Modeling of Thermal-Wave Fields in Radially Inhomogeneous Spherical Solids Using the Green Function Method

In this paper, we establish a Green-function based theoretical model for evaluating solid multi-layered spherical samples which are illuminated by a frequency modulated incident beam. The specific Green function for the multi-layered spherical structure is derived and an analytical expression for the thermal-wave field in such a spherical sample is presented. The characteristics of the thermal-wave field with respect to the thermophysical, geometrical, and measurement parameters are presented. Unlike the quadruple method, the Green function method is capable of evaluating thermal-wave fields at any point of multi-layered structures with arbitrary intensity distributions of incident laser beams. Furthermore, experimental validation is also presented in the form of experimental results with steel spheres of various diameters.

The green's function method in quantum statistics

Under illumination of a solid absorbing target by short laser pulse the acoustic waves are excited both inside the target and in the surrounding air. When the surface of the target is plane the shape of acoustic signal in the air depends on the intensity distribution in the illuminating laser beam. In this report the results of restoration of two-dimensional intensity distribution of pulse laser beam by method of acoustic tomography are presented. As the target a plane metal plate was used. Measurements of acoustic signals were carried out by nine microphones placed around the illuminating beam not far from the target. Two-dimensional intensity distribution of laser beam obtained by acoustic methods are in good agreement with data obtained by usual photometric method.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

An effective method to calculate the electrostatic force between a microscopic tip and an infinite metallic plane is proposed and tested. The Green function method is used to integrate out exactly the potential distribution in the plane. The plane plus tip problem is thus reduced to a boundary value problem for the tip surface only, enabling solution by a standard numerical method. The main advantage of this approach is that systems with an arbitrary plane potential distribution may be solved with the same method and comparable numerical efficiency to problems with a constant plane potential. The method is used to calculate the electrostatic force on a tip due to a plane with a step potential and a local quadratic potential island. The calculated perpendicular force components agree with previously published theoretical results. In addition, lateral components of the tip-surface force are computed and shown to be comparable to the vertical component close to a potential step, in agreement with the published experimental data. This suggests the possibility of using lateral, as well as vertical force data in atomic force microscopy for the detection and imaging of potential steps.

New version of FDTD with GFM program in Schwarzschild space–time

We extend the applications of the photothermal diagnostics by means of laser-infrared photothermal radiometry (PTR) to samples with curved surfaces. Specifically, we present both the theoretical and experimental PTR studies on solid cylindrical samples (surfaces). Based on the Green function method, the thermal-wave field distribution of a cylindrical surface that is under the excitation of a periodically modulated uniform beam is obtained. The laser beam, which is of a cylindrical symmetry, impinges uniformly, partially or fully, on the cylindrical surface, which is practically infinitely long along the axial direction. The characteristics of the thermal-wave field with respect to the thermal diffusivity of the material, the diameter of the sample, the size of the incident beam, and the measurement of the angle are discussed. Experimental results are in good agreement with the theory.

We extend the applications of photothermal radiometric diagnostics to continuously curved cylindrical surface solids using lock-in thermography (LIT) imaging, in which both the photothermally induced surface temperature and the angularly dependent infrared radiation emitted by the curved surface are not constant. Specifically, a theoretical photothermal model is established based on the Green Function method from which the thermal-wave field distribution at different azimuthal angles on the curved surface is obtained and characteristics of the thermal-wave field with different material and measurement parameters/schemes are discussed. A laser-infrared photothermal lock-in imaging system for solid cylindrical samples is established, and the thermal diffusivity of AISI 304 cylindrical steel samples is measured directly based on the LIT images combined with empirically obtained infrared radiation angular distributions over the curved surfaces. The experimental results are in excellent agreement with the theory, which provides a fast and non-destructive quantitative tool for thermophysical evaluation of curved surface solids.

Simulations that are meant to determine the steady-state distribution of a diffusible solute such as oxygen in tissues have typically used finite difference methods to solve the diffusion equation. Finite difference methods require a tissue mesh with enough points to resolve oxygen gradients near and between discrete blood vessels. The large number of points that are typically required can make these calculations very slow. In this paper, we investigate a numerical method known as the Green's function method which is not bound by the same constraint. The Green's function method is expected to yield an accurate oxygen distribution more quickly by requiring fewer mesh points. Both methods were applied to calculate the steady state oxygen distribution in a model simulation region. When the Green's function calculation used meshes with 1/2, 1/4 and, 1/8 of the resolution required for the finite-difference mesh, there was good agreement with the finite difference calculation in all cases. When the volume of the domain was increased 8-fold the Green's function method was able to calculate the O2 field in 22 minutes, whereas the finite difference calculation is expected to take approximately 1 week. The number of steps required for the Green's function calculation increases quadratically with the number of points in the tissue mesh. As a result, small meshes are calculated very quickly using Green's functions, while for larger mesh sizes this method experiences a significant decrease in efficiency.

We have calculated the Debye-Waller factor (DWF) of Cu from a model that was used successfully in earlier calculations of anharmonicity by Cowley and Shukla. The present calculation has been carried out using quasiharmonic theory, the lowest-order (λ2) anharmonic perturbation theory, and a Green's function (GF) method which sums an infinite series of the λ2−type anharmonic terms. The static approximation ω → 0 in the cubic contribution to the self-energy of the GF, introduced in the earlier work on the DWF by Shukla and Hubschle is further justified by showing that in the high-temperature limit the exact results for the λ2 anharmonic contributions (cubic and quartic) to the Helmholtz free energy are given in this approximation. Results for the DWF are also obtained for a modified version of the Morse potential with λ2 perturbation theory (PT) and the GF method. The GF results are in excellent agreement with the experimental Mossbauer and X-ray data in the entire temperature range, 300 K  T  120...

The objective of this study is to analyse two kinds of periodic infinite lattices widely used in acoustic filtering. The first network is formed by periodic close resonators and the second by periodic open resonators. Then we realize a combination of these two systems and we study and compare the effect on the band gap. Resonators are filters often used to reduce noise. We calculate the dispersion relation theoretically and numerically in this paper by using the matrix transfer method. Then, the results obtained are compared with those of the Green's function method often used in solid state physics.

In-plane forced vibration of curved pipe conveying fluid by Green function method

An analytic and numerical solution with spectral Green's function method for transport equation in spherical geometry

The elastic response of a vacancy in a semi-infinite fcc copper lattice containing a free surface is calculated by using a new multiscale Green's function method. The method treats the lattice distortion near the vacancy at the atomistic level and the free surface at the macroscopic continuum level in the same formalism. The lattice is modeled using the lattice statics Green's function that fully accounts for the discrete atomistic structure of the lattice and can model a large crystallite containing a million atoms without excessive CPU effort. The method is especially useful for modeling the elastic response of nanocrystals containing point defects in which surfaces and interfaces play important roles. The method bridges the length scales seamlessly by relating the microscopic lattice distortion near a point defect to measurable macroscopic parameters of the solid such as the strain and the displacement field at a free surface. Using the interatomic potential derived by Cleri and Rosato, the lattice distortion, relaxation energy, and relaxation volume due to a vacancy are calculated in an otherwise perfect copper lattice for a million-atom model containing a free (100) surface. The calculated value of the relaxation volume is in excellent agreement with the observed value. Numerical results are also presented for the strain and the displacement fields at the free surface due to a vacancy and the interaction energy between a vacancy and the free surface in anisotropic semi-infinite copper.

A new coarse-mesh computational method for the numerical solution of heat conduction and fluid flow problems is formally developed and applied to sample problems. The method is based upon formal use of Green's functions, which are defined locally over subdomains of the original system under consideration. The formal development of the local Green's function method for the solution of heat conduction problems is presented and discussed. Numerical solutions of sample problems for one-dimensional heat conduction with constant thermal conductivity, one-dimensional heat conduction with temperature-dependent thermal conductivity, and two-dimensional heat conduction with constant thermal conductivity are given, and these results are compared with results obtained using the finite difference and finite element methods. The formal development of the local Green's function method for the solution of fluid flow problems is then also presented and discussed; the numerical solution of a sample problem for simple one-dimensional incompressible fluid flow with viscous heating is also given.

A computer generated hologram (CGH) has been developed for laser transformation hardening with a fiber-coupled high-power diode laser (HPDL). The laser beam shaped with the CGH is purposely non-uniform in order to obtain uniform depth of the hardened profile. The optimum intensity distribution of laser beam has been determined with the numerical simulation of dynamic thermal analysis based on the finite element method. A binary phase CGH of silica glass was designed and fabricated to realize the optimized intensity distribution of laser beam. When a steel plate surface was hardened by the 330W laser beam with the fabricated CGH, the cross-sectional hardened profile had a uniform depth, compared with experimental results for a defocused Gaussian beam and a flat-top shaped beam.