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Physics Faculty Publications

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Articles 1561 - 1590 of 1942

Full-Text Articles in Physical Sciences and Mathematics

Strain Variation With Sample Thickness In Gan Grown By Hydride Vapor Phase Epitaxy, D. C. Reynolds, David C. Look, B. Jogai, J. E. Hoelscher, R. E. Sherriff, Richard J. Molnar Aug 2000

Strain Variation With Sample Thickness In Gan Grown By Hydride Vapor Phase Epitaxy, D. C. Reynolds, David C. Look, B. Jogai, J. E. Hoelscher, R. E. Sherriff, Richard J. Molnar

Physics Faculty Publications

High quality GaN crystals can be grown on sapphire by hydride vapor phase epitaxy. The thermal expansion mismatch between sapphire and GaN produces strain in the GaN crystal as it is cooled from the growth temperature to room temperature. The strain is evidenced by shifts in the photoluminescence and reflectance line positions. By analyzing the surface strain as the crystal thickness is increased, the thickness required to obtain zero surface strain can be estimated. This structure might provide a lattice matched and thermally matched substrate for further epitaxial growth of GaN.


Time-Resolved Photoluminescence Lifetime Measurements Of The Gamma(5) And Gamma(6) Free Excitons In Zno, D. C. Reynolds, David C. Look, B. Jogai, J. E. Hoelscher, R. E. Sherriff, M. T. Harris, M. J. Callahan Aug 2000

Time-Resolved Photoluminescence Lifetime Measurements Of The Gamma(5) And Gamma(6) Free Excitons In Zno, D. C. Reynolds, David C. Look, B. Jogai, J. E. Hoelscher, R. E. Sherriff, M. T. Harris, M. J. Callahan

Physics Faculty Publications

Time-resolved photoluminescence spectroscopy at 2 K was used to measure the radiative recombination lifetime of the allowed (Γ5) and forbidden (Γ6) free excitons in ZnO. The measurements were made on a sample containing internal strain, which altered the sample symmetry, and resulted in relaxed selection rules, allowing the Γ6 exciton to be observed. A radiative recombination lifetime of 259 ps was measured for the Γ5 exciton and 245 ps for the Γ6 exciton. The decay of the free excitons was of single-exponential form, and the decay times were obtained using a least-squares fit …


Properties Of Semi‐Insulating Gaas:Fe Grown By Hydride Vapor Phase Epitaxy, E. Rodríguez Messmer, D. Söderström, P. Hult, S. Marcinkevicius, S. Lourdudoss, David C. Look Aug 2000

Properties Of Semi‐Insulating Gaas:Fe Grown By Hydride Vapor Phase Epitaxy, E. Rodríguez Messmer, D. Söderström, P. Hult, S. Marcinkevicius, S. Lourdudoss, David C. Look

Physics Faculty Publications

In this paper we analyze GaAs grown by hydride vapor phase epitaxy (HVPE) and doped with four different iron concentrations between and . From temperature dependent current‐voltage measurements we observed the highest resistivity in the lowest doped sample. We also quantified the activation energy. These results together with those of time resolved photoluminescence measurements indicate that in the sample with the lowest Fe concentration, EL2 may be dominant. From the analysis of the time resolved photoluminescence measurements, the intrinsic EL2 concentration and the electron and hole capture cross sections of Fe in GaAs were estimated. © 2000 The Electrochemical Society. …


Electrical Properties Of Boron-Doped P-Sigec Grown On N(-)-Si Substrate, M. Ahoujja, Y. K. Yeo, R. L. Hengehold, G. S. Pomrenke, David C. Look, J. Huffman Aug 2000

Electrical Properties Of Boron-Doped P-Sigec Grown On N(-)-Si Substrate, M. Ahoujja, Y. K. Yeo, R. L. Hengehold, G. S. Pomrenke, David C. Look, J. Huffman

Physics Faculty Publications

Electrical properties of fully strained boron-doped Si0.90−yGe0.10Cy/n–Si grown by low pressure chemical vapor deposition have been investigated as a function of carbon content (0.2%–1.5%), using the variable temperature (25–650 K) Hall-effect technique. The results of Hall-effect measurements show that the Si substrate and the SiGeC/Si interfacial layer affect significantly the electrical properties of the SiGeC epitaxial layer. Thus, a three-layer conducting model has been used to extract the carrier concentration and mobility of the SiGeC layer alone. At room temperature, the hole carrier concentration decreases from 6.8×1017 to 2.4×10 …


Molecular-Dynamics Study Of Phase Transitions In Alkali Thiocyanates, M. M. Ossowski, John R. Hardy, Robert W. Smith Aug 2000

Molecular-Dynamics Study Of Phase Transitions In Alkali Thiocyanates, M. M. Ossowski, John R. Hardy, Robert W. Smith

Physics Faculty Publications

An account is presented of our studies of the order-disorder phase transitions in KSCN, RbSCN, and CsSCN. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron gas formalism extended to molecular ions. We performed static structural relaxations and supercell molecular dynamics and predicted with reasonable accuracy the temperatures for the onset of the transitions. In particular, we address the question of how the SCN2 ions disorder to yield subsequent structural transformations. We found high-temperature phases of average Fm3¯m symmetry for both KSCN and RbSCN. We argue that in reality the full appearance of these phases is …


Comment On “Direct Observation Of Stretched-Exponential Relaxation In Low-Temperature Lennard-Jones Systems Using The Cage Correlation Function”, Ulrich Zürcher, T. Keyes Jul 2000

Comment On “Direct Observation Of Stretched-Exponential Relaxation In Low-Temperature Lennard-Jones Systems Using The Cage Correlation Function”, Ulrich Zürcher, T. Keyes

Physics Faculty Publications

A Comment on the Letter by Eran Rabani, J. Daniel Gezelter, and D. J. Berne, Phys. Rev. Lett. 82, 3649 (1999). The authors of the Letter offer a Reply.


Dissociation Of Al2o3(0001) Substrates And The Roles Of Silicon And Oxygen In N-Type Gan Thin Solid Films Grown By Gas-Source Molecular Beam Epitaxy, J. E. Van Nostrand, J. Solomon, A. Saxler, Q. H. Xie, D. C. Reynolds, David C. Look Jun 2000

Dissociation Of Al2o3(0001) Substrates And The Roles Of Silicon And Oxygen In N-Type Gan Thin Solid Films Grown By Gas-Source Molecular Beam Epitaxy, J. E. Van Nostrand, J. Solomon, A. Saxler, Q. H. Xie, D. C. Reynolds, David C. Look

Physics Faculty Publications

Unintentionally doped and silicon doped GaN films prepared by molecular beam epitaxy using ammonia are investigated. Hall, secondary ion mass spectroscopy (SIMS), photoluminescence, and x-ray data are utilized for analysis of sources of autodoping of GaN epitaxial films in an effort to identify whether the n-type background electron concentration is of impurity origin or native defect origin. We identify and quantify an anomalous relationship between the Si doping concentration and free carrier concentration and mobility using temperature dependent Hall measurements on a series of 2.0-μm-thick GaN(0001) films grown on sapphire with various Si doping concentrations. SIMS is used to …


Zno Diode Fabricated By Excimer-Laser Doping, Toru Aoki, Yoshinori Hatanaka, David C. Look May 2000

Zno Diode Fabricated By Excimer-Laser Doping, Toru Aoki, Yoshinori Hatanaka, David C. Look

Physics Faculty Publications

A ZnO diode was fabricated by using a laser-doping technique to form a p-type ZnO layer on an n-type ZnO substrate. A zinc-phosphide compound, used as a phosphorous source, was deposited on the ZnO wafer and subjected to excimer-laser pulses. The current–voltage characteristics showed a diode characteristic between the phosphorous-doped p-layer and the n-type substrate. Moreover, light emission, with a band-edge component, was observed by forward current injection at 110 K.


On The Main Irradiation-Induced Defect In Gan, L. Polenta, Z-Q. Fang, David C. Look Apr 2000

On The Main Irradiation-Induced Defect In Gan, L. Polenta, Z-Q. Fang, David C. Look

Physics Faculty Publications

We show that the usual Arrhenius analysis of the main electron-irradiation-induced defect trap in n-type GaN, observed by deep-level transient spectroscopy (DLTS), is not sufficiently accurate. Instead, an exact fitting of the DLTS spectrum for this trap reveals two components, each of which has a thermal energy near 60 meV, not the apparent 140–200 meV, as given in other DLTS studies. This result resolves the discrepancy between Hall-effect and DLTS determinations of the thermal energy of this defect center.


Causal Implications Of Viscous Damping In Compressible Fluid Flows, P. M. Jordan, Martin R. Meyer, Ashok Puri Jan 2000

Causal Implications Of Viscous Damping In Compressible Fluid Flows, P. M. Jordan, Martin R. Meyer, Ashok Puri

Physics Faculty Publications

Classically, a compressible, isothermal, viscous fluid is regarded as a mathematical continuum and its motion is governed by the linearized continuity, Navier-Stokes, and state equations. Unfortunately, solutions of this system are of a diffusive nature and hence do not satisfy causality. However, in the case of a half-space of fluid set to motion by a harmonically vibrating plate the classical equation of motion can, under suitable conditions, be approximated by the damped wave equation. Since this equation is hyperbolic, the resulting solutions satisfy causal requirements. In this work the Laplace transform and other analytical and numerical tools are used to …


Quantitative Analysis Of Ultra-Fine Goethite In Rust Layer On Steel Using Mossbauer And X-Ray Diffraction Spectroscopy, Masato Yamashita, Toshihei Misawa, H. E. Townsend, D. C. Cook Jan 2000

Quantitative Analysis Of Ultra-Fine Goethite In Rust Layer On Steel Using Mossbauer And X-Ray Diffraction Spectroscopy, Masato Yamashita, Toshihei Misawa, H. E. Townsend, D. C. Cook

Physics Faculty Publications

We have proposed determination procedure of the relative amounts of rust constituents of steel. Mossbauer spectroscopy provides the relative amounts of crystalline rust constituents including ultra-fine crystals. A quantitative analysis of ultra-fine crystals is possible with the resolution of several percent by comparing the Mossbauer results with the relative amounts of rust constituents determined by X-ray diffraction spectroscopy.


Renormalons As Dilation Modes In The Functional Space, A. Babansky, I. Balitsky Jan 2000

Renormalons As Dilation Modes In The Functional Space, A. Babansky, I. Balitsky

Physics Faculty Publications

There are two possible sources of the factorial large-order behavior of a typical perturbative series. First, the number of different Feynman diagrams may be large; second, there may be abnormally large diagrams known as renormalons. It is well known that the large combinatorial number of diagrams is described by instanton-type solutions of the classical equations. We demonstrate that, from the functional-integral viewpoint, the renormalons do not correspond to a particular configuration but manifest themselves as dilatation modes in the functional space.


Deeply Virtual Compton Scattering At Small X, Ian Balitsky, Elena Kuchina Jan 2000

Deeply Virtual Compton Scattering At Small X, Ian Balitsky, Elena Kuchina

Physics Faculty Publications

We calculate the cross section of deeply virtual Compton scattering at large energies and intermediate momentum transfers.


High Energy Effective Action From Scattering Of Shock Waves In Qcd, Ian Balitsky Jan 2000

High Energy Effective Action From Scattering Of Shock Waves In Qcd, Ian Balitsky

Physics Faculty Publications

The author demonstrates that the amplitude for high-energy scattering can be factorized as a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering in QCD.


Oxygen Pressure-Tuned Epitaxy And Optoelectronic Properties Of Laser-Deposited Zno Films On Sapphire, S. Choopun, R. D. Vispute, W. Noch, A. Balsamo, R. P. Sharma, T. Venkatesan, A. Iliadis, David C. Look Dec 1999

Oxygen Pressure-Tuned Epitaxy And Optoelectronic Properties Of Laser-Deposited Zno Films On Sapphire, S. Choopun, R. D. Vispute, W. Noch, A. Balsamo, R. P. Sharma, T. Venkatesan, A. Iliadis, David C. Look

Physics Faculty Publications

Influence of oxygen pressure on the epitaxy, surface morphology, and optoelectronic properties has been studied in the case of ZnO thin films grown on sapphire ~0001! by pulsed-laser deposition. Results of Rutherford backscattering and ion channeling in conjunction with atomic force microscopy clearly indicate that the growth mode, degree of epitaxy, and the defect density strongly depend on the oxygen background pressure during growth. It is also found that the growth mode and the defects strongly influence the electron mobility, free-electron concentration, and the luminescence properties of the ZnO films. By tuning the oxygen pressure during the initial and the …


Molecular-Dynamics Study Of Phase Transitions In Alkali Azides, M. M. Ossowski, John R. Hardy, Robert W. Smith Dec 1999

Molecular-Dynamics Study Of Phase Transitions In Alkali Azides, M. M. Ossowski, John R. Hardy, Robert W. Smith

Physics Faculty Publications

An account is presented of our studies of the order-disorder phase transitions in KN3, RbN3, and CsN3. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron-gas formalism extended to molecular ions. We performed static structural relaxations and supercell molecular dynamics and predicted with reasonable accuracy the temperatures for the onset of the transitions. In particular, we address the question of how the N3- ions reorient to yield the transitions. We found the existence of NaCl-type high-temperature phases in disordered KN3 and RbN3 and argue that this …


Intercomparison Of Retrospective Radon Detectors, R. William Field, Daniel J. Steck, Mary Ann Parkhurst, Judy A. Mahaffey, Michael C.R. Alavanja Nov 1999

Intercomparison Of Retrospective Radon Detectors, R. William Field, Daniel J. Steck, Mary Ann Parkhurst, Judy A. Mahaffey, Michael C.R. Alavanja

Physics Faculty Publications

We performed both a laboratory and a field intercomparison of two novel glass-based retrospective radon detectors previously used in major radon case-control studies performed in Missouri and Iowa. The new detectors estimate retrospective residential radon exposure from the accumulation of a long-lived radon decay product, 210Pb, in glass. The detectors use track registration material in direct contact with glass surfaces to measure the α-emission of a 210Pb-decay product, 210Po. The detector's track density generation rate (tracks per square centimeter per hour) is proportional to the surface α-activity. In the absence of other strong sources of α-emission in …


Low-Frequency Noise In N-Gan With High Electron Mobility, M. E. Levinshtein, S. L. Rumyantsev, David C. Look, Richard J. Molnar, M. A. Khan, G. Simin, V. Adivarahan, M. S. Shur Nov 1999

Low-Frequency Noise In N-Gan With High Electron Mobility, M. E. Levinshtein, S. L. Rumyantsev, David C. Look, Richard J. Molnar, M. A. Khan, G. Simin, V. Adivarahan, M. S. Shur

Physics Faculty Publications

We report on the results of measurements of low frequency noise in n-type gallium nitride (GaN) grown on sapphire with 300 K electron mobility of 790 cm2/V s. The noise spectra have the form of 1/f noise with a Hooge parameter α of approximately 5×10−2. This value of α is two orders of magnitude smaller than that observed before in n-GaN. The obtained results show that the level of flicker noise in GaN, just like that in GaAs and Si, strongly depends on the structural perfection of the material (the amplitude of the …


Velocity Distributions Of C Atoms In Co+ Dissociative Recombination: Implications For Photochemical Escape Of C From Mars, Jane L. Fox, Aleksander Hać Nov 1999

Velocity Distributions Of C Atoms In Co+ Dissociative Recombination: Implications For Photochemical Escape Of C From Mars, Jane L. Fox, Aleksander Hać

Physics Faculty Publications

We have carried out Monte Carlo calculations to determine the velocity distributions of C atoms produced by dissociative recombination of CO+ using recent data for the branching ratios of various allowed channels and ion and electron temperatures appropriate to the Martian thermosphere. We find that the fractions of 12C atoms with velocities greater than the escape velocity are ∼ 0.66 and ∼ 0.62, and those for 13C are ∼ 0.47 and ∼ 0.48 at the plasma temperatures characteristic of the exobases at low and high solar activities, respectively. The ratio of the escape fractions of 13C …


Strain Splitting Of The Gamma(5) And Gamma(6) Free Excitons In Zno, D. C. Reynolds, David C. Look, B. Jogai, C. W. Litton, T. C. Collins, M T. Harris, M. J. Callahan, J. S. Bailey Nov 1999

Strain Splitting Of The Gamma(5) And Gamma(6) Free Excitons In Zno, D. C. Reynolds, David C. Look, B. Jogai, C. W. Litton, T. C. Collins, M T. Harris, M. J. Callahan, J. S. Bailey

Physics Faculty Publications

High-quality ZnO crystals have been grown by vapor-phase techniques and by the hydrothermal method. Depending on the surface preparation technique, some hydrothermally grown crystals contain strain. These strains result in energy shifts of the free excitons as well as relaxation of the selection rules. The Γ6 unallowed exciton is observed in these samples without the application of a magnetic field. The Γ6 exciton is also observed to split in a strain field, consistent with the Γ9 symmetry for the top valence band in ZnO. The Γ5 and Γ6 excitons have been observed to split in …


Production And Annealing Of Electron Irradiation Damage In Zno, David C. Look, D. C. Reynolds, Joseph W. Hemsky, R. L. Jones, J. R. Sizelove Aug 1999

Production And Annealing Of Electron Irradiation Damage In Zno, David C. Look, D. C. Reynolds, Joseph W. Hemsky, R. L. Jones, J. R. Sizelove

Physics Faculty Publications

High-energy (>1.6 MeV) electrons create acceptors and donors in single-crystal ZnO. Greater damage is observed for irradiation in the [0001] direction (Zn face) than in the [000] direction (O face). The major annealing stage occurs at about 300–325 °C, and is much sharper for defects produced by Zn-face irradiation, than for those resulting from O-face irradiation. The defects appear to have a chain character, rather than being simple, near-neighbor vacancy/interstitial Frenkel pairs. These experiments suggest that ZnO is significantly more “radiation hard” than Si, GaAs, or GaN, and should be useful for applications in high-irradiation environments, such as electronics …


Configurational Entropy And Collective Modes In Normal And Supercooled Liquids, Ulrich Zürcher, T. Keyes Aug 1999

Configurational Entropy And Collective Modes In Normal And Supercooled Liquids, Ulrich Zürcher, T. Keyes

Physics Faculty Publications

Soft vibrational modes have been used to explain anomalous thermal properties of glasses above 1 K. The soft-potential model consists of a collection of double-well potentials that are distorted by a linear term representing local stress in the liquid. Double-well modes contribute to the configurational entropy of the system. Based on the Adam-Gibbs theory of entropically driven relaxation in liquids, we show that the presence of stress drives the transition from Arrhenius to Zwanzig-Bässler temperature dependence of relaxation times. At some temperature below the glass transition, the energy scale is dominated by local stress, and soft modes are described by …


Valence-Band Ordering In Zno, D. C. Reynolds, David C. Look, B. Jogai, C. W. Litton, G. Cantwell, W. C. Harsch Jul 1999

Valence-Band Ordering In Zno, D. C. Reynolds, David C. Look, B. Jogai, C. W. Litton, G. Cantwell, W. C. Harsch

Physics Faculty Publications

The emission and reflection spectra of ZnO have been investigated in the intrinsic region and the data have been interpreted in terms of the wurtzite crystal band structure. Free-exciton emission is observed for the first time. Both the Γ5 and Γ6 state excitons associated with top valence band have been identified. This identification has established the valence-band symmetry ordering in ZnO.


Particle Sizing In Strongly Turbid Suspensions With The One-Beam Cross-Correlation Dynamic Light-Scattering Technique, Anthony J. Adorjan, James A. Lock, Thomas W. Taylor, Padetha Tin, William V. Meyer, Anthony E. Smart May 1999

Particle Sizing In Strongly Turbid Suspensions With The One-Beam Cross-Correlation Dynamic Light-Scattering Technique, Anthony J. Adorjan, James A. Lock, Thomas W. Taylor, Padetha Tin, William V. Meyer, Anthony E. Smart

Physics Faculty Publications

The utility of the one-beam cross-correlation dynamic light-scattering system for sizing small particles in suspension was previously limited by its small-intensity signal-to-baseline ratio for strongly turbid suspensions. We describe three improvements in the optical system and sample cell that raise the ratio to a value comparable with that of other cross-correlation dynamic light-scattering systems. These improvements are (i) using a square cross-sectional sample cell to minimize the attenuation of the incident beam and singly scattered light, (ii) placing a 200-mu m-wide slit between the sample cell and the detector fibers to mask off the region of weak single scattering and …


Performance Of Sinusoidally Deformed Hydrophone Line Arrays, Deanna M. Caveny, Donald R. Del Balzo, James H. Leclere, George E. Ioup Apr 1999

Performance Of Sinusoidally Deformed Hydrophone Line Arrays, Deanna M. Caveny, Donald R. Del Balzo, James H. Leclere, George E. Ioup

Physics Faculty Publications

It is well known that array deformations can distort beam patterns and introduce bearing errors if the beamformer assumes linearity. It is also known that deformed arrays can resolve left–right ambiguities, provided the shape is known. In this work, these two effects are studied for undamped and damped sinusoidally deformed arrays with small deformation amplitudes in the horizontal (x,y) plane only. By use of fixed arc-length separations along the array, the hydrophone (x,y) coordinates are determined numerically and the error in assuming equal x spacing is summarized for a sample array. Array-response …


Excitation Of Morphology-Dependent Resonances And Van De Hulst's Localization Principle, James A. Lock Apr 1999

Excitation Of Morphology-Dependent Resonances And Van De Hulst's Localization Principle, James A. Lock

Physics Faculty Publications

When a laser beam scatters from a microparticle whose shape deviates from that of a sphere, a number of partial waves of the incident beam couple to a given partial wave of the scattered and interior fields. As a result, partial-wave coupling caused by small surface irregularities of a liquid droplet provides the mechanism for exciting low-radial-order morphology-dependent resonances. (C) 1999 Optical Society of America.


Residual Native Shallow Donor In Zno, David C. Look, Joseph W. Hemsky, J. R. Sizelove Mar 1999

Residual Native Shallow Donor In Zno, David C. Look, Joseph W. Hemsky, J. R. Sizelove

Physics Faculty Publications

High-energy electron irradiation in ZnO produces shallow donors at about EC-30meV. Because the production rate is much higher for Zn-face (0001) than O-face (0001̅ ) irradiation, the donor is identified as a Zn-sublattice defect, most likely the interstitial ZnI or a ZnI-related complex. The donor energy is quite close to that of the unirradiated sample, and of other samples discussed in the literature, strongly suggesting that ZnI (and not VO) is the dominant native shallow donor in ZnO. An exceptionally high displacement threshold energy (∼1.6MeV) is quantitatively explained in terms of a …


Exposure To Atmospheric Radon, Daniel J. Steck, R. William Field, Charles F. Lynch Feb 1999

Exposure To Atmospheric Radon, Daniel J. Steck, R. William Field, Charles F. Lynch

Physics Faculty Publications

We measured radon (222Rn) concentrations in Iowa and Minnesota and found that unusually high annual average radon concentrations occur outdoors in portions of central North America. In some areas, outdoor concentrations exceed the national average indoor radon concentration. The general spatial patterns of outdoor radon and indoor radon are similar to the spatial distribution of radon progeny in the soil. Outdoor radon exposure in this region can be a substantial fraction of an individual's total radon exposure and is highly variable across the population. Estimated lifetime effective dose equivalents for the women participants in a radon-related lung cancer …


Dislocation Scattering In Gan, David C. Look, J. R. Sizelove Feb 1999

Dislocation Scattering In Gan, David C. Look, J. R. Sizelove

Physics Faculty Publications

A theory of charged-dislocation-line scattering is developed within the framework of the Boltzmann transport equation. A fit of the theory to temperature-dependent Hall-effect data in GaN gives dislocation densities which are in excellent agreement with those measured by transmission electron microscopy. This work shows that threading edge dislocations in GaN indeed are electrically active, in agreement with recent theoretical predictions.


Digital Signal Propagation In Dispersive Media., P. M. Jordan, Ashok Puri Jan 1999

Digital Signal Propagation In Dispersive Media., P. M. Jordan, Ashok Puri

Physics Faculty Publications

In this article, the propagation of digital and analog signals through media which, in general, are both dissipative and dispersive is modeled using the one-dimensional telegraph equation. Input signals are represented using impulsive, Heaviside unit step, Gaussian, rectangular pulse, and both unmodulated and modulated sinusoidal pulse type boundary data. Applications to coaxial transmission lines and freshwater signal propagation, for both digital and analog signals, are included. The analysis presented here supports the finding that digital transmission in dispersive media is generally superior to that of analog. The boundary data (input signals) give rise to solutions of the telegraph equation which …