PHYSICS AND ENGINEERING.

Chair: S. Kant Vajpayee, University of Southern Mississippi

THURSDAY MORNING

Mississippi Room

9:00 DESIGN OF SEDIMENT TRAPS FOR REDUCING SILTATION IN HARBORS

T.M. Parchure, US Army Engineer Research and Development Center, Vicksburg, MS 39180

Majority of harbors in the world are man-made and they are located on rivers, lakes, estuaries and ocean shorelines. Natural water depths at these locations is often inadequate for accommodating vessels with large draft. Depending upon the type of vessel, the requirement of water depth could be as high as 18 to 20 meters. Navigation channels and harbor areas need to be dredged to this depth to permit passage of vessels to the berthing and anchoring locations. Sediment from the surrounding shallow areas enters the deep channel under tidal currents, waves and wind, which causes reduction in navigable depth. Periodic removal of this sediment is expensive and the operation may hinder navigation. Providing a sediment trap outside the navigation channel or harbor area is sometimes feasible under certain specific natural conditions. Such a trap collects sediment before it enters the areas of interest and thus keeps them operational. Sand traps do not catch all the sediment moving in the area. Hence dredging of the main areas cannot be completely avoided but the frequency and quantity of dredging in those areas can be significantly reduced. This increases the efficiency of their use and results in cost savings on maintenance dredging. The sediment trap itself must be emptied periodically to keep it functional. This operation can be easily performed independently at convenience without adversely affecting or hindering the navigation in the area. Sediment traps are very uncommon because they can be effective only at highly selective locations and cannot be provided as a general solution to channel sedimentation problem. Physical or numerical model studies are very useful in designing sediment trap. One such trap was designed for the Visakhapatnam Outer Harbor in India in the late 60's. The trap was constructed and has been found to be quite effective. Another trap has been designed at the Rollover Pass, Texas for trapping sediment before it enters the Gulf Intracoastal Water Way (GIWW). The effectiveness of this trap will be known only after it is constructed and starts functioning. Details of design of both the traps will be offered during presentation.

9:20 CRYOGENICS IN MANUFACTURING

S. Kant Vajpayee, University of Southern Mississippi, Hattiesburg, MS 39406-5137

Manufacturing like all other fields of engineering continues to be on the lookout for physical phenomena that can be applied beneficially. Cryogenics is a recent example. Cryogenics-based technologies are making inroads in manufacturing, albeit slowly. Approximately 150 cryogenic processing companies, most of them mom-and-pop operations, exist worldwide. Cryogenic processing is claimed to improve wear resistance of tools and dies. With the resulting longer tool/die life, and reduced machine downtime and maintenance, it lowers operating costs. Simply chilling metals to sub-zero temperatures for stress relief and stabilization has long been practiced by Swiss watchmakers. In recent advances, extreme temperatures and computer-based controls are being used. In one treatment, under deep, dry, controlled systems, processing takes place at around -320[degrees]F, near the temperature of liquid nitrogen. In the shallow-type, the temperature is around -120[degrees]F. The temperature is slowly lowered by a microprocess or-based controller. Items to be treated remain at that temperature for 20 to 60 hours. Such processes are finding applications in manufacturing associated with aerospace, firearms, sports, music, and tooling.

9:40 FINITE ELEMENT ANALYSIS OF THE PRESSURE BEHAVIOR DURING THE PULTRUSION OF COMPOSITES

Tabious [Hayes.sup.*] and Tyrus McCarty, University of Mississippi, University, MS 38677

A common problem associated with the manufacture of composites is the formation of voids in the final product. The voids in the composite adversely affect the strength of the final product. A high pressure rise in the die inlet region can eliminate the voids. The elimination of voids can lead to a better quality final product. The purpose of this research is to determine the effect that various process control parameters have on the pressure rise during the pultrusion process. A numerical approach referred to as the finite element method is employed in this study. Finite element analysis is used to investigate the effect of the process control parameters of pull speed, fiber diameter, and fiber volume fraction on the pressure rise in the pultrusion die region.

10:00 Break

10:20 THE EFFECTS OF MICRO-ADAPTIVE FLOW CONTROL OVER ROTOR BLADES

Tamara [Crawford.sup.*] and Sumon K. Sinha, University of Mississippi, University, MS 38677

Flow separation control is an integral part of controlling the boundary layer of numerous aerodynamic devices. Presently there are devices known as transducers, which are available to aid in flow separation control. The transducer employs thin conductive strips of the same height to transmit vibrations over Mylar film. This is done in an effort to alter the boundary layer. Although some results have been achieved in the modification of a steady boundary layer flow, the obstacle of yielding repeatable results on pitching airfoils is still prevalent. After further analyses of the device, the transducer was redesigned. The modified transducer now has a fixed number of high and low strips which alternate throughout the array. Additionally, the Mylar membrane is pre-tensioned to prevent wrinkles on the outer surface, which if left done could lead to inconsistent and undesired effects. These changes produce better control of membrane vibration. Tests conducted via wind tunnels using the modified transducer produce d repeatable and improved results for flow separation control on a NACA-0012 airfoil. Once further research has been conducted, the modified transducer could propel aerodynamic studies to the next level.

10:40 EFFECT OF HEAVY SUBSTITUTION IN THE BENZENE RING ON THE RING-MODES OF BENZENE II. PHENYLTHALLIUM DICHLORIDE 

Chandra M. [Pathak.sup.*] and B.P. Asthana, Alcorn State University, Alcorn State, MS 39096 and Banaras Hindu University, Varanasi, 221005 (INDIA)

The vibrational frequencies related to the ring modes in benzene remain fairly constant when one of the hydrogen atoms in the benzene ring is substituted with a single lighter atom or a lighter group of atoms. The present work describes the effect of replacing a single hydrogen atom in the benzene ring with a relatively heavier group : [TICI.sub.2]. The studies included the investigation of the infrared spectra of Phenylthallium Dichloride in solid phase covering the spectral region 4000-20 [cm.sup.-1] and the normal coordinate analysis. The far-infrared spectra in the region 500-20 [cm.sup.-1] were recorded and investigated for the first time. The normal coordinate analysis was carried out using the 'least square iterative technique' assuming a geometrical model with a [C.sub.2v] symmetry for the molecule and has supported the frequency assignment quite well. Twenty-eight symmetrized principal force constants and seven interaction force constants have been found to reproduce the observed frequencies. The av erage percentage error between the calculated and observed frequencies has been found to be 2.20% with the standard deviation not exceeding 6.74 [cm.sup.-1]. The standard deviation in the force constants was found to lie in the range 0.002-0.235 mdyne/A.

11:00 VISUAL ANALYSIS OF ELECTROPHORETIC DEPOSITION OF CHAIN MACROMOLECULES WITH A COMPUTER SIMULATION

Vasudevan [Rainamijam.sup.*] and R.B. Pandey, University of Southern Mississippi, Hattiesburg, MS 39406

A computer simulation model is used to study the growth of polymer density and conformation of polymer chains in an electrophoretic deposition process. We consider a discrete lattice of size [L.sub.x] * L * L with a large aspect ratio [L.sub.x]/L. A chain macromolecule of length L, is modeled by ([L.sub.c] + 1)-nodes connected by bonds on a trail of random walk with a self-avoiding-walk constraint. Chains are released from one end (x = 0) of the sample and are driven toward an impenetrable substrate/wall at the opposite end (x = [L.sub.x]). In addition to excluded volume, we consider a polymer-polymer repulsive and polymer-wall attractive interaction. A Metropolis Monte Carlo method is used to trove chain nodes with dynamics such as kink-jump and crank-shaft. As the chains move and deposit on the substrate, polymer density grows and their conformation evolves via relaxation depending on the driving field, temperature, and molecular weight. Attempts are made to visualize this process and analyze the effects o f these parameters.

11:20 MODELING OF HUMAN LEG FOR SYSTEM STABILITY ANALYSIS

Ching-Sia [Lim.sup.*] and J.P. Sharma, University of Mississippi, University, MS 38677

Muscular and skeleton systems are the key elements for strength, support and locomotion to the human system. The shank, a part of the human leg system supports body weight for walking and running. This may be considered as an assembly of mechanical springs, mass and damping elements. Its mode of vibration and stability depends upon stiffness, damping coefficient and their arrangements in the muscular and skeletal system. The modeling and analysis of this system has shown that the rate of change of stiffness and damping takes place in several stages. In this paper four stages have been considered for these changes: stage 1 (child with age up to 3 years); stage 2 (adolescence with age ranging between 3+ years to 20 years); stage 3 (adults in the age group from 20+ years to 65 years) and stage 4 (old age considered beyond 65+ years). Results show that the rate of change in both the stiffness and the damping in the stage 3 are negligible. This also means optimum stability is achieved by the human locomotion syst em between the ages 20 to 60 years. However, towards the end of this stage, the changing rate of the damping elements decreases but not the stiffness. In stage 4, these changes lead to brittleness of the system. The brittleness occurs when the bone loses its pores and permeability and fluids dries out in the muscles fibers. A linear model is used to simplify the analysis of this system. Different cases for each stage are discussed from results computed using the circuit simulation software SPICE as a virtual analog computer.

11:40 ONE-HUNDRED-AND-ONE WAYS TO DEFINE QUALITY

S. Kant Vajpayee, University of Southern Mississippi, Hattiesburg, MS 39406-5137

In this age of quality, the most fundamental question still remains: What is quality? As an abstract term, quality is difficult to define and associate with an acceptable meaning. A large number of professionals whose job is to produce high quality products and services have recently been asked to define quality. More than eighty of them responded with definitions from the sublime to the ridiculous. It is well nigh impossible to have one definition of quality that will satisfy everyone. Quality means different things to different people in different industries in different jobs. Some interesting definitions are: "Quality is when the customer returns and the product doesn't," by Jim Taglieber; "Quality is never having to say you're sorry," by David Laschinger; "Quality is peace of mind," by Mihail Liviu Iliescu; "Quality is working without hassles," by Satish Pendharkar. For mathematically-oriented people, Dave Wiemer offers: "Quality = Maximization of perceived value = Fulfillment of tangible and intangible expectations (Good product or service performance + customer service) Attributes/Cost." A comprehensive meaning of quality, based on these responses and their analysis, will be provided in the presentation.

THURSDAY AFTERNOON

Mississippi Room

1:30 EFFECTS OF THE ELEMENT CONCENTRATION ON THE LIBS SPECTRAL INTENSITY

Sean [Lestrade.sup.*], Chun Fu Su, Fang-Yu Yueh, and Jagdish P. Singh, Mississippi State University, Mississippi State, MS 39762

In recent years, laser-induced breakdown spectrometry (LIBS) has been used to identify the elements and evaluate their concentrations present in solid, liquid, and gas samples. The effect of the sample temperature on the spectral intensities obtained by the LIBS technique is one aspect of these studies. The results have been presented at past MAS annual meetings. This current study focuses on the effects of the elemental concentrations on the LIBS spectral intensities. Two categories of samples are investigated; commercial aluminum alloy samples and vitrified glass samples produced by a transportable vitrification system (TVS). Eight samples of the former and five of the latter were used in this study. Each sample contains more than ten elements. The concentrations of some elements of each sample were analyzed by the atomic absorption technique performed at Mississippi State University. The analyzed results were used as references for the project. The element concentrations differ between samples. The result s of the LIBS technique show that the observed spectral intensities for each element have a linear relationship with the sample concentration. These results were consistent with what was expected. The experimental procedures and more detailed results will be presented.

1:50 AN EFFICIENT MODELING OF WAVEGUIDE-BASED PATCH AND SLOT ANTENNAS FOR SPATIAL POWER COMBINING APPLICATIONS

Milan [Lukic.sup.*] and Alexander B. Yakovlev, University of Mississippi, University, MS 38677-1848

In this paper, a full-wave analysis of waveguide-based patch and slot antennas is proposed for the modeling of spatial power combining amplifier arrays. The analysis is based on the integral equation formulation discretized via the method of moments for the electric and magnetic current density. This results in the Generalized Scattering Matrix for all propagating and evanescent TE and TM modes of a waveguide transition containing interactive patch and slot antennas. In this formulation, the electric dyadic Green's functions are obtained in the form of a double series expansion as the solution of Sturm-Liouville boundary-value problems for layered waveguides. Numerical results are obtained and compared with other numerical methods for the scattering parameters of single patch and slot antennas and aperture-coupled patch arrays operating at X-band. Multimoding and surface-wave coupling effects are studied leading to a better understanding of power combining mechanisms in spatially distributed structures. The proposed numerical-analytical approach can be effectively used in modeling large antenna arrays as encountered with spatial power combiners.

2:10 X-BAND P-I-N DIODE MODULATOR 

Tracy L. Jeffries, University of Mississippi, University, MS 38677

The purpose of this project is to test the feasibility of the design of a shunt switch for radio frequency (RF) waveguides or transmission lines that will be the basis of the design for an X-Band P-I-N diode modulator. The designed circuit consists of an electronic timer, transistor driver, switching diodes, and waveguide. The last phase of this project requires the layout of the driver circuit and fabrication of a printed-circuit (PC) board for the diode driver. This procedure is performed using a numerically controlled milling machine that removes the copper cladding during the engraving process for the circuit. The design of this circuit is examined using three different techniques: an analytical approach, a circuit simulation using the software program PSPICE, and experimental test and verification of the circuit performance. All three methods yielded the same basic results that verified the design of an X-band modulator. This switch is used to square wave modulate a 50 milliwatt flange mount, Gunn diode source in X-band at 1 kilohertz for microwave measurement applications.

2:30 FULLY AUTOMATED BOUNDARY ISOLATION IN HIGH-RESOLUTION SATELLITE IMAGES

Harold A. [Dunsford.sup.*] and John Patrick Lestrade, Mississippi State University, Mississippi State, MS 39762

The advent of 1-meter resolution panchromatic data and 4-meter resolution multispectral data from the IKONOS satellite provide the remote sensing community with new opportunities to study smaller areas, such as roads and urban structures. Our research focuses on the application of grouping algorithms and wavelet analyses to perform image segmentation and classification. Using edge detection algorithms in conjunction with ancillary and contextual information, this classification supplies the necessary constraints for successful fully-automated boundary isolation.

2:50 Break

3:10 ANNULAR DIELECTRIC RESONATOR LOADING A MONOPOLE ANTENNA

Swee H. [Ong.sup.*] and Ahmed A. Kishk, University of Mississippi, University, MS 38677

One widely used antenna is the monopole antenna, which is a wire antenna placed normal to a ground plane. This antenna is normally of a quarter wavelength. It is a narrowband antenna and requires a matching circuit most of the time to achieve a certain bandwidth. Instead of using a matching circuit that increases the antenna losses, we loaded the monopole antenna by an annular dielectric resonator. When the monopole is loaded with the annular dielectric resonator in a symmetric form, the radiation pattern remains the same as that of the unloaded monopole antenna and its matching bandwidth increased. The bandwidth increase is due to the excitation of the zero order mode of the dielectric resonator. Numerical results will be presented to show the effect of the dielectric loading on the antenna characteristics. When the dielectric loading becomes asymmetric, the radiation pattern's shape changes from the monopole type to the broadside type, with the radiation pattern peak points in the direction of the monopole . This is because the monopole in this case excites the non-zero order mode of the dielectric resonator and the radiation pattern is affected by the dielectric resonator mode more than the monopole antenna mode. Within the bandwidth, the radiation pattern is disturbed a little due to the mixing of the monopole mode and the dielectric resonator mode.

3:30 GAMMA-RAY BURST TIME PROFILES: ARE THE INTENSITY PEAKS RANDOMLY DISTRIBUTED IN TIME?

Sarah B. [Nage.sup.*] and John Patrick Lestrade, Mississippi State University, Mississippi State, MS 39762

Gamma-ray bursts (grb) are cosmic explosions that are more powerful than anything since the Big Bang. Their sources are cosmological, i.e., they are located outside our galaxy. Of the thousands of grb detected, we have been able to measure the redshifts of only 18 ranging from z = 0.4 to z [sim] 5. Their causes remain unknown. As a starting point in our research, we are looking for patterns in the grb intensity time profiles. The statistic that we use is the Gini-Simpson Index, a measure of dispersion based on the Poisson distribution. We use this index to determine if evidence of patterns in the distribution of inter-peak times is statistically significant. The arrival times of the intensity peaks in 100 gamma-ray burst time profiles have been measured and the results of the statistical test will be presented.

3:50 Divisional Poster Session

NUMERICAL ANALYSIS OF GROUNDED COPLANAR WAVEGUIDES

Xuexun [Hu.sup.*], Atef Z. Elsherbeni, and Charles E. Smith, University of Mississippi, University, MS 38677-1848

This research is a study of the transmission characteristics of grounded coplanar waveguides (GCPW) with the objective to improve transmission at an operating frequency of 10 GHz. Three types of GCPW configurations are investigated in this study: the ordinary GCPW(geometry A), a GCPW with large air cavity under the center line feed (geometry B), and a GCPW with two small air cavities under the gaps between the feed line and the side grounds (geometry C). The finite difference time domain (FDTD) technique for a meshed computational space with inhomogeneous lossy dielectrics is used to calculate the distribution of electromagnetic fields in these three configurations of GCPW. The computation of transmission parameters, including the attenuation and scattering parameters as a function of frequency are calculated for these examples over a desired frequency range. Two types of boundaries, perfectly electric conductor (PEC) and an absorbing boundary condition (ABC), are applied in this study. Comparison of numeric al results reveal that the geometry B yields the lowest return loss and the lowest attenuation as compared to the other two designs.

ACCURATE CHARACTERIZATION FOR THE DIELECTRIC PROPERTIES OF BIOLOGICAL TISSUES BASED ON MULTI-TERM DEBYE DISPERSIVE RELATION

Atef Z. [Elsherbeni.sup.*] and Mohamed A. Eleiwa, University of Mississippi, University, MS 38677-1848

Debye modeling for the dielectric properties of dispersive materials facilitates its incorporation into the Finite-Difference Time-Domain (FDTD) formulation. This paper generates a comprehensive list of multi-term Debye coefficients for 16 biological tissues. A numerical technique is developed to accurately fit one, two, and three-term Debye equations with the published experimental data of biological tissues. The proposed numerical technique is a two-step procedure. First, Matlab "invfreqs" is used to find the numerator and denominator real coefficients of the polynomial representing the measured dielectric constant [[[epsilon].sup.*].sub.r]([omega]). Then Matlab "residue" is used to convert the obtained quotient of the polynomial form of [[[epsilon].sup.*].sub.r]([omega]) to the partial function expansion from which the corresponding Debye coefficients are calculated. Tables of Debye coefficients (two and three terms) for a wideband of frequency are presented. For verification purposes, the obtained coeffi cients are substituted back into Debye equation to reconstruct the complex dielectric constant [[[epsilon].sup.*].sub.r]([omega]). The reconstructed [[[epsilon].sup.*].sub.r]([omega]) is shown to be in excellent agreement with the measured data over the frequency range 1 Hz to 20 GHz.

ON THE USE OF A GENETIC ALGORITHM FOR PATTERN CORRECTION OF A LINEAR ARRAY

Lee A. Harrison, Raytheon, Inc., Brandon, MS 39042

In recent years, the Genetic Algorithm (GA) has received much attention in areas of electromagnetic optimization problems. Some examples include the design of layered material for broadband microwave absorber, antenna array pattern shaping, minimization of side lobes by array thinning and the design of microwave filters. When one or more elements in an antenna array are damaged, this can lead to pattern deformation, such as a major increase in side lobe level, which may prove to be detrimental to antenna operation. A method for adjusting the functioning elements to compensate for the failing elements would prove valuable in circumstances where replacing the damaged elements is impractical, such as in the battlefield or in satellite communications. In this paper, the GA is studied as a method to correct for element failures in a linear array. This method is based on a steady state genetic algorithm that employs binary coding of the amplitude and phase coefficients of the array elements. Comparisons are made b etween the original and corrected patterns for single and double element failures.

FRIDAY MORNING

Mississippi Room

9:00 A STATISTICAL STUDY OF BACKGROUND NOISE IN GAMMA-RAY BURST TIME PROFILES

Christopher G. [Kelly.sup.*] and John Patrick Lestrade, Mississippi State University, Mississippi State, MS 39762

When the detectors of an experiment in earth orbit record a burst of high-energy gamma radiation, the burst signal is mixed with background radiation. The cause of the burst might be the collision of two neutron stars or a large mass falling into a black hole. The background "noise" is in the form of high-energy photons that emanate from both known sources such as black holes and X-ray binaries and countless unknown sources in the universe. In this project we study the statistical properties of this background radiation. In addition to learning more about the sources of the noise, we hope that this research will lead to a clearer identification of the start and end points of the burst itself.

9:20 ANALYSIS OF CONICAL SHAPED DIELECTRIC RESONATOR ANTENNAS

Yan [Yin.sup.*], Ahmed A. Kishk, and A. W. Glisson, University of Mississippi, University, MS 38677

Last year we had presented a parametric study of dielectric resonator antennas with conical shapes. The antenna was excited by a coaxial probe. This excitation method requires machining of the dielectric resonator to host the coaxial probe inside the dielectric resonator. It also excites several modes that may disturb the radiation pattern symmetry. To isolate the excitation mechanism from the radiation domain, another excitation is considered. The excitation is a narrow slot on a ground plane, where the dielectric resonator resides on the slot. From the other side of the ground plane a microstrip transmission line is coupled to the slot. To achieve this coupling the transmission line is placed normal to the slot. The microstrip line is designed to have a characteristic impedance of 50 U. Thus, it is required to match the antenna input impedance to the transmission line. This is achieved by the proper design for the slot length and width, and also by adding a matching stub to the microstrip transmission line . Through an optimization of these parameters we have achieved a wide frequency matching for the antenna that is more than 50%. This type of excitation is selected also to achieve a wide radiation bandwidth. Samples of these results will be presented with a comparison between the slot excitation and the coaxial probe excitation.

9:40 COMPARATIVE ANALYSIS BETWEEN CONICAL AND GAUSSIAN HORN

Ahmed A. Kishk, University of Mississippi, University, MS 38677

Conical horn antennas are normally excited by circular waveguides. In this case, cylindrical waves with planar phase front propagate inside the waveguide and are transformed to spherical waves in the conical horn with a spherical cap aperture. When the horn apex angle increases the aperture phase error increases causing a reduction in the horn directivity and an increase in the side lobe level. A Gaussian horn introduces a smooth transition between the circular waveguide aperture and the horn aperture in the sense that the cylindrical waves in the waveguide transform to nearly spherical waves inside the horn and then back to cylindrical waves at the horn aperture. The cylindrical wave on the Gaussian horn aperture has smaller phase error. Here, a comparison between the performance of the conical horn and the Gaussian horn will be presented. While it is recommended that the Gaussian horn should be long with small radii ratio between the waveguide radius and the horn aperture, we have analyzed horns with large radii ratio to shorten the horn length and reduce the phase center variation within the frequency band. Reducing the horn length reduces its weight and make it more attractive for space antenna applications. To improve the radiation characteristics of the horn, a corrugated Gaussian horn is studied. This horn is a promising candidate as a feed for parabolic reflectors. Therefore, the horn is analyzed as a feed for the parabolic reflector. The reflector efficiencies such as phase efficiency, spillover efficiency, and total reflector efficiency are computed. The reflector efficiency is improved to about 80%.

10:00 Break

10:20 CHARACTERISTICS OF CIRCULAR DIELECTRIC ROD LOADED WITH CONDUCTING STRIPS USING THE ASYMPTOTIC STRIP BOUNDARY CONDITIONS

Androw E. [Simon.sup.*] and Ahmed A. Kishk, University of Mississippi, University, MS 38677

Circular dielectric guides are used as fiber optics cables. Also, dielectric rods are used as antennas. The dielectric rod can be excited by a circular waveguide. The radiation characteristics of such a dielectric rod antenna can be controlled by the rod length and shaping its end. Here, we load the rod with conducting strips. The characteristics of the rod as a guiding structure is investigated and the supported modes are analyzed. The strips form a helix around the rod with very large number of turns (N) per wavelength. The number of turns is taken to be large in order to apply the approximate asymptotic strip boundary conditions (ASBC) to simplify the analysis. The ASBC is used when the spacing between the helix turns, S, approaches zero. The solutions using this assumption were found to be valid for practical cases when the period [S.sub.i]U [absolute val. of E/10 (]E is the wavelength) and when the pitch angle is 0 degree (circumferential strips) and 90 degrees (longitudinal strips). With this assumption, the tangential fields along the strips are zero electric field and continuous magnetic field, and the tangential electric field in the transverse direction to the strips is continuous. The dielectric rod with such surfaces supports the conducting waveguide modes and the dielectric rod mode. The propagation constant and cutoff frequencies are computed and compared with those of the dielectric rod and the circular waveguide. A mode chart and field distribution for different modes will be presented.

10:40 USE OF THE SYMBOLIC SOFTWARE IN THE DERIVATION OF THE GREEN'S FUNCTION DUE TO A SOURCE IN A GROUNDED DIELECTRIC SUBSTRATE

Jin [Yu.sup.*] and Ahmed A. Kishk, University of Mississippi, University, MS 38677

Analytical solutions of complicated mathematical problems sometimes require high level skilled researchers to perform a lengthy derivation of mathematical expressions. Performing that with a pencil and a sheet of paper sometimes is carried out through several trials of repeating the derivation to assure that the final expressions are correct. Most of the time, one may find that in the middle of the derivation something was written in error from one step to the next, and the error is carried over to the following steps leading to incorrect expressions. For a non-experienced person this may lead to frustration. With the available symbolic software such as Maple, one can derive very complicated expressions and reach simple form of the expressions, as much as possible. These types of symbolic software can be used for many purposes. However, we are presenting a simple example of their possible use. Here, we used Maple to derive the Green's function expressions for a grounded dielectric substrate excited by an ele ctric or magnetic current source. The procedure used in the derivation of Green's functions will be presented. Another advantage of using this symbolic software is that these expressions can be programed in FORTRAN or C by the software, which you can use. A live presentation will be carried out to show the simplicity of the procedure.

11:00 HIGHER ORDER WAVELET-LIKE BASIS FUNCTIONS IN A FINITE ELEMENT ALGORITHM

Elliott [Hutchcraft.sup.*] and Richard K. Gordon, University of Mississippi, University, MS 38677

The objective of this research is to investigate the use of higher order wavelet-like basis functions in the finite element solution of partial differential equations. These wavelet-like basis functions are obtained from the traditional higher order finite element basis functions using an algorithm developed by Stephane Jaffard. In this talk, the generation of the wavelet-like basis functions will be discussed, and numerical results obtained using these basis functions will be presented. Comparisons with results obtained using the traditional higher order finite element basis functions will be considered in order to highlight the advantages and disadvantages of this technique.

11:20 Divisional Business Meeting