My Account
Digital Library
Bookstore
News
Archives
Contact
Donate
Become A Member
Society for Industrial and Applied Mathematics
Become a Member
Login
Get Involved
Society for Industrial and Applied Mathematics
Home
Publications
Journals
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal (MMS)
SIAM Journal on Applied Algebra and Geometry (SIAGA)
SIAM Journal on Applied Dynamical Systems (SIADS)
SIAM Journal on Applied Mathematics (SIAP)
SIAM Journal on Computing (SICOMP)
SIAM Journal on Control and Optimization (SICON)
SIAM Journal on Discrete Mathematics (SIDMA)
SIAM Journal on Financial Mathematics (SIFIN)
SIAM Journal on Imaging Sciences (SIIMS)
SIAM Journal on Mathematical Analysis (SIMA)
SIAM Journal on Mathematics of Data Science (SIMODS)
SIAM Journal on Matrix Analysis and Applications (SIMAX)
SIAM Journal on Numerical Analysis (SINUM)
SIAM Journal on Optimization (SIOPT)
SIAM Journal on Scientific Computing (SISC)
SIAM / ASA Journal on Uncertainty Quantification (JUQ)
SIAM Review (SIREV)
Theory of Probability and Its Applications (TVP)
Related
Recent Articles
Information for Authors
Subscriptions and Ordering Information
Journal Policies
Open Access
Books
Book Series
For Authors
For Booksellers
For Librarians
For Educators
SIAM News
SIURO
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 7
Volume 6
Volume 5
Volume 4
Volume 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
Related
Editorial Information
Instructions for Undergraduate Authors
Reports
Digital Library
SIAM Unwrapped
Proceedings
Research Areas
Analysis and Partial Differential Equations
Applied Geometry
Applied Mathematics Education
Classical Applied Mathematics
Computational Science & Numerical Analysis
Control and Systems Theory
Data Science
Discrete Mathematics and Theoretical Computing
Dynamical Systems, Nonlinear Waves
Financial Mathematics and Engineering
Geosciences and Mathematics of Planet Earth
Imaging Science
Life Sciences
Linear Algebra
Mathematical Aspects of Materials Science
Optimization
Uncertainty Quantification
Conferences
Calendar
SIAM Conferences
Cooperating Conferences
Archives
Travel Support
SIAM Student Travel Awards
SIAM Early Career Travel Awards
About SIAM Conferences
Conference Guidelines
Navigating a SIAM Conference
Featured Lectures & Videos
Ways to Sponsor
Exhibitors and Sponsors
Propose a Conference or Workshop
FAQ
Proceedings
Careers
Job Board
Internships
Fellowships
Research Opportunities
Resources
Companies and Industries
Careers in the Math Sciences
What is Applied Mathematics and Computational Science?
Students & Education
Programs & Initiatives
BIG Math Network
Gene Golub SIAM Summer School
Mathematics and Statistics Awareness Month
MathWorks Math Modeling (M3) Challenge
SIAM Science Policy Fellowship Program
SIAM Visiting Lecturer Program
Thinking of a Career in Applied Mathematics?
Tondeur Initiatives
James Crowley Endowed Fund for Student Support
Resources
For Undergraduate Students
For K-12 Students
For Educators
Student Chapters
Start a Chapter
Student Chapter Directory
Chapter Resources
Membership
Join SIAM
Individual Members
Institutional Members
Activity Groups
Algebraic Geometry SI(AG)2
Analysis of Partial Differential Equations
Applied and Computational Discrete Algorithms
Applied Mathematics Education
Computational Science and Engineering
Control and Systems Theory
Data Science
Discrete Mathematics
Dynamical Systems
Financial Mathematics and Engineering
Geometric Design
Geosciences
Imaging Science
Life Sciences
Linear Algebra
Mathematics of Planet Earth
Mathematical Aspects of Materials Science
Nonlinear Waves and Coherent Structures
Optimization
Orthogonal Polynomials and Special Functions
Supercomputing
Uncertainty Quantification
Related
Start an Activity Group
Information for Activity Group Officers
SIAM Activity Group Leadership Suggestion
Sections
SIAM Central States Section
Great Lakes Section of SIAM
Mexico Section of SIAM
SIAM Northern States Section
SIAM Pacific Northwest Section
SIAM Southeastern Atlantic Section
SIAM Southern California Section
SIAM Texas-Louisiana Section
SIAM Washington-Baltimore Section
Argentina Section of SIAM
Bulgaria Section of SIAM
Colombia Section of SIAM
East Asia Section of SIAM
United Kingdom and Republic of Ireland of SIAM
Related
Start a Section
Information for Section Officers
Prizes & Recognition
Deadline Calendar
Major Prizes & Lectures
AWM-SIAM Sonia Kovalevsky Lecture
George Pólya Prize for Mathematical Exposition
George Pólya Prize in Applied Combinatorics
George Pólya Prize in Mathematics
Germund Dahlquist Prize
I.E. Block Community Lecture
James H. Wilkinson Prize for Numerical Software
James H. Wilkinson Prize in Numerical Analysis and Scientific Computing
John von Neumann Prize
Julian Cole Lectureship
Ralph E. Kleinman Prize
Richard C. DiPrima Prize
SIAM Outstanding Paper Prizes
SIAM Prize for Distinguished Service to the Profession
SIAM/ACM Prize in Computational Science and Engineering
Theodore von Kármán Prize
W.T. and Idalia Reid Prize
Activity Group Prizes
Dénes König Prize
Gábor Szegö Prize
J.D. Crawford Prize
Jürgen Moser Lecture
Martin Kruskal Lecture
Red Sock Award
SIAM Activity Group on Algebraic Geometry Early Career Prize
SIAM Activity Group on Applied and Computational Discrete Algorithms Early Career Prize
SIAM Activity Group on Analysis of Partial Differential Equations Best Paper Prize
SIAM Activity Group on Analysis of Partial Differential Equations Early Career Prize
SIAM Activity Group on Computational Science and Engineering Best Paper Prize
SIAM Activity Group on Computational Science and Engineering Early Career Prize
SIAM Activity Group on Control and Systems Theory Best SICON Paper Prize
SIAM Activity Group on Control and Systems Theory Prize
SIAM Activity Group on Financial Mathematics and Engineering Conference Paper Prize
SIAM Activity Group on Financial Mathematics and Engineering Early Career Prize
SIAM Activity Group on Geometric Design Early Career Prize
SIAM Activity Group on Geosciences Career Prize
SIAM Activity Group on Geosciences Early Career Prize
SIAM Activity Group on Imaging Science Best Paper Prize
SIAM Activity Group on Imaging Science Early Career Prize
SIAM Activity Group on Life Sciences Early Career Prize
SIAM Activity Group on Linear Algebra Best Paper Prize
SIAM Activity Group on Linear Algebra Early Career Prize
SIAM Activity Group on Mathematics of Planet Earth Prize
SIAM Activity Group on Optimization Best Paper Prize
SIAM Activity Group on Optimization Early Career Prize
SIAM Activity Group on Supercomputing Best Paper Prize
SIAM Activity Group on Supercomputing Career Prize
SIAM Activity Group on Supercomputing Early Career Prize
SIAM Activity Group on Uncertainty Quantification Early Career Prize
T. Brooke Benjamin Prize in Nonlinear Waves
Student Prizes
Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student
SIAM Award in the Mathematical Contest in Modeling
SIAM Student Paper Prize
SIAM Student Travel Awards
SIAM Early Career Travel Awards
Joint Prizes
George B. Dantzig Prize
George David Birkhoff Prize
Gerald and Judith Porter Public Lecture
JPBM Communications Award
Lagrange Prize in Continuous Optimization
Norbert Wiener Prize
Peter Henrici Prize
Pioneer Prize
Fellows Program
Nomination Procedures
Selection Criteria
Eligibility
All SIAM Fellows
FAQ
Policies & Guidelines
SIAM Prize Policy
Prizes & Recognition FAQ
For Selection Committees
For Prize Winners
For Nominators
Publications
SIURO
Volume 3
Text/HTML
SIAM Undergraduate Research Online
Volume 3
SIAM Undergraduate Research Online Volume 3
Modeling, Analysis and Computation of Fluid Structure Interaction Models for Biological Systems
Published electronically January 26, 2010
DOI:
10.1137/09S010496
Author:
S. Minerva Venuti (George Mason University)
Sponsor:
Padmanabhan Seshaiyer (George Mason University)
Abstract
: A mathematical modeling for the interaction of blood flow with the arterial wall surrounded by cerebral spinal fluid is developed. The blood pressure acting on the inner arterial wall is modeled using a Fourier Series, the arterial wall is modeled using a spring-mass system, and the surrounding cerebral spinal fluid is modeled via a simplified Navier-Stokes equation. The resulting coupled system of partial differential equations for this fluid structure interaction with appropriate boundary conditions are solved first analytically using Laplace Transform and then numerically using an implicit finite difference scheme. The solutions are also investigated using computational tools. An application of the model studied to intracranial saccular aneurysms is also presented.
Influences On Pattern Formation During Non-Isothermal Phase Separation in Local and Nonlocal Phase-Field Models
Published electronically March 2, 2010
DOI:
10.1137/09S010538
Author:
Thomas Stephens (George Mason University)
Sponsor:
Thomas Wanner (George Mason University)
Abstract
: The classical phase-field model represents a coupling of an Allen-Cahn type nonlinear equation with a standard diffusion equation and has been proposed to describe uniform phase separation in a pure substance. This research considers an extension of that model which incorporates a more accurate approximation to the diffuse interface between states of matter through the use of a nonlocal operator. Results of simulations under this model are compared with those of the classical model in order to understand the effects of the nonlocal contribution. Attention has been given to the behavior of the underlying temperature field during early phase separation. We use the tools of computational homology to quantitatively compare patterns in the phase field under both models. Simulations show that the complicated patterns in the phase field persist longer during the solidification process in the nonlocal extension of the classical model.
Drift-Diffusion Simulations of Potassium Channels
Published electronically April 28, 2010
DOI:
10.1137/10S010648
Author:
Jeremiah Jones (Arizona State University)
Sponsor:
Carl Gardner (Arizona State University)
Abstract
: Ionic channels play an important role in regulating the cell's membrane potential and internal charge. This paper will focus on a continuum model of the KcsA potassium channel. We will derive the Poisson-Nernst-Planck (PNP) equations in general and then provide computational solutions for a 1D KcsA channel using experimentally determined parameters. The solution to the PNP equations consists of the time-dependent charge densities of each ion, coupled with the electric potential. The results will be used to solve for the time-dependent current in the channel in response to different time-dependent voltage signals, which can be compared with experimental data.
Subset Selection Algorithms: Randomized vs. Deterministic
Published electronically May 13, 2010
DOI:
10.1137/09S010435
Authors:
Mary E. Broadbent (Amherst College), Martin Brown (University of California, Berkeley), and Kevin Penner (University of Pittsburgh)
Sponsors:
Ilse Ipsen (North Carolina State University), Rizwana Rehman (North Carolina State University)
Abstract
: Subset selection is a method for selecting a subset of columns from a real matrix, so that the subset represents the entire matrix well and is far from being rank deficient. We begin by extending a deterministic subset selection algorithm to matrices that have more columns than rows. Then we investigate a two-stage subset selection algorithm that utilizes a randomized stage to pick a smaller number of candidate columns, which are forwarded for to the deterministic stage for subset selection. We perform extensive numerical experiments to compare the accuracy of this algorithm with the best known deterministic algorithm. We also introduce an iterative algorithm that systematically determines the number of candidate columns picked in the randomized stage, and we provide a recommendation for a specific value. Motivated by our experimental results, we propose a new two stage deterministic algorithm for subset selection. In our numerical experiments, this new algorithm appears to be as accurate as the best deterministic algorithm, but it is faster, and it is also easier to implement than the randomized algorithm.
Statistical and Stochastic Modeling of Gang Rivalries in Los Angeles
Published electronically May 26, 2010
DOI:
10.1137/09S010459
Authors:
Mike Egesdal (University of California, Los Angeles), Chris Fathauer (Harvey Mudd College), Kym Louie (Harvey Mudd College), and Jeremy Neuman (University of California, Los Angeles)
Sponsors:
George Mohler (University of California, Los Angeles) and Erik Lewis (University of California, Los Angeles)
Abstract
: Gang violence has plagued the Los Angeles policing district of Hollenbeck for over half a century. With sophisticated models, police may better understand and predict the region's frequent gang crimes. The purpose of this paper is to model Hollenbeck's gang rivalries. A self-exciting point process called a Hawkes process is used to model rivalries over time. While this is shown to fit the data well, an agent based model is presented which is able to accurately simulate gang rivalry crimes not only temporally but also spatially. Finally, we compare random graphs generated by the agent model to existing models developed to incorporate geography into random graphs.
Statistical Analysis of Simulations of Coarsening Droplets Coating a Hydrophobic Surface
Published electronically July 6, 2010
DOI:
10.1137/10S010594
Author:
Jeremy Semko (Duke University)
Sponsor:
Thomas Witelski (Duke University)
Abstract
: Thin layers of slow-moving, viscous fluids coating hydrophobic surfaces are shaped by the competing forces of disjoining pressure and surface tension. These forces form the fluid layer into an array of discrete droplets connected by an ultra thin layer. However, the droplet array is unstable, and the droplets will interact with one another. To determine the structure and properties of steady droplets, we use the Reynolds' PDE in one dimension and phase-plane methods. We can then analyze the unstable droplet system by utilizing paired ODEs. Numerical solutions show how the droplets interact to produce movement and mass exchange, giving rise to coarsening events which reduce the number of droplets in the system. These events occur when a droplet collapses into the ultra thin layer or when two droplets collide, and thus, merge. Using numerical simulations and statistical analysis of their results, we aim to gain a better understanding of the dynamics of this system including the factors that influence coarsening events such as parameters and initial conditions.
A Formal Derivation of the Aronsson Equations for Symmetrized Gradients
Published electronically July 15, 2010
DOI:
10.1137/10S010582
Author:
Mark Spanier (North Dakota State University)
Sponsor:
Marian Bocea (North Dakota State University)
Abstract
: The Euler-Lagrange equations associated to the problem of minimizing a power-law functional acting on symmetrized gradients are identified. A formal derivation of the limiting system of partial differential equations stemming from these equations as
p
tends to infinity is provided. Our computations are reminiscent of the derivation of the infinity Laplace equation starting from the
p
-Dirchlet integral.
Numerical Investigation of a Stokes Model for Flow down a Fiber
Published electronically July 27, 2010
DOI:
10.1137/09S010563
Author:
Dennis S. Fillebrown (Bucknell University)
Sponsor:
Linda B. Smolka (Bucknell University)
Abstract
: We numerically solve a fourth order nonlinear partial differential equation derived by Craster and Matar [Craster and Matar, J. Fluid Mech. 553, 85 (2006)] that models a viscous fluid flowing down the outside of a vertical fiber in order to investigate the initial formation of perturbations along the fluid free surface. We compare numerical results of their model to existing experimental data [Smolka et al., Phys. Rev. E 77, 036301 (2008)]. In the simulations, perturbations consistently coalesced with neighboring perturbations during their initial formation, whereas in the experiments no coalescence was observed during this time period. We find that the amplitude growth follows two distinct exponential functions (referred to as phases I and II) in the initial formation of perturbations; in the experiments the data follows only one exponential function. The switch in growth rates from phase I to II is influenced by the coalescence of neighboring perturbations. The wavelength varies throughout the time that a perturbation forms so that the flow is unstable to a range of wavenumber. We compare the growth rates of several perturbations during phase II from the simulations to experimental data. Of the six data sets, the range of growth rate and wavenumber were in excellent agreement in two of the data sets and in fair to good agreement with two other data sets. For the last two data sets, there was no overlap in growth rate and little overlap in wavenumber. We find that linear stability results developed from Craster and Matar's Stokes flow model are in excellent qualitative agreement with the growth of the perturbations measured during phase II in simulations for all six data sets. Finally, we find that data from simulations consistently overpredict the final perturbation amplitude measured in experiments.
Mathematically Modeling the Mass-Effect of Invasive Brain Tumors
Published electronically July 29, 2010
DOI:
10.1137/09S010526
Author:
Taylor Hines (Arizona State University)
Sponsor:
Eric Kostelich (Arizona State University)
Abstract
: When developing an accurate model of the development of glioblastomas multiforme, it is important to account not only for the invasion and diffusion of tumor cells into healthy tissue but also the resulting mass effect and brain tissue deformation. This motivates the model presented here, which implements the finite element method to solve a boundary value problem defined through classical continuum mechanics. Intended to improve existing models of tumor invasion, this model predicts the mass-effect of an invading tumor in heterogeneous brain tissue. Several parameters, taken from existing literature, dictate the behavior of differing types of brain matter. The model operates on a two-dimensional (2D) domain and outputs the displacement of brain tissue as a result of the pressure surrounding and within the tumor (peri-tumor pressure).
Moody's Mega Math Challenge Champion Paper-Making Sense of the 2010 Census
Published electronically August 4, 2010
DOI:
10.1137/10S010697
M3 Challenge Introduction
Authors:
Andrew Das Sarma, Jacob Hurwitz, David Tolnay, and Scott Yu (Montgomery Blair High School, Silver Spring, MD)
Sponsor:
David Stein (Montgomery Blair High School, Silver Spring, MD)
Executive Summary:
With so much political and economic interest behind accurate results for the United States Census, the Census Bureau has implemented several strategies for dealing with the particularly pesky problem of undercounting, or the exclusion of certain individuals from the Census: These include sampling the population after the Census to gauge how many people were excluded, guessing the values for missing data, and examining public records to estimate the breakdown of the population. Of these, we found that only the last two are sufficiently helpful to merit use, whereas the first strategy of post-Census sampling can lead to error greater than what it was intended to remedy.
Of course, even with perfectly reliable Census results, proper political representation cannot be attained without a system that distributes seats in the House of Representatives in a manner that addresses the particularities of the population. Evaluating six methods (Hill, Dean, Webster, Adams, Jefferson, and Hamilton-Vinton) that Congress has historically considered for dividing seats in the House, we found that the Hamilton-Vinton method surpasses others in the arena of fair apportionment.
After Congress, the next bearers of responsibility are the fifty states of the Union, which are constitutionally charged with drawing district lines that demarcate regions for their representatives. In regard to this process, we suggest that states commit to a system that impartially divides the state according to population density. Such a system, we hold, will serve the common good of the state by achieving the democratic goal that our representative democracy should reflect the sentiments of the American people.
A Method of Calculating the Thickness of a Solid-Liquid Interface
Published electronically September 17, 2010
DOI:
10.1137/10S010636
Author:
Michael R. Atkins (George Mason University)
Sponsors:
Daniel Anderson (George Mason University), Maria Emelianenko (George Mason University), Yuri Mishin (George Mason University)
Abstract
: Microstructural evolution is a phenomenon of paramount importance in various areas of industry; its understanding is critical for designing materials with superior properties. The nonlinear and metastable nature of this mesoscale phenomenon has given rise to various models that attempt to describe it. One type of model that is often used is a phase-field model. Here we present a method to determine a constant related to the solid-liquid interface thickness found in the model via atomistic simulation.
Understanding the Eigenstructure of Various Triangles
Published electronically September 29, 2010
DOI:
10.1137/10S010612
Authors:
Anil Damle (University of Colorado at Boulder) and Geoffrey Colin Peterson (University of Colorado at Boulder)
Sponsors:
James Currry (University of Colorado at Boulder) and Anne Dougherty (University of Colorado at Boulder)
Abstract
: We examine the eigenstructure of generalized isosceles triangles and explore the possibilities of analytic solutions to the general eigenvalue problem in other triangles. Starting with work based off of Brian McCartin's paper on equilateral triangles, we first explore the existence of analytic solutions within the space of all isosceles triangles. We find that this method only leads to consistent solutions in the equilateral case. Next, we develop criteria for the existence of complete solutions in other triangles. We find that complete solutions are guaranteed in the equilateral, right isosceles and 30-60-90 triangles. We then use a method developed by Milan Prager to formulate solutions in the right isosceles triangle through folding transformations of solutions in the square.