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 Cole-Cole and Havriliak-Negami 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

The Effects of Periodic and Non Periodic Inputs on the Dynamics of a Medial Entorhinal Cortex Layer II Stellate Cell Model:

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 hyper-polarization activated (h- or Ih) currents. We focus on the effect of oscillatory inputs at various frequencies on the sub- and super-threshold activity of SCs. These include (1) the effect of high-frequency Poisson-distributed trains of combined excitatory and inhibitory conductance-based 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 (super-threshold 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 firing-frequency 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 Feed-forward Networks to Infer the Activity of Feedback Neuronal Networks:

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Xinxian Huang ~ June 15, 2010

The Role of Nonlinearities and Time Scale Separation in the Generation of Abrupt Transitions between Firing Frequency Regimes in Stellate Cells:

Abstract:  In two- and three-dimensional 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 mixed-mode oscillations (subthreshold oscillations interspersed with spikes) in biophysical (conductance-based) 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 hyper-excitable 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, threshold-like transition from theta to hyper-excitable 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, self-coupled 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

Contact Line Induced Instabilities in Two Cases: Thin Films Flowing Down Inverted Substrates and Liquid Crystal Spreading:

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Te-Sheng 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 two-dimensional, 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 two-dimensional 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:

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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 physico-thermal parameters affecting combustion.

Daniel Fong ~ July 6, 2010

Stochastic Simulation with Application to Materials:

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David Horntrop ~ July 8, 2010

Confidence Bands for Survival Functions Under Semiparametric Random Censorship Models:

Abstract:  We propose a bootstrap-based 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 Kaplan--Meier 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 model-based 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 model-based, 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

The Evolution of a Two-Dimensional Cartesian Drop in an Imposed Linear Flow: The Influence of Surfactant and Surfactant Solubility:

Abstract:  We study the evolution of a two-dimensional Cartesian drop or bubble in an imposed flow in the presence of soluble surfactant, i.e., a surface-active 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 complex-valued 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. High-order numerical schemes have been devised. These include an equal-arclength frame, a spectrally-accurate quadrature method, and a spectrum filter.

Kuan Xu ~ July 20, 2010

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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 higher-order 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:

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Shahriar Afkhami ~ July 29, 2010

Molecular Dynamics Simulation of 2D Dry Granular Materials:

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Xiaoni Fang ~ August 3, 2010

What to Do with Your Numerical Simulations:

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Roy Goodman ~ August 5, 2010