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Projects in 1977–1978


California State Architect's Office: Life Cycle Costing

Advisor
Eliot Bradford

Methods for making decisions about purchase, design and refurbishing of buildings, for choices among competing alternatives. The rationale for this approach to estimating the true cost of a structure over its lifetime was investigated and developed. A catalog of cost categories was constructed and utilized, including initial costs, site development, energy costs, maintenance and salvage costs. A computer program, and a user's manual for it, were prepared to cover a wide class of applications.

Chevron Oil Field Research Company: Supernormal Pressures: ETC

Advisor
Ellis Cumberbatch

The abnormal pressures are found during oil well drilling. A mathematical model has been developed incorporating deposition of different material layers over millions of years, and their subsequent compaction. Release of bound water (diagenesis) is included. The purpose of this project was to modify this model to include the modeling of leaks (transverse water flows), and variable densities.

Chevron Oil Field Research Company: Abnormally High Pressure in Sedimentary Basins

Advisor
Courtney Coleman

The team continued work on a complex model of vertical fluid flow over geologic time through the pore spaces of a compacting sedimentary column, taking into account fluid production by diagenesis. The computer program for approximating the solutions of the equations of the model was substantially improved.

General Dynamics: Analytic Model of the Concentration of CO2

Advisor
Jerren Gould
College
CGU

Knowledge of the distribution of atmospheric carbon dioxide concentration is valuable for determining the effects of CO$_2$ emission/absorption and alleviating the problem of nearfield interference in infra-red sensing devices. Two foci of this project's work were the lower troposphere (0-2km) and mid troposphere (2-10km). Based on meterological and meteortopical considerations, mathematical models of certain scenarios were created; numerical schemes and some closed form solutions for the governing partial differential equations were developed and implemented. In at least one case the estimates of the physical parameters were incorporated to produce a “picture” of CO$_2$ distribution for the scenario.

Honeywell Marine Systems Division: Digital Feedback Control of Targeting Devices

Advisor
Ellis Cumberbatch
College
CGU

The team developed a mathematical model of the dynamics of a T.V. camera-gun-target system controlled by digital rather than analogue devices. The problem of estimating the target locating when it has been obscured for some time was studied and the team developed an algorithm for it. The team also developed computer programs for implementing the above models.

Jet Propulsion Laboratory, Caltech President's Fund: Search for Extraterrestrial Intelligence: Data Processing Techniques

Advisors
Ken Cooke
Richard Elderkin

Efforts to discover evidence of intelligent extraterrestrial life have recently been undertaken in several places, including JPL. The essence of the JPL approach is to perform broad frequency sky-surveys, using sophisticated receiving and data processing systems. In this project the team worked with scientists from JPL to analyze the methodology associated with the design of very large fast Fourier transform data processing devices. The team was asked to conduct a mathematical study of sources and effects of errors in the data processing. Topics which were considered included effects of analog to digital conversion and sampling error, memory precision and rounding, machine arithmetic, and Fourier coefficient quantization error. A considerable search of the mathematics and engineering literature yielded many useful techniques for analysis, which in most cases needed significant adaptation to the JPL project. The team was successful in accomplishing that adaptation and in providing original analysis in some project-specific instances.

Pomona Valley Municipal Water District: A Method for Predicting Groundwater Nitrate Concentrations Vol II

Advisor
Greg Pierce

A continuation of last year's project, validation of the contour mapping program and optimal interpolation parameters and additional geographic factors were stressed. The predictive model was thoroughly tested against experimental data, and modified when necessary to increase its accuracy and efficiency. In particular, empirical models were introduced in at least two instances where the physics and chemistry is not properly researched or understood. The applicability of new mathematical procedures, including a non-linear finite-element method and perturbation techniques, were investigated.

TRASANA: Multivariate Data Analysis

Advisor
James Lucke
College
CMC/IDS

Investigations of cluster analysis, discriminant analysis and pattern recognition continued in order to develop efficient methods to organize data from simulation testing. In addition to continued search of the literature and developing the background theory, programs for different types of algorithms were written, tested, and compared on artificial and real data. In addition, some further study of the Myhre-Saunders model of reliability was undertaken to determine its area of applications and to increase its usefulness. Computer simulations were used to study the robustness of the model and to develop a lower confidence bound procedure.

U.S. Forest Service Fire Lab: Mathematical Simulation of Chaparral Management Alternatives

Advisor
Greg Pierce
College
CGU

The team developed mathematical models to assess possible fire control strategies for chaparral lands in Southern California. The mechanism of control lies in the creation of regions of younger fire-resistant chaparral interspersed among areas of older highly flammable chaparral. This could be achieved by setting controlled fires under favorable conditions for containment, by using herbicides, or by a variety of other strategies. The expectation was that the total cost of fires in terms of human and animal life and loss of watershed and property could thus be minimized. Relevant literature was searched, and with this information a computer model was developed to predict best mixes of chaparral, age-class mosaic sizes and distribution.