Photothermal Radiometry with Solid Cylindrical Samples

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.

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.

A theoretical model for evaluating solid multilayered spherical solids heated by a frequency-modulated light beam using the Green function method is presented. The specific thermal-wave Green function corresponding to the composite structure has been derived. The characteristics of the thermal-wave field with respect to the thermophysical, geometrical, and measurement parameters are presented. Unlike the quadrupole method, the Green function method is capable of evaluating thermal-wave fields at any point of multilayered structures with arbitrary intensity distributions of the incident laser beams. This study establishes applications of thermal-wave fields in both cylindrical and spherical samples using the Green function method and is of importance in characterizing radially inhomogeneous spherical solids.

The green's function method in quantum statistics

The comparison of the ray theory, the complex ray theory with the experimental results was studied in the work. The least-squares procedure was used in multiparameter fitting of experimental data and theoretical result. Some parameters of experimental setup were also determined. There was proved in the work that the complex ray theory better describes the experimental results than the ray theory. Moreover, the complex ray theory takes into account some effects that do not occur in the ray theory at all.

The effect of the laser source spotsize on the measurement sensitivity of layered system using photothermal radiometry (PTR) technique is presented. The beam size effect on the PTR measurement sensitivity is theoretically examined and experimentally demonstrated using a carbo-nitrided C1018 steel sample. The experimental results using a focused beam and an expanded beam for a carbo-nitrided C1018 sample validated the theoretical prediction, according to which the expanded beam showed a much larger magnitude change (contrast) in both amplitude and phase than results with a focused beam.

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.

In this article, a non-destructive photothermal radiometry (PTR) method is proposed to quantitatively evaluate the aging degrees of field-servicing silicone rubber composite insulators via a thermal diffusivity ratio and degradation layer thickness. A sensitivity analysis is performed to investigate the sensitivity of the PTR amplitude and phase to the thermo-physical, optical, and structural parameters of the aged silicone rubber composite insulators consisting of a degradation layer and a substrate layer. It is found that the PTR amplitude and phase are highly sensitive to the thermal diffusivity, effective infrared absorption coefficient, and thickness of the degradation layer as well as the thermal diffusivity of the substrate layer but are much less sensitive to optical absorption coefficients of the degradation and substrate layers and the effective infrared absorption coefficient of the substrate layer. Thus, parameters with high sensitivity coefficients are set as free parameters and determined by multi-parameter fitting the frequency dependences of the PTR amplitude and phase measured directly from the surfaces of the field-serviced silicone rubber composite insulators to a two-layer PTR theoretical model, while in the multi-parameter fitting, the parameters with low sensitivity coefficients are set as “known” parameters whose values are either measured separately or taken from literature. By doing so, the thermal diffusivity ratio and degradation layer thickness are accurately determined in a non-destructive way. Experimental results demonstrate that the thermal diffusivity ratio and degradation layer thickness determined by the proposed non-destructive PTR method are in good agreement with that determined by a conventional destructive PTR method, thus, proving the feasibility of the non-destructive PTR method for quantitative evaluation of aging degrees of the silicone rubber composite insulators being serviced in the high-voltage power transmission systems.

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

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.

Photoacoustic (PA) field calculations using a Green’s function approach is presented. The method has been applied to predict PA spectra generated by normal (discocyte) and pathological (stomatocyte) red blood cells (RBCs). The contours of normal and pathological RBCs were generated by employing a popular parametric model and accordingly, fitted with the Legendre polynomial expansions for surface parametrization. The first frequency minimum of theoretical PA spectrum approximately appears at 607 MHz for a discocyte and 410 MHz for a stomatocyte when computed from the direction of symmetry axis. The same feature occurs nearly at 247 and 331 MHz, respectively, for those particles when measured along the perpendicular direction. The average experimental spectrum for normal RBCs is found to be flat over a bandwidth of 150-500 MHz when measured along the direction of symmetry axis. For spherical RBCs, both the theoretical and experimental spectra demonstrate negative slope over a bandwidth of 250-500 MHz. Using the Green’s function method discussed, it may be possible to rapidly characterize cellular morphology from single-particle PA spectra.

Optical spectra of finite-momentum excitons in carbon nanotubes with gold nanostructures are theoretically studied. A Green function method is developed for self-consistently solving Maxwell equations including the quantum-mechanical nonlocal response of the nanotubes and the local response of the nanostructures. Excitons with finite momenta in the axis direction in the nanotubes are effectively excited by localized electric fields due to surface plasmons in the gold nanostructures and counteract the surface plasmons through depolarization fields, showing the crucial self-consistency of these effects.

Propagation of a short pulse through human breast tissues is studied by numerically solving the diffuse equation. Different numerical methods, such as Monte Carlo and finite difference time domain, have been used to study the short pulse laser propagation through biological tissues. In this paper, we use boundary integral method to study the laser pulse–tissue interaction. The diffuse equation is used to examine the propagation of laser into biological tissues, and boundary integral method is used to alter this equation to the integral form and the result is solved by using boundary element method. To verify the precision of a boundary element method code, we compared the obtained results with those obtained by finite difference time domain method. In addition, the effects of different optical parameters of breast tissues, i.e., reduced scattering and absorption coefficients, on time evolution of a diffusely reflected pulse are studied.

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