Yeonhyang Kim (kim4y AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
9/8/23 
TBA 

9/15/23 
TBA  TBA 
9/22/23 
TBA 
TBA 
9/29/23 
Hiruni Pallage (CMU) 
Recovery of Initial conditions through later time samples 
10/6/23 
TBA 
TBA 
10/13/23 
TBA 
TBA 
10/20/23 
TBA 
TBA 
10/27/23 
TBA 
TBA 
11/3/23 
TBA 
TBA 
11/10/23 
TBA 
TBA 
11/17/23 
TBA 
TBA 
12/1/23 
TBA 
TBA 
12/8/23 
Hongsong Feng (MSU) 
MathematicsAI for drug discovery and drug addiction studies 
Speaker: Hiruni Pallage
Title: Recovery of Initial conditions through later time samples
Abstract: Full knowledge of the initial conditions of an initial value problem (IVP) is necessary to solve said IVP but is often impossible in reallife applications due to the unavailability or inaccessibility of a sufficiently large sensor network. One way to overcome this impairing is to exploit the evolutionary nature of the sampling environment while working with a reduced number of sensors, i.e., to employ the concept of dynamical sampling. A typical dynamical sampling problem is to find sparse locations that allow one to recover an unknown function from various times samples at these locations. The classical problem of inverse heat conduction has been recently revisited by Devore and Zuazua (2014). We study conditions on an evolving system and spatial samples in a more general setup using bases. Specifically, we study when $u(x, t) = \sum_{n=1}^\infty a_nf_n(x) g_n(t)$, where $a_n \in \mathbb{R}$, $x \in [0, 1]$, $t \in [0, \infty)$ can be reasonably approximated through latertime samples at a single sampling location. The results of our research are relevant in applications, and we present examples of solving the Laplace equation and variable coefficient wave equation using our general method. Kim and Aceska (2021) retrieved the unknown initial condition function of the above systems via exponentially growing samples. However, in the approximation process, they observed exponential growth in error terms of the coefficients. Our recent research demonstrates that we can incorporate a linear growth pattern of errors in the recovered coefficients in these systems.
Speaker: Hongsong Feng
Title: MathematicsAI for drug discovery and drug addiction studies
Abstract: Traditional drug discovery is a timeconsuming and costly process, often taking over a decade to bring a new drug to market. AI has great potential to transform the entire landscape of pharmaceutical research and developments. It is promising to combine mathematics with AI to promote the drug discovery development. Due to the importance of accurate predictions of binding affinity between proteins and druglike compounds, there is pressing need for reliable mathematical predictive models. Models based on persistent Laplacian (PL) theory were proposed in this aspect by our research group and can serve as a useful tool for binding affinity predictions. In my talk, I will present our recent machine learning studies with persistent Laplacian models and natural language processing (NLP) methods for drug discovery and drug addiction problems.
Yeonhyang Kim (kim4y AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
If you would like to give a talk, please email any one of us.
Fridays, 2:00pm – 3:00pm, on Webex
Date 
Speaker 
Title 
1/20/23 
TBA 
TBA 
1/27/23

Mohsen Zayernouri (MSU) 
DataDriven Fractional Modeling, Analysis, and Simulation of Anomalous Transport & Materials 
2/3/23 
TBA 
TBA 
2/10/23 
TBA 
TBA 
2/17/23 
TBA 
TBA 
2/24/23 
TBA 
TBA 
3/3/23 
TBA 
TBA 
3/17/23 
TBA 
TBA 
3/24/23 
TBA 
TBA 
3/31/23  Andrea Liu (University of Pennsylvania) 
Machine Learning Glassy Dynamics 
4/7/23 
TBA 
TBA 
4/14/23 
Kyle Harshbarger 
Scheduling and Planning High Uncertainty Seasonal Products at Dow 
4/21/23 

TBA 
4/28/23 
TBA 
TBA 
Speaker: Mohsen Zayernouri
Title: Tittle: DataDriven Fractional Modeling, Analysis, and Simulation of Anomalous Transport & Materials
Abstract: The classical calculus and integerorder differential and integral models, due to their inherently local characters in spacetime, cannot fully describe/predict the realistic nonlocal and complex nature of the anomalous transport phenomena. Nature is abundant with such processes, in which for instance a cloud of particles spreads in a different manner than traditional diffusion. This emerging class of physical phenomena refers to fascinating processes that exhibit nonMarkovian (long range memory) effects, nonFickian (nonlocal in space) interactions, non ergodic statistics, and nonequilibrium dynamics. The phenomena of anomalous transport have been observed in a wide variety of complex, multiscale, and multiphysics systems such as: sub/superdiffusion in subsurface transport, kinetic plasma turbulence, aging polymers, glassy materials, in addition to amorphous semiconductors, biological cells, heterogeneous tissues, and fractal disordered media. In this talk, we present a series of recent spectral theories and global spectral methods for efficient numerical treatment of fractional ODEs/PDEs. Finally, a number of applications including fluid turbulence, powerlaw rheology, and material failure processes will be also presented, in which fractional modelling emerge as a natural language for highfidelity modelling and prediction.
Speaker: Andrea Liu
Title: Machine Learning Glassy Dynamics
Abstract: The threedimensional glass transition is an infamous example of an emergent collective phenomenon in manybody systems that is stubbornly resistant to microscopic understanding using traditional mathematical statistical physics approaches. Establishing the connection between microscopic properties and the glass transition requires reducing vast quantities of microscopic information to a few relevant microscopic variables and their distributions. I will demonstrate how machine learning, designed for dimensional analysis reduction, can provide a natural way forward when standard statistical physics tools fail. We have harnessed machine learning to identify a useful microscopic structural quantity for the glass transition, have applied it to simulation and experimental data, and have used it to build a new mathematical model for glassy dynamics.
Speaker: Kyle Harshbarger
Title: Scheduling and Planning High Uncertainty Seasonal Products at Dow
Abstract: Dow manufactures sells products with a joint problem of high seasonality and high uncertainty. Proper framing and modeling of the problem allows scheduling and planning processes to be brought under control. Planning for the whole season requires changing buffers with backwards scheduling. Scheduling requires balancing immediate high service level needs to avoid stockouts and restofseason analysis to minimize excess inventory. Model fitting of sales history identified a Gamma distribution as best fit to predict future demand in future periods. Monte Carlo approaches are used to accumulate periodic demand for operational requirements.
Fall 2022
Yeonhyang Kim (kim4y AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
10/14/22 
TBA 
TBA 
10/21/22 
TBA 
TBA 
10/28/22, 4pm5pm

Qian Zhang (Michigan Tech University) 
GradcurlConforming Finite Elements Based on De Rham Complexes for the FourthOrder Curl Problems 
11/4/22 
TBA 
TBA 
11/11/22 
?(MSU) 
TBA 
11/18/22 
TBA 
TBA 
11/25/22 
TBA 
TBA 
12/2/22 
TBA 
TBA 
12/9/22

LIKCHUAN LEE (MSU) 
Computer Modeling of Cardiac Microstructure and its Effects in Heart Diseases 
Speaker: Qian Zhang
Title: GradcurlConforming Finite Elements Based on De Rham Complexes for the FourthOrder Curl Problems
Abstract: The fourthorder curl operator appears in various models, such as electromagnetic interior transmission eigenvalue problems, magnetohydrodynamics in hot plasmas, and couple stress theory in linear elasticity. The key to discretizing these problems is to discretize the fourthorder curl operator. In this talk, I will present the conforming finite element method for a simplified fourthorder curl model. Discretizing the quadcurl equations using smoother elements (such as H^2conforming elements) would lead to wrong solutions. Speciﬁc ﬁnite elements need to be designed for the fourthorder curl operator. However, constructing such elements is a challenging task because of the continuity required by the curlcurlconformity and the naturally divergencefree property of the curl operator. In this presentation, we provide the construction of the curlcurlconforming elements in both 2D and 3D based on the de Rham complex. In 2D, the lowestorder grad curlconforming element has only 6 and 8 degrees of freedom on a triangle and a rectangle, respectively. In 3D, we relate the fourthorder curl problem to fluid mechanics and a de Rham complex with higher regularity. The lowestorder element has only 18 degrees of freedom on a tetrahedron. As a byproduct, we construct a family of stable and masspreserving finite element pairs for solving the NavierStokes equations.
Speaker: LIKCHUAN LEE
Title: Computer Modeling of Cardiac Microstructure and its Effects in Heart Diseases
Abstract: Microstructural pathological features such as muscle fiber disarray and excessive fibrosis are hallmarks of many heart diseases. Often present together in heart diseases such as heart failure with preserved ejection fraction (HFpEF) and hypertrophic cardiomyopathy (HCM), these features are associated with the cardiac dysfunction found in these diseases. Statistical correlation analysis can provide some insights regarding the role of microstructural pathological features on cardiac dysfunction. It is, however, difficult to distinguish or isolate the contributions of each feature using only statistical studies. Computer modeling that considers the cardiac tissue microstructure can address this limitation by isolating the effects of each pathological features on heart function. Here, we present the development of such computer models to investigate the effects of microstructural pathological features on HFpEF and HCM. First, we present a computer model of the passive left ventricular (LV) mechanics using a Lanirtype microstructural constitutive model that consider dispersion of collagen fiber waviness and orientation. The model is used to investigate the load taken up by each tissue constituent during LV passive filling. Next, we present a computer model of active LV mechanics that considers muscle fiber disarray using a structural tensor approach. This model is applied to investigate the effects of myofiber disarray on LV and cardiac myocyte function in HCM patients.
Speaker: TBA
Title:
Abstract:
Yeonhyang Kim (kim4y AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
1/21/22 
TBA 
TBA 
1/28/22 
TBA 
TBA 
2/4/22 
TBA 
TBA 
2/11/22 
TBA 
TBA 
2/18/22 
TBA 
TBA 
2/25/22 
TBA 
TBA 
3/4/22 
TBA 
TBA 
3/11/22 
TBA 
TBA 
3/18/22 
TBA 
TBA 
3/25/22 
Walter G. Chapman (Rice University) 
Density Gradient Theory for Interfacial Properties of Fluids: Stabilized and Mass Conserved Algorithms for Associating Solvents to Surfactants 
4/1/22 
TBA 
TBA 
4/8/22 
TBA 
TBA 
4/15/22 
TBA 
TBA 
4/22/22 
TBA 
TBA 
4/29/22 
Miranda Holmes (Courant Mathematical Institute, NYU) 
Numerically simulating particles with shortranged interactions 
Speaker: Walter G. Chapman
Title: Density Gradient Theory for Interfacial Properties of Fluids: Stabilized and Mass Conserved Algorithms for Associating Solvents to Surfactants
Abstract: Density gradient theory (DGT) is a form of density functional theory (DFT) that allows prediction of the interfacial tension and density profile of molecules through a fluidfluid interface. In DFT, the free energy is minimized as a function of the density distribution of molecules to obtain the equilibrium structure and properties of the fluid. DGT has roots that trace back to van der Waals. In this talk, we introduce several recent extensions of the theory and algorithms for practical calculations. While conventional algorithms require a reference substance of the system, we have developed a “stabilized density gradient theory” (SDGT) algorithm to solve DGT equations for multiphase pure and mixed systems that is robust and enables other generalizations. This algorithm makes it possible to calculate interfacial properties accurately at any domain size larger than the interface thickness without choosing a reference substance or assuming the functional form of the density profile. Further, we extend DGT to enable calculations for surfactant systems. For the first time, the surfactant head group and tail group are described separately in the DGT. Finally, these extensions are applied using a mass conserved DGT. This is a true mass conserved algorithm rather than being mass constrained. Applications of the approach are demonstrated using our SAFT equation of state.
Speaker: Miranda Holmes
Title: Numerically simulating particles with shortranged interactions
Abstract: Particles with diameters of nanometres to micrometres form the building blocks of many of the materials around us, and can be designed in a multitude of ways to form new ones. Such particles commonly live in fluids, where they jiggle about randomly because of thermal fluctuations in the fluid, and interact with each other via numerous mechanisms. One challenge in simulating such particles is that the range over which they interact attractively is often much shorter than their diameters, so the equations describing the particles’ dynamics are stiff, requiring timesteps much smaller than the timescales of interest. I will introduce methods to accelerate these simulations, which instead solve the limiting equations as the range of the attractive interaction goes to zero. In this limit a system of particles is described by a diffusion process on a collection of manifolds of different dimensions, connected by “sticky” boundary conditions. I will show how to simulate lowdimensional sticky diffusion processes, and then discuss some ongoing challenges such as extending these methods to high dimensions and incorporating hydrodynamic interactions.
Fall 2021
Yeonhyang Kim (kim4y AT cmich DOT edu)
EnBing Lin (enbing.lin AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
If you would like to give a talk, please email any one of us.
Fridays, 3:00pm – 4:00pm, on Webex
Date 
Speaker 
Title 
8/3/21 
TBA 
TBA 
9/10/21 
TBA 
TBA 
9/17/21 
TBA 
TBA 
10/1/21 
TBA 
TBA 
10/8/21 
TBA 
TBA 
10/15/21 
TBA 
TBA 
10/22/21 
Promislow, Keith (MSU) 
Packing and Entropy in Structured Polymer Blends Meeting link: https://cmich.webex.com/cmich/j.php?MTID=m909f20a889f6a01e6ceb96a868f41d2eMeeting number: 2621 028 0701 Password: cQhSZ6cxz65 Host key: 123766 
10/29/21 
TBA 
TBA 
11/5/21 
TBA 
TBA 
11/12/21 
TBA 
TBA 
11/19/21 
Ronald G. Larson (University of Michigan Ann Arbor) 
Industrial Strength Rheology: MultiScale Modeling of Polymers, Colloids, and Surfactant Solutions Meeting link: https://cmich.webex.com/cmich/j.php?MTID=m4089470c73f025afa9f2f1079fa17645 
11/26/21 
Thanksgiving Break 
TBA 
12/3/21 
TBA 
TBA 
12/10/21 
Norma OrtizRobinson (Grand Valley State University) 
Optimal Control strategies to contain Covid19 for a data driven model for the state of Michigan Meeting link: https://cmich.webex.com/cmich/j.php?MTID=m7106e8898a81cbfcb06cfb4c1eabcdbd Meeting number: 2620 857 5866 Password: 3MReJYf3BQ8 
Speaker: Promislow, Keith
Title: Packing and Entropy in Structured Polymer Blends
Abstract: Packing and entropy play crucial roles in selfassembly of structured (diblock, triblock) polymers in solvent. We start with a very simple model for the packing of star polymers in a bounded domain and show that it leads to a wide range of possible patterns, both ordered and disordered. Then we revisit the random phase reductions of selfconsistent mean field models of ChoksiRen and UneyamaDoi. By including a longerrange interaction associated to partial charges, we derive a phasefield model for the free energy. We show that reductions of this model connect to the scalar models of GompperSchick and GommperGoos for oilwatersurfactant microemulsions, and then present an analysis of a blend of long and short polymers, identifying a scaling regime in which geometric singular perturbations techniques and some simple microlocal analysis can be applied to show that interdigitations of long and short polymers, evocative of the role of sterols in phospholipid bilayers, can have a stabilizing effect.
Speaker: Ronald G. Larson
Title: Industrial Strength Rheology: MultiScale Modeling of Polymers, Colloids, and Surfactant Solutions
Abstract: Continuumlevel thermodynamic and transport properties relevant to industrial applications can now be computed from molecularscale interactions using multiscale molecular dynamics (MD) simulations and Brownian dynamics (BD) simulations, along with biasing methods, such as umbrella sampling, and forward flux sampling. We demonstrate the power of these methods by computing the dynamics and rheology of surfactant solutions, polymers, and colloidpolymer mixtures used in consumer and industrial products, such as shampoos, oil dispersants, paints, and plastic films. The complex structures of these fluids require multiscale modeling that can include atomistic and coarsegrained molecular simulations, as well as colloidal scale simulations, and modelreduction schemes to connect commercially important rheological properties to chemical composition. We also compare the predicted results to experimental data, and extract information, that is unavailable, or not easily available, from experiments.
Speaker: Norma OrtizRobinson
Title: Optimal Control strategies to contain Covid19 for
a data driven model for the state of Michigan
Abstract: In this talk I will present numerically obtained optimal strategies for
an optimal control model formulated to account for vaccination hesitancy,
social distancing, treatment and vaccination rates. The optimal
control model is based on an SIR model with parameters derived
from Covid19 epidemic data in the state of Michigan.
Yeonhyang Kim (kim4y AT cmich DOT edu)
EnBing Lin (enbing.lin AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
1/15/21 
TBA 
TBA 
1/22/21 
TBA 
TBA 
1/29/21 
TBA 
TBA 
2/5/21 
TBA 
TBA 
2/12/21 
TBA 
TBA 
2/19/21 
Wendy Robertson (CMU) 
Application of the Modified Universal Soil Loss Equation (MUSLE) in (semi) distributed watershed models: challenges and opportunities

2/26/21 
Hanliang Guo (University of Michigan) 
Modeling ciliary flow in complex geometries

3/5/21 
TBA 
TBA 
3/12/21 
TBA 
TBA 
3/19/21 
TBA 
TBA 
3/26/21 
TBA 
TBA 
4/2/21 
TBA 
TBA 
4/9/21 
Olga Kuksenok (Clemson University) 
Mesoscale modeling of controlled degradation and erosion of polymer networks

4/16/21 
Jackson Criswell (CMU) 
Wavelet Neural Networks and Applications in River Flow

4/23/21 
Anne V. Ginzburg (H. H. Dow High School) 
Modeling the Dynamics of the Coronavirus SARSCoV2 Pandemic and the Role of Vaccination in Stopping its Spread 
4/27/21, 4:00 pm 
Zachary Tickner (Scripps Florida) 
Mathematical tools for the directed evolution of RNA devices

Speaker: Wendy Robertson
Title: Application of the Modified Universal Soil Loss Equation (MUSLE) in (semi) distributed watershed models: challenges and opportunities
Abstract: The Modified Universal Soil Loss Equation (MUSLE) is an empiricallybased model that is widely applied to predict sediment yield resulting from water erosion within catchments. While it offers meaningful benefits for predicting soil loss and sediment yield (flexibility, data availability, computational power, among others), there are substantial challenges to its application and limitations for its use. This talk will discuss the theoretical framework, development and application, datasets, limitations, and future avenues of research for MUSLE and USLEtype models and their incorporation into watershed models for the prediction of sediment yield.
Speaker: Hanliang Guo
Title: Modeling ciliary flow in complex geometries
Abstract: Cilia are hairlike organelles that protrude from epithelial cell surfaces. Being one of the most conserved microstructures in nature, cilia are critical buildingblocks of life. In particular, it is known for decades that our airway systems require the periodic movements of cilia to transport mucus that carries out the dusts and toxic particles. More recently, people have realized that being the “conveyorbelt” of unwanted particles are far from the sole function of ciliaryflows. For example, cilia can create fluidmechanical micro environments for the active recruitment of the specific microbiome of the host; ciliaryflows in the brain ventricles behave like a “switch” that reliably and periodically alters the flow pattern.
Despite the fact that cilia grow in greatly complex geometries, existing numerical works have focused on simple geometries and idealized boundary conditions such as periodic, freespace or halfspace flows. In this talk, we will present a recently developed hybrid numerical method for simulating ciliary flows in complex geometries. The confining geometries are treated by FMM accelerated boundary integral method while the ciliary flows are treated by the method of regularized stokeslet. We will also present an optimization approach that can find the most efficient ciliary motion of a ciliated microswimmer. The result can have great implications on the designs of microrobots for healthrelated functions such as drug delivery.
Speaker: Olga Kuksenok
Title: Mesoscale modeling of controlled degradation and erosion of polymer networks
Abstract: Controlled degradation of hydrogels plays a vital role in a variety of applications ranging from regulating growth of complex tissues and neural networks to controlled drugs and biomolecules delivery. Further, of a particular interest is photocontrolled degradation of polymer networks, which permits spatiallyresolved dynamic control of physical and chemical properties of the materials. Notably, in a number of practical applications, either the characteristic features of degradable gels or the dimensions of the entire degradable gel particles range between nanometers to microns scales, the length scales referred to as mesoscopic. We develop a Dissipative Particle Dynamics (DPD) approach to capture degradation of polymer networks at the mesoscale. DPD is a mesoscale approach utilizing soft repulsive interactions between beads representing collections of atoms, thereby allowing low computational cost of simulations. To overcome unphysical topological crossings of bonded polymer chains (a known limitation of DPD), we adapted a modified Segmental Repulsive Potential (mSRP) formulation to model gels with degradable crosslinks. We track the progress of the degradation process via measuring the fraction of degradable bonds intact. Further, we track mass loss from the hydrogel films, along with the number, sizes, and spatial distributions of clusters (bonded beads) formed during the degradation process. The figure below shows representative snapshots of degradation from the threedimensional film (side view); for clarity, solvent beads are not shown. The cluster size distribution enables us to calculate the evolution of the weight average
Materials Science and Engineering
College of Engineering, Computing and Applied Sciences Clemson University
degree of polymerization, DPw, during degradation. The evolution of DPw depends on the crosslink density, polymer volume fraction, and solvent quality. As degradation proceeds, the hydrogel film undergoes reverse gelation and the percolating network disappears. We quantify the point at which this reverse gelation occurs (reverse gel point) from the maximum of the reduced DPw, which excludes the largest cluster in the system, and compare our measured value with previous analytical theories and experimental results. Our measured value agrees well with the value obtained from the bond percolation theory on a diamond lattice.
Image
Research Interest: Computational design of biomimetic materials; Theory and computer simulations of multicomponent polymeric systems; Modeling pattern formation in nonequilibrium systems
Speaker: Anne V. Ginzburg
Title: Modeling the Dynamics of the Coronavirus SARSCoV2 Pandemic and the Role of Vaccination in Stopping its Spread
Abstract: A modeling study of the outbreak of the Coronavirus SARSCoV2 and the implication of a global vaccination on the spread of the virus is presented. The global outbreak of the coronavirus began in the early months of 2020 and has continued for over 11 months at the time of this presentation. By early 2021, a number of vaccines have been developed in various countries, and the administration of these vaccines is now well underway. It is important to use modeling to investigate the implications of the vaccination on the spread of the coronavirus. Our simulation utilized the “Susceptible Exposed Infected Recovered” (SEIR) model in order to recreate the likely infection and exposure rates based on the known death and net hospitalization rates. The work of You Yang Gu (MIT) and other authors were used to parameterize the virus reproduction number (R(t)) and other model inputs, and to predict the death and hospitalization rates. These predictions were then compared with the reallife data. Because of the incredibly wide scope of this pandemic, our investigation was limited to 5 U.S. states with varied geographies, population sizes and vaccine distribution plans. The next step of the investigation would include broadening the investigation to the countries of the world and predicting the general trend of the pandemic.
Speaker: Jackson A. Criswell
Title: Wavelet Neural Networks and Applications in River Flow
Abstract: River flow is a chaotic natural phenomenon characterized by extreme events causing an inherent aperiodicity across multiple time scales. This dynamic nature makes development of accurate simulations and predictive models for fluvial discharge an onerous task in geophysics and hydrology. Human development often creates a large investment of life and resources along riverbanks and in floodplains. These areas can be prone to unexpected disasters such as floods and droughts. By better understanding the hydrological processes through development of predictive models, improvements can be made in disaster preparedness and response. There was a terrible disaster that occurred on May 20, 2020 along the Tittabawassee River, near Central Michigan University. Communities in the floodplain of the Tittabawassee experienced a 500year flash flooding event which threatened many lives and continues to cause loss through property damage and devaluation. The dammed river features a series of dams and this calamity occurred after the collapse of the final two in the chain.
A neurowavelet method of predictive river modeling is developed here which combines wavelet analysis and artificial neural networks to perform river flow forecasting. Several test cases are studied, and a broad sweep of network types and design parameters is performed to strengthen the quality of the predictions. Results are presented to provide comparisons based on different techniques and training parameters. The algorithm design is based on a nonlinear autoregressive multilayer perceptron artificial neural network. In order to improve predictive ability, new methods are designed to incorporate the multiresolution information from a discrete wavelet transform using the Daubechies mother wavelet. The new predictive network design is inspired by existing methods but adds more repeatability and stability to the result. A custom genetic algorithm for selecting trained networks and averaging the results of many trials provides control for the inherent randomness created from network training. Results include 30day daily average discharge forecast, and a new predictor that is being proposed in this work, the total predicted discharge. Total predicted discharge volumes in acrefeet are presented for a week, a fortnight, and a month subsequent to several test dates.
In this case study, artificial neural networks and neurowavelets are used to perform river flow forecasting of the May 2020 flood event of the Tittabawassee River. Preliminary results are promising and continuing work to improve the network design through the inclusion of additional climate data and increased neural net complexity is underway.
Speaker: Zachary Tickner
Title: Mathematical tools for the directed evolution of RNA devices
Abstract: SELEX (Systematic Evolution of Ligands by Exponential Enrichment) is an invitro directed evolution technique which enriches nucleic acids capable of specific, highaffinity binding to a variety of targets. Molecules isolated by SELEX (known as aptamers) have been applied as biosensors, diagnostic tools, and therapeutics. Careful experimental design is required for a successful selection: starting populations, known as libraries, are assembled combinatorially and may be designed to increase the probability of containing viable aptamers, while selections must be monitored and controlled to enable enrichment of aptamers while avoiding accumulation of parasitic artifacts. Following a successful selection, a variety of biochemical and computational techniques are used to identify enriched aptamers, and to evaluate their binding and structural properties. This talk will describe general considerations for planning and performing invitro directed evolution experiments, as well as the recent selection and characterization of RNA aptamers to the antibiotic doxycycline.
Yeonhyang Kim (kim4y AT cmich DOT edu)
EnBing Lin (enbing.lin AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
9/4/20 
TBA 
TBA 
9/11/20 
TBA 
TBA 
9/18/20 
TBA 
TBA 
9/25/20 
TBA 
TBA 
10/2/20 
TBA 
TBA 
10/9/20 
TBA 
TBA 
10/16/20 
TBA 
TBA 
10/23/20 
Tianyu Zhang (Montana State University) 
Multiscale FluxBased Modeling of Biofilm Communities: Linking Microbial Metabolism to Community Environment 
10/30/20 
TBA 
TBA 
11/6/20 
TBA 
TBA 
11/13/20 
TBA 
TBA 
11/20/20 
TBA 
TBA 
Speaker: Tianyu Zhang
Title: Multiscale FluxBased Modeling of Biofilm Communities: Linking Microbial Metabolism to Community Environment
Abstract: For environmental microbial communities, environment is destiny in the sense that microbial community structure and function are strongly linked to chemical and physical conditions. Moreover, most environments outside of the lab are physically and chemically heterogeneous, further shaping and complicating the metabolisms of their resident microbial communities: spatial variations introduce physics such as diffusive and advective transport of nutrients and byproducts for example. Conversely, microbial metabolic activity can strongly effect the environment in which the community must function. Hence it is important to link metabolism at the cellular level to physics and chemistry at the community level. In order to introduce metabolism to communityscale population dy namics, many modeling methods rely on large numbers of reaction ki netics parameters that are unmeasured and likely effectively unmeasur able (because they are themselves coupled to environmental conditions), also making detailed metabolic information mostly unusable. The bio engineering community has, in response to these difficulties, moved to kineticsfree formulations at the cellular level, termed flux balance anal ysis. These cellular level models should respond to system level environ mental conditions. To combine and connect the two scales, we propose to replace classical kinetics functions in community scale models and in stead use celllevel metabolic models to predict metabolism and how it is influenced by and influences the environment. Further, our methodology permits assimilation of many types of measurement data. We will discuss the background and motivation, model development, and some numerical simulation results.
Yeonhyang Kim (kim4y AT cmich DOT edu)
EnBing Lin (enbing.lin AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
1/24/20 
Peimeng Yin (Wayne State University) 
Efficient discontinuous Galerkin (DG) methods for timedependent fourth order problems 
1/31/20 
TBA 
TBA 
2/7/20 
TBA 
TBA 
2/14/20 
TBA 
TBA 
2/21/20 
Mohye Sweidan (CMU) 
Analysis of ShortleyWeller scheme I 
2/28/20 


3/6/20 
Mohye Sweidan (CMU) 
Analysis of ShortleyWeller scheme II 
3/20/20 


3/26/20 
TBA 
TBA 
4/2/20 
TBA 
TBA 
4/9/20 
TBA 
TBA 
4/16/20 
TBA 
TBA 
4/23/20 
TBA 
TBA 
4/30/20 
TBA 
TBA 



Speaker: Peimeng Yin
Title: Efficient discontinuous Galerkin (DG) methods for timedependent fourth order problems
Abstract: We design, analyze and implement efficient discontinuous Galerkin (DG) methods for a class of fourth order timedependent partial differential equations (PDEs). The main advantages of such schemes are their provable unconditional stability, high order accuracy, and their easiness for generalization to multidimensions for arbitrarily high order schemes on structured and unstructured meshes. These schemes have been applied to two fourth order gradient flows such as the SwiftHohenberg (SH) equation and the CahnHilliard (CH) equation, which are well known nonlinear models in modern physics.
Speaker: Mohye Sweidan
Title: Analysis of ShortleyWeller scheme
Abstract: This series of talks aim to present the whole proof of the superconvergence of the classic ShortleyWeller scheme for Poisson problems with curved domains. This proof was provided by LIsl Waynans in 2018( SuperConvergence in Maximum Norm of the Gradient for the ShortleyWeller Method, Journal of Scientific Computing, 75:625637).
Yeonhyang Kim (kim4y AT cmich DOT edu)
EnBing Lin (enbing.lin AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
09/13/19 
Mohye Sweidan (CMU) 
A basic introduction to finite difference schemes for elliptic problems (part 1). 
09/20/19 
Xiaoming Zheng (CMU) 
A basic introduction to finite difference schemes for elliptic problems (part 2). 
09/27/19 
Chunhua Shan (Univ of Toledo) 
Complex Dynamics of Epidemic Models on Adaptive Networks 
10/04/19 
TBA 
TBA 
10/11/19 
Xiaoming Zheng (CMU) 
Some finite difference schemes for elliptic problems with curved domain 
10/18/19 
TBA 
TBA 
10/25/19 
Yeonhyang Kim (CMU) 
Orientation distribution function estimation in single shell qball imaging using predicted diffusion gradient directions 
11/01/19 
TBA 
TBA 
11/08/19 
EnBing Lin (CMU) 
The Interplay of Big Data Analytics and Mathematics 
11/15/19 
TBA 
TBA 
11/22/19 
TBA 
TBA 
12/06/19 
TBA 
TBA 






Speaker: Mohye Sweidan
Title: A basic introduction to finite difference schemes for elliptic problems (part 1).
Abstract: This talk will present the central difference scheme for twopoint boundary problems and its error analysis. This is a standard material in numerical analysis. Any undergraduate and graduate students are welcome to attend.
Speaker: Xiaoming Zheng
Title: A basic introduction to finite difference schemes for elliptic problems (part 2).
Abstract: This talk will present some finite difference schemes for two dimensional elliptic problems and their error analysis. This is a standard material in numerical analysis. Any undergraduate and graduate students are welcome to attend.
Speaker: Shan, Chunhua
Title: Complex Dynamics of Epidemic Models on Adaptive Networks
Abstract: There has been a substantial amount of wellmixing epidemic models devoted to characterizing the observed complex phenomena (such as bistability, hysteresis, oscillations, etc.) during the transmission of many infectious diseases. A comprehensive explanation of these phenomena by epidemic models on complex networks is still lacking. In this talk, we study epidemic dynamics in an adaptive network model proposed by Gross et al, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. Such rewiring of the local connections changes the topology of network, and inevitably has a profound effect on the transmissions of infectious diseases, which in turn influences the rewiring process. We rigorously prove that such adaptive epidemic network model exhibits degenerate Hopf bifurcation, homoclinic bifurcation and BogdanovTakens bifurcation. Our study shows that human adaptive behaviors to the emergence of an epidemic may induce complex dynamics of diseases transmission, including bistability, transient and sustained oscillations, which contrast sharply to the dynamics of classic network models. Our results yield deeper insights into the interplay between topology of networks and the dynamics of disease transmission on networks.
Speaker: Xiaoming Zheng
Title: Some finite difference schemes for elliptic problems with curved domain
Abstract: This is part 3 of the introduction to finite difference schemes for elliptic problems. This part introduces three classic schemes to treat the curved domain: Collatz scheme, Ghost Fluid Method with first order extrapolation, and ShortleyWeller scheme. In this case, the Cartesian mesh points are not on the domain boundary. We will derive the truncation errors and global errors. The super convergence is observed in the ShortleyWeller scheme.
Speaker: Yeonhyang Kim
Title: Orientation distribution function estimation in single shell qball imaging using predicted diffusion gradient directions
Abstract: High Angular Resolution Diffusion Imaging (HARDI) has been proposed as a means to overcome some limitations imposed by diffusion tensor imaging (DTI), especially in complex models of fibre orientation distribution in voxels. A long acquisition time for HARDI is a major obstacle to the clinical implementation. In this paper, we propose a novel method to improve angular and radial resolution using measured apparent diffusion coefficients in given diffusion gradient (DG) directions.
Speaker: EnBing Lin
Title: The Interplay of Big Data Analytics and Mathematics
Abstract: We begin with an overview of Big Data and some current trends of big data analytics. Applications of big data analytics in biology, business and industry will be mentioned. Moreover, we present the use of big data analytics in handling large amount of information via rough set theory and analyzing DNA sequences by utilizing wavelet analysis.
Yeonhyang Kim (kim4y AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
10/12/18 
TBA 
TBA 
10/19/18 
Yip, Nung Kwan (Purdue University) 
Dynamics of a second order gradient model for phase transitions 
01/25/19 
TBA 
TBA 
02/01/19 
TBA 
TBA 
02/08/19 
TBA 
TBA 
02/15/19 
TBA 
TBA 
03/01/19 (4pm  5pm) 
Shixu Meng (University of Michigan) 
Qualitative approaches to inverse scattering and wave motion in complex media 
03/15/19 
TBA 
TBA 
03/22/19 
TBA 
TBA 
03/29/19 
TBA 
TBA 
04/12/19 
TBA 
TBA 
04/19/19 (1:30pm2:30pm) 
Lewei Zhao (Wayne State Univ.) 
Finite Element Method for Laplace Equation in Twodimensional Domains with a Singular Fracture 



Speaker: Yip, Nung Kwan
Title: Dynamics of a second order gradient model for phase
transitions
Abstract: We prove in a radially symmetric geometry,
the convergence in the sharp interfacial limit, to motion by mean
curvature of a second order gradient model for phase transition. This
is in spirit similar to the classical AllenCahn theory of phase
boundary motion. However the corresponding dynamical equation is
fourth order thus creating some challenging difficulties for its
analysis. A characterization and stability analysis of the optimal
profile are performed which are in turn used in the proof of
convergence of an asymptotic expansion. (This is joint work with Drew
Swartz.)
Speaker: Shixu Meng
Title :Qualitative approaches to inverse scattering and wave
motion in complex media
Abstract: The mathematical theory of
wave scattering describes the interaction of waves (e.g., sound or
electromagnetic) with natural or manufactured perturbations of the
medium through which they propagate. The goal of inverse wave
scattering (or in short imaging) is to estimate the medium from
observations of the wave field. It has applications in a broad
spectrum of scientific and engineering disciplines, including seismic
imaging, radar, astronomy, medical diagnosis, and nondestructive
material testing. Qualitative approaches to inverse scattering
problems have been the focus of much activity in the mathematics
community. Examples are the linear sampling method, the factorization
method, use of transmission eigenvalues, Stekloff eigenvalues and so
on. Reverse time migration methods and the closely related matched
field or matched filtering array data processing techniques are
related to such qualitative approaches. In this talk I shall first
present qualitative imaging methods in an acoustic waveguide with
sound hard walls. The waveguide terminates at one end and contains an
unknown obstacle of compact support or has deformed walls, to be
determined from data gathered by an array of sensors that probe the
obstacle with waves and measure the scattered response. To further
shed light on qualitative approaches to imaging in complex media, I
shall present higherorder wave homogenization in periodic media,
where such media have been used with success to manipulate waves
toward achieving superfocusing, subwavelength imaging, cloaking,
and topological insulation.
Speaker:
Lewei Zhao
Title: Finite Element Method for Laplace Equation in
Twodimensional Domains with a Singular Fracture Abstract: We study
the Laplace equation in 2D with a line Dirac Delta function on the
right hand side. We establish the regularity of this problem
described by weighted Sobolev space near the endpoint of the singular
line. Our numerical method relies on element not across the singular
line and graded mesh controlled by a grading parameter. Numerical
examples are shown to verify the optimal convergence rate.
Yeonhyang Kim (kim4y AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
01/26/18 
TBA 
TBA 
02/02/18 
TBA 
TBA 
02/09/18 
TBA 
TBA 
02/16/18 
TBA 
TBA 
02/23/18 
TBA 
TBA 
03/02/18 
TBA 
TBA 
03/14/18, 1011, PE224 
Chen Mu (Florida State University) 
Robust Tomographic Reconstruction Techniques in Nanomanufacturing and Improvement by Datadependent Sparse Filtered Backprojection 
03/23/18 
TBA 
TBA 
03/30/18 
TBA 
TBA 
04/06/18 
Fatih Celiker 
Novel nonlocal operators
in arbitrary dimension enforcing local 
04/13/18 
TBA 
TBA 
04/20/18 
TBA 
TBA 
04/27/18 
Michael Delaura (MSU) 
Statistical Estimation of fibers from HARDI and DTI data 
05/04/18 


Speaker: Chen Mu
Title: Robust Tomographic Reconstruction Techniques in
Nanomanufacturing and Improvement by Datadependent Sparse Filtered
Backprojection
Abstract: Tomographic reconstruction is a method
of reconstructing a high dimensional image with a series of its low
dimensional projections. Filtered backprojection is one of the
several popular analytical techniques for the reconstruction due to
its computational efficiency and easy implementation. The accuracy of
the filtered backprojection method deteriorates when the input data
are noisy or the input data are available for only a limited number
of projection angles. In these cases, some algebraic approaches
perform better, but they require computationally slow iterations. We
demonstrate an improvement of the filtered backprojection method
which is as fast as the existing filtered backprojection method and
is as accurate as the algebraic approaches under heavy observation
noises and missing wedge issue. The new approach optimizes the filter
of the backprojection operator to minimize a regularized
reconstruction error, which results in a sparse filter. We compare
the new approach with the stateoftheart filtered backprojection
and algebraic approaches using two simulated datasets and a
realworld nanomanufacturing data set to show its competitive
accuracy and fast computing speed.
Speaker: Fatih Celiker
Title: Novel nonlocal operators in arbitrary dimension
enforcing local boundary conditions
Abstract: We present novel
nonlocal governing operators in 2D/3D for wave propagation and
diffusion that enforce local boundary conditions (BC). The main
ingredients are periodic, antiperiodic, and mixed extensions of
kernel functions together with even and odd parts of bivariate
functions. We present all possible 36 different types of BC in 2D
which include pure and mixed combinations of Neumann, Dirichlet,
periodic, and antiperiodic BC. Our construction is systematic and
easy to follow. We provide numerical experiments that validate our
theoretical findings. We also compare the solutions of the classical
wave and heat equations to their nonlocal counterparts.
Speaker:
Michael Delaura
Title: Statistical Estimation of fibers from
HARDI and DTI data
Abstract: High Angular Resolution Diffusion
Imaging (HARDI) and Diffusion Tensor Imaging (DTI) are popular in
vivo brain imaging techniques that allow medical researchers to
access brain connectivity, which plays crucial role in identifying
early stages of Alzheimer's disease and other brain disorders. In
this talk we will introduce the mathematical and statistical models
for both HARDI and DTI. We will discuss how noise enters into these
models and how our statistical tractography methodology helps to
estimate the fibers locations and access the uncertainty in the
images obtained via HARDI and DTI. We will also discuss how our
approach compares with other tractography methods. This talk is based
on the joint work with Dr. Sakhanenko and Dr. Zhu.
Yeonhyang Kim (kim4y AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Date 
Speaker 
Title 
9/15/2017 (3pm4pm) 
Xiaoming Zheng (CMU) 
A viscoelastic model of capillary growth: derivation, analysis, and simulation 
9/22/2017 
Yeonhyang Kim (CMU) 
The spherical harmonic basis for a HARDI signal 
9/29/2017 
TBA 
TBA 
10/6/2017 
TBA 
TBA 
10/13/2017 (4pm5pm) 
Yingda Cheng (Michigan State University) 
A Sparse Grid Discontinuous Galerkin Method for HighDimensional Transport Equations 
10/20/2017 
TBA 
TBA 
10/27/2017 
Roza Aceska (Ball State University) 
Approximation of solutions of certain classes of PDEs via dynamical sampling 
11/3/2017 
TBA 
TBA 
11/10/17 
TBA 
TBA 
11/17/2017 
TBA 
TBA 
12/1/2017 
TBA 
TBA 
12/8/2017 
Zhengfu Xu (Michigan Technological University) 
Bound preserving flux limiters and total variation stability for computation of scalar conservation laws 

TBA 
TBA 



Abstracts
Speaker: Xiaoming
Zheng
Title: A viscoelastic model of capillary growth:
derivation, analysis, and simulation
Abstract: We derive
a onedimensional viscoelastic model of blood vessel capillary
growth under nonlinear friction with surroundings, analyze its
solution properties, and simulate various growth patterns in
angiogenesis. The mathematical model treats the cell density as the
growth pressure eliciting viscoelastic response of cells, thus
extension or regression of the capillary. Nonlinear analysis provides
some conditions to guarantee the global existence of biologically
meaningful solutions, while linear analysis and numerical simulations
predict the global biological solutions exist as long as the cell
density change is sufficiently slow in time. Examples with blowups
are captured by numerical approximations and the global solutions are
recovered by slow growth processes. Numerical simulations demonstrate
this model can reproduce angiogenesis experiments under several
biological conditions including blood vessel extension without
proliferation and blood vessel regression.
Speaker: Yeonhyang
Kim
Title: The spherical harmonic basis for a HARDI
signal
Abstract: High
AngularResolutionDiffusionImaging(HARDI)has been proposed as a means
to overcome some limitations imposed by diffusion tensor imaging
(DTI), especially in complex models of fibre orientation distribution
in voxels. The signal generated by the 3D diffusion measurement of
each voxel is called the qspace signal. Qball imaging (QBI), one of
the HARDI methods, directly derives the diffusion orientation
distribution function (ODF) of water molecules and this ODF can be
estimated directly from the raw HARDI signal S on a single sphere of
qspace. Originally the Qball representation utilized spherical
radial bases. Later, spherical harmonic bases were adopted in many
applications because they provide an analytic solution for the
reconstruction of ODFs. In this talk, we study some properties of the
spherical harmonic basis and the representation of the ODF of a HARDI
signal.
Speaker: Yingda
Cheng
Title: A Sparse Grid Discontinuous Galerkin Method
for HighDimensional Transport Equations
Abstract: In
this talk, we present sparse grid discontinuous Galerkin schemes for
solving highdimensional PDEs. We will discuss the construction of
the scheme based on hierarchical tensor product finite element
spaces, its properties and applications in kinetic transport
equations.
Speaker: Roza
Aceska
Title: Approximation of solutions of certain
classes of PDEs via dynamical sampling
Abstract: The
concept of dynamical sampling is introduced in setups where the
sensing devices available are limited due to some constraints. We
show how to reconstruct optimally the solution of certain
(non)linear PDEs in a suitable Sobolev class using a single
(locationfixed) sensor over time. We show that the optimal sampling
does not depend on the spectrum of the operators involved, but just
on the order of the PDE. We generalize the problem by working with
timevariant coefficients in the PDEs. We adapt our approach to solve
certain nonlinear integrodifferential equations and nonlinear PDEs.
(Preliminary research report  joint work with Alessandro Arsie and
Ramesh Karki )
Speaker: Zhengfu
Xu
Title: Bound
preserving flux limiters and total variation stability for
computation of scalar conservation laws
Abstract: Provable total
variation bounded high order (at least third order) method based on
variation measured on grid values will be discussed in this talk.
Most of the conventional design of TVB methods is based on Harten's
criteria. However, to strictly follow Harten's TVD criteria, one can
only provide methods of at most second order. Popular ENO/WENO
methods are very successful in producing robust numerical results
with great performance of suppressing oscillations around
discontinuities. However, it is still elusive to prove ENO/WENO
methods are TVB. As one of the most important properties we desire
for numerical methods solving conservation laws, provable TVB
property is at the center of this talk. A new criteria will be
provided to design TVB high order finite difference scheme for
onedimensional problems.
Spring 2016
Organizers
Debraj Chakrabarti (chakr2d AT cmich DOT edu)
Enbing Lin (enbing.lin@cmich.edu)
Yeonhyang Kim (kim4y AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
Schedule
Date 
Speaker 
Title 
1/29/2016 
Derek Thompson (Taylor University) 
Spectra of Some Weighted Composition Operators on H^2 
2/5/2016 
TBA 
TBA 
2/12/2016 
TBA 
TBA 
2/19/2016 
TBA 
TBA 
2/5/2016 
TBA 
TBA 
2/26/2016 
TBA 
TBA 
3/4/2016 
TBA 
TBA 
3/18/2016 
Debraj Chakrabarti (CMU) 
A counterexample of L. Nirenberg on embeddability of CR structures (1) 
3/25/2016 
Debraj Chakrabarti (CMU) 
A counterexample of L. Nirenberg on embeddability of CR structures (2) 
4/1/2016 
TBA 
TBA 
4/8/2016 
Debraj Chakrabarti (CMU) 
A counterexample of L. Nirenberg on embeddability of CR structures (3) 
4/15/2016 
TBA 
TBA 
4/22/2016 
TBA 
TBA 
4/29/2016 
TBA 
TBA 
4/29/2016 
TBA 
TBA 
5/6/2016 
TBA 
TBA 
Abstracts
Speaker: Derek Thompson
Title: Spectra
of Some Weighted Composition Operators on H^2
Abstract: We
completely characterize the spectra of weighted composition operators
T_\psi C_\phi on H^2 when the weight \psi is in H^\infty and
continuous at the DenjoyWolff point of the compositional symbol
\phi, and \phi converges uniformly under iteration to its Denjoy
Wolff point. Though this is a rather strong condition on \phi,
several wellknown symbols exhibit this behavior and applications to
weak normality conditions for weighted composition operators are
given.
Speaker: Debraj Chakrabarti
Title: A
counterexample of L. Nirenberg on embeddability of CR structures
Abstract: The aim of these talks is to discuss an early
and famous contribution of this year's Fleming lecturer Louis
Nirenberg to complex analysis and partial differential equations. We
will try to make the talks as nontechnical and exampleoriented as
possible. An outline is as follows. (1) CR structures and the CR
embedding problem. We discuss some classical embedding problems of
geometry and analysis, such as the Whitney and Kodaira embedding
theorems. We motivate the definition of CR structures, discuss some
elementary properties of CR structures, and introduce the notion of
pseudoconvexity. We then state the global and local versions of the
CR embedding problems. (2) Two discoveries of Hans Lewy We discuss
basic facts about partial differential equations, such as the
CauchyKowalevsky theorem and the MalgrangeEhrenpreis Theorem. We
then discuss an example of a nonsolvable first order PDE due to Lewy
and also a related result on the holomorphic extension of CR
functions. (3) Nirenberg's example We discuss a counterexample due to
Louis Nirenberg (1974) which shows that the local CR problem does not
have a solution in three dimensions.
Fall 2015
Date 
Speaker 
Title 
9/4/2015 
Andrew Zimmer (University of Chicago) 
Characterizing polynomial domains by their biholomorphism group 
9/11/2015 
TBA 
TBA 
9/18/2015 
TBA 
TBA 
9/25/2015 
TBA 
TBA 
10/2/2015 
Emil Straube (Texas A&M university) 
Compactness of the $\overline{\partial}$Neumann Operator: An Example 
10/9/2015 
TBA 
TBA 
10/16/2015 
Byeongseon Jeong (CMU) 
Subdivision Schemes in Geometric Design 
10/23/2015 
TBA 
TBA 
10/30/2015 
Changchuan Yin (University of Illinois at Chicago) Meeting time: 4 pm ~ 5 pm 
Whole Genome Phylogenetic Analysis by Fourier Transform 
11/6/2015 
Leela Rakesh (CMU) 
Navier Stokes equation and polymer fluid dynamics 
11/13/2015 
Divakar (University Michiga) 
Intermittency at fine scales and complex singularities of turbulent flow 
11/20/2015 
CANCELED 
TBA 
12/4/2015 
TBA 
TBA 
12/11/2015 
TBA 
TBA 
Speaker: Andrew Zimmer
Title:
Characterizing polynomial domains by their biholomorphism group
Abstract: In this talk we will discuss the
biholomorphism group of bounded domains in $\mathbb{C}^n$. Every
bounded domain has several intrinsic metrics: for instance the
Kobayashi, Carath{\'e}odory, and Bergman metric. The biholomorphism
group acts by isometries on each of these metrics and in particular
the geometry of these metrics controls the behavior of the group of
biholomorphisms. I will discuss how ideas from the theory of
nonpositively curved metric spaces can be used to prove new results
in several complex variables. The main result I will discuss is a
characterization of certain polynomial domains in terms of the
asymptotic behavior of the biholomorphism group.
Speaker: Emil Straube
Title:
Compactness of the $\overline{\partial}$Neumann Operator: An
Example
Abstract: We will introduce the
$\overline{\partial}$Neumann operator, explain why whether or not it
is compact is important, and discuss an example. More precisely, we
will discuss compactness of the $\overline{\partial}$Neumann
operator on the intersection of two (pseudoconvex) domains when the
respective operators on the two domains are compact.
Speaker: Byeongseon Jeong
Title:
Subdivision Schemes in Geometric Design
Abstract:
Subdivision scheme is a method to obtain smooth curves/surfaces
from a given set of discrete points by recursively generating denser
sets. We will introduce the basic notions of subdivision schemes and
discuss the properties of a scheme which enable us to reproduce
certain classes of curves and surfaces. Numerical examples will be
presented for the verification of design capabilities.
Speaker: Changchuan Yin
Title: Whole
Genome Phylogenetic Analysis by Fourier Transform
Abstract:
DNA sequence similarity comparison is a major step in
computational phylogenetic analysis of genomes. The sequence
comparison of closely related DNA sequences is usually performed by
multiple sequence alignments (MSA); however, MSA may produce
incorrect results when DNA sequences undergo rearrangements, as in
many bacterial and viral genomes. It is also limited by high
computational complexity when omparing large volumes of data. We
present a new method for the similarity comparison of DNA sequences
by Fourier transform . In this method, we map DNA sequences into 2D
numerical sequences and then apply Fourier transform to convert the
numerical sequences into frequency domain. In 2D mapping, the
nucleotide composition of a DNA sequence is a determinant factor. The
2D mapping reduces the nucleotide composition bias in distance
measuring. The method can be applicable to any DNA sequences of
arbitrary length. The similarity measurement in frequency domain is
successfully applied on phylogenetic analysis for large, whole
bacterial genomes.
Speaker: Leela Rakesh
Title: Navier
Stokes equation and polymer fluid dynamics
Abstract: The
NavierStokes equation (NSE) is named after ClaudeLouis Navier and
George Gabriel Stokes. NSE with appropriate initial and boundary
conditions delivers mathematical model of the motion of liquids and
gases (fluid). It is the momentous equation in computational and
experimental fluid dynamics by making use of various fundamental
principles of vector calculus. Vector fields are convenient to study
fluid dynamics and make it possible to detect the path of a fluid at
any given point. Various modifications of NSEs are used in polymer
and biomedical industries to study the optimality under various
operating conditions. In this talk I will discuss some of the
fundamental aspects of NSEs and few applications.
Speaker: Divakar Viswanath
Title:
Intermittency at fine scales and complex singularities of
turbulent flow
Abstract: Intermittency is a property of
the finest scales of turbulent flow. If one looks at a fine scale
either in time or in space, it will be quiescent much of the time (or
in much of the place) except for occasional bursts. We compute
complex plane singularities of turbulent flow and show that
intermittency is nothing but a manifestation of complex
singularities, thus numerically verifying a conjecture of Frisch and
Morf (1981). This talk is joint work with Andre Souza.
Date 
Speaker 
Title 
1/30/2015 
Kun Gou (Michigan State University) 
Modeling of human airway swelling by biomechanics 
2/6/2015 
Hana Cho (Michigan State University) 
Stable and Efficient Schemes for Parabolic Problems using the Method of Lines Transpose 
2/13/2015 
TBA 
TBA 
2/20/2015 
Michael Bolt (Calvin College) 
Szeg\H{o} kernel transformation law 
2/27/2015 
TBA 
TBA 
3/6/2015 
TBA 
TBA 
3/13/2015 
Spring Break 
TBA 
3/20/2015 
Xiaodong Wang (Michigan State University) 
An integral formula in Kahler geometry with applications 
3/27/2015 
TBA 
TBA 
4/3/2015 
Sonmez Sahutoglu (University of Toledo) 
Essential norm estimates for Hankel operators on convex domains in $\mathbb{C}^2$ 
4/10/2015 
Shravan (U of M & Courant Institute) 
Vesicle flows: simulations, dynamics and rheology 
4/17/2015 
Valery Ginzburg (Dow Chemical Scientist) 
Fieldtheoretic simulations and selfconsistent field theory (SCFT) for studying block copolymer directed selfassembly 
Speaker: Kun Gou
Title: Modeling
of human airway swelling by biomechanics
Abstract: The
human airway, also called the trachea in a professional way, is an
organ by which we breath air into the lungs. When swelling
(angioedema) occurs in the airway, it can rapidly narrow the airway,
reduce air transportation capability and thus lead to a life
threatening condition. The symptom of swelling in the airway is
studied by means of biomechanics. First we consider the airway to be
an idealized cylindrical shape, and study an 1D problem for
convenience of mathematical analysis. Then we consider a practical
3D airway geometry extracted from biomedical images, where finite
element formulation is used to obtain the solution. Airway
constriction and the internal stress distribution are tracked as
functions of swelling effect. This modeling provides a sound
continuum mechanical foundation that facilitates our understanding of
airway swelling for a better cure of the disease.
Speaker: Hana Cho TBA
Title: Stable
and Efficient Schemes for Parabolic Problems using the Method of
Lines Transpose
Abstract: As followed up to [1] , we
present a novel numerical scheme suitable for solving parabolic
differential equation model using the Method of Lines Transpose
(MOL^T) combined with the successive convolution operators. The
primary advantage is that the operators can be computed quickly in
O(N) work, to high precision; and a multi dimensional solution is
formed by dimensional sweeps. We demonstrate our solver on the
AllenCahn and CahnHilliard equation.
Speaker: Michael Bolt
Title: Szeg\H{o}
kernel transformation law
Abstract: Let $\Omega_1,
\Omega_2$ be smoothly bounded doubly connected regions in the complex
plane. We establish a transformation law for the Szeg\H{o} kernel
under proper holomorphic mappings. This extends known results
concerning biholomorphic mappings between multiply connected regions
as well as proper holomorphic mappings from multiply connected
regions to simply connected regions.
Speaker: Xiaodong Wang
Title: An
integral formula in Kahler geometry with applications
Abstract:
I will discuss an integral formula on a smooth, precompact domain
in a Kahler manifold and some of its applications. As the 1st
application I will discuss holomorphic extension of CR functions.
Then I will present an isoperimetric inequality in terms of a
positive lower bound for the Hermitian mean curvature of the
boundary. Combining with a Minkowski type formula on the complex
hyperbolic space it implies that any closed, embedded hypersurface of
constant mean curvature must be a geodesic sphere, provided the
hypersurface is Hopf. A similar result is valid for the complex
projective space.
Speaker: Sonmez Sahutoglu
Title:
Essential norm estimates for Hankel operators on convex domains
in $\mathbb{C}^2$
Abstract: Let $\Omega$ be a bounded
convex domain in $\mathbb{C}^2$ with $C^1$smooth boundary and
$\varphi\in C^1(\overline{\Omega})$ such that $\varphi$ is harmonic
on the nontrivial analytic disks in the boundary. We estimate the
essential norm of the Hankel operator $H_{\varphi}$ in terms of the
$\overline{\partial}$ derivatives of $\varphi$ ``along'' the
nontrivial disks in the boundary. This is joint work with Zeljko
Cuckovic.
Speaker: Shravan
Title: Vesicle
flows: simulations, dynamics and rheology
Abstract: In
this talk, we will present recent progress in our group on numerical
algorithms for simulating dense vesicle suspensions in viscous
fluids. Capturing the close twobody interactions of vesicles (or
other softparticles) poses significant numerical challenges owing to
the nearsingularity in the hydrodynamic interaction forces. We
present a new spectrallyaccurate algorithm for computing such
forces. A novel fast algorithm for simulating multiphase through
periodic geometries of arbitrary shape will be presented. Finally, we
will present new results on the dynamics and rheology of dense
suspensions obtained using these computational algorithms.
Speaker: Dr. Valeriy V. Ginzburg
Title:
Fieldtheoretic simulations and selfconsistent field theory
(SCFT) for studying block copolymer directed selfassembly
Abstract:
In recent years, block copolymer directed selfassembly (DSA) has
become a promising new approach to printing sub40 nm features. In
DSA, nanoscale patterns are obtained as a result of thermodynamic
microphase separation between two or more chemically distinct blocks
covalently bonded into block copolymers. By manipulating the chemical
nature of each of the individual blocks and molecular weight of the
block copolymer, one can vary the symmetry of the equilibrium
structure (lamellar, hexagonal, bodycenteredcubic, gyroid, etc.)
and its equilibrium period (often referred to as â€œpitchâ€).
Computational modeling is increasingly becoming part of the DSA
development in industry. Modeling is used to optimize block copolymer
formulations, estimate process windows, predict defect density, or
just visualize the polymer morphology inside a specific feature. I
will discuss the use of mesoscale fieldtheoretic block copolymer
models, and specifically selfconsistent field theory (SCFT) in the
context of block copolymer DSA. In recent years, SCFT has been widely
used as a tool to predict equilibrium block copolymer morphology both
in the bulk and in confined geometries, and its predictions are shown
to agree well with experiments. Specific examples include
chemoepitaxy (lamellar PSPMMA on brushed surfaces) and graphoepitaxy
(contact hole shrink and linespace applications).
Date 
Speaker 
Title 
9/5 
Purvi Gupta (Ann Arbor) 
A link between Fefferman's hypersurface measure and polyhedral approximation 
9/12 
Arundhati Bagchi Mishra (Saginaw Valley State) 
Modified Chambolle algorithm for speckle image denoising 
9/19 


9/26 
PinHung Kao (Central Michigan University) 
An Application of the MaynardTao Sieve 
10/3 
TBA 
TBA 
10/17 
Ilya Kossovskiy (University of Vienna) 
Dynamical Approach in CRgeometry and Applications 
10/24 
Liz Vivas (Ohio State University) 
Parabolic domains associated to formal invariant curves 
10/31 
Xinghui Zhong (Michigan State University) 
Discontinuous Galerkin Methods: algorithm design and applications 
11/7 
James Angelos (Central Michigan University) 
Best Approximation of Vector Valued Functions 
11/14 
TBA 
TBA 
11/21 
TBA 
TBA 
1/30/2015 
Kun Gou (Michigan State University) 
TBA 
3/20/2015 
Xiaodong Wang (Michigan State University) 
TBA 
Speaker: Purvi Gupta
Title: A link
between Fefferman's hypersurface measure and polyhedral approximation
Abstract: In convex geometry, the affine surface area
measure  studied first by Blaschke  is a measure on convex
boundaries that is preserved by the group of equiaffine
transformations. It occurs, among other things, in the asymptotics of
polyhedral approximations of convex bodies. In multivariate complex
analysis, a similar measure, due to Fefferman, exists on boundaries
of certain convexlike domains, where the relevant group is that of
volumepreserving biholomorphisms. It is natural to ask whether this
measure enjoys any connection with approximation problems as in the
affine situation. In this talk, I will motivate and formulate this
question and discuss a positive result in this direction.
Speaker: Arundhati Bagchi Misra
Title:
Modified Chambolle algorithm for speckle image denoising
Abstract:
In this paper, we introduce a new algorithm based on total variation
for denoising speckle noise images. The total variation was
introduced by Rudin, Osher, and Fatemi in 1992 for regularizing
images. Chambolle proposed a faster algorithm based on duality of
convex functions for minimizing the total variation. His algorithm
was built for Gaussian noise removal. We modify this algorithm for
speckle noise images. The first noise equation for speckle denoising
was proposed by Krissian, Kikinis, Westin and Vosburgh in 2005. We
apply Chambolle algorithm to the Krissian et al. noise equation to
develop a faster algorithm for speckle noise images.
Speaker: Ilya Kossovskiy
Title:
Dynamical Approach in CRgeometry and Applications
Abstract:
Study of equivalences and symmetries of real submanifolds in
complex space goes back to the classical work of Poincar\'e and
Cartan and was deeply developed in later work of Tanaka and Chern and
Moser. This work initiated far going research in the area (since
1970's till present), which is dedicated to questions of regularity
of mappings between real submanifolds in complex space, unique jet
determination of mappings, solution of the equivalence problem, and
study of automorphism groups of real submanifolds. Current state of
the art and methods involved provide satisfactory (and sometimes
complete) solution for the above mentioned problems in nondegenerate
settings. However, very little is known for more degenerate
situations, i.e., when real submanifolds under consideration admit
certain singularities of the CRstructure (such as nonconstancy of
the CRdimension or that of the CRorbit dimension). The recent CR
(CaucheyRiemann Manifolds)  DS (Dynamical Systems) technique,
developed in our joint work with Shafikov and Lamel, suggests to
replace a real submanifold with a CRsingularity by appropriate
complex dynamical systems. This technique has recently hepled to
solve a number of longstanding problems in CRgeometry, related to
regularity of CRmappings. In this talk, we give an overview of the
technique and the results obtained recently by using it. We also
discuss a possible development in this direction, in particular, new
sectorial extension phenomena for CRmappings.
Speaker: PinHung Ka
Title: An
Application of the MaynardTao Sieve
Abstract: Goldston,
Pintz, and Y\i ld\i r\i m made a breakthrough in the study of bounded
gaps between primes in the recent years. They used a modified Selberg
sieve to achieved bounded gaps between primes under the assumption of
the ElliottHalberstam Conjecture. Maynard and Tao expanded the idea
of GPY and used a multidimensional Selberg sieve to obtain bounded
gaps between primes unconditionally. In this talk, the speaker will
discuss an ongoing investigation of his work in the application of
the MaynardTao sieve to the study of gaps between $E_2$ numbers.
That is, the gaps between integers with exactly two distinct prime
factors.
Speaker: Liz Vivas
Title: Parabolic
domains associated to formal invariant curves
Abstract: We
investigate the existence of parabolic attracting domains for germs
tangent to the identity, when there is a formal invariant curve
associated to the given germ. Formal curves are algebraic objects
that might have geometrical meaning. However this is not always the
case. We review some classical results for holomorphic germs in one
dimension and explain the corresponding results for holomorphic germs
in several dimensions. This is joint work with Lorena LopezHernanz.
Speaker: Xinghui Zhong
Title:
Discontinuous Galerkin Methods: algorithm design and applications
Abstract: In this talk, we discuss discontinuous
Galerkin (DG) methods with emphasis on their algorithm design
targeted towards applications for shock calculation and plasma
physics. DG method is a class finite element methods that has gained
popularity in recent years due to its flexibility for arbitrarily
unstructured meshes, with a compact stencil, and with the ability to
easily accommodate arbitrary hp adaptivity. However, some challenges
still remain in specific application problems. In the first part of
my talk, we design a new limiter using weighted essentially
nonoscillatory (WENO) methodology for DG methods solving
conservation laws, with the goal of obtaining a robust and high order
limiting procedure to simultaneously achieve uniform high order
accuracy and sharp, nonoscillatory shock transitions. The main
advantage of this limiter is its simplicity in implementation,
especially on multidimensional unstructured meshes. In the second
part, we propose energyconserving numerical schemes for the
Vlasovtype systems. Those equations are fundamental models in the
simulation of plasma physics. The total energy is an important
physical quantity that is conserved by those models. Our methods are
the first Eulerian solver that can preserve fully discrete total
energy conservation. The main features of our methods include
energyconservative temporal and spatial discretization. In
particular, an energyconserving operator splitting is proposed to
enable efficient calculation of fully implicit methods. We validate
our schemes by rigorous derivations and benchmark numerical examples.
Speaker: James Angelos
Title: Best
Approximation of Vector Valued Functions
Abstract: Let X
be a metric space. The set C(X,R^k) denotes the set of continuous
functions from X to R^k with the norm
f = sup {f(x)_2 :
x ∈ X}.
Let M be a finite dimensional subspace of C(X,R^k). p
∈ M is a best approximation to f from M if
 fp ≤
fq, ∀ q ∈ M.
We consider the charactization of p,
whether or not it is unique, and properties of the best approximation
operator: B : C(X,Rk) → M where B(f) = p, p the best approximation,
for a particular class of subspaces known as generalized Haar spaces
of tensor product type.