Grace M. Kepler

Modeling HIV Immune Response and Validation with Clinical Data

A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain features that have been shown to be important by recent experimental research are incorporated in the model. These include the role of CD4+memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. We show that this more biologically detailed model can exhibit the phenomenon of transient viremia experienced by some patients on therapy with viral load levels suppressed below the detection limit. We also show that the loss of CD4+T-cell help in the generation of CD8+memory cells leads to larger peak values for the viral load during transient viremia. Censored clinical data is used to obtain parameter estimates. We demonstrate that using a reduced set of 16 free parameters, obtained by fixing some parameters at their population averages, the model provides reasonable fits to the patient data and, moreover, that it exhibits good predictive capability. We further show that parameter values obtained for most clinical patients do not admit multiple locally a.s off-treatment equilibria. This suggests that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower (or zero) viral load is not possible for these patients.

Reduced order modeling and control of thin film growth in an HPCVD reactor

This paper describes the development of a reduced order model-based feedback control methodology for regulation of the growth of thin films in a high-pressure chemical vapor deposition (HPCVD) reactor. Precise control of the film thickness and composition is highly desirable, making real-time control of the deposition process very important. The source vapor species transport is modeled by the standard gas dynamics partial differential equations, with species decomposition reactions, reduced down to a small number of ordinary differential equations through use of the proper orthogonal decomposition technique. This system is coupled with a reduced order model of the surface reactions involved in the source vapor decomposition and film growth on the substrate. Also modeled is the real-time observation technique used to obtain a partial measurement of the deposition process.The utilization of reduced order models greatly simplifies the mathematical formulation of the physical process so that it can be solved...

Reduced order model compensator control of species transport in a CVD reactor

We propose the use of proper orthogonal decomposition (POD) techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapour deposition (HPCVD) reactor. In this paper, we present a proof-of-concept computational implementation of this method with a simplified growth example for III–V layers in which we implement Dirichlet boundary control of a dilute Group III reactant transported by convection and diffusion to an absorbing substrate with no reactions. We implement the model-based feedback control using a reduced order state estimator based on observations of the flux of reactant at the substrate centre. This is precisely the type of measurements available with current sensing technology. We demonstrate that the reduced order state estimator or compensator system is capable of substantial control authority when applied to a high-order system. In principle, these ideas can be extended to more general HPCVD control situations by including multiple species with gas-phase reactions and surface reactions. Copyright

Material surface design to counter electromagnetic interrogation of targets

Utilization of controllable ferromagnetic layers coating a conducting object to provide an attenuation capability against electromagnetic interrogation is discussed. The problem is formulated as a differential game and/or a robust optimization. The scattered field due to interrogation can be attenuated with the assumption of an uncertainty in the interrogation wave numbers. The controllable layer composed of ferromagnetic materials [H. How and C. Vittoria, Implementation of Microwave Active Nulling, private communication; H. How and C. Vittoria, IEEE Trans. Microwave Theory Tech., 52 (2004), pp. 2177-2182] is incorporated in a mathematical formulation based on the time-harmonic Maxwell equation. Fresnels law for the reflectance index is extended to the electromagnetic propagation in anisotropic composite layers of ferromagnetic and electronic devices and is used to demonstrate feasibility of control of reflections. Our methodology is also tested for a nonplanar geometry of the conducting object (an NACA ...

Compensator control for chemical vapor deposition film growth using reduced-order design models

We present a summary of investigations on the use of proper orthogonal decomposition techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapor deposition (HPCVD) reactor. These investigations incorporate multiple species and controls, gas phase reactions, and time dependent tracking signals that are consistent with pulsed vapor reactant inputs. Numerical implementation of the model-based feedback control uses a reduced-order state estimator, based on partial state observations of the fluxes of reactants at the substrate center, which can be achieved with current sensing technology. We demonstrate that the reduced-order state estimator or compensator system is capable of substantial control authority when applied to the full system.

Optimal design of a high pressure organometallic chemical vapor deposition reactor

A team composed of material scientists, physicists, and applied mathematicians have used computer simulations as a fundamental design tool in developing a new prototype High Pressure Organometallic Chemical Vapor Deposition (HPOMCVD) reactor for use in thin film crystal growth. Early design of the HPOMCVD reactor dramatically evolved long before any physical reactor was built. This effort offers a strong endorsement of such multidisciplinary, computationally based modeling teams in the design of new products in areas of emerging technologies where heretofore extensive and costly experimental design was the central paradigm.

Simulation of a vertical reactor for high pressure organometallic chemical vapor deposition

The suitability of a vertical cylindrical reactor with highly constrained radial flow from a central gas injection port past a set of heated substrate wafers that are embedded in the top channel wall has been evaluated in the context of organometallic chemical vapor deposition (OMCVD) at elevated pressure. Numerical simulations showed that, in addition to the limitation on the channel height necessary for preventing buoyancy driven recirculation, negotiating the ninety-degree bend at the inlet is problematic and also constrains the channel height below a critical value, at which the radial flow area after the inlet bend is equal to the cross-sectional area of the central gas injection port. Restricting the channel height poses the danger of heating of the channel wall opposite to the substrate wafers causing potential problems with deposition of decomposition products and competitive polycrystalline film growth at this location. These problems can be avoided by actively cooling the channel wall opposite to the substrate and by keeping the retention time of the source vapor molecules and fragments thereof in the wafer location below a critical value.

Reduced order computational methods for electromagnetic material interrogation using pulsed signals and conductive reflecting interfaces

We consider the interrogation by means of a pulsed planar electromagnetic wave of a dielectric slab with a supraconductive backing. Previous work using a weak formulation with finite elements (FE) demonstrated the ability to determine material parameters and the slab thickness in the inverse problem. In this work we report on results using Proper Orthogonal Decomposition (POD) to create a more efficient set of basis functions than the standard FE basis functions. We first demonstrate the ability of the reduced basis POD formulation to capture the electromagnetic behavior in the case of the forward problem. We then apply the POD formulation to the inverse scattering problem with unknown parameters and show that the POD formulation provides a considerable reduction in computational time over standard FE methods with comparable ability to recover the unknown parameter values.

INVERSE PROBLEMS AND MODEL VALIDATION: AN EXAMPLE FROM LATENT VIRUS REACTIVATION

We consider a least squares inverse problem with a model for inducer-mediated reactivation of latent viruses. We illustrate the difficulties associated with the lack of sufficient data (quantity as well as form) in such problems. The modeling and estimation efforts described suggest new experiments as well as needed model extensions.

Heteroepitaxial processes at low and elevated pressures

Based on design criteria established in preceding work for conditions of moderately elevated pressure (less than or equal to 8 bar) we have designed and evaluated a reactor for chemical vapor deposition (CVD) at high pressure (less than or equal to 100 bar). While at moderate pressure non-turbulent unidirectional forced channel flow past a heated substrate wafer can be realized, at high pressure, the flow is expected to become turbulent. Due to phase front distortions and variations in angle of incidence associated with density fluctuations and density gradients in the high pressure vapor phase in the vicinity of the hot substrate -- the precision of methods of real-time optical process monitoring that employ polarized light, such as, p-polarized reflectance spectroscopy (PRS), is degraded. Above a critical pressure, features in the optical signals related to chemical kinetics and to the kinetics of heteroepitaxy, thus are no longer resolved. Therefore, experimentation at reduced gravity, which extends the pressure range of non-turbulent flow, and alternative robust methods of real-time optical process monitoring are considered. At very high pressures, where real-time process monitoring is severely curtailed, CVD processing must rely on predictions of numerical models -- validated by experimentation at lower pressure/low gravity. Experimentation at high pressure is needed to access materials, properties and/or structures that otherwise cannot be realized.