David J. Kirkner

The quantum transmitting boundary method

A numerical algorithm for the solution of the two‐dimensional effective mass Schrodinger equation for current‐carrying states is developed. Boundary conditions appropriate for such states are developed and a solution algorithm constructed that is based on the finite element method. The utility of the technique is illustrated by solving problems relevant to submicron semiconductor quantum device structures.

Stochastic modeling of microstructures

Preface Introduction Probability and Random Variables: A Short Resume Continuous Random Fields Random Point Fields Statistical Inference Material Media Microstructure: Modeling Issues Physical Phenomena in Random Microstructures: Selected Applications References Author Index Subject Index

Multisolute mass transport with chemical interaction kinetics

Abstract An algorithm, based on the finite-element method, for solving the multicomponent convection—dispersion equation with solid-phase chemical interaction is presented. The main feature of the method is the modularization of the chemical calculations. This unique feature makes the algorithm ideal for situations where several different chemical systems are to be explored. Example numerical results are compared with both analytical and experimental results.

Multicomponent solute transport with sorption and soluble complexation

Abstract A numerical algorithm for predicting the migration of multiple subsurface pollutants has been developed accounting for dispersion, convection, soluble complexation and solid phase accumulations (sorption). The basis of the model is a finite element solution of the mass transport equation. The essence of the algorithm is the treatment of the sorption terms as implicit functions of the total soluble concentrations facilitating a general and modularized treatment of solution phase and solid phase chemistry. Examples are presented illustrating the effects of soluble complexation and competitive sorption on the transport of multicomponent solutions.

Coupled finite element/boundary element method for semiconductor quantum devices with exposed surfaces

We present a study of the boundary conditions for the potential at exposed semiconductor surfaces in split‐gate structures, which views the exposed surface as the interface between the semiconductor and air. A two‐dimensional numerical algorithm is presented for the coupling between the nonlinear Poisson equation in the semiconductor(finite element method) and Laplace’s equation in the dielectric (boundary element method). The utility of the coupling method is demonstrated by simulating the potential distribution in an n‐type AlGaAs/GaAs split‐gate quantum wire structure within a semiclassical Thomas–Fermi charge model. We also present a comparison of our technique to more conventional Dirichlet and Neumann boundary conditions.

An eigenvalue method for open‐boundary quantum transmission problems

We present a numerical technique for open‐boundary quantum transmission problems which yields, as the direct solutions of appropriate eigenvalue problems, the energies of (i) quasi‐bound states and transmission poles, (ii) transmission ones, and (iii) transmission zeros. The eigenvalue problem results from reducing the inhomogeneous transmission problem to a homogeneous problem by forcing the in‐coming source term to zero. This homogeneous problem can be transformed to a standard linear eigenvalue problem. By treating either the transmission amplitude t(E) or the reflection amplitude r(E) as the known source term, this method also can be used to calculate the positions of transmission zeros and ones. We demonstrate the utility of this technique with several examples, such as single‐ and double‐barrier resonant tunneling and quantum waveguide systems, including t‐stubs and loops.

Finite Element Analysis of Multicomponent Contaminant Transport Including Precipitation-Dissolution Reactions

The determination of the fate of contaminants that enter groundwater systems pose difficult mathematical problems for the modeler. This is particularly true when complex multi component interactions occur among mobile and immobile species. The types of chemical reactions that can occur include; acid-base, adsorption-desorption, complex formation, ion exchange, oxidation-reduction and precipitation-dissolution. This paper will focus on the analysis of precipitation-dissolution reactions.

Compressive Strength Relationships for Concrete under Elevated Temperatures

This paper focuses on compressive strength relationships for the design of concrete structures under elevated temperatures from fire. The development of a database of previous experimental research on the temperature-dependent properties of unreinforced concrete is described. A comprehensive statistical analysis of the concrete strength data from this database is conducted using the method of multiple least-squares regression with coded variables. High-strength concrete (HSC) and normal-strength concrete (NSC) with normalweight and lightweight North American aggregates are considered in the investigation. The results are used to develop predictive relationships for the concrete strength loss under fire. Compared with existing strength loss relationships, the proposed relationships are based on a much larger data set, thus increasing statistical robustness. It is shown that a reasonable statistical fit is achieved with the available data, especially considering that the proposed relationships use relatively simple regression models suitable for design. The most significant parameters affecting the concrete strength loss with temperature are the concrete strength at room temperature, aggregate type, and heating test type. Through a critical evaluation of the current database, recommendations are presented for areas where future research should be directed. Recommendations are also made for presenting the results from future fire tests so that researchers can most effectively use this data.

A two-dimensional hot carrier injector for electron waveguide structures

Abstract The current-voltage characteristics for a constriction in a quantum waveguide channel are calculated. The constriction forms an effective barrier which can be employed as a tunneling injector. We find that such a structure may be useful in providing high-energy electrons in a single mode of the waveguide. We also examine the current in the far-from-linear response regime. Away from the linear region the current through the constriction saturates and the conductance falls to zero.

NON-LINEAR FINITE ELEMENT ANALYSIS TO PREDICT PERMANENT DEFORMATIONS IN PAVEMENT STRUCTURES UNDER MOVING LOADS.

The structural analysis of pavement systems is quite a difficult problem; it involves a layered medium, usually modeled as unbounded in extent, subjected to moving loads. A principle concern is the permanent deformation remaining when the load exceeds design values; the so-called rutting phenomenon. A steady, moving load, assumed quasi-static, can be handled by employing a moving coordinate system to advantage; in essence converting the modeling problem to one with a stationary load. However, the unbounded domain is still problematical. The common practice of using rollers on the boundaries of a truncated domain will lead to a loss of accuracy, especially for points near the truncated boundaries. In a finite element approach to the steady-state problem in which a load moves at a constant speed on an elastic-plastic layered system “boundary effects” due to the inherent nonlinear boundary conditions are so obvious that it is almost impossible to evaluate residual displacements. In this paper, a method is proposed to treat the involved, nonlinear boundary conditions and to allow accurate prediction of the residual displacements. A modified iterative scheme is constructed and infinite elements are employed to treat the unbounded domain. The infinite element formulation involves the residual displacements and, therefore, must be used together with the modified iterative scheme. Numerical results indicate that the adoption of the infinite elements together with the modified iterative scheme completely eliminate the “boundary effects” and greatly improve the accuracy of calculated residual displacements.