BEGIN:VCALENDAR CALSCALE:GREGORIAN METHOD:PUBLISH PRODID:-//appliedmath.arizona.edu//NONSGML iCalcreator 2.2// VERSION:2.0 X-WR-CALNAME:Applied Math Colloquium X-WR-CALDESC:Applied Math Colloquium Calendar, University of Arizona Progra m in Applied Mathematics X-WR-TIMEZONE:US/Arizona BEGIN:VTIMEZONE TZID:US/Arizona BEGIN:STANDARD DTSTART:19700101T000000 TZOFFSETFROM:-0700 TZOFFSETTO:-0700 TZNAME:MST END:STANDARD END:VTIMEZONE BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:There is currently tremendous interest in geometric PDEs\, due in part to the geometric flow program used recently to solve the Poincare conjecture. Geometric PDEs also play an expanding role in many other appli cations\, such as understanding the gravitational wave models of Einstein. The need to validate these models has led to the construction of gravitat ional wave detectors in the last several years\, such as the NSF-funded LI GO project. In this lecture\, we consider the coupled nonlinear elliptic c onstraints in the Einstein equations\, a geometric flow which describes th e propagation of gravitational waves generated by collisions of massive ob jects such as black holes. The constraint equations must be solved numeric ally to produce initial data for gravitational wave simulations and to enf orce the constraints during dynamical simulations. In the first part of th e lecture\, we consider a thirty-year-old open question involving existenc e of solutions to the constraint equations on space-like hyper-surfaces wi th arbitrarily prescribed mean extrinsic curvature\, and we give a partial answer using a priori estimates and a new type of topological fixed-point argument.\n\nIn the second part of this lecture\, we develop some adaptiv e numerical methods for which we can prove a number of useful results on c onvergence\, optimality\, and scalability. Based on the a priori estimates developed in the first part of the talk\, we first establish some critica l discrete estimates. We then derive error estimates for Galerkin approxim ations and describe a class of nonlinear approximation algorithms based on adaptive finite element methods (AFEM). We establish some new AFEM conver gence and optimality results for geometric PDE problems with non-monotone nonlinearities such as the Einstein constraints.\n\nWe finish by illustrat ing the algorithms with some examples using the Finite Element ToolKit (FE TK).\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080502T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Michael Holst: Some New Existence Results for a Geometric PDE Arisi ng from General Relativity and an Approximation Theory Framework UID:20080412T063721CEST-wMNFBU26T8@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:Typical porous media processes are affected by heterogeneities at different length scales. In this talk\, I will describe multiscale fini te element methods for flow and transport in heterogeneous porous media. T he main focus of the talk is on subgrid capturing using various local and global methods.\n\nI will discuss the use of local boundary conditions and the use of global information in capturing subgrid effects. The upscaling of the transport equation and its coupling to the flow equation will be p resented. The mathematical analysis of these methods will be discussed.\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080425T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Yalchin Efendiev: Multiscale Numerical Methods for Flow and Transpo rt in Heterogeneous Porous Media and Their Applications UID:20080412T063721CEST-d9InlDlOmi@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:Since the development and commercialization of the first nemati c liquid crystal display devices in the middle of the last century\, mathe matical modeling and analysis of liquid crystals has experienced significa nt progress. Liquid crystals are phases intermediate between solid and liq uid\; they occur in synthetic as well as in organic compounds. The Kevlar fiber is an example of a highly employed liquid crystal polymer\; many vir us and bacteria colonies as well as biological tissues present liquid crys tal ordering.\n\nLiquid crystals of small molecular weight consist of rigi d\, rod-like molecules that tend to follow preferential directions of alig nment. Their interaction with electric and magnetic fields is at the core of application to display devices. Recently developed liquid crystals exhi bit more complicated molecular shapes able to sustain permanent dipoles th at result in ferroelectric coupling with applied electromagnetic fields. T he speed of switching of such devices is about 10^3 to 10^4 times that of the nematic cell. Equilibrium states of ferroelectric liquid crystals resu lt from minimizing the total energy subject to packing and electrostatic c onstraints. I will present an application of such a theory to predicting s hape of material filaments.\n\nLiquid crystal elastomers are nonlinear ela stic solids that may also present liquid crystal phases. One remarkable fe ature is their capability to undergo unusually large deformations along pr eferential directions. Upon analyzing mathematical issues of such models\, I will address their gel states and discuss the potential matrix role in modeling cell motility in the brain.\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080418T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Maria-Carme T. Calderer: Elastic and Ferroelectric Properties of Li quid Crystals: Modeling and Analysis UID:20080412T063721CEST-uXeKwagT22@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:(This week's colloquium has been canceled.)\n\nWe study the spe ctrum of a linear advection-diffusion equation in a periodic domain\, wher e the diffusion coefficient changes its sign. We prove that the spectrum o f an associated linear operator consists of an infinite set of simple eige nvalues on the imaginary axis and the set of corresponding eigenfunctions is complete. However\, we also show\, assisted with numerical approximatio ns\, that the complete set of linearly independent eigenfunctions does not form a basis in a space of square integrable functions and that the Cauch y problem for the advection-diffusion equation is ill-posed. DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080411T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Dmitry Pelinovsky: CANCELED: Advection-Diffusion Equations with For ward-Backward Diffusion UID:20080412T063721CEST-RrzvAuczAF@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:I will develop and analyze stochastic models for two \nimportan t processes in cellular biophysics. The first problem concerns mRNA transl ation and protein production\, and is modeled as an interacting particle s ystem in 1D. The effects of 'slow codons\,' or defects in the mRNA\, on pr otein production rates are addressed by asymptotic matching of mean-field solutions of the problem. In the second problem\, a stochastic model for v iral entry into cells is developed. The entry of viruses turns out to be a competition between \nmembrane fusion and endocytosis. The probabilities for entry via each of these pathways are calculated within one- and two-su rface receptor models. Conditions for endocytosis are mapped. Time permitt ing\, I will also briefly introduce a stochastic inverse problem where tra nsition rates of a Markov process can or cannot be reconstructed from firs t \npassage time distributions.\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080404T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Tom Chou: Stochastic Models in Biophysics UID:20080412T063721CEST-VZLGtsedXV@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:Al Scott Lecture. The ability of the circulatory system to adeq uately match blood supply to tissue demand implies the existence of regula tory mechanisms that communicate tissue status to blood vessels. For examp le\, red blood cells have been shown to respond to low tissue oxygen level s by releasing ATP. The ATP triggers a conducted response signal to travel upstream and cause arterioles to dilate so that more blood is delivered t o the region of demand. A theoretical model focusing on the role of this m echanism in blood flow regulation is presented here. In the model\, arteri oles control blood flow by dilating or constricting in response to changes in metabolism as well as to changes in pressure and wall shear stress. Th e model predicts that responses to these three stimuli can account for the increase in blood flow that occurs with increased oxygen demand. DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080328T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Julia Arciero: Theoretical Model of Metabolic Blood-flow Regulation UID:20080412T063721CEST-9h8HB2kN7F@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION: CANCELED DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080307T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Timothy J. Healey: CANCELED: Some Problems in Second-Gradient Nonli near Elasticity UID:20080412T063721CEST-gjb8vv0uUa@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:Cnidaria is an ancient phylum that includes solitary organisms like Hydra and sea anemones and colonial organisms like corals. Because of their apparent lack of bilaterality and their simple body plan\, Cnidaria ns were considered very unsophisticated organisms that should be easy to u nderstand. This view\, however\, has changed recently due to the discovery of numerous Cnidarian genes and signaling molecules that are also present in 'higher' organisms.\n\nFor a long time Hydra has been a model system f or developmental biology and a favorite pet for theorists. It is remarkabl e for its extraordinary regeneration capabilities that enable the survival of the organism from only 1% of the body tissue. In the course of regener ation Hydra forms a hollow sphere that undergoes cycles of oscillations. T he purpose of the oscillations has not yet been completely understood but is likely due to osmoregulation\, as I will argue in my talk.\n\nCorals gi ve rise to one of the world's most diverse ecosystems and fascinate becaus e of their bright colors and fantastic shapes. How these different shapes are created is still very much unclear. On the one hand\, genetic disposit ions must be important\; on the other hand\, environmental factors such as light and water flow modulate the growth significantly. In my talk I will summarize experimental work geared towards deciphering the rules of growt h in the coral Stylophora pistillata and present a model setup for studyin g these rules.\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080222T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Michael Kuecken: Modeling Cnidarians: Oscillations in Hydra and Gro wth Rules in Corals UID:20080412T063721CEST-8H8ZIKvVDf@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:Compared to the plant and animal kingdoms\, diversity of microb ial life is considerably less explored and less understood (even the notio n of microbial species is a current topic of debate). Prokaryotes (bacteri a and archaea) are estimated to make up approximately half of extant bioma ss\; for example\, each human harbors about 100 trillion microbes (bacteri a and archaea)\, ten times more microbial than human cells. The familiar v iew of microbes in their free (planktonic) state is however not the norm\; rather it is believed that much of the microbial biomass\, perhaps 95-99% \, is located in close-knit communities\, designated biofilms and microbia l mats\, consisting of large numbers of organisms living within self-secre ted matrices constructed of polymers and other molecules. (Microbes in col lective behave very differently from their planktonic state\; even genetic expression patterns change.) These matrices serve the purposes of anchori ng and protecting their communities in favorable locations while providing a framework in which structured populations can differentiate and self-or ganize. \n\nOne can and will find biofilms in almost any damp or wet envir onment\, and they are often key players in problems such as human and anim al infections\, fouling of industrial equipment and water systems\, and wa ste remediation\, just to name a few. Medical relevance is quite dramatic. Quoting from the National Institutes of Health: 'Biofilms are clinically important\, accounting for over 80 percent of microbial infections in the body. Examples include: infections of the oral soft tissues\, teeth and de ntal implants\; middle ear\; gastro-intestinal tract\; urogenital tract\; airway/lung tissue\; eye\; urinary tract prostheses\; peritoneal membrane and peritoneal dialysis catheters\, in-dwelling catheters for hemodialysis and for chronic administration of chemotherapeutic agents (Hickman cathet ers)\; cardiac implants such as pacemakers\, prosthetic heart valves\, ven tricular assist devices\, and synthetic vascular grafts and stents\; prost heses\, internal fixation devices\, percutaneous sutures\; and tracheal an d ventilator tubing.'\n\nViewed as materials\, biofilms are quite interest ing: they are living\, growing viscoelastic fluids with surprising ability to respond to and defend against their environments. This talk will prese nt a general overview of efforts to characterize and model biofilms on a c ontinuum macroscale\, addressing some of the issues mentioned above. \n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080215T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Isaac Klapper: Microbial Biofilms UID:20080412T063721CEST-lKGUv4G65r@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:In the past several years it has come to be appreciated that in low Reynolds number flow the nonlinearities provided by non-Newtonian str esses of a complex fluid can provide a richness of dynamical behaviors mor e commonly associated with high Reynolds number Newtonian flow. For exampl e\, experiments have shown that dilute polymer suspensions being sheared i n simple flow geometries can exhibit highly time-dependent dynamics and sh ow efficient mixing. The corresponding experiments using Newtonian fluids do not show such nontrivial dynamics. To better understand these phenomena we study numerically the 2D Oldroyd-B Viscoelastic model at low Reynolds number. A background force is used to create a periodic cell with four-rol l mill vertical structure around a hyperbolic fixed point. We consider bot h steady and time-periodic forcing. For low Weissenberg number (Wi) the el astic stresses are bounded to the forcing\, with mixing confined to small sets near the hyperbolic point. At larger Wi an analog to the coil-stretch transition occurs\, yielding large stresses and stress gradients concentr ated on sets of small measure. The flow then becomes very sensitive to per turbations in the forcing and there is a transition to global mixing in th e fluid.\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080208T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Becca Thomases: Singularities and Transport in Viscoelastic Fluids UID:20080412T063721CEST-lVKwPAnCEm@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:The engineering community has been actively pursuing the develo pment of self-organization of particles in order to design smaller\, faste r and more efficient electronic elements. In order to achieve theoretical understanding of these processes\, we suggest a dissipative analogue of ki netic equations that describe the motion of probability distribution in th e momentum-coordinate space. This work is based on the double bracket diss ipation ideas that were originally suggested for astrophysical application s.\n\nWe then show how to extend the double bracket method to include part icles with interaction dependent on orientation\, for example\, magnetized particles in colloidal solution. We derive evolution equations for densit y and magnetization that reduce to the celebrated Landau-Lifshitz-Gilbert equations for non-moving magnets and to Debye-Huckel equations for particl es without orientation. We also show how our equations naturally give the motion for of an elastic self-interacting curve\, and discuss the applicat ion of our technique to folding of biologically-relevant strands.\n\nColla borators: Darryl D. Holm\, Cesare Tronci (Mathematics\, Imperial College\, London\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080125T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Vakhtang Putkaradze: Models of Dissipation and Self-Organization in Physical Systems: From Kinetic Equations to Self-Organization of Magnetic Particles to Protein UID:20080412T063721CEST-bBXa2UcGMV@appliedmath.arizona.edu END:VEVENT BEGIN:VEVENT CATEGORIES:Colloquium DESCRIPTION:Art Winfree's first scientific paper\, published in 1967 and ba sed on research he did as a senior in college\, was about synchronization of biological oscillators. In his honor\, this talk will survey what we kn ow (and don't know) about synchronization\, 40 years later.\n\nThe tendenc y to synchronize is one of the most mysterious and pervasive drives in all of nature. Every night along the tidal rivers of Malaysia\, thousands of fireflies flash in silent\, hypnotic unison\; the moon spins in perfect re sonance with its orbit around the Earth\; the intense coherence of a laser comes from trillions of atoms pulsing together. All these astonishing fea ts of synchrony occur spontaneously --- almost as if the universe had an o verwhelming desire for order.\n\nOn the surface\, these phenomena might se em unrelated. After all\, the forces that synchronize fireflies have nothi ng to do with those in a laser. But at a deeper level\, they are all conne cted by the same mathematical theme: self-organization\, the spontaneous e mergence of order out of chaos. Video footage of synchronous fireflies and the notorious crowd synchrony that triggered the wobbling of London's Mil lennium Bridge will be shown.\n DTSTAMP:20080412T043721Z DTSTART;TZID=US/Arizona:20080118T160000 DURATION:PT1H LOCATION:Math 501 SUMMARY:Steven Strogatz: Synchronization in Nature UID:20080412T063721CEST-THSfjEkWJB@appliedmath.arizona.edu END:VEVENT END:VCALENDAR