Nonlinear waves in adhesive strings

We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state, beyond such a value the stress discontinuously drops to zero. Therefore the semilinear equation is characterized by a source term presenting jump discontinuity. Well-posedness of the initial boundary value problem of Neumann type, as well as qualitative properties of the solutions are studied and the evolution of different initial conditions are numerically investigated

Index to 1981 NASA Tech Briefs, volume 6, numbers 1-4

Short announcements of new technology derived from the R&D activities of NASA are presented. These briefs emphasize information considered likely to be transferrable across industrial, regional, or disciplinary lines and are issued to encourage commercial application. This index for 1981 Tech Briefs contains abstracts and four indexes: subject, personal author, originating center, and Tech Brief Number. The following areas are covered: electronic components and circuits, electronic systems, physical sciences, materials, life sciences, mechanics, machinery, fabrication technology, and mathematics and information sciences

Using smart sensor strings for continuous monitoring of temperature stratification in large water bodies

Copyright © 2006 IEEEA "smart" thermistor string for continuous long-term temperature profiling in large water bodies is described allowing highly matched yet low-cost spatial and temporal temperature measurements. The sensor uses the three-wire SDI-12 communications standard to enable a low-powered radio or data logger on supporting buoys to command measurements and retrieve high-resolution temperature data in digital form. Each "smart" temperature sensor integrates a thermistor element, measurement circuitry, power control, calibration coefficient storage, temperature computation, and data communications. Multiple addressable sensors at discrete vertical depths are deployed along a three-wire cable that provides power and allows data transfer at regular intervals. Circuit, manufacturing, and automated calibration techniques allow temperature measurements with a resolution of plusmn0.003degC, and with intersensor matching of plusmn0.006degC. The low cost of each sensor is achieved by using poor tolerance thermistor and circuit components in conjunction with a 15-bit charge-balance analog-to-digital converter. Sensor inaccuracies and temperature coefficients are corrected by a two-point calibration procedure made possible by a standard-curve generator within the sensor, based upon the method of finite differences. This two-point calibration process allows in-field sensor string calibration in stratified water bodies and provides a means to correct for long-term calibration drift without having to return the string to a laboratory.Andrew J. Skinner and Martin F. Lamber

Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap

One-dimensional nonlinear phononic crystals have been assembled from periodic diatomic chains of stainless steel cylinders alternated with Polytetrafluoroethylene spheres. This system allows dramatic changes of behavior (from linear to strongly nonlinear) by application of compressive forces practically without changes of geometry of the system. The relevance of classical acoustic band-gap, characteristic for chain with linear interaction forces and derived from the dispersion relation of the linearized system, on the transformation of single and multiple pulses in linear, nonlinear and strongly nonlinear regimes are investigated with numerical calculations and experiments. The limiting frequencies of the acoustic band-gap for investigated system with given precompression force are within the audible frequency range (20–20,000 Hz) and can be tuned by varying the particle’s material properties, mass and initial compression. In the linear elastic chain the presence of the acoustic band-gap was apparent through fast transformation of incoming pulses within very short distances from the chain entrance. It is interesting that pulses with relatively large amplitude (nonlinear elastic chain) exhibit qualitatively similar behavior indicating relevance of the acoustic band gap also for transformation of nonlinear signals. The effects of an in situ band-gap created by a mean dynamic compression are observed in the strongly nonlinear wave regime

Characterizing Optical Loss in Orientation Patterned III-V Materials Using Laser Calorimetry

This research examines the optical loss in orientation patterned III-V materials. Laser calorimetry technique was assembled to measure the absorption loss in GaAs, GaP and Fe2+ZnSe samples. Three different methods are explained and utilized to calculate the absorptance value from the calorimetry data. Absorption coefficient values were found for three different samples of GaAs ranging from 0.025+-0.009 cm-1 to 0.80+-0.08 cm-1, all within the sphere of published values for GaAs. A Complete Angle Scatter Instrument (CASI) was used to determine scatter at incident angles ranging from 0 to 55.5 degrees from two OPGaAs samples using an 8.16 micrometer, p-polarized incident laser light. Diffraction peaks were observed in the samples with high impurities, with domains in the material acting as diffraction gratings. FTIR measurements were conducted using a wire grid polarizer on the CASI samples to investigate transmission signal variations with change in incident polarization. Both patterned GaAs samples exhibited some polarization effect from the grated material. The amount of transmission detected changed by as much as 20% for both samples as they were rotated to change incident polarization

Nonlinear waves in Newton's cradle and the discrete p-Schroedinger equation

We study nonlinear waves in Newton's cradle, a classical mechanical system consisting of a chain of beads attached to linear pendula and interacting nonlinearly via Hertz's contact forces. We formally derive a spatially discrete modulation equation, for small amplitude nonlinear waves consisting of slow modulations of time-periodic linear oscillations. The fully-nonlinear and unilateral interactions between beads yield a nonstandard modulation equation that we call the discrete p-Schroedinger (DpS) equation. It consists of a spatial discretization of a generalized Schroedinger equation with p-Laplacian, with fractional p>2 depending on the exponent of Hertz's contact force. We show that the DpS equation admits explicit periodic travelling wave solutions, and numerically find a plethora of standing wave solutions given by the orbits of a discrete map, in particular spatially localized breather solutions. Using a modified Lyapunov-Schmidt technique, we prove the existence of exact periodic travelling waves in the chain of beads, close to the small amplitude modulated waves given by the DpS equation. Using numerical simulations, we show that the DpS equation captures several other important features of the dynamics in the weakly nonlinear regime, namely modulational instabilities, the existence of static and travelling breathers, and repulsive or attractive interactions of these localized structures