Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Email: rockhopper@mcihispeed.net
Mentor: Yi Jiang
A Cellular Model of Angiogenesis
"We wish to investigate the effects of 3 different types of chemical source pro-files: 1) a point source, 2) a line source, and 3) a parabolic source, to determine which source profile most closely resembles actual blood vessel growth nearby and within a real tumor."
Email: ayelet@hwr.arizona.edu
Mentors: Daniel Tartakovsky and Pieter Swart
Stochastic analysis of transient flow to a well in a heterogeneous aquifer
"It is the intention of this research to develop a methodology to infer medium properties from pressure interference tests for heterogeneous aquifers while taking into account the uncertain nature of the subsurface. "
Email: kbold@princeton.edu
Mentors: Aric Hagberg and Shlomo Neuman
Differential Equations on a Network: from Dynamics to Structure
"We compare classical theoretical results with numerical results in the discrete case."
Email: nawaf@caltech.edu
Mentor: Darryl Holm
Topics in Geometric Mechanics: Geometrical Monodromy
"Mathematically, this means the fiber bundle associated with the natural mechanical connection for these problems (again, for example, the magnetic vector potential in the Aharanov-Bohm effect) is non-trivial. This multivaluedness is known as geometric monodromy, in analogy with the same term arising in analytic function theory."
Email: bures@linux.fjfi.cvut.cz
Mentors: Mikhail Shashkov, Burton Wendroff, Raphael Loubere, and Konstantin Lipnikov
A 1D Lagrangian Adaptive Mesh Refinement (AMR) Algorithm
"Our objective is to implement refinement and coarsening operators that can be plugged into the existing 1D ALE code [1]."
Email: nakul@grad.math.arizona.edu
Mentors: James (Mac) Hyman and J M Cushing
Modeling the spread of malaria
"Our goal with this model is to compare some of the control strategies used against malaria today and some of the ideas for future control to determine the most effective ways of reducing malarial transmission, morbidity and mortality."
Email: dohnal@math.unm.edu
Mentor: Avner Peleg
Effects of disorder on solitary waves of the cubic-quintic nonlinear Schrödinger equation
"During this summer we focused on the special case of a linear gain perturbation"
Email: cdonahue@t7.lanl.gov
Mentor: Brendt Wohlberg
Temporal Coding in the Visual Cortex
"We are interested in building biologically inspired models of primary visual cortex (V1) that are based upon temporal coding theories. In particular, we would like to find models that reproduce these gamma oscillations, and show a direct correlation to the stimulus input."
Email: hawkan@wwc.edu
Mentor: Kevin Vixie
"In this paper, we introduce a statistical model to capture the similarities in images with various types of noise, and to compare the recovered image of different reconstruction models in the literature. The types of noise considered are additive gaussian, multiplicative, salt and pepper, poisson, and cracks. Currenty, our focus is on additive gaussian noise."
Email: skandada@nmsu.edu
Mentor: Brendt Wohlberg
Directional Multiresolutional Image Analysis
"A major part of the work done this summer was to study and comprehend the rapidly growing literature on directional multiresolutional image analysis and classify the different methods based on some common approach they use. The other part of the work was to study the different properties of these methods and choose appropriate transforms for either image compression or denoising."
Email: tle@math.ucla.edu
Mentor: Kevin Vixie
"In this paper, we introduce a statistical model to capture the similarities in images with various types of noise, and to compare the recovered image of different reconstruction models in the literature. The types of noise considered are additive gaussian, multiplicative, salt and pepper, poisson, and cracks. Currenty, our focus is on additive gaussian noise."
Email: emanalo@math.uci.edu
Mentor: Susan Kurien
Parameter Study of the 2D-Navier-Stokes-α Model
"The goal of this research study is to explore the practicality and the effectiveness of a particular model, the NS-α (pronounced NS-alpha) model, as a subgrid model to 2D-turbulence."
Email: J.C.Miller@damtp.cam.ac.uk
Mentor: James (Mac) Hyman
Preventing or Reducing the Spread of Epidemics
"We have shown that in the population produced by Episims, there are vaccination strategies which improve on simply vaccinating those people who have the most contacts."
Email: apetersen@math.arizona.edu
Mentors: James (Mac) Hyman, Martin Staley, and Juan Restrepo
Nonlinear, Dispersive Partial Differential Equations
"My research at Los Alamos this summer focused on the dynamics of solutions to another nonlinear, dispersive equation."
Email: rozenfhd@clarkson.edu
Mentors: Aric Hagberg and Pieter Swart
Extremal Properties on Bipartite Networks
"In this project we found the maximal clustering coefficient and assortativity on projected networks by choosing the right wiring model in the bipartite graph."
Email: brendan.sheehan@colorado.edu
Mentor: Travis Austin
Adaptive Refinement for Neutron Transport
"The goal of my project was to apply adaptive spatial refinement to the neutron transport equation in two spatial dimensions."
Email: fang@math.arizona.edu
Mentors: Brendt Wohlberg and Kevin Vixie
Wavelets and Their Applications
"We shall study wavelets from multi-resolution analysis."
Email: maxim@email.arizona.edu
Mentor: Yeo-Jin Chung
Error Rate Fluctuations in High Speed Optical Fiber Communication Systems
"Objective: to verify of general results on statistical properties of error fluctuations in comunication systems with structural disorder and temporal noise."
Email: joshs@math.arizona.edu
Mentor: Avner Peleg
Effects of Stimulated Raman Scattering on Multichannel Soliton Transmission
"The main goal of this project is to determine the effects of stimulated Raman scattering on soliton collisions while taking the stochastic nature of bitstreams into account."
Email: stechman@CIMS.nyu.edu
Mentor: Darryl Holm
Singular Solutions to a Partial Differential Equation for Computer Imaging
"We have studied the dynamics with respect to this norm on manifolds with symmetry, including the sphere and hyperbolic space."
Email: dasvyat@ld54.math.uh.edu
Mentors: Mikhail Shashov and Konstantin Lipnikov
"The main goal of this summer project is the investigation and the program realization of mimetic finite difference algorithms for a diffusion-type equation on unstructured polyhedral meshes."
Email: turitsyn@mail.ru
Mentor: Ildar Gabitov
Solitary waves stability in Maxwell-Duffing equation
"The solitary wave survives when the perturbation has one sign and it totally breaks down for the other sign. Such behaviour is property of nonintegrable equations and was not observed in any known integrable models. Analytical description of such semistability is the main aim of this work."
Email: vachal@galileo.fjfi.cvut.cz
Mentors: Mikhail Shashkov, Konstantin Lipnikov, and Markus Berndt
Mesh Reconnection Method for Solution of Elliptic Problems
"One of my tasks for this summer was to implement a set of routines which will adapt the mesh by node reconnection instead of refinement."
Email: zakharovdmitry@mail.ru
Mentors: Ildar Gabitov and Mikhail Stepanov
Isoperiodic deformations of solutions of the Harry Dym hierarchy
"Together with Mikhail Stepanov, we have written a program that implements the deformations and explicitly constructs finite-gap solutions of KdV."
Email: sleepytime22_86503@yahoo.com (Tommy)
nicke@sonic.net (Nick)
cantstopmat@yahoo.com (Mat)
okun4275@eudoramail.com (Olaoluwa)
sllevarge@math.arizona.edu (Sheree)
man16@cornell.edu (Miriam)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
Cellular Noise and The Aging Process
"We propose two mathematical models to investigate the progression of aging at the cellular level."
Email: d_chowell@hotmail.com (Diego)
TheIT1@aol.com (Pablito)
dperez7@lion.lmu.edu (David P.)
hixahuary@ucol.mx (Cynthia)
fas9@cornell.edu (Fabio)
dlm35@mathpost.la.asu.edu
(David M.)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
The Impact of Mosquito-Bird Interaction on the Spread of West Nile Virus to Human Populations
"We establish the existence of possible multiple endemic equilibria."
Email: jalmora@email.unc.edu (Jose)
aizarrar@uci.edu (Albert)
rabbit@unm.edu (Qiao)
cnnesmith@smcm.edu (Crystal)
dlm35@mathpost.la.asu.edu
(David M.)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
Agent based modeling of Eciton burchelli swarm patterns
"We observe their reactions to different initial food distributions in a simulated ant world and determine the stability of their swarm patterns to perturbations and external factors."
Email: antonio_b50@yahoo.com
(Antonio)
kayruche@hotmail.com (Katie)
gonzales@mathpost.la.asu.edu
(Chad)
magdaliz@hotmail.com (Magdaliz)
mubayi@mathpost.la.asu.edu
(Anuj)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
HIV and Its Impact on the Infant Immune System
"We observe their reactions to different initial food distributions in a simulated ant world and determine the stability of their swarm patterns to perturbations and external factors."
Email: billups.a@neu.edu
(Anthony B.)
Reynaldo.Castro@asu.edu
(Reynaldo)
wfc151986@yahoo.com
(Wilbert)
roque@math.binghamton.edu (Tairi)
tongen@math.arizona.edu
(Anthony T.)
ariel@cam.cornell.edu
(Ariel)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
Does gravitational gossip weigh heavy on your local area network?
"We examine the effect of different networks within this mathematical framework. We propose a general mathematical model that incorporates the susceptibility and infectivity of a given machine in a local area network."
Email: jgjorgjieva@hmc.edu
(Julijana)
s krsmith1@clarion.edu
(Kelly)
gtg208a@mail.gatech.edu
(Jessica)
gc82@cornell.edu (Gerardo)
fas9@cornell.edu (Fabio)
chavez@math.la.asu.edu
(Carlos)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
The Role of Vaccination in the Control of SARS
"We assess pre-outbreak and during-outbreak vaccination as control strategies for SARS epidemics. Our model includes susceptible, latent (traced and untraced), infectious, quarantined/isolated and recovered classes. We take parameter estimates from published literature."
Email: arlene@mathpost.asu.edu
(Arlene)
angela.ortiz@asu.edu
(Angela)
krr22@cornell.edu (Karen)
urdapill@mathpost.asu.edu (Alicia)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
U.S.A. the Fast Food Nation: Obesity as an Epidemic
"The aim of this project is to study the potential role of peer-pressure in fast-food consumption as well as its effect on an individual's weight. We explore these effects on the dynamics of obesity at the population level using an epidemiological model."
Email: kevin83@umail.ucsb.edu
(Kevin)
lhannah@princeton.edu
(Lauren)
ylin7@emory.edu (Yi)
Mentors: Carlos Castillo-Chávez and James "Mac" Hyman
Modeling of Tumor Growth and its Control via Paclitaxel Using a Delay Differential Equation
"Our research considers a mathematical model that describes tumor growth and response to treatment with a continuous, low dose treatment of the antimitotic drug Paclitaxel."
Last modified: October 15, 2004