Summer 2010
All seminars are held on Tuesdays and Thursdays at 2:00PM  3:00PM in
Cullimore
Hall Room 611 (Math Conference Room),
unless noted
otherwise.
If you have any questions about a particular seminar, please contact
the person hosting the speaker.


Host 

Tuesday, May 25, 2010 
Matt Causley, Department
of Mathematical Sciences, NJIT 
Jacek Wróbel 
Tuesday, June 1, 2010 
Dongwook Kim,
Department of Mathematical Sciences,
NJIT 
Jacek Wróbel 
Thursday, June 3, 2010 
Linda Cummings, Department of Mathematical Sciences,
NJIT 
Daniel Fong 
Tuesday, June 8, 2010 
Hui Wu,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, June 10, 2010 
Yuan Nan Young,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
Tuesday, June 15, 2010 
Xinxian Huang,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, June 17, 2010 
Horacio G. Rotstein,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
Tuesday, June 22, 2010 
TeSheng Lin,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, June 24, 2010 
Shidong
Jiang,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
Tuesday, June 29, 2010 
Rudrani Banerjee,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, July 1, 2010 
Lou Kondic,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
Tuesday, July 6, 2010 
Daniel Fong,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, July 8, 2010 
David Horntrop,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
Tuesday, July 13, 2010 
Peixin Zhang,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, July 15, 2010 
Michael Booty,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
Tuesday, July 20, 2010 
Kuan Xu,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, July 22, 2010 
Yassine Boubendir,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
Tuesday, July 27, 2010 
Jacek Wrobel,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, July 29, 2010 
Shahriar Afkhami,
Department of Mathematical Sciences, NJIT The Motion and Deformation of Elongated Drops and Bubbles in a Microchannel 
Daniel Fong 
Tuesday, August 3, 2010 
Xiaoni Fang,
Department of Mathematical Sciences, NJIT 
Jacek Wróbel 
Thursday, August 5, 2010 
Roy Goodman,
Department of Mathematical Sciences, NJIT 
Daniel Fong 
ABSTRACTS
An Efficient Numerical Method for Anomalously Dispersive Dielectrics: Abstract: Recent numerical techniques have been developed for the efficient implementation of convolution integrals whose kernels possess integrable singularities. By employing such techniques we have designed several algorithms that allow for the simulation of the ColeCole and HavriliakNegami dielectric permittivity models using finite difference schemes. We construct and independently validate solutions for these anomalously dispersive models, and show explicitly that the standard error and stability conditions of the finite difference method are preserved. Matt Causley ~ May 25, 2010 
Abstract: Information flows from the neocortex to the hippocampus through the superficial layers (II and III) of the entorhinal cortex (EC). Stellate cells (SCs) are the most abundant cell type in layer II of the medial EC and provide the main afferent system to the hippocampus. SCs display subthreshold rhythmic oscillations at theta frequencies (4  12 Hz). These patterns are generated mainly as the result of the interaction between a persistent sodium (Ip) and a hyperpolarization activated (h or Ih) currents. We focus on the effect of oscillatory inputs at various frequencies on the sub and superthreshold activity of SCs. These include (1) the effect of highfrequency Poissondistributed trains of combined excitatory and inhibitory conductancebased synaptic inputs on the SC's subtheshold oscillatory activity, and (2) the effect of sinusoidal inputs at various frequencies on the SC's firing frequency (superthreshold activity). We present the results of our simulations and show that for values of the control parameter (maximal synaptic conductance or sinusoidal input amplitude) not small enough but still in a biophysically plausible range these results depart from the linear prediction. More specifically, in (1) our simulations show that the peak in power spectrum for the SC's output voltage first decreases, for low values of the maximal synaptic conductance, but increases significantly for higher values. The peak frequency remains almost unchanged. In (2), we found more than one peak in the output firingfrequency vs. input sinusoidal frequency graphs. These findings suggest a special role for the SC's intrinsic currents Ih and Ip. Dongwook Kim ~ June 1, 2010 
Problems in Thin Film Fluid Dynamics: Abstract: Many problems of industrial and biomedical interest involve the flow of a thin film of liquid over a substrate. In this talk we will briefly review how simplified models for such "thin film" flows can be derived, and will focus on one particular case of a thin liquid film lining a cylindrical tube. In particular, the relative effects of surface tension and gravity on the liquid lining will be considered. The talk will conclude by mentioning several other related problems for which similar methods can usefully be applied. Linda Cummings ~ June 3, 2010 
Pattern Formation in Oscillatory Systems: Abstract: The topic has two parts: Kuramoto model and Oscillators in the Oregonator and FHN type models with global inhibitory feedback term. Kuramoto's original analysis of his model gives the critical synchronization value for a critical coupling constant K, he also gives an estimate for the value of order parameter r when K is close to the critical value K_c. When we have different initial values for the oscillators, the order parameters are different from his estimation.The objective of the first topic is to give the distribution of the value of order parameter r under different initial conditions. The main idea of the second topic is to find the phase property of Oscillators in the Oregonator and FHN type models with global inhibitory feedback term. Numerical simulations suggest that, the cubic system has the same phase property as the piecewise linear system. So we reduce the cubic system to piecewise linear system to estimate the phase pattern. The STDM (Strike time difference map) combines the STRC (Strike time response curve) of both participating oscillators to provide information about their synchronization properties. For PWL models of FHN type, STRCs can be computed analytically. We use STRC to see how the pattern of PWL model change with the parameters. Hui Wu ~ June 8, 2010 
Viscous Drops and Vesicles in Stokes Flow: Abstract: Many biological systems consist of enclosed drops or membranes separating two fluids. In this talk I will present a selected summary of work on encapsulated compounds in fluid mechanics. These compounds are made of at least two drops, with the biggest one enclosing all other drops. There are many potential applications to these systems, such as biological cells or vesicles. In addition, I will also talk about the dynamics of vesicles and their applications. Yuan Nan Young ~ June 10, 2010 
Using Feedforward Networks to Infer the Activity of Feedback Neuronal Networks: Abstract content: Xinxian Huang ~ June 15, 2010 
Abstract: In two and threedimensional systems, the term canard structure refers to the combination of nonlinearities (nullclines and nullsurfaces) and time scale separation that have the potential to produce the canard phenomenon. In the context on neural dynamics, canard structures have been shown to underlie the mechanism of generation of subthreshold and mixedmode oscillations (subthreshold oscillations interspersed with spikes) in biophysical (conductancebased) models of single cells. A prototypical example is a model of stellate cells (SCs) in layer II of the medial entorhinal cortex of the brain. These cells are known for their ability to display robust rhythmic subthreshold spiking activity in the theta frequency range (4  10 Hz) that persist in both excitatory and inhibitory networks including SCs. Recent experimental studies have shown that SCs become hyperexcitable in animal models of temporal lobe epilepsy. These studies have also demonstrated the existence of recurrent connections among SCs (excitatory), reduced levels of recurrent inhibition in epileptic networks as compared to control ones, and comparable levels of recurrent excitation among SCs in both network types. In this work, we show that minimal, recurrently connected networks of SCs and interneurons (inhibitory cells) exhibit an abrupt, thresholdlike transition from theta to hyperexcitable spiking (about 60 Hz) as the result of small increases in the amount of recurrent excitation. These abrupt transitions are observed in the absence of inhibition and in single, selfcoupled SCs, which represent a network of coupled synchronous SCs, but not in synaptically isolated SCs. Experimental results confirm our theoretical predictions. We use dynamical systems tools to explain how synaptic excitation interacts with the canard structure present in the SC model to generate these abrupt transitions between firing frequency regimes. Horacio G. Rotstein ~ June 17, 2010 
Abstract content: TeSheng Lin ~ June 22, 2010 
Introduction to Fast Algorithms and Integral Equations: Abstract: Abstract content:In this talk, we will give a short introduction to fast algorithms and integral equations. We will also discuss the connections between these two and their combined application to solving certain PDE problems. Shidong Jiang ~ June 24, 2010 
A Usage Rate Sensitive Warranty Servicing Strategy With Imperfect Repairs: Abstract: A warranty policy for a product should balance the interests of both producer and consumer. Consumer protection is typically provided by a guarantee of replacement or some form of repair of the product failing within a promised warranty period, while an approach to provide a corresponding protection for the manufacturer is to limit the maximum usage allowed under warranty. Such warranty policies are twodimensional, and the warranty expires at the end of the promised warranty period or upon reaching the maximum usage allowed, whichever occurs sooner. From a manufacturer's point of view, reducing warranty costs is an issue of great interest. In this work, we look at two different servicing strategies for a twodimensional warranty scheme involving minimal and imperfect repairs. Our work demonstrates the modeling and analysis of costs under these servicing strategies and compare their performance to other strategies that have been investigated in the literature. Rudrani Banerjee ~ June 29, 2010 
Particulate Matter: Networks, Chains, Energies, and their Role in Signal Propagation: Abstract content: Lou Kondic ~ July 1, 2010 
Asymptotic Structure of Diffusion Flames at High Pressure with Soret Transport: Abstract: Mathematical models of nonpremixed flames usually assume Fick's law applies to the molecular diffusivities. However, at elevated pressures, it is known that the Soret effects, mass transport via temperature gradients, become important. Moreover, at very high pressures, including supercritical conditions, Soret effects may become dominant. We investigate the asymptotic structure of diffusion flames with Soret mass transport. Our theory provides explicit expressions for flame temperature, location and extinction conditions in terms of physicothermal parameters affecting combustion. Daniel Fong ~ July 6, 2010 
Stochastic Simulation with Application to Materials: Abstract content: David Horntrop ~ July 8, 2010 
Confidence Bands for Survival Functions Under Semiparametric Random Censorship Models: Abstract: We propose a bootstrapbased simultaneous confidence band for survival functions under the setting of semiparametric random censorship models and prove its asymptotic validity. The proposed approach, which is based on a semiparametric survival function estimator, produces a tighter confidence band than those based on the KaplanMeier estimator. We have derived a key result involving the bootstrap maximum likelihood estimator of the finite dimensional parameter in the model for a conditional probability. Preliminary simulation results corroborate the theory that incorporation of modelbased estimators would produce an improved confidence band. We will perform more simulations to further study the operating characteristics of the proposed approach. To illustrate the proposed confidence band, we will analyze a lung cancer clinical trial data set. Since the proposed band is modelbased, we will also carry out a misspecification study to evaluate its robustness properties. Peixin Zhang ~ July 13, 2010 
Classical Aerofoil Theory and Variations on a Theme: Abstract: After a brief overview of classical 2D aerofoil theory some generalizations or extensions will be presented that lead to as yet unresolved questions. Michael Booty ~ July 15, 2010 
Abstract: We study the evolution of a twodimensional Cartesian drop or bubble in an imposed flow in the presence of soluble surfactant, i.e., a surfaceactive agent. The surfactant is distributed both on the drop surface and in the exterior bulk fluid. The governing equations in the zero Reynolds number of Stokes flow limit are solved by the boundary integral method using a complexvalued density. Specifically, the Goursat representation of the flow is used, in which solution of the biharmonic equation for the stream function and all primitive variables are given by construction of a pair of complex analytic functions, which can be found by constructing a single complex density that satisfies a Fredholm integral equation of second type. A recent study on solvability of this boundary integral equation is reported, as well as the results of several numerical examples. Highorder numerical schemes have been devised. These include an equalarclength frame, a spectrallyaccurate quadrature method, and a spectrum filter. Kuan Xu ~ July 20, 2010 
Seminar Title: Abstract content: Yassine Boubendir ~ July 22, 2010 
Adaptive Methods For Computing Invariant Manifolds of Maps: Abstract: We present efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve (surface), we propose using higherorder interpolation (approximation) techniques from geometric modeling. We use Bezier curves (triangles), one of the fundamental objects in curve (surface) design, to create an adaptive method. The methods are based on tolerance conditions derived from properties of Bezier curves (triangles). We develop and test the methods for ordinary parametric curves; then we adapt these methods to invariant manifolds of planar maps. Next, we develop and test the methods for parametric surfaces and begin their implementation to invariant manifolds of higher dimensional maps. Jacek Wrobel ~ July 27, 2010 
The Motion and Deformation of Elongated Drops and Bubbles in a Microchannel: Abstract content: Shahriar Afkhami ~ July 29, 2010 
Molecular Dynamics Simulation of 2D Dry Granular Materials: Abstract content: Xiaoni Fang ~ August 3, 2010 
What to Do with Your Numerical Simulations: Abstract content: Roy Goodman ~ August 5, 2010 
http://math.njit.edu/seminars/