O sistema de FitzHugh-Nagumo possui um tipo especial de solução chamadas ondas viajantes, que são da forma &micro(x,t)=&oslash(x+ct) e w(x,t)=&#1137(x+ct) e além disso sabe-se que ela é estável. Tem-se o interesse de obter uma caracterização de seu perfil (&oslash,&#1137) e sua velocidade de propagação c. Fazendo uma mudança de variáveis, transformamos tal problema em encontrar equilíbrios de uma equação não local. Esta equação não local possui uma onda viajante de velocidade zero cujo perfil é o mesmo da equação original e, com esta equação, é possível aproximar, ao mesmo tempo, o perfil e a velocidade da onda viajante. Como a intenção é usar métodos numéricos para aproximar tais soluções, o problema não local foi analisado em um intervalo limitado verificando a existência e algumas propriedades espectrais em domínios limitados. / The FitzHugh-Nagumo systems have a special kind of solution named traveling wave, which has a form &micro(x,t)=&oslash(x+ct) and w(x,t)=&#1137(x+ct) and furthermore it is a stable solution. It is our interest to obtain a characterization of its profile (&oslash,&#1137) and speed of propagation c. Changing variables, we transform the problem of finding these solutions in the problem of finding an equilibria in a nonlocal equation. This nonlocal equation has a traveling wave with zero speed whose profile is the same of the original equation, and the nonlocal equation is used to approximate the profile and speed of the traveling wave at the same time. To use numerical methods for approximating such solutions, the nonlocal problem was analyzed in a finite interval to check that the existence and some spectral properties on bounded domains.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING / Includes bibliographical references. / by Scott Roger Shepard. / M.S.

The need for potable water is increasing with the ever-increasing world population. Further development of fast, portable, and cost effective analytical tools is necessary in order to create diagnostic techniques capable of supporting the water needs of the world’s population. Within the last decade microfluidics and Lab-on-a-Chip (LOC) technologies have increased the portability and speed of detection for aqueous samples. Photolithography techniques serve as a cost effective fabrication tool to create LOC electrodes on the micron scale. An in-depth look at the fabrication process is undertaken in this paper in order to further the development of micro-scale detection techniques. An electrode array capable of detecting multiple targets within one aqueous sample was designed and fabricated. The electrode array was assessed for performance characteristics to determine if reproducibility is possible. The fabrication process was also detailed for a new chemical separation technique, traveling-wave electrophoresis (TWE). TWE could serve as a separation tool capable of separating out specific charged molecules for biological and chemical samples. The TWE device was assessed on the capabilities to move charged molecules.

This thesis takes a fresh approach to cochlear mechanics. Over the last quarter of a century, we have learnt that the cochlea is active and highly tuned, observations suggesting that something may be resonating. Rather than accepting the standard traveling wave interpretation, here I investigate whether a resonance theory of some kind can be applied to this remarkable behaviour.¶ A historical survey of resonance theories is first conducted, and advantages and drawbacks examined. A corresponding look at the traveling wave theory includes a listing of its short-comings.¶ A new model of the cochlea is put forward that exhibits inherently high tuning. The surface acoustic wave (SAW) model suggests that the three rows of outer hair cells (OHCs) interact in a similar way to the interdigital transducers of an electronic SAW device. Analytic equations are developed to describe the conjectured interactions between rows of active OHCs in which each cell is treated as a point source of expanding wavefronts. Motion of a cell launches a wave that is sensed by the stereocilia of neighbouring cells, producing positive feedback. Numerical calculations confirm that this arrangement provides sharp tuning when the feedback gain is set just below oscillation threshold.¶ A major requirement of the SAW model is that the waves carrying the feedback have slow speed (5-200 mm/s) and high dispersion. A wave type with the required properties is identified - a symmetric Lloyd-Redwood wave (or squirting wave) - and the physical properties of the organ of Corti are shown to well match those required by theory.¶ The squirting wave mechanism may provide a second filter for a primary traveling wave stimulus, or stand-alone tuning in a pure resonance model. In both, cyclic activity of squirting waves leads to standing waves, and this provides a physical rendering of the cochlear amplifier. In keeping with pure resonance, this thesis proposes that OHCs react to the fast pressure wave rather than to bending of stereocilia induced by a traveling wave. Investigation of literature on OHC ultrastructure reveals anatomical features consistent with them being pressure detectors: they possess a cuticular pore (a small compliant spot in an otherwise rigid cell body) and a spherical body within (Hensens body) that could be compressible. I conclude that OHCs are dual detectors, sensing displacement at high intensities and pressure at low. Thus, the conventional traveling wave could operate at high levels and resonance at levels dominated by the cochlear amplifier. ¶ The latter picture accords with the description due to Gold (1987) that the cochlea is an ‘underwater piano’ - a bank of strings that are highly tuned despite immersion in liquid.¶ An autocorrelation analysis of the distinctive outer hair cell geometry shows trends that support the SAW model. In particular, it explains why maximum distortion occurs at a ratio of the two primaries of about 1.2. This ratio also produces near-integer ratios in certain hair-cell alignments, suggesting that music may have a cochlear basis.¶ The thesis concludes with an evaluation and proposals to experimentally test its validity.

by L.J. Chu and J.D. Jackson. / "April 28, 1947." / Bibliography: p. 25-26. / Army Signal Corps Contract No. W-36-039 sc-32037

External modulators will become key components in fiberoptical communica- tion systems operating at 40Gbit/s andhigher bitrates. Semiconductor electro- absorption (EA)modulators are promising candidates because of their high-speed potential, and their process compatibility with thecorresponding semi- conductor laser light sources. Thetraveling-wave (TW) electrode concept for electro-opticmodulators has been used for a long time in order to resolvethe con°ict between high modulation depth and highmodulation bandwidth. Re- cently, it has been adopted for EAmodulators as well. This thesis presents the work carried out on design,fabrication and analysis of traveling-wave EA modulators(TWEAM) based on InP-InGaAsP. The lengths of TWEAM arecomparable to the lengths of their lumped counterparts. Theexperimental data of this work were analyzed in order show thatthe traveling- wave concept results in better performance evenfor short EA modulators. One key issue is the impedancematching. The low intrinsic characteristic modulator impedancehas to be matched with a corresponding load. In this case, theTW con figuration leads to a much higher bandwidth than for alumped EA modulator with the same length and the same connectedload. An InP process was developed allowing the fabrication ofTWEAM with integrated termination resistors. Experimentalmicrowave properties were ob- tained for different TWEAMgeometries. It is reported on long TWEAM that showstate-of-the-art bandwidth. A 450&#956m long TWEAM reached43GHz, and 67GHz (beyond characterization limit) were indicatedfor a 250&#956m device. The experimental results onmicrowave properties were compared to full-wave, and circuitmodel simulations. The analysis reveals an impedance bandwidthtrade- off for the cross sectional electrode configuration. Results of a new high-impedance design in form of asegmented TWEAM are presented. The devices were processedwithin the frame of this work and record bandwidth performanceis reported. At 50&#937­ impedance a bandwidth in the90GHz region was indicated.

Laminar flow control holds major promise for increasing aircraft efficiency and increasing laminar flow over aerodynamic surfaces could decrease drag by up to 30 percent. The Flight Research Lab at Texas A&M University has studied laminar flow over a wing with 30 degrees of leading edge sweep with Discrete Roughness Elements (DREs) installed and has indicated that DREs can be used to increase laminar flow at Reynolds numbers up to 7.5 million at Mach 0.3. A new project, termed SARGE, has been commissioned in conjunction with NASA for studying DREs on a swept wing glove at conditions relevant to jet transports. The SARGE project must have an instrumentation system capable of accurately measuring flow conditions and transition location on the suction side of the glove. Infrared (IR) thermography has been selected as the primary transition detection tool. A heat transfer analysis has shown that solar radiation will warm the surface of the glove above the adiabatic wall temperature and therefore the laminar region will appear to be warmer. The FLIR SC8000 IR camera has been selected for this application due to its ability to produce high-resolution images in the appropriate IR band. High quality air data is also required for the experiment. A five-hole probe will be used to measure flow angle and velocity near the glove. This instrument will provide meanflow conditions due to its limited frequency response. High quality pressure transducers coupled with careful probe calibration will allow for differential measurements to be made with an uncertainty of +/- 0.03 degrees. Static pressure ports and high frequency response Kulite transducers will also be employed. Hotfilm sensors will be used to verify the state of the boundary layer on the glove through spectral analysis. A unique hotfilm array has been proposed that will enable the measurement of traveling wave vectors through a spectral technique. An experiment on the Flight Research Lab's Cessna O-2 to investigate the veracity of this technique has also been suggested. Thermocouples will also be installed on the glove's surface to monitor temperatures and verify transition location. The layout of the hotfilms and thermocouples is also detailed.

Many physical phenomena can be described by nonlinear models. The last few decades have seen an enormous growth of the applicability of nonlinear models and of the development of related nonlinear concepts. This has been driven by modern computer power as well as by the discovery of new mathematical techniques, which include two contrasting themes: (i) the theory of dynamical systems, most popularly associated with the study of chaos, and (ii) the theory of integrable systems associated, among other things, with the study of solitons. In this dissertation, we study two nonlinear models. One is the 1-dimensional vibrating string satisfying wtt − wxx = 0 with van der Pol boundary conditions. We formulate the problem into an equivalent first order hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary conditions. Thus, the problem is reduced to the discrete iteration problem of the type un+1 = F (un). Periodic solutions are investigated, an invariant interval for the Abel equation is studied, and numerical simulations and visualizations with different coefficients are illustrated. The other model is the Korteweg-de Vries-Burgers (KdVB) equation. In this dissertation, we proposed two new approaches: One is what we currently call First Integral Method, which is based on the ring theory of commutative algebra. Applying the Hilbert-Nullstellensatz, we reduce the KdVB equation to a first-order integrable ordinary differential equation. The other approach is called the Coordinate Transformation Method, which involves a series of variable transformations. Some new results on the traveling wave solution are established by using these two methods, which not only are more general than the existing ones in the previous literature, but also indicate that some corresponding solutions presented in the literature contain errors. We clarify the errors and instead give a refined result.

<p>External modulators will become key components in fiberoptical communica- tion systems operating at 40Gbit/s andhigher bitrates. Semiconductor electro- absorption (EA)modulators are promising candidates because of their high-speed potential, and their process compatibility with thecorresponding semi- conductor laser light sources. Thetraveling-wave (TW) electrode concept for electro-opticmodulators has been used for a long time in order to resolvethe con°ict between high modulation depth and highmodulation bandwidth. Re- cently, it has been adopted for EAmodulators as well.</p><p>This thesis presents the work carried out on design,fabrication and analysis of traveling-wave EA modulators(TWEAM) based on InP-InGaAsP. The lengths of TWEAM arecomparable to the lengths of their lumped counterparts. Theexperimental data of this work were analyzed in order show thatthe traveling- wave concept results in better performance evenfor short EA modulators. One key issue is the impedancematching. The low intrinsic characteristic modulator impedancehas to be matched with a corresponding load. In this case, theTW con figuration leads to a much higher bandwidth than for alumped EA modulator with the same length and the same connectedload.</p><p>An InP process was developed allowing the fabrication ofTWEAM with integrated termination resistors. Experimentalmicrowave properties were ob- tained for different TWEAMgeometries. It is reported on long TWEAM that showstate-of-the-art bandwidth. A 450&#956m long TWEAM reached43GHz, and 67GHz (beyond characterization limit) were indicatedfor a 250&#956m device. The experimental results onmicrowave properties were compared to full-wave, and circuitmodel simulations. The analysis reveals an impedance bandwidthtrade- off for the cross sectional electrode configuration.</p><p>Results of a new high-impedance design in form of asegmented TWEAM are presented. The devices were processedwithin the frame of this work and record bandwidth performanceis reported. At 50&#937­ impedance a bandwidth in the90GHz region was indicated.</p>

In power transmission systems, locating faults is an essential technology. When a fault occurs on a transmission line, it will affect the whole power system. To find the fault location accurately and promptly is required to ensure the power supply. In this paper, the study of traveling wave theory, fault location method, Karrenbauer transform, and Wavelet transform is presented. This thesis focuses on single ended fault location method. The signal processing technique and evaluation study are presented. The MATLAB SimPowerSystem is used to test and simulate fault scenarios for evaluation studies.