**Seminars and Colloquiums**

for the week of August 26, 2019

for the week of August 26, 2019

*SPEAKERS*

**Monday
**B. G. Kang, POSTECH

**Wednesday**

Zerihun Birhanu, Visiting Scholar, UTK & Hawassa Univ, Ethiopia

**Friday**

Theodora Bourni, UTK

**Monday, August 26**

*ALGEBRA SEMINAR*

**Title**: Dedekind-Mertens Lemma for Power Series

**Speaker**: B. G. Kang, POSTECH** **

**Time**: 3:35 PM-4:25 PM

**Room**: Ayres 114

**Abstract**: Let R be a commutative ring with unity. The famous Dedekind- Mertens Lemma states that for polynomials *f, g *∈ *R*[*x*], *C*(*f*)*k**C*(*f**g*) = *C*(*f *)*k*+1*C*(*g*)

where *C*(*f *) denotes the ideal of *R *generated by the coefficients of *f *and *k *is the degree of *g*. In this talk, we introduce the new result of ours that the Dedekind-Mertens Lemma also holds for power series *f *, *g *in *R*[[*x*]] provided *C*(*g*) is finitely generated. In our case the choice of *k *depends only on *g *but this dependence is not as easily understood as in the polynomial case.

**Wednesday, August 28**

*COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR *

**Title**: Mathematical Modeling and Simulation of Groundwater Flow and Aquifer Thermal Energy Storage

**Speaker**: Zerihun Birhanu, Visiting Scholar, UTK & Hawassa Univ, Ethiopia

**Time**: 3:35 PM-4:25 PM

**Room**: Ayres 113

**Abstract**: ** **We discuss analytical and numerical radial solutions of the differential equations for heat transport in water-saturated porous media. In particular, a similarity solution is obtained for a 2D-horizontal confined aquifer with constant radial flow. Numerical solutions are derived using a high-resolution Lagrangian approach avoiding spurious oscillations and artificial dispersion, and are shown to match the analytical solutions. The primary purpose of the investigation has been to calculate the recovery factor of an Aquifer Thermal Energy Storage (ATES) system with a cyclic repetition of injection and pumping. Solutions covering both instantaneous and delayed heat transfer between fluid and solid, as well as time varying water flow, are derived and applied to a one-well test case.

We present also a robust forward model for simulating extraction and storage of thermal energy in an aquifer. The model is a local three-dimensional finite element model with boundary conditions derived from an analytic large-scale model based on the regional water balance. Numerical investigations and thermo-hydraulic evaluation of a typical dipole injection–extraction system are presented. Most of the simulation results are focused on the spatio-temporal extension of the hot water plume close to the injection well where the main challenges occur with respect to numerical stability. Because the (aquifer thermal energy storage system is located close to the groundwater divide, the energy recovery is less sensitive to the well configuration with respect to the groundwater flow direction.

**Friday, August 30**

*COLLOQUIUM*

**Title**: Ancient Solutions to Mean Curvature Flow

**Speaker**: Theodora Bourni, UTK

**Time**: 3:35 PM-4:35 PM

**Room**: Ayres 405

** Abstract**: Mean curvature flow (MCF) is the gradient flow of the area functional; it moves the surface in the direction of steepest decrease of area. An important motivation for the study of MCF comes from its potential geometric applications, such as classification theorems and geometric inequalities. The biggest problem in the study of MCF is the appearance of singularities (curvature blow-up), which obstruct the flow from existing for all times. This phenomenon is studied by ``zooming in" around such points, a procedure that produces what is known as ancient solutions. These are solutions that have existed for all times in the past and they model singularities. In this talk we will discuss their importance and ways of studying, constructing and classifying such solutions.

*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:**

2018-19