Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
C O N T R I B U T E D PA P E R S CHRISTINA AMBROSIO New Jersey Institute of Technology Frequency Control of a Rhythmic Network Through the Interaction of Both Fast and Slow Inputs Rhythmic movements are often controlled by systems containing coupled subnetworks whose oscillations are of different frequencies. We show how fast inhibition from the pyloric network interacts with a slow modulatory input to control the frequency of the gastric mill rhythm of the crustacean stomatogastric ganglion. We deduce that the timing of the pyloric input is crucial in determining what affect it has on the frequency of the gastric network. Over one set of timings, the modulatory input and the pyloric input work together to determine the frequency and over another set of timings, the affect of the pyloric input is mitigated by the modulatory input. P A U L AT Z B E R G E R Rensselaer Polytechnic Institute Thermal Fluctuations of the Immersed Boundary Method as a Model of Small Length-Scale Fluid Dynamics and Applications In many biological fluid problems, it is desirable to model immersed elastic structures that interact with the surrounding fluid. The Immersed Boundary Method (IB) of Peskin has been demonstrated to be a plausible model to numerically simulate such systems. At small length scales, the molecular nature of a fluid system starts to manifest itself in the form of thermal fluctuations of the macroscopic variables. In this poster, we will discuss an extension to the IB method that models the thermal fluctuations by an appropriate stochastic forcing term in the Navier-Stokes equation. We will discuss some diagnostic tests and applications of the new method including the diffusion of coupled particles, polymers, and a model for osmotically induced flows motivated by physiological processes. S I B A B R ATA B A N E R J E E New Jersey Institute of Technology Finite Sample Efficiency of Local Linear Estimation in EXPAR Models (Exponential Autoregressive Model: Non-Linear Time Series) A popular amplitude dependent autoregressive (AR) process is an exponential AR process (EXPAR) model. Estimating the parameters of this model requires nonlinear estimation techniques. A local linearization approach for estimation was suggested by Ozaki (1981). We have studied the finite sample properties of the local linearization approach. Concepts from dynamical systems, such as chaos and limit cycles, have critical roles in the nonlinear autoregressive models. We have also investigated the effects of chaotic forms and limit cycles on statistical estimation in the context of amplitude dependent autoregressive processes. G A U TA M B A R O T New Jersey Institute of Technology (Joint work with I. Joga Rao) Constitutive Modeling of Crystallizable Shape Memory Polymers Shape memory polymers are novel materials that can be easily formed into complex shapes, retaining memory of their original shape even after undergoing large deformations. They can be made to return to their original shape by heating above a recovery temperature. Because of their useful properties they are finding increasing use in a number of cutting edge applications ranging from actuators, MEMS devices, biomedical devices to space technology. 25 Inspite of their technological significance and in marked contrast to the situation in shape memory alloys, there is a dearth of constitutive models that are able to predict the thermo-mechanical behavior of shape memory polymers undergoing complex thermal and mechanical loadings. In this work we outline the development of constitutive equations to model the thermo-mechanical behavior of crystallizable shape memory polymers. This is done using a framework that was developed recently for studying crystallization in polymers. The constitutive equations are formulated in a full thermodynamic framework using the notion of multiple natural configurations. Changes in symmetry, that are crucial for predicting the properties of the crystalline phase, are handled in a direct manner and the symmetry induced in the newly formed crystalline phase depends on the deformation in the rubbery phase. In addition to presenting the main components of such a model, we investigate its response for a crystallizable shape memory polymer undergoing a typical thermo-mechanical cycle. The boundary value problems considered include uni-axial deformations, circular shear and other inhomogeneous deformations. The model is able to capture the main features of a typical shape memory cycle, namely, the drop in stress observed on crystallization and the increase in stiffness of the semi-crystalline polymer. The results of the model are shown to compare favorably with experimental observations. OLEH BARAN New Jersey Institute of Technology (Joint work with Lou Kondic) Sheared Granular Systems: Velocity Profiles, Stresses, and Bagnold Scaling We will present the results of three-dimensional hard-sphere molecular dynamics simulations of sheared granular system in Couette geometry. The simulations use realistic boundary conditions that may be expected in physical experiments. For a range of boundary properties we report velocity and volume fraction profiles and stresses on the boundaries and their distributions. In particular, we simulate "constant pressure'' boundary conditions, and we discuss the differences between the results in constant volume and constant pressure settings. A key observation here is different reactions to the increase of shearing velocity in the system with constant pressure boundary condition compared to the systems with constant volume boundary condition. In the first case, the shearing velocities are increasing, while in the second case, they are decreasing. Analysis of the stresses on the boundaries leads to some interesting new results regarding the influence of the details of averaging procedure on the computed force distributions. Movies of the simulations can be found at http://math.njit.edu/~oleh/shear_shake. LY U D M Y L A B A R A N N Y K University of Michigan (Joint work with Robert Krasny and Demetrius T. Papageorgiou, New Jersey Institue of Technology) Vortex Sheets in a Channel The flow of two immisible inviscid incompressible fluids of different densities and velocities separated by a free interface that supports surface tension is considered. Our approach involves derivation of fully nonlinear evolution equations using long-wave asymptotics and the ensuing analysis and computations of these models. When surface tension is absent, it is shown that the solution of the system of governing equations terminates in a singularity after a finite time. This is achieved by studying a 2 x 2 system of nonlinear conservation laws in the complex plane and by numerical solution of the evolution equations. The form and the time of the nascent singularity are also studied by analyzing the numerically computed Fourier spectrum. The decay of the spectrum is estimated through a least squares fit over the range of wavenumbers with the asymptotic model for the Fourier coefficients. The exact nonlinear problem is addressed numerically using a boundary integral method. Numerical solutions are presented. The results are compared with those of the fully nonlinear long-wave model. 26 J O S E P H B I E L LO New York University (Joint work with A.J. Majda) Rossby Wave Interaction Connecting the Tropics and Midlatitudes: A New Asymptotic Theory and Solitary Waves Equatorial baroclinic Rossby waves are equatorially trapped and can respond to equatorial diabatic heating. Equatorial barotropic Rossby waves also have a significant midlatitude projection. Both of these families of Rossby waves are weakly dispersive in the limit of long zonal wavelength and their wave speeds allow for resonant interactions and intraseasonal timescales. We have developed simplified asymptotic equations for the nonlinear interaction of long wavelength equatorial Rossby waves and barotropic Rossby waves with a significant midlatitude projection in the presence of suitable horizontally and vertically sheared zonal mean flows. The simplified equations allow for nonlinear energy exchange between the barotropic Rossby waves and the baroclinic equatorial waves for non-zero zonal mean vertical shear through wave-wave interactions. Idealized examples in the model demonstrate that midlatitude Rossby wave trains in a baroclinic mean shear can transfer their energy to localized equatorially trapped baroclinic Rossby waves through a nonlinear "westerly wind burst" mechanism. Conversely, equatorially trapped baroclinic Rossby wave trains in the idealized model can transfer substantial energy to the midlatitude barotropic Rossby waves. From the viewpoint of applied mathematics, the asymptotic equations derived here have several novel features. In particular, they admit analytic solitary wave solutions which correspond to interesting localized vortical flows in the equatorial troposphere. A M I TA B H A B O S E New Jersey Institute of Technology Two-Oscillator Model of Ventilatory Rhythmogenesis in the Frog Frogs produce two distinct yet highly coordinated ventilatory behaviors, buccal and lung. Lung ventilation occurs in short episodes, interspersed with periods of buccal ventilation. Recent data suggests that two brainstem oscillators are involved in generating these behaviours, one primarily responsible for buccal ventilation, the other for lung. Here we use a modeling approach to demonstrate that the episodic pattern of lung ventilation might be an emergent property of the coupling between the oscillators, and may not require a perturbing input from another, as yet unidentified but previously postulated, neuronal oscillator. A L O K N AT H C H A K R A B A R T I Indian Institute of Science, Bangalore, India (Joint work with B.N. Mandal and Rupanwita Gayen) Carleman Integral Equations in the Dock Problem The classical dock problem is re-examined here by reducing it to two different Carleman singular integral equations by employing two procedures essentially based on Fourier analysis. The singular integral equations are solved by reducing them to two Riemann Hilbert problems involving the positive real axis. Both the methods produce the same value for the reflection coefficient. The velocity potential describing the motion in water can be obtained easily. 27 J Y OT I C H A M PA N E R K A R New Jersey Institute of Technology (Joint work with Denis Blackmore) Applications of Pitchfork Bifurcations Theorems about pitchfork bifurcations in one-dimension and pitchfork bifurcations of invariant manifolds in higher dimensions are stated and their applications are described. Applications include bifurcations of spheres and bifurcations of invariant circles in discrete dynamical population models. SUNIL DHAR New Jersey Institute of Technology Evaluating Randomness and Related Tests Data generated through various random number generators are evaluated for their randomness. This evaluation is carried through exploratory data analysis and using tests of hypotheses. The goodness-of-fit test evaluates the comparison of these data sets to the uniform distribution. The Kolmogorov-Smirnov goodness-of-fit type hypotheses test is introduced afresh, motivated by meaningfully combining several nonparametric tests. DOBROMIR DIMITROV University of Texas Complete Mathematical Analysis of Predator-Prey Models with Linear Prey Growth and Beddington-DeAngelis Functional Response The dynamics of predator-prey models with a Beddington-DeAngelis functional response and linear intrinsic growth rate of the prey population is fully analyzed. Conditions on local and global stability of the interior equilibrium are established. The equilibria types are determined. All possible global asymptotic behaviors of the system are considered, including the determination of the extinction conditions and existence of periodic orbits. It is shown that mutual interference between predators can alone stabilize predator-prey interactions even when only a linear intrinsic growth rate of the prey population is considered in the mathematical model. Additional biological implications and a set of numerical simulations supporting the analysis are also presented. TOMAS DOHNAL University of New Mexico (Joint work with Alejandro B. Aceves) Localized Stable Solitary Wave Bullets in 2D Periodic Structures We present the problem of optical pulses propagating in 2D photonic structures and propose a study of interaction of such pulses with localized defects. The medium has a waveguide geometry in one transverse direction and the refractive index is periodic in both the direction of propagation and the other transverse direction. The periodicity of the refractive index (i.e.,‘grating') in the direction of propagation is assumed to be in Bragg resonance with the electric field, thus creating strong back reflection. The governing mathematical model is the system of two-dimensional Coupled Mode Equations. We present our numerical results in the search for a stable solution localized in both space and time (i.e., ‘bullet'). In our simulations, we use the Discontinuous Galerkin method with an Additive Runge Kutta time-stepping scheme and we employ Perfectly Matched boundary layers to take care of radiation. We also propose a way of studying interactions of such bullets with localized defects. The expected nature of interactions is either trapping, reflection or transmission. Possible engineering applications of such systems include optical memory, buffers and switches. 28 DIEGO DOMINICI State University of New York at New Paltz Asymptotic Analysis by the Saddle Point Method of the Anick-Mitra-Sondhi Model We consider a fluid queue where the input process consists of N identical sources that turn on and off at exponential waiting times. The server works at the constant rate c and an on source generates fluid at unit rate. This model was first formulated and analyzed by Anick, Mitra and Sondhi. We obtain an alternate representation of the joint steady state distribution of the buffer content and the number of on sources. This is given as a contour integral that we then analyze in the limit N . We give detailed asymptotic results for the joint distribution, as well as the associated marginal and conditional distributions. In particular, simple conditional limits laws are obtained. These show how the buffer content behaves conditioned on the number of active sources and vice versa. Numerical comparisons show that our asymptotic results are very accurate even for N = 20. ANNA FIORENTINO New Jersey Institute of Technology (Joint work with Deepangi Pandit, Milind Misra, Kathleen Gilbert, Rose Dios, and Carol A.Venanzi) Singular Value Decomposition of Analogs of GBR 12909 Analogs of GBR 12909 are drugs that could potentially be used to treat cocaine addiction. Singular Value Decomposition (SVD) is a multivariate analysis technique used to show relationships between the data and the variables associated with the data. The input data consists of the conformations of each analog (analog 2, 728 conformers; analog 3, 739 conformers) along with the eight torsional angles (A1, A2, B1-B6). The data were analyzed separately as well as combined into one 1467 x 8 matrix. Analysis of the scores and loadings plots shows that analog 2 separates into three distinct groups along principal component 1, whose major contributor are angles A1 and A2. Analog 3 also separates into three distinct groups. However the separation is seen on principal component 7 whose major contributor is angle B4. Singular value decomposition has been shown to be helpful in classifying the two analogs of GBR 12909 into distinct groups. This information, along with the molecular shape of representative structures from each group, can be used for pharmacophore modeling with the ultimate goal of designing a drug useful in the treatment of cocaine abuse. IAN S. FISCHER New Jersey Institute of Technology Velocity Analysis of the RSSR Mechanism A formulation is developed using 3x3 dual-number coordinate-transformation matrices to calculate joint speeds in spatial mechanisms with ball joints. The RSSR spatial four-bar mechanism is used as an example, demonstrating how the methodology is amenable to object-oriented programming calculations. The relationship between the calculated speeds and physical speeds in a ball joint is explained. 29 ROY GOODMAN New Jersey Institute of Technology The Two-Bounce Resonance in Hamiltonian Wave-Interactions The two-bounce resonance is a phenomenon that has been seen in the interaction of waves with localized structures and between pairs of nonlinear waves. A new framework, involving the calculation of certain Melnikov integrals and matched asymptotic expansions, is developed for the study of ordinary differential equations describing this phenomenon, yielding new quantitative results for a few such systems. ARNAUD GOULLET New Jersey Institute of Technology (Joint work with Nadine Aubry) Mixing Enhancement by a Dual Speed Rotating Stirrer Stirring is a well-known means of fluid mixing due to the emergence of complex patterns in the flow, even at low Reynolds number. In this work, we consider a stirrer rotating along a circular trajectory at constant speed. The fluid flow, considered incompressible, inviscid and two dimensional (in a circular container), is modeled by a point vortex model consisting of a vortex rotating in a circular container at constant angular speed. The mixing problem is addressed by considering the Hamiltonian form of the advection equations formulated in the frame of reference moving with the vortex. The dynamics of passive fluid particles is considered using dynamical systems theory. The bifurcation diagram reveals the presence of various degenerate fixed points and homoclinic/heteroclinic orbits whose nature varies for different parameter values. By considering an initially concentrated set of marker particles and using the various structures of the phase space in the bifurcation diagram, we generate complex dynamics which, in turn, can generate efficient mixing. The latter is studied using both numerical simulations and physical experiments. RODOLFO HAEDO Rutgers University/New Jersey Institute of Technology (Joint work with Jorge Golowasch) Regulation of Rhythmic Activity in Cultured Neurons by Patterned Electrical Activity The central nervous system of Crustaceans such as crabs and lobsters contains the stomatogastric ganglion (STG) that contains the cellular components of two rhythm generating neural networks, the pyloric and the gastric networks. The neurons that make up these networks are known to be highly plastic both in the intact ganglion as well as in dissociated culture conditions. In the intact network, it is known that the mechanisms of rhythm generation by the pyloric network can switch between two modes: one in which rhythm generation depends on neuromodulatory substances released by the axonal terminals of centrally located projection neurons, and another mode in which rhythmic activity is generated entirely endogenously. The switch appears to be due to changes in the expression of diverse ion channel proteins as a function of the levels of activity expressed by the network. We also know that the intrinsic electrical activity displayed by these neurons can be affected by changes in activity imposed on them either experimentally or by their synaptic neighbors. We are studying the properties of these plastic changes induced by activity. We have observed that freshly dissociated neurons of the crab STG can be induced to change their intrinsic pattern of activity by imposing on them specific patterns experimentally. We observe intrinsically quiescent neurons that can be induced to express bursting (a barrage of action potentials riding on top of a periodic slow wave of depolarization) or tonic firing of action 30 potentials. We also observe older bursting neurons that can be induced to become silent or to tonically fire action potentials. Correlated with these changes, we are measuring the accompanying changes in the expression of different ionic currents. We conclude that these neurons are highly plastic in culture as well as in situ, and we are beginning to understand the biophysical mechanisms of this plasticity. MUHAMMAD HAMEED New Jersey Institute of Technology (Joint work with Michael Siegel, Demetrius T. Papageorgiou, and Charles Maldarelli, City College of New York) Influence of Surfactant on the Breakup of a Fluid Jet The effect of insoluble surfactant on the breakup of a fluid jet surrounded by another viscous fluid at low Reynolds number is studied both theoretically and experimentally. Equations governing the evolution of the interface and surfactant concentration are derived using long wavelength approximations. These one-dimensional partial differential equations are solved numerically using the method of lines for given initial interface and surfactant concentration. The relationship between surface tension and surfactant concentration is given by a linear equation of state. It is found that the presence of an insoluble surfactant at the interface retards the pinch-off process. To check the predictions of our model, we performed experiments both for a clean interface, as well as in the presence of surfactants. We made movies of the pinching bubble and extracted the minimum neck radius. The experimental results support the prediction of the theoretical model that the presence of surfactant slows down the pinch-off process. J. KADAKSHAM New Jersey Institute of Technology (Joint work with Pushpendra Singh and Nadine Aubry) Electrorheological Suspensions of Brownian Particles The transient motion of submicron sized particles of electrorheological (ER) suspensions is simulated using a new finite element scheme in which the Brownian forces are modeled and the rigid body motion inside the particles is enforced using the distributed Lagrange multiplier method. Simulations show that in a nonuniform electric field the spatial distribution of particles depends on the relative magnitudes of the dielectrophoretic (DEP) and Brownian forces. The Brownian forces make the spatial distribution of particles uniform. The DEP forces, on the other hand, make it nonuniform, as the DEP force moves them to the regions of local minimum or maximum of the electric field, depending on the sign of Clausius-Mosotti factor. For positive dielectrophoresis, simulations show that when the DEP force dominates the particles collect near the electrode edges and that when the Brownian forces dominate the spatial distribution of particles remains uniform. When the DEP and Brownian forces are of the same order the particles near the electrode edges are collected relatively quickly, but those away from the edges take much longer to collect, as the magnitude of the DEP force decreases with increasing distance from the electrode edges. 31 B H A R AT K H U S H A L A N I University of Southern California An Ergodic Method for the Vortex Discretized Flows Turbulent flow is characterized by chaotic motion and random vortices. The dynamics and the time evolution of the coherent vortices in a fully developed turbulent flow is not well understood. The interacting vortices generate a chaotic flow and are born from the turbulent nonlinearly evoluting dynamical flow due to the self-organization of the vorticity field. Assuming that the vorticity field is concentrated into the point vortices and peaks at the location of these vortices, the system of nonlinear differential equations obtained by using the delta function singularities into the Biot-Savart integral (which is obtained as a solution to the Poisson equation) governs the velocity in the resultant flowfield. This point vortex relaxed system is a Hamiltonian system and its phase space is a symplectic manifold. In this paper, a scheme will be described which preserves this symplectic structure. The pdf of such a scheme exhibits the Gaussian distribution. The scheme is ergodic in the sense that the ensemble averages equal the time-averages. NICKOLAS KINTOS New Jersey Institute of Technology (Joint work with Farzan Nadim) Modeling Actions of a Neuromodulator on a Rhythmic Network The stomatogastric ganglion (STG) of the crab Cancer borealis includes both the gastric mill and pyloric rhythms, which are coactive and oscillate at different frequencies. The gastric mill rhythm has a period of about 10 sec, while the faster pyloric rhythm has a period of about 1 sec. Moreover, the STG is modulated by over twenty different substances. These substances are released by projection neurons. One such projection neuron is modulatory commissural neuron 1 (MCN1), whose activity elicits a gastric mill rhythm. Previous modeling and experimental work has shown that this gastric mill rhythm is controlled by input from the much faster pyloric rhythm. Recent experiments have shown that bath application of a family of pyrokinin peptides elicits a gastric mill rhythm that is very similar to the MCN1-activated rhythm. We use a compartmental model of this network to examine the similarities and differences between the peptide-activated and MCN1-activated rhythms. This model can be reduced to three variables representing the membrane potentials of two coupled neurons that generate the gastric mill rhythm and a slow modulatory drive. The model can be further reduced to two variables by exploiting the difference in time scales and assuming that the voltage variable in one of the neurons has instantaneous kinetics. Using these models, we show that the effects of the projection neuron MCN1 could be mimicked by the peptide through activation of an inward current in one of the two pattern-generating neurons. EMEK KOSE Drexel University Achieving Wide Field of View Using Double-Mirror Catadioptric Sensors For many applications such as surveillance, medical imaging, photography and robot navigation, it is required that the camera have a wide field of view. Traditional approaches to solve this problem include using a rotating camera, stitching images, complex lenses or multiple cameras. We are proposing a catadioptric sensor with a camera-mirror pair for enhancing the field of view. Devices consisting of a reflective surface (catoptrics) and a camera (dioptrics) are called catadioptric sensors. Our single viewpoint double-mirror system formed of a conical mirror coupled with a proper secondary mirror arises as a solution to a nonlinear first order ordinary differential equation. The ordinary differential equations are obtained as a geometric solution to the problem. Our system is designed to image a plane at infinity, without distortion, requiring no digital unwarping. In this work, we are analyzing the family of conics and corresponding secondary mirrors to obtain a correct image and a large field of view. 32 GREGOR KOVACIC Renesselaer Polytechnic Institute Reverse-Time Correlation and the Architecture of Neuronal Networks Reverse-time correlation measurements give the average orientation dynamics of individual neurons within a highly excited visual cortical neuronal network. The resulting orientation tuning curves provide specific information about the nature of cortico-cortical connections, in particular, the strength and extent of cortical inhibition. We present a set of models that uncover and explain the connection between the experimentally observed tuning curves and the relevant cortical architecture. TA E W O N L E E State University of New York at Stony Brook (Joint work with Y. Yu and M. Zhao) Errors in Numerical Solutions of Shock Physics Problems We seek robust and understandable error models for shock physics simulations. The purpose of our study is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones. The problem is generated by a shock wave interacting with a contact located near a reflecting wall for planar geometry and near the origin for spherical geometry. The transmitted shock reflects between the contact and the wall or origin. For each interaction, we performed numerical simulations on an ensemble of 200 initial conditions perturbed from a base case to find input/output relations for the errors in such interactions. We develop a wave filter, which is the fundamental diagnostic tool that identifies individual waves, and measures the position and the width of numerical waves. We see that a very simple model of the solution error is sufficient for the study of a highly nonlinear problem. The error is linear in the input wave strengths. A composition law for combining errors and predicting errors for composite interactions on the basis of an error model of the simple constituent interactions is formulated and validated. We find how each interaction contributes to the errors at the end of three wave interactions, and factor the sources of errors. TONG H. LEE New Jersey Institute of Technology (Joint work with Chao Zhu) 3-D Simulation of Crossflow Evaporating Sprays in Circulating Fluidized Beds A hybrid Eulerian-Lagrangian method has been applied to simulate the 3-D flow structure with evaporating sprays injected into a circulating fluidized bed of rectangular cross-section. The gas-solid flows are simulated using the multifluid method while the sprays are described using Lagrangian trajectory method. In order to compare with our experimental results, liquid nitrogen sprays in FCC suspension flows are simulated in this study. Our simulation shows that the spray penetration is significantly affected by the solids loading. It is interesting to find that, due to the strong convection, the temperature contours of gas and solids phases do not represent the spray region. It also shows that the spray evaporation leads to a very low solids concentration within the spray region while there is a dense layer of solids surrounding the spray, which agrees with our experimental observations and measurements. 33 S A M U E L C . L I E B E R 1, 2 S T E P H E N F. V AT N E R 2 GISSELA DIAZ2 NADINE AUBRY1 1 Department of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ, 07102 2 Department of Cell Biology & Molecular Medicine, University of Medicine and Dentistry of New Jersey, Newark, NJ, 07101 Aging Increases Stiffness of Cardiac Myocytes Measured by Atomic Force Microscopy We used the nanoindentation function on the atomic force microscope (AFM) to test our hypothesis that aging affects the passive mechanical properties of single cardiac myocytes. A measure of stiffness, i.e. apparent elastic modulus, was determined by analyzing the relationship between AFM indentation force and probe indentation area through modeling of the AFM probe as a blunted conical indenter and following classical infinitesimal strain theory (CIST) assumptions. This is the first study to demonstrate a significant increase (~21 %, P < 0.01) in the apparent elastic modulus of single, aging cardiac myocytes (from 35.1 ± 0.7 kPa (n = 53) to 42.5 ± 1.0 kPa (n = 58)). In conclusion, these data support the novel hypothesis that the mechanism mediating increased stiffness in adult hearts resides, in part, at the level of the myocyte. BIYUE LIU Monmouth University Computer Simulation of Blood Flow in Curved Atherosclerotic Arteries Factors influencing blood flow patterns in curved atherosclerotic arteries are investigated by computer simulations. Numerical calculations of pulsatile blood flow in curved arteries with or without the presence of plaque are performed to examine the effects of the geometry of the artery on the hemodynamic characteristics such as the wall shear stress, blood pressure and flow pattern. Three-dimensional incompressible Navier Stokes equations are used as the governing equations. The finite element method is applied to spatial variables for solving the differential equations numerically. Computations are carried out with various values of physiological parameters. The numerical results demonstrate how the wall shear stress and blood pressure are affected by the angle of the curved artery, the presence of plaque and Reynolds number. R O B E R T LO M A U R O Rutgers University (Joint work with Lian Zhou and Farzan Nadim) Spike-Mediated Facilitation in the Pyloric Network of the Crab Cancer Borealis The synapse from LP to PD neurons in the crab Cancer borealis has both a graded and a spike-mediated component. It has previously been shown that the graded component is depressing. In this study, we show that the spike-mediated component of this synapse is facilitating. We have developed a model of synaptic release based on quantal analysis. We used this model to fit data from both the graded and the spike-mediated components of the LP to PD synapse and thus quantified the opposite dynamics of these two components. This facilitation is determined by the interspike interval with shorter intervals being more likely to facilitate than long intervals. 34 VA L E R Y LU K YA N OV New Jersey Institute of Technology (Joint work with G.A. Kriegsmann) On Computation of Electromagnetic Field in Photonic Crystals We show how to apply the scattering matrix approach for computation of the electromagnetic field in periodic structures. According to this method, we need at first to find a generalized scattering matrix for one element of the periodic structure and then use it to calculate transmission and reflection coefficients. We show that evanescent waves play an important role in periodic structures such as photonic crystals. By comparing the numerical results obtained from the solution of an integral equation on two cylinders in the waveguide and a solution based on the scattering matrix approach, we conclude that taking into account several evanescent modes gives a good approximation for the solution. MARC Q. MA New Jersey Institute of Technology (Joint work with Honghua Li, Kai Zhang, Guohong Hu, Hui-Yun Wang, and Minjie Luo) Iterative Support Vector Machine Classification of Data in High-Throughput Multiplex Genotyping Microarray Technological breakthroughs have enabled researchers to amplify thousands of single nucleotide polymorphisms as genetic markers in one multiplex polymerase chain reaction (PCR) microarray assay. However, apparently there is a lack of algorithmic and software support for automation in making accurate genotype calls for all the microarray assays. We report an algorithmic and software solution for performing accurate genotype calls. We use support vector machine (SVM), a commonly used supervised machine learning technique, to handle classification of two-color genotyping data generated from Genepix or Imagene. The SVM learns from a set of normalized data with known genotype calls, and the learned classifiers are used in the subsequent classification of new data. The learning step and data re-normalization are iterated until the normalized data for heterozygous alleles in the learning set is centered around the bisector of the first quadrant of the coordinate system. These iterations result in a canonical system of classifiers. We use a similar iterative approach in the subsequent classification step. This iterative SVM classification algorithm results in highly accurate genotype calls (99% accuracy confirmed by two other independent methods), and it is suitable for high throughput data analysis. YURIY MILEYKO New Jersey Institute of Technology Intersections of Swept Manifolds The problem of finding and characterizing intersections of manifolds is analyzed. Manifolds under consideration are assumed to be swept manifolds, where a swept manifold is defined as a set of trajectories of a differential equation, with the initial set being a smooth manifold of codimension 1. An approach to the general manifold intersection problem is developed using the fact that any smooth manifold is a locally swept manifold. Advantages and drawbacks of this approach are presented along with several algorithms for finding the intersection of two swept surfaces. Also, a characterization of transverse intersections based on homology theory is presented, which provides an efficient method of detecting transverse intersections of triangulated representations of objects. 35 P E T R O N I J E M I LOJ E V I C New Jersey Institute of Technology Solvability and the Number of Solutions of Hammerstein Equation We will discuss the (unique) approximation solvability and the number of solutions of nonlinear Hammerstein operator equations: x-KFx=f in Banach spaces using a projection-like method, Brouwer’s degree and the degree theory for condensing vector fields. The linear part K is assumed to be either selfadjoint or nonselfadjoint. Depending on the structure of the linear part, we impose different types of conditions on the nonlinearity N that imply a priori estimates on the solution set of the equation. Unlike earlier studies, we consider also nonlinearities that are the sum of strongly monotone and k-ball condensing maps. Applications to Hammerstein integral equations and BVP’s for ordinary and partial differential equations will be given. MILIND MISRA New Jersey Institute of Technology (Joint work with Amit Banerjee, Rajesh N. Davé, and Carol A. Venanzi) Fuzzy Clustering as a Means of Classifying Molecular Conformations The identification of natural groups among hundreds of molecular conformations requires the selection of features that allow generation of similarity data and subsequent detection of natural groupings. Fuzzy c-means (FCM) clustering is a promising technique for classifying and selecting representative molecular conformations. This paper involves the use of FCM-based clustering on a class of drugs that might be potentially useful in the treatment of cocaine abuse. Over 700 conformers of an analog of GBR 12909 were identified by a random search technique and subjected to fuzzy clustering, which involved a five step protocol - identification of a minimal set of features to represent the conformers; definition of a suitable feature vector based on the set of minimal features, to be used as the input for the FCM algorithm; implementation of the algorithm; identification of a representative conformation for every natural group and validating the resulting partition. We validate the results using several cluster validity measures from the literature, such as the partition coefficient, partition entropy and the compactness indices. ROBERT M. MIURA New Jersey Institute of Technology Study of Ion Dispersal in the Brain-Cell Microenvironment In the brain-cell microenvironment, an increase in the extracellular potassium concentration [K+] can depolarize neurons and affect their excitability, as well as affect glial cells. The K+ dynamics result from diffusion in the extracellular and intracellular spaces, passive and active ion transport across the membranes, and a spatial buffering mechanism. From a realistic tissue structure, we build a theoretical model and study the migration of K+ due to the injection of KCl, as well as the induced migrations of Na+ and Cl-. A square lattice is used on which the K+, Na+, and Cl- particles move with discrete temporal and spatial steps. Different rules for each ion determine their movements according to the lattice Boltzmann equations and membrane current equations. We show several important effects due to the microscopic structure of the brain-cell environment. A new mechanism of buffering potassium, namely, temporal buffering, is proposed and demonstrated. 36 RICHARD O. MOORE University of Delaware Pulse Dynamics in Thermally Loaded Optical Parametric Oscillators Optical parametric amplification is the process whereby optical power at one frequency is converted to optical power at another frequency (or frequencies) through the nonlinear polarization response of a material. Gain devices based on optical parametric amplification have several attractive features, such as large bandwidth, narrow linewidth, tunability and potentially noiseless operation, that make them an attractive alternative to competing amplification and frequency conversion devices. They can, however, be subject to problems related to self-heating at high-powered continuous-wave operation. Here, we consider a reduced model of an optical parametric oscillator (an optical parametric amplifier inside a cavity) to analyze the effect of self-induced heating on pulse interactions. D E M E T R I U S T. P A P A G E O R G I O U New Jersey Institute of Technology (Joint work with J.-M. Vanden-Broeck) Capillary Waves in Electrified Fluid Sheets Large amplitude capillary waves on fluid sheets are computed in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The fluid is taken to be inviscid, incompressible and nonconducting. Traveling waves of arbitrary amplitudes and wavelengths are calculated and the effect of the electric field is studied. The solutions found generalize the exact symmetric solutions of Kinnersley (Exact large amplitude capillary waves on sheets of fluid, J. Fluid Mech., 77 (1976) 229-241) to include electric fields, for which no exact solutions have been found. Long wave nonlinear waves are also constructed using asymptotic methods. The asymptotic solutions are compared with the full computations as the wavelength increases, and agreement is found to be excellent. In addition, we show that there exist antisymmetric waves extending those of the non-electrified case. These waves are calculated numerically for arbitrary amplitudes and wavelengths and the effect of the electric field is studied. The numerical procedure is based on a reformulation of the problem as a system of nonlinear integro-differential equations. MICHELE PICARELLI St. Peter’s College A Gibbs Sampling Approach To Maximum A Posteriori Time Delay And Amplitude Estimation Research concerned with underwater propagation in a shallow ocean environment is a growing area of study. In particular, the development of fast and accurate computational methods to estimate environmental parameters and source location is desired. In this work, only select features of the acoustic field are investigated, namely, the time delays and amplitudes of individual paths, the signal-to-noise ratio, and the number of multi-path arrivals. The amplitudes and delays contain pertinent information about the geometry associated with the environment of interest. Estimating the time delays and amplitudes of select paths in a manner that is both accurate and time efficient, however, is not a trivial task. A Gibbs Sampling Monte Carlo technique is proposed to recover these arrivals and their features. The method is tested on synthetic data as well as data from the Haro Straight experiment for the estimation of the number of arrivals, the amplitude and time delay associated with each arrival, and the variance of noise. Signals involved in shallow water propagation closely resemble signals obtained in other areas such as radar and communication problems. Therefore, the estimation techniques presented here may be useful in these, among several other applications. 37 S H R I R A M P I L L A PA K K A M New Jersey Institute of Technology (Joint work with Pushpendra Singh) Transient Motion of Bubbles Rising in Viscoelastic Liquids The transient behavior of Newtonian bubbles rising in Oldroyd-B liquids is investigated numerically using a threedimensional finite element code which uses the level set method to track the interface. We have used our code to analyze the transient behavior over a range of Deborah numbers and polymer concentration parameter. When Deborah number is O(1) the rise velocity of the bubble oscillates before reaching a steady value. The frequency of oscillation and the amplitude of overshoot and undershoot vary with the rheological property of the fluid, and the volume of the bubble. The evolution of negative wake during transience, as a function of the Oldroyd-B model parameters, is also analyzed. PA S C A L E R A B B A H Rutgers University/New Jersey Institute of Technology (Joint work with Cristina Soto-Trevino and Farzan Nadim) A Multi-Compartmental Model of the Electrically Coupled AB-PD Neurons, the Lobster Pyloric Pacemaker The anterior burster (AB) and pyloric dilator (PD) neurons of the spiny lobster stomatogastric ganglion (STG) constitute the pacemaker unit of the rhythmically active pyloric network. In the intact pyloric network, these cells are electrically coupled and burst synchronously. In isolation, however, each of these neurons has different activities. While the AB neuron is an endogenous burster that produces oscillations in a wide frequency range (frequency can be varied by current injection), the PD neuron typically spikes tonically in the absence of current injection. Our goal is to model these two neurons, as realistically as possible, reproduce the synchronous bursting of the coupled neurons and their qualitative activity in isolation. Intuitively, the electrical coupling should produce synchronous AB-PD oscillations. However, the coupling could also cause the PD neuron to prevent the AB neuron from bursting. Each neuron was modeled with two compartments using mostly current measurements from lobster STG cultured neurons. The experimental data was used to tune the model to qualitatively mimic the activity of the biological neurons under various current injections and different modulatory regimes (Front end ON and OFF). ROSA RODRIGUEZ Rutgers University/New Jersey Institute of Technology (Joint work with Luis Correa and Jorge Golowasch) Is Neuronal Rhythmic Activity Dependent on Network Activity Itself? The stomatogastric ganglion (STG) of crustaceans contains two rhythm generating neural networks that drive muscles of two of the chambers of the animal’s complex stomach. The rhythmic activity produced by one of these networks, the pyloric network, is conditional upon the presence of neuromodulatory substances released by axonal terminals. If these terminals are destroyed, or action potential transmission along these axons is inhibited (decentralization), the rhythmic activity of the pyloric networks ceases. However, this activity is restored spontaneously to stable levels comparable to the pre-decentralization state after ~55hrs of decentralization in vitro. We have proposed that a reorganization of internal components of the pyloric network (synaptic weights, intrinsic properties) occurs during this process. Our experiments are testing the hypothesis that it is the absence of rhythmic electrical activity of the network that drives this reorganization. We do that by modifying the levels of activity in different ways before decentralization and measuring the dynamics and time of recovery after the subsequent decentralization. Our experiments suggest that activity seems to play an important role but we cannot exclude other factors, possibly trophic effects by the centrally produced neuromodulatory substances. 38 MAX ROMAN New Jersey Institute of Technology (Joint work with Nadine Aubry) Design and Fabrication of Electrostatically Actuated Synthetic Microjets An analysis of the coupled physics (electrostatic/solid membrane deformation/ generated fluid flow) of a synthetic microjet actuator is presented. A reduced order model, based on the unsteady governing differential equations, is used for predicting the generated flow. The influence of the membrane and throat geometry and of the driving frequency on the performance of the jet is evaluated. The results are validated using CFD. The insight obtained from the analysis is incorporated into the design of a MEMS-scale device. A two wafer bonded sandwich is proposed for the fabrication of the devices. A N T H O N Y R O S AT O New Jersey Institute of Technology (Joint work with Denis Blackmore, Liam Buckley, Chris Oshman, and Mark Johnson) Experimental, Simulation and Dynamical Analysis of Galton's Board An investigation of the dynamics of a single particle rolling down a Galton's board is carried out in detail. Experiments on an actual Galton's board apparatus, molecular dynamics based simulations, and simplified discrete dynamical systems models are used to analyze and predict the motion of the particle. Good qualitative agreement, and reasonably good quantitative agreement, among the experimental, simulation and dynamical models are found with regard to such properties as lateral diffusion coefficients and end distributions. T E T YA N A S E G I N New Jersey Institute of Technology (Joint work with L. Kondic and B.S. Tilley, Franklin W. Olin College of Engineering) On Undercompressive Shocks in Gas-Liquid Countercurrent Flow in an Inclined Channel We consider the countercurrent flow of two incompressible immiscible viscous fluids in an inclined channel. The lower fluid is denser than the upper one. This configuration is relevant to air-water systems. Flow is driven by an imposed pressure gradient and possibly gravity. From a lubrication approximation based on the ratio of the channel height to the downstream disturbance wavelength, we derive a nonlinear system of evolution equation that governs the interfacial shape separating the two fluids, and the leading-order pressure. This system includes the physical effects of advection, capillarity, inertia and hydrostatic pressure. To close this system, we consider the prescribed inlet interfacial height and gas volumetric flow rate, since this is relevant to previous mathematical approaches to this problem. However, another approach more relevant to experiments is to fix pressure drop and liquid volumetric flow rate. The latter case results in an additional constraint imposed on the flow. In both of these driven systems, Lax shocks, undercompressive shocks and rarefaction waves are investigated. Numerical simulations show that these two scenarios lead to different dynamics. In case of flow driven by liquid flow rate and gas pressure drop, we observe unsteady interfacial profiles. 39 A S H I S H TA N E J A Levich Institute at the City College of CUNY Remobilization of Spherical Bubbles Rising in a Micellar Surfactant Solutions It is known that the velocity of bubbles rising by buoyancy in dilute surfactant solutions is reduced because of the presence of surfactants. In this presentation, we will focus on a regime in which the surfactant concentration, rather than being dilute, is large enough that aggregates begin forming in the bulk (i.e., monomer concentrations larger than the critical micelle concentration or CMC). The aggregates exchange with surfactant monomer. We assume that this kinetic exchange is much faster than the rates of bulk diffusion of monomers and aggregate so that there is a local equilibrium in which aggregates maintain the monomer concentration at the CMC. For this kinetically fast regime, as the bulk concentration approaches the CMC, a micelle zone forms at the back end adjacent to the bubble surface since the accumulation of convected surfactant at the back end leads to concentrations of monomer larger than the far field bulk value. In this zone, the concentration of monomer is uniform; the zone is surrounded completely by a micelle free region which extends to the far field. If the kinetic exchange of surfactant between the bulk and the surface is fast relative to the micelle/monomer exchange, the monomer concentration in the sublayer adjacent to the surface is in equilibrium with the surface. In the part of the surface at the back end adjacent to the micelle zone, the uniform concentration in the zone maintains a uniform surface concentration. This eliminates the surface gradient which immobilizes the surface, and the interfacial mobility and terminal velocity are increased. We obtain solutions for this remobilization of the surface and increase in velocity as the CMC is approached by solving the surfactant mass transport equations for the monomer and aggregate to obtain the surface concentration and interfacial tension gradients, and the hydrodynamic equations for the bubble motion (in the regime of zero inertia) due to buoyancy and the surface gradients to obtain the velocity. From these solutions, we determine the extent of remobilization as a function of the bulk concentration near the CMC. D M I T R I T S E LU I KO New Jersey Institute of Technology Numerical and Analytical Studies of Modified Kuramoto-Sivashinsky Equations Arising in Interfacial Electrohydrodynamics We consider equations that arise in the modeling of the wave motion in a thin film of a perfectly conducting viscous fluid falling down an inclined plane when a uniform electric field is applied normal to the surface. These are modified Kuramoto-Sivashinsky equations with an additional non-local term due to the Maxwell stresses exerted at the interface by the electric field. We make these equations 2pi-periodic using a rescaling of the variables. First, we perform a basic linear stability analysis and find the stability regions of the parameters of the equations. Then we solve these equations numerically for different sets of the parameters using a Fourier spectral method. To increase stability of the scheme we use the method of integrating factors and approximate the time derivative by the fourth-order Runge-Kutta formula. We find that in regions where the electric field is destabilizing, the solutions seem to retain analyticity but evolve in a dynamically complex manner. We also report some conjectures regarding analyticity properties of the solution. 40 DARKO VOLKOV New Jersey Institute of Technology (Joint work with Demetrius T. Papageorgiou and Peter G. Petropoulos) Accurate and Efficient Boundary Integral Methods for Electrified Liquid Bridge Problems We derive and implement boundary integral methods for axisymmetric liquid bridge problems in the presence of an axial electric field. The liquid bridge is bounded by solid parallel electrodes placed perpendicular to the axis of symmetry and held at a constant potential difference. The fluid is assumed to be non-conducting and has permittivity different from that of the passive surrounding medium. The problem reduces to the solution of two harmonic problems for the fluid and voltage potential inside the bridge and another harmonic problem for the voltage potential outside the bridge. The shape of the moving interface is determined by imposition of stress, kinematic and electric field boundary conditions, the former condition accounting for discontinuous electric stresses across the interface. We propose fast and highly accurate boundary integral methods based on fast summations of appropriate series representations of axisymmetric Green's functions in bounded geometries. We implement our method to calculate equilibrium shapes for electrified liquid bridges in the absence and presence of gravity. Such calculations appear in the literature using finite element methods and our boundary integral approach is a fast and accurate alternative. YUAN-NAN YOUNG Stanford University Mixing of Two-Phase Flows We simulate the coupled Navier-Stokes-Cahn-Halliard equations (NS-CH system) to study how the characteristic domain size scales with diffusion in spinoidal phase separation stirred by a chaotic background flow. As in the passive mixing case (Berthier et al, 2001), scaling of the characteristic domain size with the effective diffusion coefficient exists, and we find that the scaling exponent may change from 1/3 (with no capillary stress) to 1/2 if capillary stress is large. Drop size distribution from our turbulence simulations of two-phase flows is found to be in agreement with those from experiments on mixing of two immiscible fluids (Muzzio et al, 1991 Martinez-Bazan et al, 2000 and Lemenand et al, 2003). We also propose a new numerical algorithm for simulating two immiscible fluids with non-diffusive interfaces by combining the particle level set method with phase-field models. From turbulence simulations of non-diffusive twophase flow, we find quantities such as the number of drops and the total circumference of the drops to scale with the surface tension at the statistical equilibrium state. YILI ZHANG Rutgers University/New Jersey Institute of Technology (Joint work with Jorge Golowasch) Modeling Rhythmic Activity Recovery after Decentralization The stomatogastric ganglion (STG) of crustaceans is part of the animals central nervous system and contains two rhythm generating neural networks that drive muscles of two chambers in the animal anterior digestive system. The rhythmic activity produced by the pyloric network, which is one of these two networks, depends upon the axonal terminals’ tonic release of neuromodulatory substances. After these terminals are destroyed or action potential transmission along these axons is inhibited (decentralization), the rhythmic activity of the pyloric networks ceases. The rhythmic pyloric activity is restored spontaneously several hours after decentralization. The process of activity recovery follows a very complex dynamics that involves the alternating turning on and off of the pyloric rhythm (that we term 41 ‘bouts’) for a long period of time before a stable rhythm is recovered. We are studying the dynamics of rhythmic activity recovery using conductance-based models of the pyloric network. We model decentralization by turning off ionic conductances known to be activated by these neuromodulatory substances. We have proposed that a reorganization of internal components of the pyloric network (synaptic weights and intrinsic properties) occurs during this process. In these models, we are studying the effects of long-term regulation of ionic currents via intracellular feedback mechanisms that are sensitive to neuronal activity. Influx of Ca++ via Ca++ currents leads to its accumulation inside neurons of the network. We use Ca++ as our activity "sensor". We have found that simple rules of how Ca++ feeds back onto ionic currents to regulate their levels of expression allow these networks to express rudimentary "bouts" resembling those observed during the recovery of pyloric activity after decentralization. YONGMIN ZHANG State University of New York at Stony Brook (Joint work with James Glimm, R. Paul Drake, Srabasti Dutta, and Xiaolin Li) Supernova and ICF Simulations by Front Tracking Method We have recently developed a curved geometry front tracking algorithm for interface instabilities. The code has been verified by comparing simulations to analytical solutions and various experiments. We present a simulation of a laser compressed supernova experiment performed at the National Laser Users Facility (NLUF) at the University of Rochester (experiment NLUF2). We demonstrate the agreement of our simulation with NLUF2 experiment. We have extended the algorithm and its physical basis for preshock interface evolution due to radiation preheat. ICF simulations have also been carried out in both single and random modes. We also present a tracked sharp flame numerical model for thermonuclear explosion of Chandrasekhar mass white dwarfs, also is called Type Ia supernova. Simulations for turbulent combustion in Type Ia supernova have been carried out by using this model. LIN ZHOU New Jersey Institute of Technology (Joint work with G.A. Kriegsmann and P. Petropoulos) Perturbation Analysis on Dispersive Properties of Microstrip A systematic mathematical approach is given to find the dispersive properties of a microstrip at low frequencies. Specifically, an asymptotic method is employed to determine an approximation of the propagation constant when the wavelength is much bigger than the thickness of the substrate. A system of boundary value problems are deduced and solved numerically using integral formulations involving Green's function. The solvability conditions for these problems yield an aymptotic approximation to the propagation constant. IVAN ZORYCH New Jersey Institute of Technology (Joint work with D. Madigan) A Bayesian Modeling Approach to Location Estimation The Bayesian modeling approach is used to study wireless location problems via Markov Chain Monte Carlo methods in DAGs (directed acyclic graphs). Our key finding is that a hierarchical Bayesian approach, incorporating prior physical knowledge about the nature of Wi-Fi signals, can provide good location estimates. Two different data sets are used to illustrate the method 42