Page Not Found
Page not found. Your pixels are in another canvas.
Sitemap
A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Personal Website
About me
Page not in menu
This is a page not in th emain menu
Posts
Future Blog Post
Published:
This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.
Blog Post number 4
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 3
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 2
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 1
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
portfolio
Portfolio item number 1
Short description of portfolio item number 1
Portfolio item number 2
Short description of portfolio item number 2
publications
Boundary integral equation analysis for spheroidal suspensions
Published in , 2026
Spectra of the Laplace boundary integral operators on prolates and oblate spheroids are derived and verified. Capabilities and limitations of the approach are investigated.
talks
Perturbation Approach to Stokes-Whitehead Paradox: Oseen Approximation
Published:
The Stokes equation describes low-Reynold’s number flow dynamics. Consider an uniform flow past a sphere. Although the solution to the Stokes equation satisfies both surface and far-field boundary conditions, the next order approximation to the Navier-Stokes equation does not. This is the Whitehead paradox. Instead, we consider the low Reynold’s number as an asymptotic parameter, and look at a perturbation problem to steady state, incompressible Navier Stokes equation. The Stokes equation is the unperturbed equation in this problem. Considering flow near the surface of the sphere as a boundary layer, a second order uniform approximation can be made to resolve the Whitehead paradox. This is the Oseen approximation.
Boundary integral equation analysis for spheroidal suspensions
Published:
Boundary integral equation (BIE) methods are numerical PDE methods well suited to study soft materials in nature and industry. They reduce the dimension of the problem, but are plagued by singular and near-singular integrals on and near surfaces. We use solid spheroidal harmonics to evaluate BIO on and near the surface. Coupled with smooth quadrature for far evaluation, we present a fast, spectrally accurate method for computing BIO on spheroidal suspensions.
BIE method for Stokes Flow in Axisymmetric and Periodic Geometry
Published:
Peristalsis is an important biological process in which tubes in our body contract and relax to move solid or fluid along. One important inverse problem in mimicing this behavior artificially is to find the optimal wall configuration that generates the optimal flow, or minimizes the energy loss. During the forward direction, one solves for the flow generated by a certain wall geometry. This can be done using boundary integral equations (BIEs), by imposing a surface source density on the wall. In this paper, we reformulate the periodic geometry using proxy sources and periodic boundary discrepancies. We then use axisymmetry to reduce the surface BI into a 1D integral by analytically integrating over the angle of revolution. We also discuss the special quadrature needed to address singular and near-singular integrals that appears from BIE. Finally we give convergence and simulation results.
A scalable boundary integral method for simulating particulate flows through complex periodic geometries
Published:
Understanding low Reynolds number flows and constituent particle dynamics in confined, periodic geometries is fundamental to many biophysical applications. While Boundary Integral Equation (BIE) methods are powerful for Stokes flow, they typically rely on periodic Green’s functions, which can be restrictive for complex geometries and arbitrary periodic flow conditions.
teaching
Teaching: U-M Math Department
Undergraduate course, University of Michigan, Ann Arbor, Math Department, 2023
- Fall 2023: Math 115 (Calculus 1) Primary instructor, individual section
- Winter 2024: Math 116 (Calculus 2) Primary instructor, group section
- Fall 2024: Math 115 Primary instructor, individual section