### Seminars and Colloquiums for the week of October 7, 2019

SPEAKERS

Monday

Louis Gross, UTK
MGSC Panel
Tuesday
Xia Chen UTK
Wednesday
Marie Jameson, UTK
Thursday
Wendy Caldwell, Arizona State University
Florian Johne, Columbia
Friday
Wendy Caldwell, Arizona State University

Tea Time
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Kimberlyn Eversman & Emily Campbell
Topics:    Tips for dissertation writing; Preparing for the "Big Day"; Weekly check-in

Monday, October 7

MATH BIOLOGY SEMINAR
TITLE: Overview of Catastrophe Theory from the perspective of Bifurcation Theory
SPEAKER: Louis Gross, UTK
TIME: 10:10 am
ROOM: Claxton 105

SPEAKER: Drs. Plaut, Freire, and Brodskiy
TIME: 3:35 PM
ROOM: Ayres 405

Tuesday, October 8

PROBABILITY AND STOCHASTICS SEMINAR
TITLE: Precise intermittency for the parabolic Anderson Equation with an $(1+1)$-dimensional time-space white noise
SPEAKER: Xia Chen, UTK
TIME: 2:10 PM
ROOM: Ayres 112
Abstract: The moment Lyapunov exponent is computed for the solution of the parabolic Anderson equation with an (1+1)-dimensional time-space white noise. Our main result positively confirms an open problem that originated from the observations made in the physical literature (J. Statist. Phys. 78(1995) 1377-1401) and (Nuclear Physics B290(1987) 582-602). By a link through the Feynman-Kac's formula, our theorem leads to the evaluation of the ground state energy for then-body problem.

Wednesday, October 9

COLLOQUIUM
TITLE: Modular forms and related objects
SPEAKER: Marie Jameson, UTK
TIME: 3:35 PM
ROOM: Ayres 405
Abstract: Modular forms are holomorphic functions on the upper half of the complex plane that satisfy certain transformation properties. By considering their Fourier expansions, modular forms give rise to q-series which allow us to study a variety of objects in number theory, algebra, and combinatorics, including partitions, elliptic curves, class numbers, and quadratic forms. In this talk, we will study the existence (and non-existence) of congruences satisfied by these Fourier coefficients in arithmetic progressions. We will also consider the importance of certain values of their L-functions, which give rise to newly defined objects called zeta-polynomials.

Thursday, October 10

JUNIOR COLLOQUIUM
TITLE: Hydrocode Modeling of Impact Craters
SPEAKER: Wendy Caldwell, Arizona State University
TIME: 3:35 pm
ROOM: Ayres 405
Abstract: Asteroid 16 Psyche is the largest M-type (metallic) Main Belt Asteroid (MBA). Radar albedo data indicate Psyche’s surface is rich in metallic content, but estimates for Psyche’s bulk structure vary widely. Psyche has two large impact structures in its Southern hemisphere. In this work, we present results from 2D and 3D simulations of the formation of these craters using the FLAG hydrocode, developed and maintained by Los Alamos National Laboratory. FLAG has been verified and validated for impact cratering simulations, with good agreement to theoretical and experimental results. Through quantitative comparison of the simulated crater dimensions with measured values, our models suggest that Psyche is largely composed of porous, metallic material. In addition, our work indicates that the impacts were likely oblique, with angles at least 45 degrees from vertical

GEOMETRIC ANALYSIS SEMINAR
TITLE: Surgery for an extended Ricci flow system
SPEAKER: Florian Johne, Columbia
TIME: 4:00 PM
ROOM: Ayres 113
Abstract: List flow is a geometric flow for a pair (g,u), where g is a Riemannian metric and u a smooth function. This extended Ricci flow system has applications to static vacuum solutions of the Einstein equations and to Ricci flow on warped products. The coupling in this flow induces additional difficulties compared to Ricci flow, which we overcome by proving an improved bound on the Hessian. This allows us to prove a convergence result, a singularity classification result and a surgery result in three dimensions.

Friday, October 11

COLLOQUIUM
TITLE: Understanding Asteroid 16 Psyche's Composition through 3D Hydrocode Impact Crater Models
SPEAKER: Wendy Caldwell, Arizona State University
TIME: 3:35 PM
ROOM: Ayres 405
Abstract: Asteroid 16 Psyche is the largest M-type (metallic) asteroid in the Main Asteroid Belt (MBA), and an upcoming NASA mission will be the first of its kind to visit a metallic body rather than one composed of rock or ice. Psyche is likely the remnant of a differentiated planet core from a time when planetary accretion was disrupted by frequent solid-body collisions. However, because of its distant location and the limits of available measuring techniques, basic information about Psyche is under debate. Estimates of Psyche's diameter vary considerably and typically fall in the range from 213 km to 264 km. Estimates of Psyche's bulk density typically range from 1.4 + 0.3 g/cm3 to 4.5 + 1.4 g/cm 3 . Psyche has two large impact structures in its Southern hemisphere. The goal of this work is to study the composition of Psyche by modeling its impact craters. To our knowledge, this work is the first of its kind to use impact crater simulations to determine likely material compositions as well as the first 3D models of the craters on Psyche. We study various possible material compositions and porosity levels, and we compare the crater profiles in 2D and 3D to estimate Psyche's material composition. We used a variety of materials and models for both impactor and Psyche, including iron, nickel, Monel (a nickel-copper alloy that contains titanium, aluminum, silicon, and iron), and silicon dioxide (SiO2 ). The constitutive models we used for these materials were Preston-Tonks-Wallace, Steinberg-Guinan, and perfect plasticity. For equations of state (EOS), we used the tabular SESAME EOS and the analytic Mie-Gruneisen EOS. Our 3D simulations tested impact angles of 45 and 60 from vertical. From these simulations, we predict that Psyche is indeed likely mostly metallic with a porosity of about 50%. Lower density materials resulted in craters far too large, and some highly porous materials resulted in asteroid disruption. These predictions are consistent with the idea that M-type asteroids are differentiated planet cores. Figure 1 shows crater formation 93 s after impact in our solid Monel-Monel oblique impact simulation. We will show additional simulation images and animations from 3D simulations with final crater dimensions within the expected error bars.

#### 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 Dr. Christopher Strickland, cstric12@utk.edu

Past notices:

Sept. 30, 2019

Sept. 23, 2019

Sept. 16, 2019

Sept. 9, 2019

Sept. 2, 2019

Aug. 26, 2019

2018-19

2017-18

###### last updated: October 2019

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu