Applied Mathematics Colloquium  Fall 2017


Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact David Shirokoff.
To join the Applied Mathematics Colloquium mailing list visit https://groups.google.com/a/njit.edu/forum/?hl=en#!forum/mathcolloquium/join (Google Profile required). To join the mailing list without a Google Profile, submit the seminar request form.
Date  Speaker, Affiliation, and Title  Host 
September 8  Allison Bishop, Columbia University In Pursuit of Obfuscation We will survey developments in cryptographic research on program obfuscation: the quest to make working code that can keep secrets. 
Christina Frederick 
September 15 
Maxence Cassier, Columbia University In this talk, we are interested in a transmission problem between a dielectric and a metamaterial. The question we consider is the following: does the limiting amplitude principle hold in such a medium? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. An answer is proposed here in the case of a twolayered medium composed of a dielectric and a particular metamaterial (Drude model). In this context, we reformulate the timedependent Maxwell’s equations as a Schrödinger equation and perform its complete spectral analysis. This permits a quasiexplicit representation of the solution via the ”generalized diagonalization” of the associated unbounded selfadjoint operator. As an application of this study, we show finally that the limiting amplitude principle holds except for a particular frequency, called the critical frequency, characterized by a ratio of permittivities and permeabilities equal to 1 across the interface. This frequency is a resonance of the system and the response to this excitation blows up linearly in time. 
Roy Goodman 
September 22 
Robert Pego, Carnegie Mellon The leastaction problem for geodesic distance on the `manifold' of fluidblob shapes exhibits an instability due to microdroplet formation. This reflects a striking connection between Arnold's leastaction principle for incompressible Euler flows and geodesic paths for Wasserstein distance. A connection with fluid mixture models via a variant of Brenier's relaxed leastaction principle for generalized Euler flows will be outlined also. This is joint work with JianGuo Liu and Dejan Slepcev. 
David Shirokoff 
September 29 
Alex Townsend, Cornell University Matrices that appear in computational mathematics are so often of low rank. Since random ("average") matrices are almost surely of full rank, mathematics needs to explain the abundance of low rank structures. We will give a characterization of certain low rank matrices using Sylvester matrix equations and show that the decay of singular values can be understood via an extremal rational problem. We will give another characterization involving the JohnsonLindenstrauss Lemma that partially explains the abundance of low rank structures in big data. 
Michael Booty 
October 6 
Gennady Gor, NJIT Ultrasound is a versatile tool which has been used for investigation of matter for decades. Since the wavelength of ultrasound in solids exceeds the sizes of nanopores by several orders of magnitude, ultrasound cannot resolve any individual features on the pore scale, but it provides information on the sample as a whole. In particular, the velocity of ultrasound propagation in a fluidsaturated sample gives the values of the sample's elastic moduli. In my presentation I will discuss recently published experimental data on ultrasound propagation in nanoporous glass saturated with liquid argon. I will show the results of a Monte Carlo molecular simulation for this system, providing a relation between the measured bulk modulus of a fluidsaturated sample and the pore size. These findings suggest that ultrasound can be effectively used as a characterization tool for nanoporous materials. 
Linda Cummings 
October 13 
Andrew Bernoff, Harvey Mudd College A wide variety of physical and biological systems can be described as continuum limits of interacting particles. Many of these problems are gradient flows and their dynamics are governed by a monotonically decreasing interaction energy that is often nonlocal in nature. We show how to exploit these energies numerically, analytically, and asymptotically to characterize the observed behavior. We describe three such systems. In the first, a Langmuir layer, line tension (the twodimensional analog of surface tension) drives the fluid domains to become circular and the rate of relaxation to these circular domains can be used to deduce the magnitude of the line tension forces. In the second, a HeleShaw problem, vexing changes in topology are observed. The third system models the formation of the convoluted fingered domains observed experimentally in ferrofluids for which pattern formation is driven by line tension and dipoledipole repulsion. We show that noise in this system plays an unexpected but essential role and deduce an algorithm for extracting the dipole strength using only a shape's perimeter and morphology. 
David Shirokoff 
October 20 
Daniel Szyld, Temple University GMRES with multiple preconditioners (MPGMRES) is a method that allows for several preconditioners to be used simultaneously. In this manner, the effect of all preconditioners is applied in each iteration. An implementation of MPGMRES is proposed for solving shifted linear systems with shiftandinvert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrixvector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of preconditioners. This allows for a more efficient implementation of the algorithm. The proposed implementation is tested on shifted systems that arise in computational hydrology and the evaluation of different matrix functions. The numerical results indicate the effectiveness of the proposed approach. 
Yassine Boubendir 
October 27 
Peter Monk, University of Delaware In the last few decades, finite element methods for approximating the time harmonic Maxwell system governing electromagnetic wave propagation have undergone profound changes. Whereas in the 1980's there was confusion about how to choose the finite elements to obtain a robust solver, it is now clear not only how to discretize the Maxwell system using edge elements, but also how to analyze the resulting method. Spinoffs from this analysis include the Finite Element Exterior Calculus and the realization that the discrete de Rham diagram is a useful tool to guarantee conservation of charge. More recently several open source implementations of common finite element families for the Maxwell system have appeared making edge elements much more accessible. I shall give a historical survey of the finite element method for Maxwell's equations and comment on the main open problems still facing users. I shall also present current uses of finite elements in computational photonics, particularly light transport in nanoscale diffraction gratings where unusual surface phenomena have been observed. A particular application of this analysis is in the design of thin film solar cells. 
Yassine Boubendir 
November 3 
Johannes Tausch, Southern Methodist University Time dependence in boundary integral reformulations of parabolic PDEs is reflected in the fact that the layer potentials involve integrals over time in addition to integrals over the boundary surface. 
Michael Siegel 
November 10 
Javier Diez, UNICEN We report experimental, theoretical and numerical results on the hydrodynamic instabilities involved in the breakup of patterned thin liquid films on solid substrates, such as single filaments and bidimensional grids formed by the intersection of them. We focus on the effects of contact angle hysteresis on the flow dynamics and the type of drops patterns that are formed by these unstable flows. In particular, we describe in detail the motion of the contact line in the region nearby the end of a retracting liquid filament. Since the flow develops under conditions of partial wettability, the filament end recedes and forms a bulge (head) which lately develops a thinning neck behind it. This neck finally breaks up giving place to the generation of a separated drop, while the rest of the filament repeats the cycle. The contact angle hysteresis plays a fundamental role in this type of processes since, not only defines the dynamics, but also the geometrical features and size of the resulting drops as well as the distance between them. We use a combined model for the relation between the contact line velocity and contact angle, which takes into account the hydrodynamic viscous dissipation and the molecular kinetics at the liquidsolid interface. This relationship allows to reproduce the experimental results by means of numerical simulations of the full NavierStokes equation. We also develop a simple hydrodynamic model to account for the observed dynamics as well as to determine the number of drops resulting from the breakup of a filament of given length. These studies are applied to the nanometric scale in experiments with metalic filaments on a silicon oxide substrate, which are melted by short laser pulses. This is work joint with Alejandro G. González, Pablo D. Ravazzoli, Ingrith Cuellar. 
Lou Kondic 
November 17 
Mike O'Neil, New York University Full threedimensional highorder codes for electromagnetic scattering from complex geometries are currently out of reach in most cases. However, in particular (nontrivial) geometries very efficient algorithms can be constructed. In this talk, we will detail a separation of variables method along bodies of revolution that results in a sequence of boundary integral equations along only a onedimensional curve. The overall scheme, accelerated by the FFT, results in an overall O(N^3/2) direct method for solving scattering problems from perfect electric conducting and dielectric bodies of revolution. Several numerical examples will be included, as well as an overview of the evaluation of “modal Green’s functions” and the various numerical tools needed in the construction of this solver. 
David Shirokoff 
December 1 
Michael Shelley, New York University / Flatiron Institute Many fundamental phenomena in eukaryotic cells  nuclear migration, spindle positioning, chromosome segregation  involve the interaction of (often transitory) mechanical structures with boundaries and fluids. I will discuss the recent interactions of mathematical modeling and simulation with experimental measurements of active biomechanical processes within the cell. This includes studying how the spindle finds its proper place prior to cell division, and trying to explain coherent fluctuations within the nucleus. 
Anand Oza 
December 8 
Mette Olufsen, North Carolina State University The state of the cardiovascular system can be assessed from timeseries signals including heart rate and blood pressure. Characteristics of these signals are used to determine pathophysiology. Experienced clinicians can visually inspect signals and with high level of certainty diagnose patient outcome, yet they may do so without knowing the cascade of events triggering the outcome. This talk will address how mathematical modeling can be adapted to predict patient specific behavior, and how the optimized system equations can be used to predict emergent behavior. Focus will be on studying dynamics observed in patients diagnosed with postural orthostatic tachycardia (increased heart rate brought on by change in posture, headup tilt) and/or vasovagal syncope (fainting in response to overaction to some trigger) observed in patients diagnosed with functional somatic syndrome. Data analyzed here are from girls experiencing side effects (dizziness and fatigue) after vaccination against the human papilloma virus (HPV). It has been hypothesized that this condition can be explained by the presence of agonistic autoantibodies against beta2 adrenoceptors and M2 muscarinic receptors inducing slow heart rate and blood pressure oscillations emerging during headup tilt. In this talk we will use modeling to stimulate this condition as well as describe how to induce syncope (fainting) by switching the stable negative feedback to a positive feedback triggered by reduced filling of the heart. 
Casey Diekman 
Updated: November 21, 2017