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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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‘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
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