Algorithms for geodesics

Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of geodesics to be computed.Comment: LaTex, 12 pages, 8 figures. Version 2 corrects some errors and adds numerical examples. Supplementary material is available at http://geographiclib.sourceforge.net/geod.htm

A Model of Temporal Intensity Modulation for Laser Generated Ultrasound

Q-switched lasers are often used as a non-contact ultrasound source in non-destructive evaluation (NDE) of materials [1]. Q-switched lasers typically have ns pulse durations and generate broadband ultrasound waves, though longer laser pulses, of 100 microseconds or greater, have also been used [2] for NDE. These longer pulses tend to produce somewhat lower center frequencies than do Q-switched pulses, though they are still a broadband source. But it would be desirable in some NDE applications to narrow the signal bandwidth to improve the signal to noise ration (SNR), and also to have direct control over the center frequency of the generated ultrasound. In principle, this may be achieved by temporal [3,4] or spatial modulation [5,6] of the laser pulse, or both [7]. The purpose of this work was to develop a numerical model of a single, temporally modulated laser source of ultrasound in the thermoelastic regime, for isotropic metals

Reflection of Bounded Acoustic Beams from a Layered Solid

It is well known that when a bounded beam of acoustic waves is incident on a fluid-solid interface at certain critical angles, the reflected beam is significantly distorted and displaced due to the interference between specularly and nonspecularly reflected waves. Measurement and analysis of the reflected field can be used to estimate certain near surface elastic properties of the solid by means of several alternative nondestructive experimental arrangements [1,2]. In most of these experiments the interface generated leaky waves play a significant role. Thus a good understanding of the interface phenomena is a prerequisite to the design of experiments for their practical applications

Evaluation schemes in the ring of quaternionic polynomials

In this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.Research at CMAT was financed by Portuguese Funds through FCT - Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013. Research at NIPE was carried out within the funding with COMPETE reference number POCI-01-0145-FEDER-006683 (UID/ECO/03182/2013), with the FCT/MEC’s (Fundação para a Ciência e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on “Competitiveness and Internationalization - COMPETE 2020” under the PT2020 Partnership Agreement.info:eu-repo/semantics/publishedVersio

Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of these measures and the logarithmic capacity of their support. Since our approach is based on a reversible transformation between pairs of Jacobi matrices, we also discuss its application to an inverse / approximation problem. Numerical experiments show that the proposed algorithms are stable and can reliably compute Jacobi matrices of large order.Comment: 20 pages 6 figure

Numerical Methods for Computing Laser Generated Ultrasound Waves

The purpose of this work is to describe the implementation of a numerical Hankel-Laplace inverter for computing thermoelastic laser generated ultrasound waves in isotropic solids. It was found in this work that numerical error controls that were generally adequate, for common laser pulse parameters and material properties, were not given in the literature. The authors also found that there were no numerical values available in the literature [1,2], which researchers could use for comparison while developing their own computer codes. In this work, a numerical Hankel inverter is described for computing laser generated ultrasound waves. Empirically developed error controls, for both the Hankel and Laplace inverters, are also described, and the difficulties in implementing these inverters are discussed. Numerical values of waveforms are given at the end, which future researchers may use as benchmarks for developing their own computer programs. Note that space limitations did not permit a complete description of the numerical methods here, and the interested reader is referred to Sanderson [3].</p

Regulation of spatially-specific expression of the mouse homeobox gene Hox b-3

Computer programs for solving the thermoelastic equations describing wave generation and propagation caused by the interaction of a laser pulse with a metal surface have been developed over the last several years [1–3]. One approach is to manipulate the thermoelastic equations using transform techniques and then use numerical methods to invert the equations and solve for wave displacements. Another approach is to spatially discretize the geometry of the model using finite elements and integrate the equations of motion through time. The finite element formulation may be fully coupled or as a further approximation the thermal problem can be solved separately from the mechanical problem. The work reported here sought to develop a technique to use a commercial finite element code (ABAQUS [4]) to simulate surface waves generated in laser ultrasonics. A general purpose finite element code provides the advantages of large element and material libraries and the ability to consider complex geometries and boundary conditions. Sanderson’s [3] computer code, which solves the coupled thermoelastic problem using numerical transform techniques, was used to validate the finite element model developed. Validation was erformed using simple models and boundary conditions. Subsequent finite element simulations were used to examine the effects of simulated stress gradients (in-plane and through-thickness) on waveforms. Temperature dependent properties and the effect of including an elastic-plastic constitutive material model in the mechanical analysis were also briefly examined