SIAM Student Chapter Seminar/Fall2020
Contents
Fall 2020
date | speaker | title |
---|---|---|
9/29 | Yu Feng (Math) | Phase separation in the advective Cahn--Hilliard equation |
10/14 | Dongyu Chen (WPI) | A Half-order Numerical Scheme for Nonlinear SDEs with one-sided Lipschitz Drift and H\:{o}lder Continuous Diffusion Coefficients |
10/28 | Evan Sorensen (math) | Unsupervised data classification via Bayesian inference |
11/23 | Weijie Pang (McMaster University) | Pandemic Model with Asymptomatic Viral Carriers and Health Policy |
Abstracts
9/29, Yu Feng (Math)
Phase separation in the advective Cahn--Hilliard equation
The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection-hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection-diffusion equation.
10/14, Yuchen Dong (WPI)
A Half-order Numerical Scheme for Nonlinear SDEs with one-sided Lipschitz Drift and Hölder Continuous Diffusion Coefficients
We consider positivity-preserving explicit schemes for one-dimensional nonlinear stochastic differential equations. The drift coefficients satisfy the one-sided Lipschitz condition, and the diffusion coefficients are Hölder continuous. To control the fast growth of moments of solutions, we introduce several explicit schemes including the tamed and truncated Euler schemes. The fundamental idea is to guarantee the non-negativity of solutions. The proofs rely on the boundedness for negative moments and exponential of negative moments. We present several numerical schemes for a modified Cox-Ingersoll-Ross model and a two-factor Heston model and demonstrate their half-order convergence rate.
10/28, Evan Sorensen (math)
Unsupervised data classification via Bayesian inference
Bayesian inference is a way of “updating” our current state of knowledge given some data. In this talk, I will discuss how one can use Bayesian inference to classify data into separate groups. Particularly, I will discuss an application of this to outlier detection in contamination control within semiconductor manufacturing. Time permitting, I will talk about some computational tools for these models.
11/23, Weijie Pang (McMaster University)
Pandemic Model with Asymptomatic Viral Carriers and Health Policy
By October 13, 2020, the total number of COVID-19 confirmed cases had been 37,880,040 with 1,081,857 death in the world. The speed, range and influence of this virus exceed any pandemic in history. To find reasons of this incredible fast spread, we introduce asymptomatic category into a SEIR pandemic model. Based on published data of Italy, we calibrated exposed rates of COVID-19 in this model and then simulated the spread of COVID-19 for different asymptomatic rates. To measure the effects of different types of public health policies on this pandemic, we construct a pandemic model including health policies. By the simulation of this model, we provide feasible suggestions of containment to regulators.