocation-disclination ensemble.Tomsk Construction-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 13–19, October, 1992.     

Discrete stochastic evolution rules and continuum evolution equations

The continuum evolution equations are derived from updating rules for three classes of stochastic models. The first class corresponds to models whose stochastic continuum equations are of the Langevin type obtained after carrying out a “local average” known as coarse-graining. The second class consists of a hierarchy of continuum equations for the correlations of the dynamical variables obtained after making an average over realizations. This average generates a hierarchy of deterministic partial differential equations except when the dynamical variables do not depend on the values of the neighboring dynamical variables, in which case a hierarchy of ordinary differential equations is obtained. The third class of evolution equations for the correlations of the dynamical variable constitutes another hierarchy after calculating an average over both realizations and all the sites of the lattice. This double average generates a hierarchy of deterministic ordinary differential equations. The second and third classes of equations are truncated using a mean field (m,n)-closure approximation in order to obtain a finite set of equations. Illustrative examples of every class are given.     

Error threshold for spatially resolved evolution in the quasispecies model.

The error threshold for quasispecies in 1, 2, 3, and infinity dimensions is investigated by stochastic simulation and analytically. The results show a monotonic decrease in the maximal sustainable error probability with decreasing diffusion coefficient, independently of the spatial dimension. It is thereby established that physical interactions between sequences are necessary in order for spatial effects to enhance the stabilization of biological information. The analytically tractable behavior in an infinity-dimensional (simplex) space provides a good guide to the spatial dependence of the error threshold in lower dimensional Euclidean space.     

MRI based diffusion and perfusion predictive model to estimate stroke evolution.

In this study we present a novel automated strategy for predicting infarct evolution, based on MR diffusion and perfusion images acquired in the acute stage of stroke. The validity of this methodology was tested on novel patient data including data acquired from an independent stroke clinic. Regions-of-interest (ROIs) defining the initial diffusion lesion and tissue with abnormal hemodynamic function as defined by the mean transit time (MTT) abnormality were automatically extracted from DWI/PI maps. Quantitative measures of cerebral blood flow (CBF) and volume (CBV) along with ratio measures defined relative to the contralateral hemisphere (r(a)CBF and r(a)CBV) were calculated for the MTT ROIs. A parametric normal classifier algorithm incorporating these measures was used to predict infarct growth. The mean r(a)CBF and r(a)CBV values for eventually infarcted MTT tissue were 0.70 +/- 0.19 and 1.20 +/- 0.36. For recovered tissue the mean values were 0.99 +/- 0.25 and 1.87 +/- 0.71, respectively. There was a significant difference between these two regions for both measures (p < 0.003 and p < 0.001, respectively). Mean absolute measures of CBF (ml/100g/min) and CBV (ml/100g) for the total infarcted territory were 33.9 +/- 9.7 and 4.2 +/- 1.9. For recovered MTT tissue, the mean values were 41.5 +/- 7.2 and 5.3 +/- 1.2, respectively. A significant difference was also found for these regions (p < 0.009 and p < 0.036, respectively). The mean measures of sensitivity, specificity, positive and negative predictive values for modeling infarct evolution for the validation patient data were 0.72 +/- 0.05, 0.97 +/- 0.02, 0.68 +/- 0.07 and 0.97 +/- 0.02. We propose that this automated strategy may allow possible guided therapeutic intervention to stroke patients and evaluation of efficacy of novel stroke compounds in clinical drug trials.