Optimal Control of Markov Processes with Age-Dependent Transition Rates

We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterise the value function and optimal controls for both discounted and average cost cases.

Radiative transition in delta-doped GaAs superlattices

Radiative transition in delta-doped GaAs superlattices with a weak coupling was investigted at low temperature, The experimental results show that the transitions from both electron ground state and excited state to hole state have been observed, Based on the effective mass approximation theory, the structures of energy band and photoluminescence spectra for the samples used were calculated. Comparing the experiment with theory, a good agreement was abtained.

On transition rates in surface hopping

Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for nonadiabatic molecular dynamics. Despite its empirical effectiveness and popularity, a rigorous derivation of TSH as the classical limit of a combined quantum electron-nuclear dynamics is still missing. In this work, we aim to elucidate the theoretical basis for the widely used hopping rules. Naturally, we concentrate thereby on the formal aspects of the TSH. Using a Gaussian wave packet limit, we derive the transition rates governing the hopping process at a simple avoided level crossing. In this derivation, which gives insight into the physics underlying the hopping process, some essential features of the standard TSH algorithm are retrieved, namely (i) non-zero electronic transition rate ("hopping probability") at avoided crossings; (ii) rescaling of the nuclear velocities to conserve total energy; (iii) electronic transition rates linear in the nonadiabatic coupling vectors. The well-known Landau-Zener model is then used for illustration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770280]

Collisional-radiative calculations of He line emission in low-temperature plasmas

We present spectral modeling results for neutral helium. Our underlying atomic data contains radiative transition rates that are generated from atomic structure calculations and electron-impact excitation rates, that are determined from both the standard R-matrix method and the R-matrix with pseudostates RMPS method. In this paper, we focus on transitions of particular importance to diagnostic line ratios. For example, our calculated rate coefficient for the electron-impact transition 1s3s 1S→1s3p 1P, which has a pronounced effect on the 728.1 nm diagnostic spectral line, is found to be in good agreement with previous experimental mea- surements. We also consider transitions from the 1s2 1S ground and 1s2s 3S terms to terms of the n=4 shell. They are found to be affected significantly by coupling of the bound states to the target continuum continuum coupling, which is included in our RMPS calculation, but not in our standard R-matrix calculation. We perform collisional-radiative calculations to determine spectral line intensity ratios for three ratios of particular interest, namely the 504.8 nm/471.3 nm, 492.2 nm/471.3 nm, and 492.2 nm/504.8 nm line ratios. Comparing our results determined from the RMPS excitation rates with those from the standard R-matrix excitation rates, we find that continuum coupling affects the rate coefficients significantly, leading to different values for all three line ratios. We also compare our modeling results with spectral measurements taken recently on the Auburn Helicon plasma device, finding that the ground and metastable populations are not in equilibrium, and that the experimental measurements are more consistent with the 1s2s 3S metastable term populations being short lived in the plasma.

The effects of radiative cascades on the x-ray diagnostic lines of Fe16+

We present complete collisional-radiative modelling results for the soft x-ray emission lines of Fe16+ in the 15 Å–17 Å range. These lines have been the subject of much controversy in the astrophysical and laboratory plasma community. Radiative transition rates are generated from fully relativistic atomic structure calculations. Electron-impact excitation cross sections are determined using a fully relativistic R-matrix method employing 139 coupled atomic levels through n = 5. We find that, in all cases, using a simple ratio of the collisional rate coefficient times a radiative branching factor is not sufficient to model the widely used diagnostic line ratios. One has to include the effects of collisional-radiative cascades in a population model to achieve accurate line ratios. Our line ratio results agree well with several previous calculations and reasonably well with tokamak experimental measurements, assuming a Maxwellian electron-energy distribution. Our modelling results for four EBIT line ratios, assuming a narrow Gaussian electron-energy distribution, are in generally poor agreement with all four NIST measurements but are in better agreement with the two LLNL measurements. These results suggest the need for an investigation of the theoretical polarization calculations that are required to interpret the EBIT line ratio measurements.

Critical behavior of a contact process with aperiodic transition rates

We performed Monte Carlo simulations to investigate the steady-state critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

Estimating Multiple Tumor Transition Rates Based on Data from Survival/Sacrifice Experiments

In this paper, we focus on the model for two types of tumors. Tumor development can be described by four types of death rates and four tumor transition rates. We present a general semi-parametric model to estimate the tumor transition rates based on data from survival/sacrifice experiments. In the model, we make a proportional assumption of tumor transition rates on a common parametric function but no assumption of the death rates from any states. We derived the likelihood function of the data observed in such an experiment, and an EM algorithm that simplified estimating procedures. This article extends work on semi-parametric models for one type of tumor (see Portier and Dinse and Dinse) to two types of tumors.

Declining transition rates to psychosis: The role of diagnostic spectra and symptom overlaps in individuals with attenuated psychosis syndrome

Transition to psychosis in at-risk individuals has markedly declined in recent years. So far it has never been discussed in detail that with the growing awareness and increasing availability of early psychosis services, a much broader diagnostic spectrum is now being seen in these services. Subsequently, subjects present with symptoms that meet psychosis risk on a purely psychometric basis but may be the phenotypical expression of another underlying mental disorder. Here we critically review four groups of symptoms and clinical features that are frequently reported by individuals with suspected psychosis risk states, yet share strong commonalities with other mental disorders and conditions: isolated hallucinations; unusual bodily perceptions, hypochondriatic fears and cenesthetic psychotic symptoms; depersonalization; obsessive–compulsive, overvalued and delusional ideas. Of the 616 individuals so far assessed in the Bruderholz Early Psychosis Outpatient Service for Adolescents and Young Adults, 218 (30.5%) met ultra-high risk (UHR) criteria, 188 (86.2%) of whom suffered from one of the four above-mentioned symptom groups. The appraisal of the diagnostic spectra and their overlapping symptoms constitute a tremendous challenge in the clinical assessment of each referred individual. The final conclusion of a clinical assessment should not end with the mere assignment – or non-assignment – to a presumed psychosis risk group, but needs to take into account the ‘Gestalt’ of these particular symptoms and clinical features and thus be based on many more facets than solely a psychometric or nosological approach. Such an approach may break down the heterogeneous psychosis risk group and enable appropriate treatment regimes.

Parametrization of the average ionization and radiative cooling rates of carbon plasmas in a wide range of density and temperature

In this work we present an analysis of the influence of the thermodynamic regime on the monochromatic emissivity, the radiative power loss and the radiative cooling rate for optically thin carbon plasmas over a wide range of electron temperature and density assuming steady state situations. Furthermore, we propose analytical expressions depending on the electron density and temperature for the average ionization and cooling rate based on polynomial fittings which are valid for the whole range of plasma conditions considered in this work.

Stochastic stability of nonlinear discrete-time Markovian jump systems with time-varying delay and partially unknown transition rates

This paper is concerned with stochastic stability of a class of nonlinear discrete-time Markovian jump systems with interval time-varying delay and partially unknown transition probabilities. A new weighted summation inequality is first derived. We then employ the newly derived inequality to establish delay-dependent conditions which guarantee the stochastic stability of the system. These conditions are derived in terms of tractable matrix inequalities which can be computationally solved by various convex optimized algorithms. Numerical examples are provided to illustrate the effectiveness of the obtained results.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}

Spectroscopic properties of Nd3+:(La,Sr)(Al,Ta)O-3 crystal

A new laser crystal Nd3+:(La, Sr)(Al, Ta)O-3 (abbreviated as Nd3+:LSAT) has been grown by the conventional Czochralski method. The absorption and luminescence spectra of trivalent neodymium in Nd3+:LSAT crystal were measured at room temperature. The value of absorption and emission cross-section was calculated. The Judd-Ofelt analysis was applied to the crystal to get the phenomenological parameters (Omega(i), i = 2,4,6), the line strengths, the radiative transition rates, the branching ratios and the radiative lifetime. (C) 2006 Elsevier B.V. All rights reserved.

Transparent Er3+-activated lead fluorogermanate glass ceramics

Transparent glass ceramics containing β-PbF2:Er 3+ nanocrystals were obtained through appropriate thermal treatments of a glass of molar composition 60PbGeO3-10PbF2-30CdF 2 doped with 0.5 mol% Er3+. Their optical properties, as well as upconversion processes among erbium ions in the glass and glass ceramic matrix were studied. From absorption spectra, Judd-Ofelt parameters and radiative transition rates for several excited levels were calculated. Emission spectra in the visible and NIR regions were collected, and stimulated emission cross sections were obtained by McCumber theory for the 4F 13/2→4I15/2 transition at 1.5 μm. Red and green upconversion emissions were measured in glass and glass ceramics upon excitation at 980 nm; lifetimes were measured in order to assess the upconversion mechanisms.