Proton transport model in the ionosphere .1. Multistream approach of the transport equations

The suprathermal particles, electrons and protons, coming from the magnetosphere and precipitating into the high-latitude atmosphere are an energy source of the Earth's ionosphere. They interact with ambient thermal gas through inelastic and elastic collisions. The physical quantities perturbed by these precipitations, such as the heating rate, the electron production rate, or the emission intensities, can be provided in solving the kinetic stationary Boltzmann equation. This equation yields particle fluxes as a function of altitude, energy, and pitch angle. While this equation has been solved through different ways for the electron transport and fully tested, the proton transport is more complicated. Because of charge-changing reactions, the latter is a set of two-coupled transport equations that must be solved: one for protons and the other for H atoms. We present here a new approach that solves the multistream proton/hydrogen transport equations encompassing the collision angular redistributions and the magnetic mirroring effect. In order to validate our model we discuss the energy conservation and we compare with another model under the same inputs and with rocket observations. The influence of the angular redistributions is discussed in a forthcoming paper.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.

On the inverse parabolicity of pdf equations in turbulent flows

The focus of the present work is the well-known feature of the probability density function (PDF) transport equations in turbulent flows-the inverse parabolicity of the equations. While it is quite common in fluid mechanics to interpret equations with direct (forward-time) parabolicity as diffusive (or as a combination of diffusion, convection and reaction), the possibility of a similar interpretation for equations with inverse parabolicity is not clear. According to Einstein's point of view, a diffusion process is associated with the random walk of some physical or imaginary particles, which can be modelled by a Markov diffusion process. In the present paper it is shown that the Markov diffusion process directly associated with the PDF equation represents a reasonable model for dealing with the PDFs of scalars but it significantly underestimates the diffusion rate required to simulate turbulent dispersion when the velocity components are considered.

Finite element modeling of fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins. (C) 2001 Elsevier Science B.V. All rights reserved.

A dynamic model with on-line identification for rotary sugar drying processes

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to reidentified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.place the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.

On the relation between the conditional moment closure and unsteady flamelets

We consider the relation between the conditional moment closure (CMC) and the unsteady flamelet model (FM). The CMC equations were originally constructed as global equations, while FM was derived asymptotically for a thin reaction zone. The recent tendency is to use FM-type equations as global equations. We investigate the possible consequences and suggest a new version of FM: coordinate-invariant FM (CIFM). Unlike FM, CIFM complies with conditional properties of the exact transport equations which are used effectively in CMC. We analyse the assumptions needed to obtain another global version of FM: representative interactive flamelets (RIF), from original FM and demonstrate that, in homogeneous turbulence, one of these assumptions is equivalent to the main CMC hypothesis.

A mechanistic model for carbon dioxide corrosion of mild steel in the presence of protective iron carbonate films - Part 3: Film growth model

A model of iron carbonate (FeCO3) film growth is proposed, which is an extension of the recent mechanistic model of carbon dioxide (CO2) corrosion by Nesic, et al. In the present model, the film growth occurs by precipitation of iron carbonate once saturation is exceeded. The kinetics of precipitation is dependent on temperature and local species concentrations that are calculated by solving the coupled species transport equations. Precipitation tends to build up a layer of FeCO3 on the surface of the steel and reduce the corrosion rate. On the other hand, the corrosion process induces voids under the precipitated film, thus increasing the porosity and leading to a higher corrosion rate. Depending on the environmental parameters such as temperature, pH, CO2 partial pressure, velocity, etc., the balance of the two processes can lead to a variety of outcomes. Very protective films and low corrosion rates are predicted at high pH, temperature, CO2 partial pressure, and Fe2+ ion concentration due to formation of dense protective films as expected. The model has been successfully calibrated against limited experimental data. Parametric testing of the model has been done to gain insight into the effect of various environmental parameters on iron carbonate film formation. The trends shown in the predictions agreed well with the general understanding of the CO2 corrosion process in the presence of iron carbonate films. The present model confirms that the concept of scaling tendency is a good tool for predicting the likelihood of protective iron carbonate film formation.

Modeling of optical detection of spin-polarized carrier injection into light-emitting devices

We investigate the emission of multimodal polarized light from light emitting devices due to spin-aligned carrier injection. The results are derived through operator Langevin equations, which include thermal and carrier-injection fluctuations, as well as nonradiative recombination and electronic g-factor temperature dependence. We study the dynamics of the optoelectronic processes and show how the temperature-dependent g factor and magnetic field affect the degree of polarization of the emitted light. In addition, at high temperatures, thermal fluctuation reduces the efficiency of the optoelectronic detection method for measuring the degree of spin polarization of carrier injection into nonmagnetic semicondutors.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Charge transport in a quantum electromechanical system

We describe a quantum electromechanical system comprising a single quantum dot harmonically bound between two electrodes and facilitating a tunneling current between them. An example of such a system is a fullerene molecule between two metal electrodes [Park et al., Nature 407, 57 (2000)]. The description is based on a quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise. This dynamical description is related to observable features of the system including the stationary current as a function of bias voltage

Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

Quantum noise in optical fibers. I. Stochastic equations

We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or 1P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.

Elliptic Gaudin models and elliptic KZ equations

The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.