2021 Faculty and Student Summer Talks

Ryan Allaire

Detailed Thermal Modelling of Droplet Assembly in Nanoscale Molten Metal Films

The focus of this talk is the accurate modelling of thermal effects in nanoscale liquid
metal films that are deposited on thermally conductive substrates, melted by an external heat source, and dewet into droplet patterns. Using asymptotic analysis we develop a novel model that accurately portrays heat conduction in the liquid film and such effects as temperature varying material parameters and phase changes. By developing a 3D GPU code that solves the underlying partial differential equations we are able to simulate both film evolution and heat conduction on large domains. We find that many effects, such as temperature varying viscosity, strongly influence the dewetting mechanism of the film and can, in many instances, lead to partial drop formation that are frozen in place.

Professor Zuofeng Shang

Calibrating Multi-Dimensional Complex ODE from Noisy Data via Deep Neural Networks

Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In this work, we propose a two-stage nonparametric approach to address this problem. We first extract the denoised data and their higher order derivatives using boundary kernel method, and then feed them into a sparsely connected deep neural network with ReLU activation function. Our method is able to recover the ODE system without being subject to the curse of dimensionality and complicated ODE structure. When the ODE possesses a general modular structure, with each modular component involving only a few input variables, and the network architecture is properly chosen, our method is proven to be consistent. Theoretical properties are corroborated by an extensive simulation study that demonstrates the validity and effectiveness of the proposed method. Finally, we use our method to simultaneously characterize the growth rate of Covid-19 infection cases from 50 states of the USA.

Kosuke Sugita

A Fast and Accurate Boundary Integral Method for Superhydrophobic Flow Computations

We present a fast and accurate boundary integral method for the computation of incompressible Stokes flow over surfaces featuring corners and mixed boundary conditions. Such surfaces arise in simple models of superhydrophobic (SH) materials. Boundary integral methods have several advantages in SH flow computations, such as a reduction in the dimension of the problem and the ability to deal with complex boundary geometries. However, such problems exhibit flow singularities at boundary transition points and geometric corners, and thus standard quadrature rules for smooth integrals result in a severe loss of accuracy. Adaptive mesh refinement mitigates the issue, however, the size of the discrete problem grows significantly with refinement level, and it can still be difficult to obtain satisfactory accuracy due to the ill-conditioning of the linear system. To resolve these issues, we combine the recently developed Recursively Compressed Inverse Preconditioning (RCIP) method with kernel-split quadratures, a scaling technique, and the Fast Multipole Method to obtain a fast and accurate numerical scheme for SH flow computations. Several applications are presented to illustrate the performance of the method.
 

Yuexin Liu

Mechanical Rotation at Low Reynolds Number via Reinforcement Learning 

There is growing interest in the development of artificial microscopic machines that can perform complex maneuvers like swimming microorganisms for potential biomedical applications. At the microscopic scales, the dominance of viscous over inertial forces imposes stringent constraints on locomotion. In the absence of inertia, Purcell first proposed an elegant way to generate net translation using kinematically irreversible motions. In addition to net translation, a more recent prototype known as Purcell’s “rotator” has been proposed in Dreyfus et al. as a mechanical implementation of net rotation at low Reynolds numbers. These ingenious designs rely on knowledge of the surrounding environment and the physics of locomotion within the environment, which may be incomplete or unclear in more complex scenarios. More recently, reinforcement learning has been used as an alternative approach to enable a machine to learn effective locomotory gaits for net translation based on its interaction with the surroundings. In this work, we demonstrate the use of reinforcement learning to generate net mechanical rotation at low Reynolds numbers without requiring prior knowledge of locomotion. For a three-sphere configuration, the reinforcement learning recovers the strategy proposed by Dreyfus et al. As the number of spheres increases, multiple effective rotational strategies emerge from the learning process. However, given sufficiently long learning processes, all machines considered in this work converge to a single type of rotational policies that consist of traveling waves of actuation, suggesting its optimality of the strategy in generating net rotation at low Reynolds numbers.

*This seminar will be held at 1:50PM* 

Axel Turnquist

Optical Inverse Problems and Optimal Transport

It is well known that a parabolic antenna can take light emanating from its focus and transmit it to nearly parallel lines away from the dish. Suppose though you have a more general setup where you do not want simply parallel lines in the far-field, but instead want to customize the far-field intensity pattern. This would obviously require a more generalized antenna. This is the essence of a well-known inverse problem in geometric optics known as the reflector antenna problem. There exists a PDE formulation of this problem which allows one to solve for the shape of the antenna, but the PDE is very difficult to solve theoretically and numerically. Fortunately, observations over the last twenty years by various authors have connected this problem, via a simple change of variables, to an equivalent optimal transport problem on the sphere. Unfortunately, solving this transport problem on the sphere numerically has not, up to now, been proven to have convergent schemes. Here, we show the numerical convergence guarantees we have established for this problem, show how one goes about setting up a numerical discretization, and demonstrate the computations with various figures.

Jose L. Pabon

Elucidating an Empirical Exposition of Diversity in U.S. Museums via Data Clustering and Optimization, and Conglomerating Collective Motion Mechanics

Our succinct presentation threads together two disparate yet exciting research excerpts. Our exposition starts by examining the tools from Data Mining and Optimization to frame an empirical discussion of diversity in U.S. museums via data clustering and optimization. Some data clustering theory foundations and rudimentary concepts will be defined. Agglomerative Hierarchical Clustering specifications will be discussed including canonical algorithms as well as various industry standard proximity schemes. Data Validation Theory concepts will be explained, including cluster cohesion, cluster separation and silhouette widths. These are key for the optimization techniques used in the data analysis of the work discussed, including the results that give evidence of the very weak association between museum collection mission and diversity. The last part of our work will briefly summarize our current research into the collective motion of lattices of hydrodynamically interactive flapping swimmers. Specifically, we seek higher accuracy results by adding to the existing iterative maps forces determined via slender body potential theory.

Professor Ji Meng Loh

Spatial Sampling Design using the Generalized Neyman-Scott Process

In this talk I will introduce a new procedure for spatial sampling design. Previous studies (Zhu and Stein, 2006) have shown that the optimal sampling design for spatial prediction with estimated parameters is nearly regular with a few clustered points. The pattern is similar to a generalization of the Neyman-Scott (GNS) process (Yau and Loh, 2012) which allows for regularity in the parent process. This motivates the use of a realization of the GNS process as sampling design points. This method translates the high dimensional optimization problem of selecting sampling sites into a low dimensional optimization problem of searching for the optimal parameter sets in the GNS process. Simulation studies indicate that the proposed sampling design algorithm is more computationally efficient than traditional methods while achieving similar minimization of the criteria functions. While the traditional methods become computationally infeasible for sample size larger than a hundred, the proposed algorithm is applicable to a size as large as n = 1024. A real data example of finding the optimal spatial design for predicting sea surface temperature in the Pacific Ocean is also considered.

This is joint work with Szehim Leung, Chunyip Yau and Zhengyuan Zhu.

Diego Rios

Shallow Water Inversion

Sound propagates through all media in a fashion that is determined by the medium sound speed, density, attenuation properties, and interface characteristics between layers (seabed properties). We investigate the forward problem modeling the sound (understanding what sound “looks like”) when all the seabed properties are known. Using a variety of techniques (ray tracing, normal modes, parabolic equation to name a few) we achieve this task albeit with some effort and numerical challenges. Obtaining information about the factors that determine sound propagation given the data and the sound model is the solution to the inverse problem. Similarly, we also classify the the type of media (sediment) that our sound propagates through as a parallel problem when we want to learn different seabed characteristics. We note that solving the often ill-conditioned inverse problem takes much more work than formulating the forward problem, involving an accurate sound propagation model and a multi-dimensional estimation technique that may lead into a multi-dimensional search that requires global optimization. 

Professor Enkeleida Lushi

Collective Behavior of Interacting Active Particles in Confinement

We present a new hybrid Vicsek-ABP model for interacting active particles and look at the collective motion for such swimmers in non-trivial confinement. We discuss the collective behavior arising in convex domains, racetracks and pillar forests for a variety of densities, confinement sizes and interaction distances and compare them to collective behavior seen in free space. Phase diagrams for different geometries summarize the behavior and give insight into how we can tune the confinement to achieve a particular desired dynamics. Lastly, we compare the results to experiments in active matter systems such as Quincke colloids, swimming bacteria or larval zebrafish, and note the qualitative similarities and differences.

Work with undergraduate students Katherine Wall, Nathaniel Netznik and postdoc associate Shang-Huan Chiu.

Yasser Almoteri

Bacterial Motion and Spread in Wet Porous Materials

We investigate through mathematical modeling, analysis and nonlinear simulations, the collective motion of micro-swimmers in fluids with resistance, which approximate a porous wet material. We use a continuum model to describe the collective dynamics of bacteria that each perform a run-and-tumble motion. The swimmer dynamics is coupled to the fluid dynamics that is modeled through a Stokes-Brinkman equation with an added active stress. The linear stability of the uniform isotropic state reveals that the suspension transitions from a long-wave instability to a finite-range one where the collective bacterial chaotic motion is weakened by the resistance. Simulations of the full nonlinear PDE system confirm the analytical results. We discuss the spread of an initial accumulation of bacteria and show that it depends non-trivially on the medium resistance which suppresses the spread. Last, we outline ongoing work on high performance simulations of the coupled motion of thousands of individually-traced swimmers in a fluid with resistance.

Souaad Lazergui 

High Frequency Asymptotic Expansions of the Helmholtz Equation Solutions Using Neumann to Dirichlet and Robin to Dirichlet Operators

This talk is concerned with the asymptotic expansions of the amplitude of the solution of high-frequency Sound-hard scattering problems in the exterior of two-dimensional smooth convex scatterers. The original
expansion was obtained by using a pseudo-differential decomposition of the Dirichlet to Neumann operator and a microlocal model of the Kirchhoff operator. This work uses Neumann to Dirichlet operator to derive
the asymptotic expansion of the Kirchhoff amplitude over the scatterer boundary. Similarly to the Robin to Dirichlet operator, we seek the same ansatz for Robin boundary condition. It is obvious that the
resulting expansions can be used to appropriately choose the ansatz in the design of high-frequency numerical solvers, such as those based on integral equations, in order to produce more accurate highfrequency asymptotic numerical solution of the Helmholtz equation.

Professor Michael Booty

Studies of Surfactant Solubility

The role of a surfactant or “surface active agent” is to reduce the surface tension at an interface between immiscible liquids such as an oil and a water-based or aqueous phase.  They occur naturally although many surfactants are synthesized, and they are useful in a wide range of applications.  

Because of their molecular structure surfactants seek out an interface, or are energetically favored to be there, but they are also soluble, or can occur in the bulk phase away from an interface.  However, since surfactant molecules are much larger than their host solvent molecules they diffuse very slowly in the bulk.  Exchange of surfactant between an interface and the neighboring bulk phase leads to interesting dynamics that can be properly resolved only by careful analysis. 

Binan Gu

A Graphical Representation of Membrane Filtration

In this talk we describe a model for the filtration process in a membrane network involving multiple fouling mechanisms. We first formulate the governing equations of fluid flow on a general network, and we model transport and adsorption of particles (foulants) within the network by imposing an advection equation with a sink term on each pore (edge) as well as conservation of fluid and foulant flux at each pore junction (network vertex). Under adsorption alone, we find that total throughput satisfies a strong power law vs. initial void volume, while accumulated foulant concentration at membrane outlet follows an exponential decay against membrane tortuosity.  In addition to adsorption, we also consider sieving as a simultaneous fouling mechanism. It is modelled by sending particles of size at the order of pore radii as Poisson arrivals on the membrane top surface and random walkers on the graph following a transition law involving fluid flux. A mean-field model is proposed by solving a traffic equation for the effective arrival rate at each vertex. Lastly, we model pore size variations by imposing a random initial condition for pore radii and discuss some interesting phenomena.

Professor James MacLaurin

Metastability of Stochastic Waves and Patterns

In this talk I present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of continuous isometries (such as translation or rotation). This formalism can accommodate patterns, waves and oscillations in reaction-diffusion systems and neural field equations. To do this, I define the phase by precisely projecting the infinite-dimensional system onto the manifold of isometries. Two differing types of stochastic phase dynamics are de ned: (i) a variational phase, obtained by insisting that the difference between the projection and the original solution is orthogonal to the non-decaying eigenmodes, and (ii) an isochronal phase, defined as the limiting point on manifold obtained by taking time to infinity in the absence of noise. We outline precise stochastic differential equations for both types of phase. The variational phase SDE is then used to show that the probability of the system leaving the attracting basin of the manifold after an exponentially long period of time is exponentially unlikely. In the case that the manifold is periodic (such as for spiral waves, spatially-distributed oscillations, or neural-field phenomena on a compact domain), the isochronal phase SDE is used to determine asymptotic limits for the average occupation times of the phase as it wanders in the basin of attraction of the manifold over very long times. In particular, we find that frequently the correlation structure of the noise biases the wandering in a particular direction, such that the noise induces a slow oscillation that would not be present in the absence of noise.

Professor James MacLaurin Recording - June 29, 2021

Nicholas Dubicki

Variational Analysis of Magnetic Skyrmions in Thin-Film Materials

Nanoscale structures in ferromagnetic materials are now of great importance to computer engineering.  One such structure is the magnetic Skyrmion, a localized magnetic vortex in a 2-D ferromagnet.  Our long-term task is to ensure the micromagnetic theory can predict the existence of Skyrmion solutions in all cases.  This talk will present an overview of the micromagnetic modeling procedure.  Then, a reproduction of the result of Belavin (1975) which forms Skyrmion profiles using only the exchange interaction.  This so-called Belavin-Polyakov Profile is the basis for a class of ansätze necessary for pursuing more complicated Skyrmion problems.  We then show an example of such a Skyrmion stabilized by the Exchange, Anisotropy, and Dzyaloshinskii-Moriya Interactions together, accomplished by minimization of the combined energies over the suitable class of ansätze.

Tadanaga Takahashi

A Finite Element Domain Decomposition Method for Wave Scattering

Behind every telecommunication, radar, and imaging technology is the theory of wave scattering. The expensive computational cost at high frequencies is still the crux of wave scattering simulations. Modern wave solvers that emphasize speed employ a combination of finite elements and domain decomposition. This talk is an overview of the field accompanied with ongoing research. 

Mark Fasano

Spreading Dynamics of a Partially Wetting Water Film Atop a MHz Substrate Vibration

We consider a MHz Rayleigh surface acoustic wave (SAW) propagating in a lithium niobate substrate with either a fully wetting or partially wetting fluid atop. Previous studies have revealed that these conditions support the convective spreading of a fully wetting silicon oil film. However, partially wetting de-ionized water seemed unaffected by this spreading mechanism. Through both the development of the theoretical understanding of the system and experimentation, we will demonstrate the existence of a parametric regime where a partially wetting liquid will in fact spread under the above conditions. We will demonstrate that distinct capillary and convective spreading regimes are governed by a balance between convective and capillary mechanisms, manifested in a single non-dimensional parameter. Finally, I will discuss plans for expanding on this research by considering the problem of using SAWs to induce the separation of oil-water mixtures.   

Connor Robertson

Data-Driven Modeling for Active Nematic Systems

In recent decades, there has been steady progress in the collection of high-quality, large data sets that record the behavior of complex systems in a variety of scientific disciplines. In "data-driven modeling", the goal is to use machine learning techniques to extract a low order model that reasonably reproduces the behavior of such data sets. One important challenge in data-driven modeling is to extract continuum models directly from experimental data. We here present the results of a data-driven modeling approach applied to a biophysical system of recent interest, which consists of a collection of rod-like filaments (microtubules) driven by motor proteins and immersed in a fluid. Existing continuum models for these "active nematic" systems are typically based on liquid-crystal theory and include many phenomenological terms. As a result, there are outstanding questions about the correct model for these systems, and a data-driven modeling approach may yield new insights. In this talk, I will outline the application of Sparse Identification of Nonlinear Dynamics (SINDy) to the active nematic system and highlight the various challenges associated with data-driven modeling using noisy data. These include: integrating known physics into the learning techniques, data extraction from experimental images, numerical differentiation of noisy data, and sparse regression.

Matthew Illingworth

The Arrow of Time and Its Relation to Causality

The intuitive notion of causality depends on time having a specific order, where events proceed from past to future and cause always precedes effect; this is referred to as the “arrow of time”. For example, the second law of thermodynamics, which says that entropy never decreases and therefore has temporal irreversibility built in–that is, the distinction between past and future actually makes a difference to the production of entropy. However, there are special cases that arise in quantum physics where the arrow of time may be reversed or bifurcated; in these cases, effect might precede cause (retrocausality), or multiple orderings of a set of events can occur simultaneously (indefinite causality). This talk will provide a brief introduction to and overview of these topics.

Lauren Barnes

Modeling of Colloid-Polymer Mixtures in Microgravity

We present a theoretical model of colloid-polymer mixtures in a microgravity environment. Studying such mixtures gives us valuable insight into phase transition processes—insight that can be applied to various materials on earth. The addition of polymer to a colloidal suspension induces weakly attractive forces between the colloids and leads to a three-phase coexistence region, wherein a "liquid" phase coexists with a low-density gas phase and a high-density crystal phase. We construct, analyze and numerically simulate a phase-field model for phase separation in colloid-polymer mixtures. The results of our model simulations will be compared against experiments performed on the International Space Station, using image data available on the NASA Physical Sciences Informatics system.

Moshe Silverstein

An Introduction to Mathematical Neuroscience and Autonomous Field Equations for Balanced Neural Networks

In this talk I hope to briefly introduce and motivate the topic of mathematical neuroscience. Some of the key challenges and equations of mathematical neuroscience will be presented and discussed. I will then go on to present our work involving autonomous field equations for balanced neural networks. Specifically, I will try to motivate and derive the Fokker-Planck equation used in our model. In doing so, we briefly discuss an application of the Radon–Nikodym derivative in the form of the Girsonov Theroem. Finally, we will reduce our model to a system of ODEs which can be solved numerically.  

Joseph D'Addesa

Phase Separation of Two-Fluid Mixtures using Surface Acoustic Waves

In this talk we will present some theoretical and computational aspects of flow of thin fluid films. The theoretical part involves basic fluid mechanics and presents a brief derivation of the thin film equation using the long wave approximation. A simplified version of this equation is then analyzed numerically followed by future adaptation to include phase separation of multi-phase systems and in particular of oil-water-surfactant mixtures. The mechanism is based on application of surface acoustic waves (SAWs), which propagate in the solid substrate in contact with oil-water-surfactant mixtures. In parallel, we will work on developing a theoretical model based on coupling of Cahn-Hilliard formulation for phase separation with the thin film dynamics within the longwave formulation. The analysis will result in development of basic insight into the physical mechanisms governing the phase separation. Reaching the proposed goals will lead to establishment of proof-of-principle for use of SAW for the purpose of phase separation.

Rituparna Basak

Application of Computational Topology to Analysis of Granular Material Force Networks in the Stick-Slip Regime

We discuss the properties of force networks in a two-dimensional annular Couette geometry for both experiments and simulations in which a small intruder is pulled by a spring. In particular, the connection between topological features of the force network and fluctuations of the intruder velocity is studied in the stick-slip regime. The force networks are analyzed using persistent homology methods, focusing on the statistics of clusters and loops composed of particles experiencing strong forces. We find that the networks evolve in a nontrivial manner as the system approaches a slip event. The presentation will discuss this evolution for systems of disks and pentagonal particles at several different packing fractions.

Zheng Zhang

Consistent Estimation of the Number of Communities in Nonuniform Hypergraph Model

In the real world, many complex networks can be formulated as hypergraphs. Unlike ordinary graphs, hypergraphs allow an edge to contain arbitrarily many vertices. We are interested in how to estimate the number of communities in such networks. In this talk, I will introduce a cross-validation approach for estimating the number of communities in general nonuniform hypergraph models. I will then present some simulation studies to support the effectiveness of this approach.

Professor Travis Askham

A Periodic Fast Multipole Method

Periodic Green’s functions arise naturally in boundary integral methods for the solution of partial differential equations on periodic domains. In general, there are no closed form expressions for these Green’s functions and they are computed by numerically approximating the sum over periodic images of the free space Green’s function. We will present a simple fast algorithm for evaluating these sums which is efficient even when the unit cell has a high aspect ratio and/or significant shear. We will also spend some time reviewing the underlying mathematics of these types of sums, which have some amusing features. Joint work with Ruqi Pei, Shidong Jiang, and Leslie Greengard.

Professor Travis Askham Recording - July 15, 2021

Yixuan Sun

Modeling and Design Optimization for Membrane Filters

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work we propose mathematical models, derived from first principles and simplified using asymptotic analysis, for: (1) pleated membrane filters, where the macroscale flow problem of Darcy flow through a pleated porous medium is carefully coupled to the microscale fouling problem of particle transport and deposition within individual pores of the membrane; (2) dead-end membrane filtration with feed containing multiple species of physicochemically-distinct particles, which interact with the membrane differently; and (3) filtration with reactive particle removal using porous media composed of chemically active granular materials. Asymptotically-simplified models are used to describe and evaluate the membrane performance numerically and filter design optimization problems are formulated and solved for a number of industrially-relevant scenarios. Our study demonstrates the potential of such modeling to guide industrial membrane filter design for a range of applications involving purification and separation.

Erli Wind-andersen

The Integral equations of Sound-Soft and Sound-Hard Scattering

In this talk I will introduce the basics of solving the two dimensional time harmonic scattering problem with Direchlet and Neumann boundary conditions for single and multiple bounded scatterers. To this end, I will make use of Boundary Integral equations and their Nystrom discretization, which can be generalized to solve non-smooth boundaries.  

Professor Casey Diekman

Data Assimilation and Conductance-Based Modeling of Circadian Clock Neurons

Data assimilation (DA) is a framework for optimally combining experimental observations with preexisting knowledge (in the form of a mechanistic model) of a dynamical system in order to perform state and parameter estimation. We have developed a variational DA algorithm (4D-Var) to construct conductance-based models from electrical recordings of suprachiasmatic nucleus (SCN) neurons. The SCN is the central circadian (~24-hour) clock in mammals coordinating daily rhythms in physiology and behavior. Most of what is known about the electrical activity of SCN neurons comes from studies of nocturnal (night-active) species, hindering the translation of this knowledge to diurnal (day-active) humans. Here we use DA and current-clamp recordings from Rhabdomys pumilio, a diurnal rodent, to build the first models of SCN electrophysiology in a diurnal organism. We then use the models to make predictions about the key differences in the electrical properties of circadian clock neurons between nocturnal and diurnal species.

Professor Casey Diekman Recording - July 20, 2021

Soheil Saghafi

Deep Hybrid Modeling with cGAN as an Inverse Surrogate Model for Parameter Estimation in Morris-Lecar Model

Any machine learning approach learns from experiential data, which can be provided by direct observation, measurement, and/or extensive data records. On the other hand, mechanistic models are based on an understanding of the behavior of a system’s components. Mechanistic models of biological systems incorporate underlying biophysical mechanisms to give an appropriate deterministic approximation of reality. Often, neither mechanistic modeling nor machine learning approaches are sufficient individually. In particular, mechanistic modeling suffers from model and parameter uncertainty whereas the results of any machine learning model are often hard to interpret and usually ignore the underlying biophysical mechanisms. Here we are going to build a Deep Hybrid Model (DeepHM) which takes advantage of integrating both machine learning (deep learning) and mechanistic models to build a more reliable model. We will introduce Generative Adversarial Networks (GANs), which is a machine learning framework to provide an inverse mapping of data to identify the distribution of mechanistic modeling parameters coherent to the data. 

Xiao Han

Modeling the Flow of Nanoparticles in the Blood Vessel Guided by a Cylindrical Magnet

Magnetic drug targeting is a method of delivering drugs to targets within the body by loading magnetic nanoparticles with therapeutic drugs, delivering them into the bloodstream, and guiding them with external magnets towards a tumor. A mathematical model is developed to describe the trajectories of a cluster of magnetic nanoparticles in a blood vessel guided by a cylindrical magnet. Parameter analyses were performed, including the properties for the cylindrical magnet, the distance between the magnet and the blood vessel, and the release position of the particles. Differences between including and excluding Brownian motions from the model will also be discussed.

Hewei Zhang

Predicting Solar Flare Index Using Statistical And Machine Learning Methods

Solar flares are marked by giant bursts of X-rays and energy that travel at the speed of light, sometimes accompanied with corona mass ejection, which can damage facilities including satellites, communication systems and even ground-based technologies. Hence, the prediction of flares is vital to protect the facilities. Extensive studies have been conducted focusing on predicting the occurrence of flares in different classes for a certain active region (AR) in the next 24 hours with "yes" or "no" answers. In this talk, we introduce a different perspective of prediction involving the Flare Index (FI) that quantifies flares with occurrence probability and energy released. Specifically, we analyze ARs from May 2010 to Dec 2017 and their associated flares identified by the GOES, wherein 25 SHARP parameters are extracted to produce the FIs. With the SHARP parameters and their related FIs, we predict the FI for an AR in the next 1-day period by SMOGN algorithm, power transformation and B-spline regression, improving the accuracy of flare prediction for large FIs. In addition, we rank the 25 SHARP parameters based on their importance in flare prediction. 

Samantha Evans

The Effects of Combining the Sherman-Lauricella Integral Equation with Slow Convolution Method for Two-Phase Flow with Soluble Surfactant

This presentation will give an introduction to previous work involving two-phase flow with soluble surfactant. The problem and governing equations will be defined, as well as explaining how it was tackled using the Sherman-Lauricella equation with a mesh to solve for soluble surfactant as well as a separate way that uses a mesh-free slow convolution method for the surfactant. After that the talk will detail how we are expanding upon this work by taking the Sherman-Lauricella and mesh based code and replacing the mesh with the slow convolution Green’s function based solution. Finally the results of the Sherman-Lauricella with slow convolution method code will be presented.

Professor Yuan-Nan Young

The Many Behaviors of Deformable Active Droplets

Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can ex- plain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well un- derstood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to iden- tify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators.

Professor Yuan-Nan Young Recording - July 29, 2021

Jimmie Adriazola

Optimal Control of Hamiltonian Systems Arising from Bose-Einstein Condensates

Technologies involving quantum computation, simulation, and metrology are often dependent on efficient manipulations of Bose-Einstein condensates, an ultra-cold quantum fluid whose mean dynamics resemble that of a single atom. In this talk, we show how to construct desired condensate manipulations using tools from Hamiltonian mechanics and optimal control theory. We use a Hamiltonian dynamical systems approach to reveal the mechanisms behind the controlled condensate's dynamics. This informs us of more intuitive and lower dimensional control problems than those of the current literature. Numerical results are facilitated by a coupling of global and local optimization methods, and we provide different metrics for analyzing the efficiency of the resulting control strategy.

Subhrasish Chakraborty

Classification of Imbalanced Multiple Class Datasets: A Statistical Approach

Learning to classify or to predict numerical values prelabelled patterns is one of the central research topics in machine learning and data mining. However less attention has been paid to ordinal regression (also called ordinal classification) problems, where the labels of the target variable exhibit a natural ordering. For example, student satisfaction surveys usually involve rating teachers based on ordinal scale { poor, average, good, very good, excellent}. Hence, class labels are imbued with order information, e.g. a sample vector associated with class label average has higher rating than another from poor class, but good class is better than both. When dealing with this kind of problems, two facts are decisive: 1) misclassification costs are not same for different errors; 2) the ordering information can be used to construct more accurate models. Our motive is to propose an algorithm based on Neyman-Pearson lemma for ordinal classification but with conservative attitude towards the type I error. Further the performance of the new algorithm would be compared with the traditional classification algorithms. But before that we would discuss ordinal classification methods that had been proposed previously. Further there also is a survey on deep learning techniques for the multiclass classification. Deep learning techniques has been used to in for multiclass classification. Now we would concentrate in the case when there is class imbalances. So deep learning techniques are used with resampling techniques in order to analyze data with class imbalances.