DE Seminar: Chris Bispels and Evan Sheldon
UMBC Undergraduate Students
Location
Mathematics/Psychology : 401
Date & Time
April 28, 2025, 11:00 am – 12:00 pm
Description
Title: Miller-Rabin
Primality Test and its Applications
Speaker: Chris Bispels
Abstract: Primality
tests are discussed with a focus on the Miller-Rabin probabilistic primality
testing algorithm. After discussing different definitions of Miller-Rabin
witnesses, an outline for the modern version of a proof that establishes the
probabilistic error bound for the Miller-Rabin primality test it presented.
Finally, applications of the algorithm in cryptography are detailed.
Title: Periodic
Solutions and Resonance in Wave-Heat Systems
Speaker: Evan Sheldon
Abstract: Oscillatory
behaviors are ubiquitous in physical systems. Many natural oscillatory systems
couple different dynamics, and an important class are hyperbolic-parabolic
(i.e. wave-heat) systems of partial differential equations (PDEs). In this
sense, a heat-wave system can be viewed as an idealized fluid-structure
interaction (FSI) model. Some examples of FSI models include aeroelastic
systems, arterial dynamics in the body, and geophysical poro-elastic flow.
However, mathematical challenges for hyperbolic-parabolic systems arise due to
the difference in behavior of the hyperbolic and parabolic components, as well
as their complex interaction along a coupling interface. The phenomenon of
resonance is an important aspect of coupled wave-heat PDE dynamics, and very
recently, geometric conditions have been proposed to characterize when
resonance is possible in our wave-heat system. From these conditions, it has
been theorized that our system can demonstrate resonance in two spatial
dimensions. Using the finite difference method, we have simulated the dynamics
of our wave-heat system in both one and two spatial dimensions. Results show
that these simulations can accurately model the behavior of our wave-heat
system, and we can now search for cases of resonance in our wave-heat system.
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