Seminars and Colloquiums
for the week of August 27, 2018
Ryan Unger, University of Tennessee
Jimmy Scott, University of Tennessee
Yehuda Braiman, UTK MABE and ORNL
Suzanne Lenhart, University of Tennessee
Mahir Demir, University of Tennessee
MINIMAL SURFACES SEMINAR
TITLE: Combinatorial Stiefel--Whitney classes
SPEAKER: Ryan Unger, University of Tennessee
TIME: 4:00 PM-5:30 PM
ROOM: Ayres 121
The problem of lifting an SO(n) frame bundle to a Spin(n) principal bundle can be intuitively understood in terms of the vanishing of a Cech-H^2 class. We prove a folklore theorem which says that this is exactly the second Stiefel--Whitney class. This approach works for both SO(n) and SO(n,1) bundles. As an application, we will show that any globally hyperbolic 4-dimensional spacetime is spin.
TITLE: A Characterization of Vector-Valued Function Spaces Which Characterize Differentiability Properties – Part I
SPEAKER: Jimmy Scott, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 113
In this series of talks we prove an equivalence of two optically different classes of function spaces. We show that a class of spaces of vector fields whose semi-norms involve the magnitude of “directional” difference quotients is in fact equivalent to the class of Besov spaces. The equivalence can be considered a “Korn’s inequality” for Besov spaces. We also show the same type of equivalence between the class of vector-valued Bessel potential spaces and a class of spaces of vector fields whose semi-norms involve certain linear combinations of potentials. To further investigate these equivalences, we examine the finer structure of these new function spaces via an analogue of the auxiliary g-function.
This talk will focus on the material necessary to understand the results; specifically, the required background of singular integrals, the classical Korn’s inequality for Sobolev spaces, and the basics of the Bessel spaces, Besov spaces, and the g-function will be presented.
COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
TITLE: Principles of a cryogenic memory cell design using small arrays of coupled Josephson junctions
SPEAKER: Yehuda Braiman, UTK MABE and ORNL
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 113
One of the main challenges in modern computing systems is developing fast, small size, and energy efficient memory. As the requirements for memory grow immensely in modern times, so does the total cost to operate memory in exascale and other types of computing. One possible way to speed up memory access while reducing power consumption is cryogenic computing. Cryogenic electronics based on superconducting devices (such as Josephson junctions and superconducting quantum interference devices) are generically very fast and energy efficient. A single Josephson junction can operate at a speed close to THz and switching between the states may require as little as 10-18–10-19 J. A variety of cryogenic memory designs have been proposed, including memories based on single flux quantum digital logic, hybrid superconducting complementary metal-oxide semiconductor designs, magnetic random-access memory (RAM), and others.
In this seminar we will present a memory cell design that is based on the dynamics of small coupled arrays of Josephson junctions. In such a design, write, read, and reset operations can be executed on the same basic circuit. The operating principles of the proposed design refer to the existence of multiple stable states that may exist in coupled nonlinear arrays of Josephson junctions. Multiple states in a Josephson junction array can be simultaneously stable, and transitions between these states can be achieved by incrementally varying accessible parameters of the system or by applying an external pulse. Write, read, and reset operations may be executed from the same or different junctions, depending on the mode of operation. When no memory operations (read, write, reset) are implemented in the circuit, the voltage of each junction is zero and consequently energy dissipation is minimal (energy will dissipate mainly at the time of memory access operations). Moreover, if the circuit operation mode and parameter set are chosen appropriately then both memory access times and energies can be simultaneously minimized.
DIFFERENTIAL EQUATIONS SEMINAR
TITLE: Optimal control techniques applied to management of natural resource models
SPEAKER: Suzanne Lenhart, University of Tennessee
TIME: 2:10 PM-3:00 PM
ROOM: Ayres 113
Optimal control techniques have been used to investigate management strategies in a variety of models for natural resources. Two applications involving FISH and FIRE will be discussed, incorporating the economic impacts. Harvesting of fishery stock has led to habitat damage. We present a model with spatiotemporal dynamics of a fish stock and its habitat. Techniques of optimal control of PDEs are used to investigate the harvest rates that maximize the discounted value while minimizing the negative effects on the habitat. The number of large-scale, high-severity forest fires occurring is increasing, as is the cost to suppress these fires. We incorporate the stochasticity of the time of a forest fire into our model and explore the trade-offs between prevention management spending and suppression spending.
MATH BIOLOGY SEMINAR
TITLE: Optimal Fishery Management for the Black Sea Anchovy Ecosystem Model
SPEAKER: Mahir Demir, University of Tennessee
TIME: 10:10 AM-11:00 AM
ROOM: Ayres 401
If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.
If you have questions, or a date you would like to confirm, please contact mlangfo5 AT utk DOT edu