Physical Sciences and Mathematics Commons^™

Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty

Honors College Theses

As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete …

Using Odes To Model Drug Concentrations Within The Field Of Pharmacokinetics, Andrea Mcnally

Mathematics: Student Scholarship & Creative Works

No abstract provided.

Interdisciplinary Modeling For Water-Related Issues Graduate Course, Laurel Saito, Alexander Fernald, Timothy Link

All ECSTATIC Materials

The science and management of aquatic ecosystems is inherently interdisciplinary, with issues associated with hydrology, atmospheric science, water quality, geochemistry, sociology, economics, environmental science, and ecology. Addressing water resources issues in any one discipline invariably involves effects that concern other disciplines, and attempts to address one issue often have consequences that exacerbate existing issues or concerns, or create new ones (Jørgensen et al. 1992; Lackey et al. 1975; Straskraba 1994) due to the strongly interactive nature of key processes (Christensen et al. 1996). Thus, research and management of aquatic ecosystems must be interdisciplinary to be most effective, but such truly …

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

An Individual-Based Model Of Chaparral Vegetation Response To Frequent Wildfire, Timothy Lucas, Dayna Mann, Reanna Dona

Seaver College Research And Scholarly Achievement Symposium

In recent years, the Santa Monica Mountains (SMM) have been plagued by frequent wildfires which threaten the native chaparral species. Nonsprouting chaparral species are completely killed by a fire, but their seeds germinate in response to fire cues. Facultative sprouters both resprout after a wildfire and release seeds that germinate post-fire. This project is based on data collected since 1986 at a biological preserve adjacent to the Malibu campus of Pepperdine University with an average fire return interval of 7.5 years. We present a spatial model that simulates the growth, seed dispersal and resprouting behavior of individual shrubs that compete …

Numerical Algorithms For Solving A Generalized Cancer Chemotherapy Problem, Frank Nani, Mingxian Jin

Math and Computer Science Faculty Working Papers

In this paper, two elaborate numerical algorithms are presented for solving the Nani- Oguztoreli functional differential equations associated with cell-cycle specific cancer chemotherapy. The generalized cell-cycle specific cancer chemotherapy model of Nani- Oguztoreli contains discrete time delays which represent the times that the cancer cells spend in each cell-cycle phase. The model also takes into account that inter-cell cycle phase transition rate constants, recruitment of resting cells from the GO phase, and effect of chemotherapy drug on cells in each phase. The algorithms utilize a modified version of the Method of Steps algorithms. The constructed numerical schemes can be implemented …

Fully Coupled Fluid And Electrodynamic Modeling Of Plasmas: A Two-Fluid Isomorphism And A Strong Conservative Flux-Coupled Finite Volume Framework, Richard Joel Thompson

Doctoral Dissertations

Ideal and resistive magnetohydrodynamics (MHD) have long served as the incumbent framework for modeling plasmas of engineering interest. However, new applications, such as hypersonic flight and propulsion, plasma propulsion, plasma instability in engineering devices, charge separation effects and electromagnetic wave interaction effects may demand a higher-fidelity physical model. For these cases, the two-fluid plasma model or its limiting case of a single bulk fluid, which results in a single-fluid coupled system of the Navier-Stokes and Maxwell equations, is necessary and permits a deeper physical study than the MHD framework. At present, major challenges are imposed on solving these physical models …

Lead-Acid Battery Model Under Discharge With A Fast Splitting Method, R. Corban Harwood, Valipuram S. Manoranjan, Dean B. Edwards

Faculty Publications - Department of Mathematics

A mathematical model of a valve-regulated lead-acid battery under discharge is presented as simplified from a standard electrodynamics model. This nonlinear reaction–diffusion model of a battery cell is solved using an operator splitting method to quickly and accurately simulate sulfuric acid concentration. This splitting method incorporates one-sided approximation schemes to preserve continuity over material interfaces encompassing discontinuous parameters. Numerical results are compared with measured data by calculating battery voltage from modeled acid concentration as derived from the Nernst equation.

Software Development For A Three-Dimensional Gravity Inversion And Application To Study Of The Border Ranges Fault System, South-Central Alaska, Rolando Cardenas

Open Access Theses & Dissertations

The Border Ranges Fault System (BRFS) bounds the Cook Inlet and Susitna Basins, an important petroleum province within south-central Alaska. A primary goal in the research is to test several plausible models of structure along the Border Ranges Fault System using a novel three-dimensional inversion utilizing gravity and magnetic data, constrained with other geophysical, borehole and surface geological information. This research involves the development of inversion modeling software using a Borland C++ compiler as part of the Rapid Application Development (RAD) Studio. The novel inversion approach directly models known geology, and "a priori" uncertainties on the geologic model to allow …

Estimating The Efficacy Of Mild Heating Processes Taking Into Account Microbial Non-Linearities: A Case Study On The Thermisation Of A Food Simulant, Vasilis Valdramidis, Brijesh Tiwari, Patrick Cullen, Alain Kondjoyan, Jan Van Impe

Articles

Traditional and novel approaches for the calculation of the heat treatment efficiency are compared in this work. The Mild Heat value (MH-value), an alternative approach to the commonly used sterilisation, pasteurisation and cook value (F, P, C–value), is calculated to estimate the efficiency of a mild heat process. MH-value is the time needed to achieve a predefined microbial reduction at a reference temperature and a known thermal resistant constant, z, for log-linear or specific types of non log-linear microbial inactivation kinetics. An illustrative example is given in which microbial inactivation data of Listeria innocua CLIP 20-595 are used for estimating …

Time Domain Probabilistic Risk Assessment:, George H. Baker, Charles T. C. Mo

George H Baker

For critical facilities, survivability and reconstitution in stressful environments generated by electromagnetic transients, sabotage, terrorist activity, military conflict, or Murphy’s laws are issues of concern. Critical fixed facilities are likely to be functionally complex and their system-wide failure probabilities, modes, and consequences are often not obvious. To analyze and quantify survivability, existing probabilistic risk assessment tools usually provide a “snapshot” of failure modes at a single point of time for certain initiating conditions. Likewise, elaborate physics models developed to treat weapons effects on structures and individual functional components compute effects at a single time point.

We have developed a tool …

Resqme And Stand-Alone Simulation On A Workstation, Robert F. Gordon Ph.D., Paul G. Loewner, G J. Burkland, J-C Chen, Edward A. Macnair

Faculty Works: MCS (1984-2023)

RC 16037 (#71232)

The Research Queueing Package Modeling Environment (RESQME) provides a graphical environment for constructing and solving extended queueing network models ofmanufacturing systems, for plotting graphs of results and for viewdng animations of models. The modeling environment can be run entirely on a workstation or optionally can execute large simulations on a host system using cooperative processing. In this paper we give a brief introduction to RESQME and to the RESQ modeling elements. We demonstrate how to use the package by constructing a simple model of part of a manufacturing line and solve this model to produce charts of …

Higher Level Modeling In Resqme, Robert F. Gordon Ph.D., Kurtiss J. Gordon

Faculty Works: MCS (1984-2023)

RC 13554 (#60544)

The RESearch Queueing Package Modeling Environment (RESQME) is a graphical workstation environment for iteratively constructing, running and analyzing models of resource contention systems. It is built on top of the RESearch Queueing Package (RESQ) which provides the functionality to evaluate extended queueing networks. In this paper we describe the high-level building component design for RESQME. The modeler is provided with tools to create his own icons and to associate them with submodels. He then uses ilicsc building blocks to construct his model. This capability extends the funtlaiiicnlal building blocks of RESQ and allows the user to create …

Generalized Linear Inversion Using Tau-P Forward Modeling, Stephen Dade Walker

Graduate Theses

The Generalized Linear Inversion (GLI) method is used in conjunction with a tau-p forward model to successfully perform inversions of test and real-data examples. All data examples used are one-dimensional velocity profiles that represent several different cases. The stability of the technique is demonstrated in all the test-data sets. The use of simple models and wel1-control 1ed test data results in a minimum of iterations of the inversion process. Different levels of perturbation of the model and test-data examples are used to reveal insight into the robust nature of the inversion.