Abstract : A great number of real-life problems, important for engineering and biological applications, involve time-dependent boundaries, whose motion is controlled by interactions among microscopic and macroscopic driving forces. At the continuum level, one derives models via energy variation approach so that the resulting formulation, usually posed as systems of coupled PDEs and boundary conditions, is consistent with physical laws. To date, grand challenges remain in high-fidelity modeling and efficient computation of these multiscale problems. This minisymposium will $(1)$ address some of most recent topics in modeling and computation; $(2)$ nurture collaborations among investigators in mathematics, biophysics, and engineering.
Organizer(s) : Shuwang Li, Yongcheng Zhou, Xiaofan Li
[01873] Solving motions of an incompressible interface with bending in Navier-Stokes flows
Format : Talk at Waseda University
Author(s) :
Yunchang Seol (Sungkyunkwan University)
Ming-Chih Lai (National Yang Ming Chiao Tung University, Taiwan)
Kian Chuan Ong (Fields Institute for Research in Mathematical Sciences)
Yongsam Kim (Chung-Ang University)
Abstract : We present two numerical approaches in the immersed boundary method for solving motions of an incompressible biological cell membrane, a vesicle structure sharing similar behaviors with red blood cells. In the original problem, the surface tension enforcing the interfacial incompressibility is unknown, so the fluid variables and the tension shall be found together via an iterative method which requires huge computational cost. To overcome this difficulty, we introduce a penalty idea and a projection approach.
[01918] Convergence of boundary integral methods for interfacial Stokes and Darcy flow with surface tension
Format : Online Talk on Zoom
Author(s) :
David M Ambrose (Drexel University)
Abstract : We consider efficient numerical methods for interfacial fluid flow. For interfacial Darcy flow in three space dimensions and interfacial Stokes flow in two space dimensions, we demonstrate convergence of boundary integral methods. The problems are subject to the effect of surface tension and/or elastic membrane forces. The proofs rely on energy estimates. This will include joint work with Yang Liu, Michael Siegel, Svetlana Tlupova, and Keyang Zhang.
[02287] A Cartesian Grid-Based Boundary Integral Method for Moving Interface Problems
Format : Talk at Waseda University
Author(s) :
Han Zhou (Shanghai Jiao Tong University)
Wenjun Ying (Shanghai Jiao Tong University)
Abstract : Moving interface problems are ubiquitous in natural sciences. Often the interface motion is coupled with PDEs in the bulk domain. This talk will present a Cartesian grid-based boundary integral method for solving moving interface problems. Layer potentials are evaluated by solving simple interface problems on a Cartesian grid to take advantage of fast solvers such as FFTs and the geometric multigrid method. Numerical simulations, including crystal growth and two-phase flows, will be reported.
[02762] An explicit numerical method for the Cahn-Hilliard equation
Format : Talk at Waseda University
Author(s) :
Junseok Kim (Korea University )
Soobin Kwak (Korea University)
Abstract : In this talk, I present an explicit conservative numerical method for the Cahn–Hilliard (CH) equation, which is a famous mathematical model for conservative phases. The CH equation has been applied in many important problems and a lot of computational methods were developed to numerically compute the CH equation. So far most of numerical methods were based on implicit numerical methods because of very stiff timestep restriction of the explicit scheme. To overcome this severe time-step restriction of the explicit scheme, we developed an explicit conservative numerical scheme. To demonstrate the superior performance of the proposed scheme, we present the computational experiments.
[02792] Viscous fingers in a Hele-Shaw cell under an electric field
Format : Talk at Waseda University
Author(s) :
Meng Zhao (Huazhong University of Science and Technology)
Abstract : We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw cell subject to an in-plane applied electric field. We develop a spectrally accurate numerical method for solving a coupled integral equation system. Our nonlinear results reveal that currents are able to promote/suppress the interface dynamics depending on its direction. When no fluid is injected, and a negative current is utilized, the interface tends to approach the origin and break up into several drops.
[02813] Computing viscoelastic and elastoplastic deformations induced by volumetric growth
Format : Talk at Waseda University
Author(s) :
Min Wu (Worcester Polytechnic Institute)
Abstract : Based on a discretized energy formulation, I will present a numerical method to solve various nonlinear mechanical systems involving finite elastic deformation, Maxwell-type viscoelasticity, or elastoplasticity. I will show its application to simulate deformations of living and nonliving soft materials during volumetric growth with free boundaries. These simulations can give insight into swelling gel experiments, in vitro wound closure dynamics, and cell and tissue morphogenesis.
[02818] Disturbance flow generated by particles in linear viscoelastic fluids
Format : Talk at Waseda University
Author(s) :
Xiaofan Li (Illinois Institute of Technology)
Hualong Feng (California State Univ, Bakersfield)
Amlan Barua (Indian Institute of Technology Dharwad)
Shuwang Li (Illinois Institute of Technology)
Abstract : Studying effects of moving particles on fluids is of fundamental importance for understanding particle dynamics and binding kinetics. We compute the fluid dynamics using an accurate boundary integral method with 3rd order accuracy in space. A unique feature of our method is that we can calculate the stress on the particle surface for a prescribed particle velocity profile. It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. When the flow becomes viscoelastic, however, the boundary layers are fundamentally different than those observed in Newtonian fluids.
[02820] Mathematical Modeling and Computation of Tumor Growth
Format : Online Talk on Zoom
Author(s) :
Min-Jhe Lu (University of California, Irvine)
John Lowengrub (University of California, Irvine)
Chun Liu (Illinois Tech)
Shuwang Li (Illinois Tech)
Yiwei Wang (University of California, Riverside)
Abstract : The building of the mechano-chemical tumor models aims to understand how the mechanical interaction and the biochemical reactions can influence the dynamics of tumor growth. The mechanical interaction within cells produces stress and the biochemical reactions involve chemical species supplying tumor with nutrients. In this talk I will demonstrate how we build the tumor models with energetic variational approaches and the numerical simulation results in both sharp interface and diffuse interface formulation will also be given.
Yuan Nan Young (New Jersey Institute of Technology)
Bryan Quaife (Florida State University)
Szu-Pei Fu (Trinity College)
Abstract : We use a model recently developed for the many-body hydrodynamics of amphiphilic JPs under a viscous background flow to investigate distinct particle phases that arise when accounting for asymmetric and polar hydrophobes. We quantify the macroscopic properties of novel JP phases under a linear shear and a Taylor-Green mixing background flow and quantify their macroscopic, complex-fluid behavior. These numerical results provide insight into dynamic control of non-equilibrium active biological systems with similar self-organization.
[02823] Sharp interface problem of Ohta-Kawasaki Model
Format : Talk at Waseda University
Author(s) :
Amlan K Barua (IIT Dharwad)
Abstract : The Ohta Kawasaki (OK) model investigates mesoscopic phase separation in block copolymers. In this talk, we discuss a sharp interface version of OK equations using matched asymptotic expansions. The resultant equations resemble a Hele-Shaw type system. We suggest a boundary integral formulation of the problem and propose highly accurate numerical techniques to solve the equations. We conduct long-time simulation using our numerical methods. The simulation results show the emergence of various interesting configurations.
[02835] Phase-field modeling and simulation of controllable dendritic growth
Format : Talk at Waseda University
Author(s) :
Darae Jeong (Kangwon National University)
Abstract : In this study, we consider the controllable dendritic growth model with phase-field method. The governing system consists of three equations that are for capturing the interface between solid and melt phases, diffusion of the temperature, and structure by molecular orientations in solid. We propose the time-dependent adaptive mesh and finite-difference algorithm, which is designed to efficiently solve the governing system. After that, we present several numerical simulation to show the various patterns and its corresponding parameter effect for crystal formation. And we demonstrate the effectiveness of our approach by comparing numerical results with other method.
[05666] Self-consistent field simulations for liquid-liquid phase separation of proteins'
Author(s) :
Yongcheng Zhou (Colorado State University)
Abstract : Liquid–liquid phase separation (LLPS) is a process that compartmentalizes proteins and nucleic acids into microscale, liquid-like, membraneless bodies with specific functions. It regulates intracellular spatiotemporal coordination of various critical biological activities. Quantitive simulations of LLPS has been challenging since there is no membrane and thus previous developed curved energy based Cahn-Hilliard theory does not work. Here we developed a self-consistent field theory for LLPS and adopted a deep learning approach to explore the biological parameters that could drive LLPS.
