Department of Mathematics
University of North Carolina
Chapel Hill, North Carolina
Weekly Calendar Spring 2015
Monday, April 20
GMA Seminar
Nick Battista, UNC, 381 Phillips Hall, 4:00 pm
Title: I <3 Weightlifting, and sometimes, on occasion, math:
Abstract: Part 1: Optimized Bar Path In Olympic Weightlifting
Part 2: A story of love, deceit, and betrayal: Hematocrit and Trabeculation in Cardiogenesis
Applied Mathematics Seminar
Howard Winet, UCLA, 328 Phillips Hall, 12:00 pm
Title: Muscle pump influence on bone circulation: A Physiological model for forced percolation
in search of a fluid dynamic model
Abstract: The blood vessels supplying long bones enter their target after passing between or
through skeletal muscles that move the bone. Contraction of these “muscle pumps” squeezes the
flexible—but of limited elasticity—vessels, setting up pressure waves in blood, an
incompressible Non-Newtonian fluid. We have tested the hypothesis: “Sufficient muscle pump
pressure reaches downstream bone capillaries to significantly influence transport across their
walls and into the surrounding bone tissue.” To test this hypothesis we used a bone window (the
bone chamber) that allows observation of bone microcirculation in a living rabbit’s tibia, and
electrical stimulation of its gastrocnemius muscle pump. Fluorescent microspheres indicated flow
velocity within the capillaries and fluorescent dextrans of specific molecular weights indicated
diffusive vs. convective transport across their walls. Significant increases in transmural
convective transport was measured in response to relatively small contractions (the leg jumped
too much at greater stimuli.). In addition, increase in bone formation was measured after weeks
of a daily stimulation regimen. These data support well-documented evidence for enhanced
osteogenesis in response to exercise. Alone, however, they do not explain how astronauts who
lose bone during space flight cannot counteract the effect by exercise. We hypothesize that
exercise in space does not bring enough blood to long bone capillaries because blood cannot pool
in the lower extremities (region of major microgravity bone loss) as it does on Earth. In order to
develop a form of exercise (or some other treatment) that would bring bloodflow and transmural
flow in long bone capillaries to normal levels, a more accurate fluid mechanical model of
circulatory blood distribution in normal and micro-gravity under various exercise regimens is
needed.
Wednesday, April 22
PDE/Analysis Seminar
Fang Wang, Shanghai Jiaotong University, 381 Phillips Hall, 4:00 pm
Title: Radiation field on Schwarzschild space-time.
Abstract: I will talk about the radiation field for the wave equation on the Schwarzschild black
hole space-time. It has two components: the rescaled restriction of the time derivative of a
solution to null infinity and to event horizon. I will mainly study the mapping property of the map
from initial data to the radiation field and and show that the regularity of the solution across the
event horizon and across null infinity is determined by the regularity and decay rate of the initial
data.
Thursday, April 23
Colloquium
David Lannes, Bordeaux, 332 Phillips Hall, 4:00 pm
Title: Modelling water waves
Abstract: We will present in this talk several mathematical issues related to the water waves
problem, many of them suggested by phenomena arising in coastal oceanography. After a brief
historical survey, we will present several mathematical approaches to the water waves problem
(based on complex analysis, harmonic analysis, geometry, etc). We will in particular show how
this free boundary problem (the domain in which the solution lives is itself the main unknown of
the problem) can be reduced to a more standard evolution equation. We will then comment on
some of the mathematical issues arising in the local well posedness theory for these equations.
Finally, we will also explain how the solutions thus constructed can be described using simpler
equations that are used in oceanography for the numerical simulation of coastal flows and
comment on the mathematical challenges raised by specific physical problems, such as wave
breaking for instance.
Friday, April 24
Applied Mathematics Seminar
Johanna Rosman, UNC, 332 Phillips Hall, 4:00 pm
Title: Flow and Mixing over Complex Biological Substrates: Understanding Linkages between
Organism- and Reef-Scales
Abstract: One of the biggest challenges in addressing questions about physical-biological
interactions on reefs is that topography varies over a wide range of spatial scales. Currents
predicted by circulation models usually represent spatially-averaged conditions over large areas.
However, in these types of systems, topography varies at scales as small as cm, and flow occurs
through layers containing solid obstacles as well as above them. Two major challenges are
therefore: 1) how to properly represent small-scale processes in circulation models, and 2) how to
interpret circulation model results if questions require knowledge of flow conditions at a
particular point on a reef. This talk will draw examples from two systems: coral reefs and oyster
reefs. We will present results from field measurements and computer simulations that provide
insight into spatial and temporal patterns in flow at scales ranging from a single organism to
clusters of organisms. We will discuss the ways in which organism-scale processes affect and are
affected by flow at larger (reef) scales, and some feedbacks that exist between reef structure,
hydrodynamics, and reef development.