Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Fokker-Planck Equation for a Metastable Time Dependent Potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

AN ILLNESS-DEATH PROCESS WITH TIME-DEPENDENT COVARIATES

A general model for the illness-death stochastic process with covariates has been developed for the analysis of survival data. This model incorporates important baseline and time-dependent covariates to make proper adjustment for the transition probabilities and survival probabilities. The follow-up period is subdivided into small intervals and a constant hazard is assumed for each interval. An approximation formula is derived to estimate the transition parameters when the exact transition time is unknown.^ The method developed is illustrated by using data from a study on the prevention of the recurrence of a myocardial infarction and subsequent mortality, the Beta-Blocker Heart Attack Trial (BHAT). This method provides an analytical approach which simultaneously includes provision for both fatal and nonfatal events in the model. According to this analysis, the effectiveness of the treatment can be compared between the Placebo and Propranolol treatment groups with respect to fatal and nonfatal events. ^

Time-dependent monoenergetic neutron transport in two adjacent semi-infinite media

An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence.

The general result is expressed as a sum of definite, multiple integrals, one of which contains the uncollided wave of neutrons originating at the source plane. It is possible to obtain a simplified form for the solution at the interface, and certain numerical calculations are made there.

The interface flux in two adjacent moderators is calculated and plotted as a function of time for several moderator materials. For each case it is found that the flux decay curve has an asymptotic slope given accurately by diffusion theory. Furthermore, the interface current is observed to change directions when the scattering and absorption cross sections of the two moderator materials are related in a certain manner. More specifically, the reflection process in two adjacent moderators appears to depend initially on the scattering properties and for long times on the absorption properties of the media.

This analysis contains both the single infinite and semi-infinite medium problems as special cases. The results in these two special cases provide a check on the accuracy of the general solution since they agree with solutions of these problems obtained by separate analyses.

Photoregulated or energy dependent process of hormogonia differentiation in Nostoc sphaeroides Kutzing (Cyanobacterium)

Hormogonium, which was thought to play an important role in the dispersal and survival of these microorganisms in their natural habitats, is a distinguishable developmental stage of heterocystous cyanobacteria. The present study examined the effects of different light conditions and sugars on the differentiation of Nostoc sphaeroides Kutzing to the hormogonia stage. Results showed that differentiation of hormogonia was light dependent in the absence of sugar, but that close to 100% of cyanobacteria differentiated to hormogonia in the presence of glucose or sucrose, irrespective of the light conditions. This differentiation was inhibited, even in the presence of sugars, upon application of an inhibitor of respiration. Following the testing of different sugars, the effects of different lights were examined. It was found that 5 10 μ mol.m(-2)• s(-1) photon flux density was optimal for hormogonia differentiation. One hundred percent differentiation was obtained with white light irradiation, in contrast with irradiation with green light (80% differentiation) and red light (0-10% differentiation). Although they showed different efficiencies in inducing hormogonia differentiation in N. sphaeroides, the green and red radiation did not display antagonistic effects. When the additional aspect of time dependence was investigated through the application of different light radiations and an inhibitor of protein synthesis, it was found that the initial 6 h of the differentiation process was crucial for hormogonia differentiation. Taken together, these results show that hormogonia differentiation in N. sphaeroides is either a photoregulated or an energy dependent process.

TIME-DEPENDENT DENSITY FUNCTIONAL STUDY OF MULTIELECTRON TRANSFER IN Cq+-Na-4 COLLISIONS

The process of multielectron transfer from a Na-4 cluster induced by highly charged C6+, C4+, C2+ and C+ ions is studied using the method of time-dependent density functional theory within the local density approximation combined with the use of pseudopotential. The evolution of dipole moment changes and emitted electrons in Na-4 isobtained and the time-dependent probabilities with various charges are deduced. It is shown that the Na-4 cluster is strongly ionized by C6+ and that the number of emitted electrons per atom of Na-4 is larger than that of Na-2 under the same condition. One can find that the detailed information of the emitted electrons from Na-4 is different from the same from Na-2, which is possibly related to the difference in structure between the two clusters.

Time-dependent wavepacket approach to the influence of intense fields on the population of molecular excited states

The influence of laser-field parameters, such as intensity and pulse width, on the population of molecular excited state is investigated by using the time-dependent wavepacket method. For a two-state system in intense laser fields, the populations in the upper and lower states are given by the wavefunctions obtained by solving the Schrodinger equation through split-operator scheme. The calculation shows that both the laser intensity and the pulse width have a strong effect on the population in molecular excited state, and that as the common feature of light-matter interaction (LMI), the periodic changing of the population with the evolution time in each state can be interpreted by Rabi oscillation and area-theorem. The results illustrate that by controlling these two parameters, the needed population in excited state of interest can be obtained, which provides the foundation of light manipulation of molecular processes. (C) 2005 Elsevier B.V. All rights reserved.

Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Time dependent electric, magnetic and hydrodynamic interaction in aluminium electrolysis cells

The waves in commercial cells for electrolytic aluminium production originate at the interface between the liquid aluminium and electrolyte, but their effect can spread into the surrounding busbar network as electric current perturbation, and the total magnetic field acquires a time dependent component. The presented model for the wave development accounts for the nonuniform electric current distribution at the cathode and the whole network of the surrounding busbars. The magnetic field is computed for the continuous current in the fluid zones, all busbars and the ferromagnetic construction elements. When the electric current and the associated magnetic field are computed according to the actual electrical circuit and updated for all times, the instability growth rate is significantly affected. The presented numerical model for the wave and electromagnetic interaction demonstrates how different physical coupling factors are affecting the wave development in the electrolysis cells. These small amplitude self-sustained interface oscillations are damped in the presence of intense turbulent viscosity created by the horizontal circulation velocity field. Additionally, the horizontal circulation vortices create a pressure gradient contributing to the deformation of the interface. Instructive examples for the 500 kA demonstration cell are presented.

Vacuum arc remelting time dependent modelling

Vacuum arc remelting (VAR) aims at production of high quality, segregation-free alloys. The quality of the produced ingots depends on the operating conditions which could be monitored and analyzed using numerical modelling. The remelting process uniformity is controlled by critical medium scale time variations of the order 1-100 s, which are physically initiated by the droplet detachment and the large scale arc motion at the top of liquid pool [1,2]. The newly developed numerical modelling tools are addressing the 3-dimensional magnetohydrodynamic and thermal behaviour in the liquid zone and the adjacent ingot, electrode and crucible.

Time-dependent modelling and experimental validation of the metal/flux interface in a continuous casting mould

A finite volume computer model of the continuous casting process for steel flat products has been developed. In this first stage, the model concentrates on the hydrodynamic aspects of the process and in particular the dynamic behavior of the metal/slag interface. The model was validated against experimental measurements obtained in a water model apparatus.

Modelling the time-dependent behaviour of solder pastes used in the electronics assembly applications

Solder paste is the most widely used bonding material in the assembly of surface mount devices in electronic industries. It generally has a flocculated structure (show aggregation of solder particles), and hence are known to exhibit a thixotropic behavior. This is recognized by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterisation of this timedependent rheological behaviour of solder pastes is crucial for establishing the relationships between the pastes’ structure and flow behaviour; and for correlating the physical parameters with paste printing performance. In this paper, we present a novel method which has been developed for characterising the timedependent and non-Newtonian rheological behaviour of solder pastes as a function of shear rates. The objective of the study reported in this paper is to investigate the thixotropic build-up behaviour of solder pastes. The stretched exponential model(SEM) has been used to model the structural changes during the build-up process and to correlate model parameters with the paste printing process.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600404]

Time-dependent alterations of soluble and cellular components in human milk

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)