Student Talks - Summer 2017

Student Talks - Summer 2017

Talks are held from 12 - 2PM inside Cullimore 611 on the dates listed below.

Date Day Speaker, Affiliation, and Title
June 7 W Ivana Seric
Direct Numerical Simulations of Variable Surface Tension Flows Using a Volume-of-Fluid Method

We develop a general methodology for including a variable surface tension coefficient into a Volume-of-Fluid based Navier-Stokes solver. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation applies to both temperature and concentration dependent surface tension coefficient, along with the setups involving a large jump in the temperature between the fluid and its surrounding.

In this talk, I will demonstrate the convergence of our method for various interfacial geometries, and comparison with existing literature for a classical problem of a thermocapillary drop migration. I will also discuss the applications to the breakup of liquid metal filaments and drop coalescence.
June 9 F Pejman Sanaei
Mathematical Modeling of Membrane Filtration

The purpose of this talk is to formulate and investigate new mathematical models for membrane filtration. The work presented is divided into four parts. In the first part, a new mathematical model for flow and fouling in a pleated membrane filter is presented. Pleated membrane filters are widely used in many applications, and offer significantly better surface area to volume ratios than equal area unpleated membrane filters. However, their filtration characteristics are markedly inferior to those of equivalent unpleated membrane filters in dead-end filtration. While several hypotheses have been advanced for this, one possibility is that the flow field induced by the pleating leads to spatially nonuniform fouling of the filter, which in turn degrades performance. This hypothesis was investigated by developing a simplified model for the flow and fouling within a pleated membrane filter. The model accounts for the pleated membrane geometry (which affects the flow), for porous support layers surrounding the membrane, and for two membrane fouling mechanisms: (i) adsorption of very small particles within membrane pores; and (ii) blocking of entire pores by large particles. Asymptotic techniques are used based on the small pleat aspect ratio to solve the model, and solutions are compared to those for the closest-equivalent unpleated filter.

In the second and third parts, mathematical models are proposed to describe the effects of filter membrane morphology on filtration efficiency. A reasonable question that membrane filter manufacturers may ask is: what is the optimal configuration of filter membranes, in terms of internal morphology (pore size and shape), to achieve the most efficient filtration? In order to answer this question, a robust measure of filtration performance must be first proposed. Filter membrane performance can be measured in a number of different ways. As filtration occurs, the membrane becomes blocked, or fouled, by the impurities in the feed solution, and any performance measure must take account of this. For example, one performance measure might be the total throughput -- the amount of filtered feed solution -- at the end of filtration process, when the membrane is so badly blocked that it is deemed no longer functional. A simplified mathematical model is proposed, which (i) characterizes membrane internal pore structure via pore or permeability profiles in the depth of the membrane; (ii) accounts for various membrane fouling mechanisms (adsorption and blocking in part 2, and cake formation in part 3); and (iii) defines a measure of filter performance; and (iv) predicts the optimum pore or permeability profile for the chosen performance measure.

In the fourth part, a model for more complex pore morphology is described. Many models have been proposed to describe particle capture by membrane filters and the associated fluid dynamics, but most such models are based on a very simple structure in which the pores of the membrane are assumed to be simple circularly-cylindrical tubes spanning the depth of the membrane. Real membranes used in applications usually have much more complex geometry, with interconnected pores which may branch and bifurcate. Pores are also typically larger on the upstream side of the membrane than on the downstream side. An idealized mathematical model is presented, in which a membrane consists of a series of bifurcating pores, which decrease in size as the membrane is traversed. The membrane's permeability decreases as the filtration progresses, ultimately falling to zero. The dependence of filtration efficiency on the characteristics of the branching structure is discussed.
June 14 W Szu-Pei Fu
One-Particle-Thick Coarse-Grained Lipid Bilayer Membrane Simulations in LAMMPS

Lipid bilayer membranes have been extensively studied by coarse-grained molecular dynamics simulations. Numerical efficiencies have been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4 ∼ 6 nm so that there is only one particle in the thickness direction. Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane, such as gel–fluid–gas phase transitions of lipids, diffusion, and bending rigidity. In this work we implement such an interaction potential in LAMMPS to simulate large-scale lipid systems such as a giant unilamellar vesicle (GUV) and red blood cells (RBCs). We also consider the effect of cytoskeleton on the lipid membrane dynamics as a model for RBC dynamics, and incorporate coarse-grained water molecules to account for hydrodynamic interactions. The interaction between the coarse-grained water molecules (explicit solvent molecules) is modeled as a Lennard-Jones (L-J) potential. To demonstrate that the proposed methods do capture the observed dynamics of vesicles and RBCs, we focus on two sets of LAMMPS simulations: 1. Vesicle shape transitions with enclosed volume; 2. RBC shape transitions with different enclosed volume.
June 21 W Andrew deStefan
Numerical Methods for Finding Optimal Sampling Paths for Autonomous Vehicles

Autonomous surface vehicles and autonomous underwater vehicles (collectively referred to as AVs) are self-propelled waterborne drones which are commonly used to study various oceanographic properties. In this research, we are particularly interested in using AVs to better understand uncertain surface currents in oceanic domains. This requires determining an optimal sampling path, along which the AV can acquire the most information regarding the ocean currents. We accomplish this by means of the level set method, which is an algorithm capable of solving optimal control problems such as the minimum time-to-travel between two points in a given domain. Kalman filtering techniques are used in conjunction with the level set method for data assimilation purposes.
June 23 F Rui Cao
Numerical Simulation of Time-dependent Electrophoresis

Electrophoresis refers to the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. With the application of the electric field, a charged ‘Debye’ layer forms between the particle surface and surrounding fluid. Outside the charged layer the fluid is approximately charge neutral. This causes dispersed particles to move or migrate. The phenomenon was first observed in 1807 by Ferdinand Frederic Reuss. Ory Schnitzer, Itzchak Frankel and Ehud Yariv investigated the electrophoretic speed of a bubble in the steady state by asymptotic analysis in the limit when the Debye layer thickness is small compared to the drop radius. To simulate the process of ion transport between the layer and the region outside we solve the problem numerically including time dependent effects without the thin Debye layer assumption. By assuming the bubble is rigid and spherical, the problem is expressed in spherical coordinates with axisymmetry. The angular dependence is expressed by expansion in Legendre polynomials. Nonlinear terms are then treated in a pseudo-spectral manner. As a result, at each time step we solve a system of forced linear ODEs and PDEs in r and t in each Legendre polynomial mode. With the assumption of charge neutrality outside the Debye layer, we develop a semi-analytical method for solving the system including the boundary layer on a semi-infinite domain. This eliminates the influence of an inaccurately imposed zero far-field boundary condition at an artificial finite location and improves the numerical results significantly. Comparison will be made between our numerical results in the quasi-steady state with the results from the analysis of Schnitzer et al.
June 28 W Mahdi Bandegi
A Study of Minimizers for Pairwise Interaction Problems Using Convex Relaxation

In this talk, I will discuss both continuum and discrete energy models for a system of large particles. These models can be found in materials or biological aggregations. Finding minimizers of these models is important since energy of systems of many particles approach a minimum value at equilibrium.

The new approach is to introduce a convex relaxation to the non-convex energy. This approach gives a linear programming problem which is computationally efficient to solve and can provide a verification on a states optimality.
June 30 F Tensae Andargachew
June 30 F Subha Tirtha Datta
Joint Screening of Ultra-High Dimensional Variables for Family-Based Genetic Studies

Mixed models are a useful tool for evaluating the association between an outcome variable and genetic variables from a family-based genetic study, taking into account the kinship coefficients. When there are ultra-high dimensional genetic variables, it is challenging to fit any mixed effect model. We propose a two-stage strategy, screening genetic variables in the first stage and then fitting the mixed effect model in the second stage to those variables that survive the screening. We evaluate the performance of the proposed screening procedure via a simulation study and an application to the GAW20 data.
July 5 W Haiyang Qi
July 7 F Valeria Barra
Numerical Study of Thin Viscoelastic Films

We present a computational investigation of thin viscoelastic films. The first part of this study concerns thin films and drops on a flat solid substrate subject to the van der Waals interaction force, in two spatial dimensions. The governing equations are obtained within a long-wave approximation of the Navier-Stokes equations with Jeffreys model for the viscoelastic stress. We investigate the effects of viscoelasticity, Newtonian viscosity, and the substrate slippage on the dynamics of thin viscoelastic dewetting films, and spreading/receding drops. The second part of this study concerns numerical simulations of gravity-driven instabilities of thin viscoelastic films on an inverted plane. Finally, the third part introduces a transient finite element analysis concerning viscoelastic sheets in three spatial dimensions, in which the viscoelastic stress is included as planar stress for membrane elements.
July 12 W Yalin Zhu
A Selective Inference-based Two-stage Procedure for Clinical Safety Studies

Many complex biomedical studies, such as clinical safety studies and genome-wide association studies, often involve testing multiple families of hypotheses. Most existing multiple testing methods cannot guarantee strong control of appropriate type 1 error rates suitable for such increasingly complex research questions. In this paper, we will introduce a novel two-stage procedure based on the recently developed idea of selective inference for clinical safety studies. In the first stage, some significant families are selected by using some family-level global test, which guarantees control of generalized familywise error rate (k-FWER) among the selected families. In the second stage, individual hypotheses are tested for each selected families, which guarantees control of conditional false discovery rate (cFDR) based on the fact that the family is selected. By applying the proposed procedure to clinical safety studies, one can not only efficiently flag the significant clinical adverse events (AEs) but also select body systems of interest (BSoI) as extra information for further research. The proposed procedure for multiple families structure is implemented in the R package MHTmult. Our simulation studies show that the proposed procedure can be more reliable than alternative methods such as Mehrotra and Heyse's double FDR procedure in the setting of clinical safety.
July 14 F Linwan Feng
Penalty Methods and the Numerical Solutions of Shallow Water Wave Equations

In the talk, I will briefly introduce the penalty equation as well as the convergence rate for both Dirichlet boundary condition and Neumann boundary condition. I will use some examples to show the results of that. Then I am going to have several examples to discuss the spectral method based on the heat equation.

The second part contains the numerical solution of the 1D shallow water wave system. I will discuss the linear case, weakly nonlinear case and strongly nonlinear case. Also I will show graphs to prove the convergence rate of the numerical method. After that, I will show some recent researches of the 2D systems and use some examples to check the numerical methods of that case.

The ongoing work is to fine the conservative form of the 2D case and do the evolution code of that.
July 19 W Michael Pedneault
What are Financial Derivatives and How to Price Them Fairly
July 21 F RJ Leiser
Heterogeneous Networks: Connectivity and Periodic Forcing

Relaxation oscillations occur when the time scales between an activator and inhibitor of a system are well separated. These systems can also exhibit smaller amplitude oscillations as well as an abrupt transition between them known as the canard phenomenon. While individual oscillators are monostable (exhibiting either small or large amplitude oscillations, but not both), oscillators within a network are not. Any transition between regimes then is a network phenomenon comprised of the intrinsic properties of the isolated cells, the connectivity, and the interaction with the other cell. Using a piece-wise linear Fitzhugh-Nahumo model, we investigate the mechanisms that generate these transitions and localized patterns in a globally coupled minimal network. We also examine the ability of exponentially small periodic forcing to restore and control full relaxation oscillations.

An impedance profile represents the interaction between a neuron and periodic forcing. The interplay of frequency preference and amplitude response give us insight into the preferred forcing for optimal output. However, this idea becomes much more complex when applied to a network. Although resonance has been observed in several neuron types, the resonant properties of neuronal networks and the functionality of the impedance profile are still not well understood. The interactions of multiple frequency preferences can open op behaviors that individual cell would not be capable of alone. The frequency preference of a network is unable to be determined given the intrinsic frequency preference of its cells. We aim to develop a tool that allows us to predict and analyze the resonant properties of a coupled network from the resonant properties of the participating neurons. We test these ideas in a minimal network model of two electrically coupled neurons, measuring the network response in terms of impedances of the two coupled cells.
July 26 W Yan Zhang
Conditional Confidence Interval Based on Uncorrelated and Correlated Screening

Procedure for multiple two-sample testing is widely used. However, we are also interested in selective inference, which provides more information than the p-value in the multiple families hypotheses testing. To begin with this study, we first introduce the single conditional confidence interval for two-sample case. Then we will develop some methods for conditional confidence interval based on uncorrelated and correlated screening. Meanwhile, we will discuss conditional false coverage rate and gamma false coverage probability.
July 28 F Jacob Lesniewski
Numerical Methods for Optimal Transport

In this talk, I shall briefly introduce the Monge-Ampere Equation and its application to Optimal Transport. I shall then discuss some of the Methods developed by Froese and Oberman for solving the equation and what I have done to implement them for different problems. Following some early examples, the development of Meshfree point clouds for computing eigenvalues of the Hessian matrix in order to find the solution to the Monge-Ampere equation will be discussed. Both obsolete and current methods will be explained. Examples will then be shown of solutions to problems along with convergence plots on different domains with Dirichlet boundary conditions.
July 28 F Ryan Allaire
Heat Transfer in Thin Liquid Metals

In this talk I will discuss the Marangoni effect and its influence on thin liquid metals. This topic has been analyzed by linear stability analysis and volume of fluids in the past. I will discuss how to attack the problem using finite difference methods and its challenges. Moreover, I will discuss approximations that can be made to speed up the process and the 2-D simulations that are developed to validate this approach.
August 2 W Xieyang Jia
Modeling Semi-competing Risk Data Using Copula

We consider a competing risk data problem where a terminal event censors a non-terminal event, but not vise versa. Archimedean copula is used to model the dependence structure between events, and an estimation of the association parameter is formulated via minimum discrepancy method.
August 4 F Keyang Zhang
Convergence of a Boundary Integral Method for Interfacial Stokes Flow

Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of discretization points and allows the treatment of complicated interfaces. Despite their popularity, there is no little or no analysis of the convergence of these methods. We present our ideas on the convergence analysis of the boundary integral method for Stokes flow, focussing on a recent method by Veerapaneni, Gueyffier, Zorin, and Biros for vesicles in 2D flow.
August 9 W Matthew Moye
Data Assimilation and Electrophysiological Modeling of Mammalian Circadian Clock Neurons

Recently there has been interest in the application of data assimilation tools to the improvement of neuronal models. Often, the only data one has access to is the measured voltage from a current-clamp experiment with a prescribed injected current. Our work aims to improve understanding of the impact that injected current stimuli has on the identifiability of parameters in a neuronal model. Parameter estimation results will be shown from an Unscented Kalman Filter (UKF). We will test the performance of characteristic currents, including steps, ramps, and chaotic currents. The ability of these various stimulus protocols to enable state and parameter estimation will be assessed using simulated data from the Morris-Lecar model and a biophysical model of mammalian circadian clock neurons in the suprachiasmatic nucleus.
August 11 F Yixuan Sun
August 11 F Zhongcheng Lin
A Statistical Test for Dependent Censoring

Dependent censoring is a very important issue in medical research.We need to deal with the situation under which a failure time T and a censoring time C are dependent with each other quite often.Suppose there is one more assumption that T and C are both independent with another censoring time C',then the question will become how to check the dependence between T and C effectively.In this talk,I will briefly discuss a new statistical test to check the dependence between T and C.
August 16 W Axel Turnquist
August 16 W Binan Gu
August 18 F Jimmie Adriazola
August 18 F Yinbo Chen
August 23 W Brandon Behring
August 23 W Guangyuan Liao
August 25 F Summer Program Sign-Off

Updated: August 1, 2017