UCLA SIAM Student Chapter Home Events People Links Conferences Activities for 2007-2008 Academic Year Back to main events page. Spring 2008 Monday, June 2 4-5pm, MS 6627 Perspectives: Lauren Caston - The Rand Corporation Tuesday, May 27 4-5pm, MS 6627 Student Seminar: Jeremy Brandman Tuesday, May 27 3-4pm, MS 6620 2008-2009 Organizational Meeting Monday, May 19 4-5pm, MS 6627 Perspectives: Jianlin Xia Winter 2008 Monday, March 3 4-5pm, MS 6627 Perspectives: Martin Short Thursday, February 7 5pm, MS 6620 Qual Panel Monday, January 14th 4-5pm, MS 6627 Intro to Multigrid - Brendan Sheehan Fall 2007 Monday, November 5 4-4:50pm, MS 5137 Perspectives: Jeff Eldredge Wednesday, October 17 4:00pm, MS 6943 Graduate Experience Panel for Undergrads Perspectives in Mathematics Seminar Series Jianlin Xia, Department of Mathematics (S08) Title: "Statistical Condition Estimation Tutorial" Abstract: This talk reviews the basic ideas of the statistical condition estimation (SCE) method. Traditional numerical condition and condition estimators may be insufficient in many situations. SCE provides componentwise condition estimates for numerical problems based on small-sample perturbation analysis. It is generally not more expensive than traditional methods, and can achieve high accuracy with multiple samples. It is also good at respecting the structures of numerical problems and provides less conservative estimates. In this talk we use linear systems and eigenvalue problems as examples to show the SCE estimators and their performance. SCE can be applied to many other problems such as least squares, matrix functions, differential equations, control problems, etc. Martin Short, Department of Mathematics (W08) Title: The Mathematics of Crime Abstract: In this talk, we shall discuss a statistically based model of criminal behavior, using the specific example of residential burglaries. Based upon the empirically measured phenomena of repeat and near-repeat burglaries (which we shall also discuss) and crime hotspots, we develop a simple model of how burglars move through their environment and choose which houses to strike. Nonlinear feedback within the model system generates crime hotspots similar those observed in police data, with sizes and lifetimes of spots adjustable via parameters. We examine a continuum approximation of this discrete model as well, and go in-depth to discuss various behaviors present, including subcritical bifurcations and coarsening. Perspectives in Applied Mathematics Series Jeff Eldredge, Mechanical and Aerospace Engineering (F07) Title: "An Exploration of Fundamental Mechanisms of Swimming and Flying in Nature using High-Fidelity Numerical Simulation" Abstract: Most aquatic creatures and airborne insects achieve motility through the dynamic interaction of their flexible body/fins/wings with the surrounding medium. This flexibility is used to provide a spectrum of active and passive control, allowing the creature to sometimes prescribe its shape changes and at other times extract energy from the fluid. This mix is particularly important in the moderate Reynolds number regime, in which wake vortices play an important energetic role. A well-devised control strategy for a bio-inspired vehicle should -- perhaps must -- exploit such flexion and energy exchange; as yet, we lack sufficient understanding to develop such a strategy. In this work, I will present several two-dimensional canonical problems that distill fundamental modes of fluid/flexible body mechanics in biological systems, which are analyzed using high-fidelity numerical simulation. The simulations are based on the viscous vortex particle method with coupled fluid-body dynamics.  The first system consists of an articulated three-link swimmer, considered in free-swimming as well as in a passive configuration in the wake of an obstacle. The shape-change kinematics of the free swimming system are explored parametrically to find optimal gaits.  When in the wake of a static obstacle, under some circumstances the passive system extracts energy from the ambient flow to propel itself forward. The second system consists of flapping of a two-component wing with a torsion spring, which allows a portion of the wing to passively deflect. The power budgets and lift generation are investigated for different hovering kinematics prescribed for this flexible wing. The third problem involves an articulated jellyfish model, in which the active/passive flexibility mix is explored by designation of the individual hinges. Brendan Sheehan, Department of Mathematics (F07) Title: Introduction to Multigrid Abstract: Multigrid is a numerical method for approximately solving certain linear systems in order N operations. This talk is intended for those with no previous exposure to multigrid. The basic concepts will be explained, and illustrated in 1-D using Matlab. Time permitting, a multi-D application to neutron transport may also be discussed. Perspectives in Industry Series Lauren Caston, The Rand Corporation (S08) Title: "Statistical Mechanics and Behavioral Models" Abstract: How do changes in local or global policy affect fundamentally uncertain phenomena? For example, what levers are available to social leaders that may help reduce crime or smoking in certain communities or populations? RAND, a U.S.-based nonprofit think tank, often seeks out practical solutions to such public policy-relevant questions by developing and employing mathematical models to help understand social behavior, resource management, and decision-making under deep uncertainty. One fundamental component of policy research is an individual's or a group's decision calculus, a concept that has developed significantly over the last century or more; the notion of an expected value, risk analysis, game theory, and subjective probabilities mark various stages of this evolution. In this talk I will give a brief background of RAND, then review some current applications of statistical mechanics models to the study of social trends. I will attempt to assess the potential impact such methods may have on policy, and therefore shed some light on their value to economic and social modeling. Lauren Caston is an associate mathematician at the RAND Corporation in Santa Monica. He currently studies catastrophe and litigation modeling, informational retrieval and search processes, risk management, and airbase operability. Lauren received a BA in mathematics from the University of California, Berkeley in 2000. He then went on to study mathematical supersymmetry under V.S. Varadarajan at the University of California, Los Angeles where he received his Ph.D. in 2005. From 2005-2006, Lauren received an "assengo di ricerca" fellowship from the University of Bologna, Italy to continue his study of superschemes and group actions. Lauren joined RAND in August, 2006. Student Seminars Jeremy Brandman, Department of Mathematics (S08) Title: An introduction to level-set methods for PDE on surfaces Abstract: PDE on surfaces arise in a variety of areas, including fluid dynamics, computer graphics, biological pattern formation, and geometry. Recently, level-set methods for solving PDE on surfaces have been introduced which rely on standard numerical methods and which work for surfaces that are not triangulated or polygonal. The main idea behind these methods is to represent the surface implicitly; using such a representation, all calculations can be done on the Cartesian grid using regular finite differences or finite elements. In this talk we introduce level-set methods for solving elliptic and parabolic PDE on surfaces and discuss recent work on elliptic eigenvalue problems. Miscellaneous Qual Panel (W08) Panel discussion for graduate students on the Applied Qualifying exams (Numerical and ADE). Come get all your questions answered on what to study, what not to study, what types of questions commonly appear on exams, where to look for more information on specific topics and more. Questions will be fielded by an expert team of advanced graduate students, full of qual-passing experience. Events for Undergraduates Graduate Experience Panel (F07) Panel discussion providing undergraduate students a chance to ask a panel of graduate students questions about their graduate school experience, the application process, funding, exams, and anything else they would like to know. The panel consists of a mix of both pure and applied math graduate students. This is a joint activity with the undergraduate student society. 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