Time-dependent Dynamic Model Research Articles

Experimental and numerical investigations of an orifice type cryogenic pulse tube refrigerator

A helium filled orifice type pulse tube refrigerator (OPTR) was designed, built and operated to provide cryogenic cooling. The OTPR is a traveling wave thermoacoustic refrigerator that operates on a modified reverse Stirling cycle. The experimental studies are carried out to characterize the performance of the OPTR at various values of the mean pressure of helium (0.35 MPa–2.2 MPa), amplitudes of pressure oscillations, frequencies of operation and sizes of orifice opening. A detailed time-dependent axisymmetric computational fluid dynamic (CFD) model of the OPTR is also developed to predict its performance. In the CFD model, the continuity, momentum and energy equations are solved for both the refrigerant gas (helium) and the porous media regions (the regenerator and the three heat-exchangers) in the OPTR. An improved representation of heat transfer in the porous media is achieved by employing a thermal non-equilibrium model to couple the gas and solid (porous media) energy equations. The computational results are compared with specific experimental results to validate the numerical model. The model predictions show better temporal comparisons with the experimental results when the effects of wall thicknesses and natural convective losses of the various components of the OPTR to the surroundings are included in the model.

The dynamic prediction of criminal recidivism: A three-wave prospective study.

A three-wave, prospective panel design was used to assess the extent to which static and dynamic risk factors could predict criminal recidivism in a sample of 136 adult male offenders released from Canadian federal prisons. Static measures were assessed only once, prior to release while dynamic measures were assessed on three separate occasions: pre-release, 1 month, and 3 months post-release. Recidivism was coded during an average of 10.2-month follow-up period (SD=19.2). A series of Cox regression survival analyses with time-dependent covariates and Receiver Operator Characteristic (ROC) analyses were conducted to assess predictive validity. Although the combined static and time-dependent dynamic model (AUC=.89, CI=.81-.93) significantly (p<.01) outperformed the pure static model (AUC=.81, CI=.73-.87) the confidence intervals did overlap to some extent. Implications for dynamic risk assessment and management are discussed.

Cost-effectiveness analysis of universal childhood vaccination against varicella in Brazil

This study conducts a cost-effectiveness analysis of a childhood universal varicella vaccination program in Brazil. An age and time-dependent dynamic model was developed to estimate the incidence of varicella for 30 years. Assuming a single-dose schedule; vaccine efficacy of 85% and coverage of 80%, the program could prevent 74,422,058 cases and 2905 deaths. It would cost R$ 3,178,396,110 and save R$ 660,076,410 to the society and R$ 365,602,305 to the healthcare system. The program is cost-effective (R$ 14,749 and R$ 16,582 per life-year saved under the societal and the healthcare system's perspective, respectively). The program's cost-effectiveness is highly sensitive to the vaccine price and number of doses.

Coherent Microwave Rayleigh Scattering from Resonance-Enhanced Multiphoton Ionization in Argon

Multiphoton ionization and electron recombination processes are studied in argon using coherent microwave Rayleigh scattering from a localized, resonance-enhanced multiphoton ionization produced plasma. A time dependent one-dimensional plasma dynamic model is developed to predict the time evolution of the microwave scattering from the plasma. Experimental results of the argon ionization spectrum and electron recombination rates are in good agreement with the model predictions.

Dynamical collapse in a degenerate binary fermion mixture using a hydrodynamic model

We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion–fermion mixture (DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances, there cannot be a collapse for repulsive interspecies fermion–fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion–fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model, we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion–fermion interaction (scattering length) to a large negative (attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose–Einstein condensation

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schrödinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose–Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type.

State-space modeling and analysis of fault arcs

This paper presents a state-space technique for the transient analysis of power systems arcing faults, using the time-dependent dynamic resistance model. The state equations describing the system behavior are derived and these equations are solved by the use of numerical integration. Based on the solution technique, a computer program in the MATLAB environment is developed. The computer program is capable of directly formulating the state equations for a transmission line with a fault arc and it produces data for the arc voltage, current and resistance.

Exact time-dependent decoherence factor and its adiabatic classical limit

The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis–Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what is obtained by other authors, and furthermore we obtain more general results concerning time-dependent nonadiabatic quantum decoherence. It is shown that the invariant theory is appropriate for treating both the time-dependent quantum decoherence and the geometric phase factor. PACS Nos.: 03.65.Ge, 03.65.Bz

Response of the Baltic Sea to climate change—theory and observations

The dynamics controlling the response of the Baltic Sea to changed atmospheric and hydrologic forcing are reviewed and demonstrated using simple models. The response time for salt is 30 times longer than for heat in the Baltic Sea. In the course of a year, the Baltic Sea renews most of its heat but only about 3% of its salt. On the seasonal scale, surface temperature and ice-coverage are controlled by the atmospheric conditions over the Baltic Sea as demonstrated by e.g. the strong inter-annual variations in winter temperature and ice-coverage due to variations in dominating wind directions causing alternating mild and cold winters. The response of surface temperature and ice-coverage in the Baltic Sea to modest climate change may therefore be predicted using existing statistics. Due to the long response time in combination with complicated dynamics, the response of the salinity of the Baltic Sea cannot be predicted using existing statistics but has to be computed from mechanistic models. Salinity changes primarily through changes in the two major forcing factors: the supply of freshwater and the low-frequency sea level fluctuations in the Kattegat. The sensitivity of Baltic Sea salinity to changed freshwater supply is investigated using a simple mechanistic steady-state model that includes baroclinic geostrophic outflow from the Kattegat, the major dynamical factor controlling the freshwater content in the Kattegat and thereby the salinity of water flowing into the Baltic Sea. The computed sensitivity of Baltic Sea surface salinity to changes of freshwater supply is similar to earlier published estimates from time-dependent dynamical models with higher resolution. According to the model, the Baltic Sea would become fresh at a mean freshwater supply of about 60 000 m 3 s −1, i.e. a 300% increase of the contemporary supply. If the freshwater supply in the different basins increased in proportion to the present-day supply, the Bothnian Bay would become fresh already at a freshwater supply of about 37 000 m 3 s −1 and the Bothnian Sea at a supply of about 45 000 m 3 s −1. The assumption of baroclinic geostrophic outflow from the Kattegat, crucial for the salinity response of the Baltic Sea to changed freshwater supply, is validated using daily salinity profiles for the period 1931–1977 from lightship Läsö Nord.

Surface transport kinetics in low-temperature silicon deposition determined from topography evolution

In this article, surface transport kinetics during low-temperature silicon thin film deposition are characterized using time dependent surface topography and dynamic scaling models. Analysis of surface morphology indicates that diffusion of adsorbed species dominates surface transport, with a characteristic diffusion length that increases with surface temperature. A diffusion activation barrier of $\ensuremath{\sim}0.2 \mathrm{eV}$ is obtained, consistent with hydrogen-mediated adspecies diffusion on the growth silicon surface. Samples are compared over a range of deposition temperatures (25 to $350\ifmmode^\circ\else\textdegree\fi{}\mathrm{C})$ and film thickness (20 to $5000 \AA{})$ deposited using silane with helium or argon dilution, on glass and silicon substrates. Self-similar surface structure is found to depend on detailed film growth conditions, but is independent of film thickness after nuclei coalescence. For films deposited using helium dilution, static and dynamic scaling parameters are consistent with self-similar fractal geometry scaling, and the lateral correlation length increases from 45 to 150 nm as temperature increases from 25 to $150\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}.$ These results are discussed in relation to current silicon deposition models and with topography evolution observed during low temperature growth of other amorphous material systems.

Modelling of LIBS plasma expansion

A one-dimensional time-dependent fluid dynamic model has been developed to describe the expansion of the plume produced by laser ablation. The model includes chemical reactions considered in local thermodynamic equilibrium to describe the expansion of a TiO plasma. The results are discussed in connection with LIBS plasmas.

The Postshock Chemical Lifetimes of Outflow Tracers and a Possible New Mechanism to Produce Water Ice Mantles

We have used a coupled time-dependent chemical and dynamical model to investigate the lifetime of the chemical legacy in the wake of C-type shocks. We concentrate this study on the chemistry of and O2, two molecules which are predicted to have abundances that are significantly affected in shock-heated gas. Two models are presented: (1) a three-stage model of preshock, shocked, and postshock gas; and (2) a Monte Carlo cloud simulation where we explore the effects of stochastic shock activity on molecular gas over a cloud lifetime. For both models we separately examine the pure gas-phase chemistry as well as the chemistry including the interactions of molecules with grain surfaces. In agreement with previous studies, we find that shock velocities in excess of 10 km/s are required to convert all of the oxygen not locked in CO into before the gas has an opportunity to cool. For pure gas phase models the lifetime of the high water abundances, or H2O legacy, in the postshock gas is approximately (4-7) x 10(exp 5) yr, independent of the gas density. A density dependence for the lifetime of is found in gas-grain models as the water molecules deplete onto grains at the depletion timescale. Through the Monte Carlo cloud simulation we demonstrate that the time-average abundance of H2O, the weighted average of the amount of time gas spends in preshock, shock, and postshock stages, is a sensitive function of the frequency of shocks. Thus we predict that the abundance of H2O, and to a lesser extent O2, can be used to trace the history of shock activity in molecular gas. We use previous large-scale surveys of molecular outflows to constrain the frequency of 10 km/s shocks in regions with varying star formation properties and discuss the observations required to test these results. We discuss the postshock lifetimes for other possible outflow tracers (e.g., SiO and CH3OH) and show that the differences between the lifetimes for various tracers can produce potentially observable chemical variations between younger and older outflows. For gas-grain models we find that the abundance of water-ice on grain surfaces can be quite large and is comparable to that observed in molecular clouds. This offers a possible alternative method to create water mantles without resorting to grain surface chemistry: gas heating and chemical modification due to a C-type shock and subsequent depletion of the gas-phase species onto grain mantles.

Observational signatures of nanoflare heated solar stellar coronae

Using time-dependent dynamical models of the radiating gas in coronal flux tubes, we identify features in UV spectral line profiles that can reveal the direction in which energy flows through the solar transition region, in observations without temporal or spatial resolution. The profile features survive spatial and temporal averaging through non-linear dependencies of the line emission coefficients on thermal properties of the plasma that are correlated with the material velocity. This approach requires only low noise data of high spectral resolution and could naturally be applied to stars as well as the solar corona. We make predictions for the SUMER instrument that can in principle test whether energy propagates upwards or downwards in coronal flux tubes, suggesting a new angle of attack on the long standing problem of determining coronal heating mechanisms.

Interstellar Grains in Elliptical Galaxies: Grain Evolution

We consider the lifecycle of dust introduced into the hot interstellar medium in isolated elliptical galaxies. Dust grains are ejected into galactic-scale cooling flows in large ellipticals by normal mass loss from evolving red giants. Newly introduced dust rapidly enters the hot gas environment and is sputtered away by thermal collisions with ions. Before the grains are completely sputtered away, they emit prodigious amounts of infrared radiation which may contribute to the large far infrared luminosities observed in ellipticals. In order to study the global properties of grains in ellipticals we construct a new series of King-type galactic models which are consistent with the fundamental plane, galactic mass to light ratios and other relevant observational correlations. We describe a new ``continuity'' procedure to construct simple time-dependent gas dynamic models for cooling flows. In all galaxy models, although grains can flow a considerable distance from their radius of origin before being sputtered away, the grain size distribution is accurately determined by assuming {\it in situ} sputtering, completely ignoring advection. The dominant source of grain heating is absorption of starlight; grain heating by collisions with energetic thermal electrons or X-ray absorption are negligible. However, we also show that when self-consistent grain sputtering is included the dust-to-gas ratio is reduced and radiative cooling, not electron-grain interactions dominates plasma cooling, even for the most massive ellipticals.

Inverse methods and data assimilation in nonlinear ocean models

An overview is given of the current status of inverse methods and data assimilation for nonlinear ocean models. The inverse theory for time dependent dynamical models is formulated and the most promising solution methods like simulated annealing, the representer method, and sequential methods based on Monte Carlo simulations, are discussed with special focus on applications with nonlinear dynamics. A rather general “model independent” presentation has been used to make the methodology more accessible for different scientific areas dealing with dynamical models and data.

The application of reverse flow reactors to endothermic reactions

The concept of the reverse flow reactor traditionally used for mildly exothermic reactions has been extended to endothermic reactions and applied to the dehydrogenation of ethylbenzene. Periodic alternation of a reactant and a regenerating medium countercurrently over a fixed bed of catalyst in endothermic processes can be shown to result in higher conversions than traditional non-periodic systems. With this configuration several new process parameters are introduced such as total cycle time and the ratio of countercurrent flows. By judicious choice of operating conditions the hottest point of the reactor can be placed at the exit of the reactant stream allowing for much more favourable equilibriums and outlet conversions than if it were the coldest spot in the reactor as is common in steady-state processes. Two types of modeling are utilized. The first employs a technique which assumes that the switching is so rapid that the temperature distribution in the catalyst is in time independent steady-state. This high switching frequency model is compared against a more complicated time dependent dynamic model which traditionally is employed in reverse flow systems. Results for the first model are shown to be the limiting case of the dynamic model with fast switching. The models show significant conversion improvement with respect to existing steady state processes.

A Numerical Modeling Technique for Estimating Sulfur Dioxide Dry Deposition Due to Local Source Emissions

This paper describes a methodology for estimating the effect of local source emissions on dry deposition of sulfur dioxide in regions of complex terrain. Airflow in complex terrain is simulated by a time-dependent dynamical model for the meteorological fields. The results of the dynamical model are used to drive a semi-stochastic Lagrangian dispersion model in order to evaluate concentrations resulting from local source emissions. The Lagrangian dispersion model is coupled with a dry deposition treatment which includes the effects of both surface properties and micrometeoroiogical factors on deposition. A sample application is discussed for a source in the Shenandoah Valley. The largest concentrations and deposition rates were obtained shortly after sunrise, during the transition from the nocturnal to the daytime flow regime. These results suggest that dry deposition may be episodic.

Mixing by time-dependent convection

Two-dimensional numerical flow models are employed to study the mixing of passive heterogeneities in the earth's mantle. Both simple kinematic models of time-dependent flow and dynamic convection models are studied. Initially small blocks of tracers are inserted into the flow and their progressive dispersal is monitored through time. Some of the tracers also serve as infinitesimal strain markers. Three different regimes of mixing are observed: (A) all heterogeneities are rapidly strained and stirred according to a turbulent mixing law, where the size of a blob decreases exponentially with time; (B) most heterogeneities are only slowly strained and possibly follow a laminar mixing law with a linear decrease with time of the size of a heterogeneity; (C) the size reduction proceeds rapidly in part of the fluid, but some poorly stirred “islands” persist for a long time. All three regimes are found in various kinematic flow models, while in the dynamic convection models only regime A is observed. The effective strain rate in the exponential (turbulent) mixing law is more than an order of magnitude smaller than the average flow strain rate. When the results from the dynamic convection models with variable viscosity are scaled to the upper mantle, mixing over small length scales would be achieved after a few hundred million years. For whole-mantle convection with a significant increase of viscosity with depth, mixing times could be in the order of 1–2 Ga. In the latter case it appears marginally possible that part of the isotopic heterogeneity observed in oceanic basalts has evolved within the convecting mantle rather than in physically separated reservoirs.

Pion multiplicities in dynamical models of heavy ion collisions.

The effects of different ingredients of time-dependent dynamical simulation models are investigated. The variable of interest is the net ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$ production. I study the Ar+KCl data from ${E}_{\mathrm{lab}}$=0.36 to 1.808 GeV/nucleon with the momentum-dependent Boltzmann-Uehling-Uhlenbeck approach. Implications for the determination of the nuclear equation of state are mentioned and limitations of the model are considered.

Modelling and simulation of styrene-acrylonitrile emulsion polymerization kinetics

The emulsion polymerization kinetics of the styrene-acrylonitrile system have been studied. A dynamic time-dependent model has been developed, which successfully describes the course of the conversion of styrene as compared with that of acrylonitrile. This model avoids the difficulties encountered by previous models when applied to high acrylonitrile-content polymers, and is able to predict the conversion process for both batch and continuous reactors. The model is aimed at the simulation and operation of composition-controlled semibatch and continuous processes.