Finite-difference Calculations Research Articles

Variational sensitivity analysis and design optimization

Variational method (VM) is employed to derive the co-state equations, boundary (transversality) conditions, and functional sensitivity derivatives. The converged solutions of the state equations together with the steady state solution of the co-state equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational method to aerodynamic shape optimization problems is demonstrated on internal flow problems at supersonic Mach number range of 1.5. Optimization results for flows with and without shock phenomena are presented. The study shows that while maintaining the accuracy of aerodynamical objective function and constraint within the reasonable range for engineering prediction purposes, variational method provides a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference computations.

Localized surface plasmon resonance-based hybrid Au–Ag nanoparticles for detection of Staphylococcus aureus enterotoxin B

A triangular hybrid Au–Ag nanoparticles array was proposed for the purpose of biosensing in this paper. Constructing the hybrid nanoparticles, an Au thin film is capped on the Ag nanoparticles which are attached on glass substrate. The hybrid nanoparticles array was designed by means of finite-difference and time-domain (FDTD) algorithm-based computational numerical calculation and optimization. Sensitivity of refractive index of the hybrid nanoparticles array was obtained by the computational calculation and experimental detection. Moreover, the hybrid nanoparticles array can prevent oxidation of the pure Ag nanoparticles from atmosphere environment because the Au protective layer was deposited on top of the Ag nanoparticles so as to isolate the Ag particles from the atmosphere. We presented a novel surface covalent link method between the localized surface plasmon resonance (LSPR) effect-based biosensors with hybrid nanoparticles array and the detected target molecules. The generated surface plasmon wave from the array carries the biological interaction message into the corresponding spectra. Staphylococcus aureus enterotoxin B (SEB), a small protein toxin was directly detected at nanogramme per milliliter level using the triangular hybrid Au–Ag nanoparticles. Hence one more option for the SEB detection is provided by this way.

Wavelength-scale photonic-crystal laser formed by electron-beam-induced nano-block deposition

A wavelength-scale cavity is generated by printing a carbonaceous nano-block on a photonic-crystal waveguide. The nanometer-size carbonaceous block is grown at a pre-determined region by the electron-beam-induced deposition method. The wavelength-scale photonic-crystal cavity operates as a single mode laser, near 1550 nm with threshold of approximately 100 microW at room temperature. Finite-difference time-domain computations show that a high-quality-factor cavity mode is defined around the nano-block with resonant wavelength slightly longer than the dispersion-edge of the photonic-crystal waveguide. Measured near-field images exhibit photon distribution well-localized in the proximity of the printed nano-block. Linearly-polarized emission along the vertical direction is also observed.

MULTISCALE MODELING OF THE VACUUM ARC REMELTING PROCESS FOR THE PREDICTION ON MICROSTRUCTURE FORMATION

The final solidification structures of Vacuum Arc Remelting (VAR) ingots depend on the temperature distribution and fluid motion within the molten pool. In this paper, a three-dimensional multi-physics macroscale model for VAR is developed, based on the modular CFD software PHYSICA. This model is used to provide estimates of process parameters and to study complex physical phenomena, such as liquid metal flow with turbulence, heat transfer, solidification, and magnetohydrodynamics in the VAR process. The macromodel is coupled to a microscale solidification model. The micromodel combines stochastic nucleation and a modified decentred square/octahedron method to describe dendritic growth with a finite difference computation of solute diffusion. The resulting multiscale model allows prediction of the formation of microstructures in the solidifying mushy zone. This gives a better understanding of the whole VAR process from operational conditions to final ingot microstructures, as well as an essential first step in defect prediction.

Analytical sensitivity of interpolatory quadrature in force‐based frame elements

AbstractRecent literature shows the choice of an integration method in the state determination of force‐based frame finite elements has a significant influence on the computed element response. To assess the modeling uncertainty associated with integration methods in force‐based elements, analytical sensitivity of one‐dimensional interpolatory quadrature is developed via direct differentiation of the governing Vandermonde equations. Comparisons with finite difference calculations show that the combination of the Vandermonde equation sensitivity with equations that govern force‐based element response sensitivity leads to an accurate approach to stand‐alone response sensitivity analysis. Consistent with previous findings for material, load, and geometric parameters in finite element response sensitivity analysis, sensitivity with respect to parameters associated with the integration method in force‐based elements improves the efficiency of gradient‐based algorithms where the locations and/or weights of the integration method are treated as uncertain random variables. Copyright © 2009 John Wiley & Sons, Ltd.

Modulation of Main Lobe for Superfocusing Using Subwavelength Metallic Heterostructures

A subwavelength metallic heterostructure is put forth for the purpose of suppressing sidelobes and improving superfocusing at a quasi-far field region. Improvement has been made by means of optimization of the heterostructure composed of structured Au and Ag thin films. By tuning thicknesses of both the structured Au and Ag films, we can modulate propagation distance of the plasmonic lens and beam width of main lobe for the superfocusing. A finite-difference and time-domain (FDTD) algorithm-based computational numerical calculation was carried out for analyzing the focusing performance and tuning ability of the metal films. Our computational calculation results show that the sidelobes which play negative role for the focusing can be suppressed significantly in the case of the metal film thicknesses of hAu = 50 nm and hAg = 10 nm. Theoretically, the metallic structure with smaller thicknesses of the structured Au and Ag films is helpful for improving the focusing performance. This heterostructure-based device is possible to be used as a superlens or nanoprobe in data storage, nanometrology/inspection, and biosensing etc.

Comparison of Finite-Difference and Finite-Element Schemes for Magnetization Processes in 3-D Particles

This paper compares two numerical schemes for the simulation of magnetization dynamics in 3-D particles. The first one is based on the finite-difference computation of the Landau-Lifshitz equation and on the magnetostatic field evaluation by fast Fourier transforms. The second one handles the spatial discretization of the effective field expression by a nodal finite-element method and solves the Poisson equation with a finite-element/boundary-element technique. The convergence of the methods is studied by varying the time and space discretization.

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case ( a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X 1 Σ + and a 3 Σ + states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ + states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3) 3 Σ + states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ -doubling constants of the (1,2) 1 Π states and magnetic g -factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.

Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides

We investigate coupled-mode theory in designing high index contrast silicon-on-insulator waveguide couplers and arrayed waveguides. We develop and demonstrate a method of solution to the inverse problem of reconstructing the coupling matrix from the modal profiles obtained, in this case, from finite-difference frequency-domain field calculations. We show that whereas supermode theory provides a good approximation of the mode profiles, next-to-nearest-neighbor coupling becomes significant at small separation distances between arrayed waveguides. These distances are quantified for three different silicon-on-insulator material platforms. We also point out the phenomenon of field skewing and deformation at small separations.

J0406-3-1 超音波法による鋳造金型および凝固材料の温度分布モニタリングの基礎的検討(超音波計測・解析法の新展開(3))

An ultrasonic method has been applied to internal temperature measurements of heated materials during casting process. The principle of the method is based on the temperature dependence of the velocity of ultrasonic wave propagating through a material. An inverse analysis coupled with a finite difference calculation is used to determine a one-dimensional temperature distribution. In this work, an attempt to monitor both temperatures of a solidifying alloy and a die during casting process has been made. A low melting-point alloy is employed as the melt. Ultrasonic pulse-echo measurements are performed and the changes in the transit times of the reflected echoes through the die and the alloy are continuously acquired, and then the temperature distributions inside the die and the alloy have been estimated during the casting process.

105 超音波による鋳造プロセスの温度モニタリングに関する検討(構造部材や加工プロセスの信頼性を支える計測・評価技術)

In this work, an application of the ultrasonic method to internal temperature measurements of materials during casting has been studied. The principle of the method is based on the temperature dependence of the velocity of ultrasonic wave propagating through a material. An inverse analysis coupled with a finite difference calculation is used to determine a one-dimensional temperature distribution. An attempt to monitor both temperatures of a solidifying alloy and a die during casting process has been made. A low melting-point alloy is employed as the melt. Ultrasonic pulse-echo measurements are performed and the changes in the transit times of the reflected echoes through the die and the alloy are continuously acquired, and then the temperature distributions inside the die and the alloy have been estimated during the casting process.

102 レーザー超音波による材料表面の2次元温度分布の非接触モニタリング(構造部材や加工プロセスの信頼性を支える計測・評価技術)

An ultrasonic method for measuring a two-dimensional temperature distribution on a material surface is presented. The method provides non-contact measurements of surface temperature. The principle of the method is based on surface acoustic wave (SAW) measurements using a laser-ultrasonic technique and its two-dimensional scanning on a material surface. The surface temperature distribution is basically determined by an effective method consisting of SAW measurements and an inverse analysis coupled with a one-dimensional finite difference calculation. The ultrasonic method has been applied to the surface temperature measurement of an aluminum plate whose single side is being heated. The surface temperature distributions determined by the ultrasonic method almost agree with those measured using an infrared camera.

Non-invasive monitoring of temperature distribution inside materials with ultrasound inversion method

A novel ultrasound inversion method for monitoring the temperature distribution inside materials being heated is presented. The method consists of an ultrasonic pulse-echo measurement and a finite difference calculation for determining a 1D temperature distribution. At first, the inversion method has been applied to a numerical model of a heated plate having a temperature gradient to verify the validity of the method. To demonstrate the practicability of the method, a steel plate of 30 mm thickness being heated by contacting with 700°C molten aluminium is evaluated. Ultrasonic pulse-echo measurements are performed for the steel during heating and the inversion method is used to determine the temperature distribution inside the steel. The internal temperature distributions determined by the ultrasound inversion almost agree with those measured using thermocouples installed in the steel.

Numerical model to calculate microphysical influences on sound wave propagation in forests

There is a growing need for increasingly accurate and reliable numerical models to predict micrometeorological and turbulence conditions in complex sound wave propagation environments. In this paper, a prototype finite-difference computer model is developed to calculate the microphysical influences on sound speed in forested areas. Several numerical tests are conducted to assess model code capabilities using micrometeorological field data collected in June 2006. For the current analysis, the model domain and total number of grid points are greatly increased from earlier reported versions and the finite-difference numerical schemes for advection are modified to permit different inflow and outflow boundaries. Preliminary results for three cases are encouraging. Micrometeorological profiles and calculated fields of sound speed are presented. Some initial approximations of short-range acoustic transmission loss for the experimental test site are also discussed.

Numerical solving of the track wall equation in LR115 detectors etched in direct and reverse directions

Our equation of the track wall was solved numerically by using finite difference method and computer software MATHEMATICA. This method was applied for alpha particle tracks in LR115 detector, assuming both directions of etching, from the top and bottom of the sensitive layer. The equation of the track wall etched in reverse direction was derived, and has the same form as one for direct etching, with some difference in argument of V function. We will analyse the consequences of direct and reverse etching on the shape of alpha particles tracks with energies ranging from 2 to 4 MeV in thin LR115 NTDs.

Finite-Difference and Edge Finite-Element Approaches for Dynamic Micromagnetic Modeling

This paper presents the comparison between two different numerical schemes for the analysis of switching phenomena in magnetic thin films. The first one is based on the finite-difference computation of the Landau-Lifshitz equation and on the magnetostatic field evaluation by fast Fourier transforms. The second one handles the spatial discretization of the Landau-Lifshitz equation by the edge finite-element method and solves the Poisson equation for the magnetostatic field with a hybrid finite element/boundary element technique.

Electromagnetic field distribution calculation in solenoidal inductively coupled plasma using finite difference method

The electromagnetic field (both E and B fields) is calculated for a solenoidal inductively coupled plasma (ICP) discharge. The model is based on two-dimensional cylindrical coordinates, and the finite difference method is used for solving Maxwell equations in both the radial and axial directions. Through one-turn coil measurements, assuming that the electrical conductivity has a constant value in each cross section of the discharge tube, the calculated E and B fields rise sharply near the tube wall. The nonuniform radial distributions imply that the skin effect plays a significant role in the energy balance of the stable ICP. Damped distributions in the axial direction show that the magnetic flux gradually dissipates into the surrounding space. A finite difference calculation allows prediction of the electrical conductivity and plasma permeability, and the induction coil voltage and plasma current can be calculated, which are verified for correctness.

Experimental studies of the internal Goos–Hänchen shift for self-collimated beams in two-dimensional microwave photonic crystals

We study experimentally the Goos–Hänchen effect observed at the reflection of a self-collimated beam from the surface of a two-dimensional photonic crystal and describe a method for controlling the beam reflection through surface engineering. The microwave photonic crystal, fabricated from alumina rods, allows control of the output position of a reflected beam undergoing an internal Goos–Hänchen shift by changing the rod diameter at the reflection surface. The experimental data are in good agreement with the results of the finite-difference time-domain numerical calculations.

ACE—A FORTRAN subroutine for analytical computation of effective grid parameters for finite-difference seismic waveform modeling with standard Earth models

Despite the broad use of the heterogeneous finite-difference (FD) method for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of densities in grid cells. This scheme enables us to place a material discontinuity in an arbitrary position in the spatial grids. Standard Earth models have made a significant contribution to synthetic seismogram calculations with a variety of numerical procedures such as the FD method. For the FD computation of seismic waveform with these models, we must first ensure accurate treatment of material discontinuities in the radius (or depth). The present paper introduces a FORTRAN subroutine ACE which calculates effective parameters analytically for an arbitrary spatial region in either the radius or depth direction for four major standard Earth models, namely, the PREM, IASP91, SP6, and AK135. This program is intended for all FD users who are concerned with seismic wave simulation for these models.

Hypervelocity impact penetration mechanics

Abstract Inert dense metal penetrators having a mass and geometry capable of missile delivery offer significant potential for countering underground facilities at depths of tens of meters in hard rock. The proliferation of such facilities among countries whose support for terrorism and potential possession of Weapons of Mass Destruction (WMD) constitutes threats to world peace and U.S. Security. The Defense Threat Reduction Agency (DTRA), in cooperation with the U.S. Army Corps of Engineers, the Department of Energy National Laboratories and private sector R&D firms have pursued an aggressive research effort to explore the attributes of high velocity impact penetrators for countering such facilities. The penetration of crustal rocks with metal rods (such as tungsten or steel alloys) at high velocities involves complex wave propagation phenomena within the rod and inelastic response of both the penetrator and target material. In this paper we examine the sensitivity of penetration depth (for a fixed tungsten alloy mass impacting a limestone target) to impactor velocity, strength and geometry. Analyses are based upon a matrix of first principle finite difference calculations using the Sandia CTH (release 7.1) Shock Physics Code. Results indicate that impact velocity, penetrator yield strength and target yield strength strongly influence the penetration depth. Maximum penetration depth is achieved by a delicate trade off between penetrator kinetic energy and penetrator inelastic deformation (erosion). Numerical analyses for the parameter variations exercised in this study (impact velocities 1–3.5 km/s and penetrator yield strengths of 1–4 GPa) produced penetration depths of a tungsten alloy rod (length 200 cm, diameter 20 cm) which varied from 5.1 m to 28 m in a homogeneous limestone target.