Events
Department of Mathematics and Statistics
Texas Tech University
The work deals with the existence of solutions of an integro-differential equation in the case of the normal diffusion and the influx/efflux term proportional to the Dirac delta function. The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for non Fredholm elliptic operators in unbounded domains are used.
This week's Biomath seminar details available at this pdf
This week's PDGMP seminar details available at this pdf
Please virtually attend Ms. Atampalage's presentation at 3 PM on Wednesday the 24th at this zoom link.
In the first part of the talk, we will study about the distribution of
gaps between eigenvalues of Hecke operators in both horizontal and
vertical settings. As an application of this we will obtain a strong
multiplicity one theorem and evidence towards Maeda conjecture. The
horizontal setting is a joint work with M. Ram Murty. In the second
part of the talk, using recent developments in the theory of l-adic
Galois representations we will study the normal number of prime
factors of sums of Fourier coefficients of eigenforms. Moreover, we
will see an all purpose Erd ̈os-Kac theorem. The final part is joint
work with M. Ram Murty and V. Kumar Murty.
Join Zoom Meeting https://zoom.us/j/96217128540?pwd=NjU5dzE2RjZvV0prejhOOWVjVENadz09
Meeting ID: 962 1712 8540
Passcode: 474170
Erosion is a fluid-mechanical process that is present in many geological phenomena such as groundwater flow. We present a boundary integral equation formulation to simulate two-dimensional erosion of a porous media. A numerical challenge to simulate low porosities is accurately resolving the interactions between nearly touching eroding bodies. We present a Barycentric quadrature method to resolve these interactions and compare its accuracy with the standard trapezoid rule. By using a fast summation method, such as the Fast Multipole Method (FMM), the cost of applying the standard trapezoid rule can be reduced to O(N) operations where N is the total number of source and target points. However, this advantage is gone when applying the Barycentric quadrature rules with FMM which involve several N-body calculations. To reduce the computational time, we develop a hybrid method that combines this quadrature rule and an accelerated version of the trapezoid rule. We compute the velocity, vorticity, and tracer trajectories in the geometries that include dense packings of 20, 50, and 100 eroding bodies. Similar to our previous work (B. D. Quaife et al., J. Comput. Phys. 375, 1 (2018).), we observe quickly expanding channels between close bodies, flat faces developing along the regions of near contact, and bodies eventually vanishing. Finally, having computed tracer trajectories, we characterize the transport inside of eroding geometries by computing and analyzing the tortuosity and anomalous dispersion rates. We present the validation of the tortuosities based on two different definitions and apply a reinsertion method to compute asymptotic anomalous dispersion rates.
Please virtually attend the Applied Math seminar via this zoom link Wednesday the 24th at 4 PM.