Improvement of a Differential Method for Metallic Diffraction Gratings by Means of an Integral Method

Abstract

It is shown how a result from the integral method for calculating the diffraction from a metallic grating can be used to improve the differential method. The result from the integral formalism can be regarded as a vigorous theoretical basis for those methods that employ surface impedance boundary conditions.     

Comparative study of various methods of primary energy estimation in nucleon-nucleon interactions

The various available methods for the estimation of primary energy in nucleon-nucleon interactions have been examined by using the experimental data on angular distributions of shower particles from p-N interactions at two accelerator energies, 67 and 400 GeV. Three different groups of shower particle multiplicities have been considered for interactions at both energies. It is found that the different methods give quite different estimates of primary energy. Moreover, each method is found to give different values of energy according to the choice of multiplicity groups. It is concluded that the E_ch method is relatively the better method among all the methods available, and that within this method, the consideration of the group of small multiplicities gives a much better result. The method also yields plausible estimates of inelasticity in high energy nucleon-nucleon interactions.     

Depth-Resolved Surface Thermophysical Property Measurement by Laser-Produced Plasmas

A new laser-based method for real-time in situ measurement of thermophysical properties of materials has been developed. It entails production by a high-power laser pulse of a plasma plume from the surface of a condensed-phase specimen and simultaneous measurement of a material's response to the excitation. The specimen may be a solid or in a molten state at high temperatures. It has been shown that the thermal diffusivity can be determined, for instance, from the mass loss due to laser excitation. In one implementation the mass loss is determined from the impulse imparted on the surface by the ablated matter which is measured by an impulse transducer. In this paper, we present a new spectroscopic method for measurement of the mass loss, facilitating in situ non-contact measurement of the thermal diffusivity for the first time. An implementation of this method is described, whereby the thermal diffusivity of a complex layered surface is determined as a function of depth with resolutions as small as 13 nm.     

Finite-element analysis of unsteady temperature fields in parts of gas turbine engines

A method is proposed for the numerical solution of a problem of unsteady heat conduction which arises in the analysis of the thermal strength of power-generating equipment. The method employs finite-element techniques. It is of secondorder accuracy and is absolutely stable. The method is compared with the traditional Euler, Galerkin, and Crank-Nicolson methods. It is shown that the new method is more advantageous for solving unsteady heat-conduction problems in which the boundary conditions change rapidly with time. Examples are presented to illustrate the high degree of accuracy and reliability of the method.Leningrad Polytechnic Institute. Translated from Problemy Prochnosti, No. 12, pp. 82–87, December, 1989.     

Molecular dynamics calculation of the J-integral fracture criterion for nano-sized crystals

The critical J-integral is recognized as a valuable criterion for evaluating elastic-plastic fracture behavior of materials. It is, however, computationally complicated at the atomic scale for a nano-sized crystal when using the traditional integral method to reckon the traction force, strain, strain energy, etc. atom by atom. This paper attempts to propose an effective J-integral calculation method based on molecular dynamics (MD) simulations. The proposed method takes advantage of the potential energy interpretation of the J-integral, the main task in which is to calculate the potential energy difference of two identical crystal models with the neighboring crack length. As the potential energy of crystals at the atomic scale can be obtained easily from molecular dynamics simulations, the proposed method is thus computationally simple and especially applicable to complex crystal structures. A nickel crystal having an opening model I crack is investigated using this method. The critical J-integral in the ductile fracture plane (1\bar10) is calculated to be 4.424 Jm^–2. It is also found in this study that the onset of crack propagation does not coincide with the occurrence of the maximum tension stress for nano-sized crystals, which is different from conventional fracture mechanics observation.     

Conservative Eulerian method for numerical investigation of the hydrodynamics of liquids with a free surface

An effective numerical method is suggested for investigation of the hydrodynamics of liquids with a free surface. The method is a conservative Eulerian method that is useful for investigation of processes with turbulent behavior of the surface of the liquid that are accompanied by generation of waves, splash, spatter, etc. In the present method, apart from hydrodynamic equations, a transfer equation is used to describe transfer of the liquid phase. A method of numerical solution free from grid diffusion is suggested for this equation. It is proved that the conservative Eulerian method is adequate quantitatively for modeling the motions of a liquid with a slight deformation on its surface and adequate qualitatively for complicated motions.Dneprodzerzhinsk Industrial Institute, Dneprodzerzhinsk, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 3–4, pp. 228–234, September–October, 1994.     

Accurate reanalysis of structures by a preconditioned conjugate gradient method

A preconditioned conjugate gradient (PCG) method that is most suitable for reanalysis of structures is developed. The method presented provides accurate results efficiently. It is easy to implement and can be used in a wide range of applications, including non‐linear analysis and eigenvalue problems. It is shown that the PCG method presented and the combined approximations (CA) method developed recently provide theoretically identical results. Consequently, available results from one method can be applied to the other method. Effective solution procedures developed for the CA method can be used for the PCG method, and various criteria and error bounds developed for conjugate gradient methods can be used for the CA method. Numerical examples show that the condition number of the selected preconditioned matrix is much smaller than the condition number of the original matrix. This property explains the fast convergence and accurate results achieved by the method. Copyright © 2002 John Wiley & Sons, Ltd.     

Improved interpolation method suitable for very high-precision data applied to ge resistance thermometry

An improved method is proposed for eliminating the commonly occurring spurious ripples which arise from interpolation fits to very accurate data and have an unknown functional form. This method is illustrated by fitting an interpolation curve to a commercial Ge resistance thermometer characteristic. For data with a rms scatter of ± 0.8 mK, an interpolation accuracy of about ± 0.2–0.4 mK is achieved. This accuracy is about four times higher than that obtained from the generally used high-order, polynominal, least-squares fitting method. It is also explicitly shown that the proposed method is superior to other interpolation methods.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

Ultrasonic and Viscoelastic Properties of Small-Volume Mesogen Samples at the Phase Transition

The ultrasonic method is very informative for research of viscoelastic properties of mesogens at changing thermodynamic parameters of state. At phase transitions, anomalies of the velocity of propagation and coefficient of absorption of ultrasound waves as well as of viscoelastic properties are observed. These anomalies for liquid crystals are most pronounced at frequencies lower that 1 MHz. Up to now acoustic resonators with volumes of about 5 cm³ have been used, which considerably prevents the application of this method for science-based newly synthesized mesogenic compounds. This article presents experimental results obtained by means of a new resonator method with samples with volumes of 0.06 cm³ to 0.15 cm³. The velocity and coefficient of absorption of ultrasound were measured at frequencies from 0.68 MHz to 1.63 MHz for four mesogens: esters of alkyloxyphenylcyclo-hexane-2-carbonic acid and n-amylphenol. It has been shown that temperature dependencies of ultrasonic parameters obtained in small-volume cells correspond to those established previously by traditional methods using measuring cells with larger volumes. It is also shown that the temperature dependencies of the bulk viscosity and the bulk elasticity modulus derived from our ultrasonic measurements, in general features, duplicate the corresponding dependencies obtained by standard methods. It confirms that the proposed acoustic method is suitable for routine investigations of viscoelastic properties of small-volume samples of mesogenic compounds.     

Bayesian Inference of Nanoparticle-Broadened X-Ray Line Profiles

A single-step, self-contained method for determining the crystallite-size distribution and shape from experimental x-ray line profile data is presented. It is shown that the crystallite-size distribution can be determined without invoking a functional form for the size distribution, determining instead the size distribution with the least assumptions by applying the Bayesian/MaxEnt method. The Bayesian/MaxEnt method is tested using both simulated and experimental CeO₂ data, the results comparing favourably with experimental CeO₂ data from TEM measurements.     

A residual‐based finite element method for the Helmholtz equation

A new residual‐based finite element method for the scalar Helmholtz equation is developed. This method is obtained from the Galerkin approximation by appending terms that are proportional to residuals on element interiors and inter‐element boundaries. The inclusion of residuals on inter‐element boundaries distinguishes this method from the well‐known Galerkin least‐squares method and is crucial to the resulting accuracy of this method. In two dimensions and for regular bilinear quadrilateral finite elements, it is shown via a dispersion analysis that this method has minimal phase error. Numerical experiments are conducted to verify this claim as well as test and compare the performance of this method on unstructured meshes with other methods. It is found that even for unstructured meshes this method retains a high level of accuracy. Copyright © 2000 John Wiley & Sons, Ltd.     

Micromechanical analysis of effective properties of magneto-electro-thermo-elastic multilayer composites

An exact matrix method, originally proposed for evaluating effective elastic constants of generally anisotropic multilayer composites, is further developed for a micromechanical analysis of multilayers with various coupled physical effects including piezoelectricity, piezomagnetism, thermoelasticity (in consideration of entropy), and the Biot’s poroelasticity. The results for a BaTiO₃-CoFe₂O₄ magneto-electro-thermo-elastic (METE) multilayer coincide with those calculated using other micromechanical models based on the Mori-Tanaka method and the asymptotic homogenization method. It is shown that the present method can efficiently handle the most general type of multilayers with an arbitrary number of general anisotropic layers. Analytical expressions for effective material properties of a transversely isotropic METE multilayer composite are derived, from which those for functionally graded METE multilayers can be directly obtained. The effects of crystallographic orientations and volume fractions of constituting layers on the magnetoelectric coefficients are investigated for BaTiO₃-CoFe₂O₄ and LiNbO₃-CoFe₂O₄ multilayer composites. It is thus demonstrated that the present model can be used for the layout/material optimization of these METE multilayers to obtain a maximum product property such as the magnetoelectric, pyroelectric, and pyromagnetic coefficients. It is also shown that the same method can be used to predict the effective properties of poroelastic multilayers.     

A divide and conquer-based greedy search for two-machine no-wait job shop problems with makespan minimisation

This paper addresses a two-machine no-wait job shop problem with makespan minimisation. It is well known that this problem is strongly NP-hard. A divide-and-conquer approach (DC for short) is adopted to calculate the optimal timetable of a given sequence. It decomposes the given sequences into several independent parts and conquers them separately. A timetable enhancing method is introduced to further improve the timetable obtained by DC. It constructs a set of flow shop type jobs based on the result from DC and calculates the best timetable for these newly constructed jobs by the well-known Gilmore and Gomory method (GG for short). An efficient greedy search is proposed by integrating DC with GG to search for the best sequence. Experimental results show that the proposed algorithm can find the optimal solutions for 96% of the randomly generated test instances on average.     

Preparation of monodispersed mesoporous silica spheres with tunable pore size and pore-size effects on adsorption of Au nanoparticles and urease

Monodispersed mesoporous silica spheres (MMSS) with controllable porosity and pore size were successfully prepared by calcination method in the presence of complex salts. The effect of calcination temperature on the pore size of MMSS was examined. The results show that the pore size of MMSS samples can be tuned in the range from 3.20 to 46.80 nm by varying the calcination temperature. It is worth mentioning that the pore size of MMSS can be controlled on a much larger scale by this method compared to the templating approach, by which the pore size can only be expanded up to 10 nm. It is very advantageous for the application in loading enzymes. Moreover, it could be found that the method is feasible, effective and simple. In addition, the use of various MMSS samples as adsorbents for Au nanoparticles of different sizes as well as urease has also been demonstrated. It was confirmed that MMSS with adequate surface charge and optimum matching pore size showed excellent adsorption properties for Au nanoparticles and urease.     

Determination of metastable atom concentration by use of electrostatic probe technique

A method for determination of the metastable atom concentration in high pressure (>100 Torr) high density (> 10¹²cm²³); helium plasma from current–voltage characteristics of a single electrostatic probe is described. It is shown, that the flux of metastable atoms to the probe is controlled by ion sheath thickness and consequently by probe bias. The method for calculation of metastables concentration from the negative part of the current–voltage probe characteristics is proposed. The metastables concentrations measured in pulsed microwave discharge are in agreement with values calculated from the metastable balance equation.     

Effect of the scale factor on long-term strength

The author proposes a method of evaluating the effect of the transverse dimensions of specimens on long-term strength. The method is based on taking into account different roles of surface and internal layers of the metal in real tests. The concept of the damaged layer, formed on all side surfaces of the tested specimens as a result of corrosion, is introduced. The thickness of this layer is calculated from the condition according to which the long-term strength curve, determined for the unfractured central part of the cross section, does not depend on the geometry and dimensions of the specimens. It is shown that to calculate this parameter it is sufficient to have two long-term strength curves corresponding to test series of specimens of two thicknesses. A statistical method of determining all characteristics of the material has been proposed. The method is suitable for describing the available experimental data. It has been shown that the integral quantitative characteristics of the scatter of the experimental and theoretical values of the fracture time as a result of using the proposed method for a number of materials decrease by a factor of 10 or more.Translated from Problemy Prochnosti, No. 3, pp. 13–18, March, 1995.     

Approximate accounting of material damage in problems of the equilibrium of elastic shells

Expressions for determination of effective elasticity characteristics of materials weakened by plane elliptical cracks with interacting edges are derived using the energy method in the approximation of a small concentration. It is demonstrated that in the case of a complex stress state, the damaged material is modeled by a continuous physically nonlinear medium. Approaches to solution of problems of the equilibrium of shells formed from a similar kind of materials are discussed. An approximate method is proposed for investigation of the stability of shells formed from damaged materials; this method is similar to the concept of the tangent- modulus loading employed in the theory of the stability of elastoplastic bodies.Translated from Problemy Prochnosti, No. 3, pp. 20–30, March, 1996.     

Determination of effective surface energy of dynamic failure

A method is presented for determining the effective surface energy under dynamic loading. It is based on combining the effect of a valuewise different static tensile load and similar tensile pulses on identical specimens. It is shown that the method is insensitive to the sharpness of the originally made notch. This facilitates the form of the moving crack front to be controlled and eliminates the need to set up a fatigue crack. Graphs of variation in time of the SIF and length and velocity of the crack are given.Translated from Problemy Prochnosti, No. 7, pp. 10–14, July, 1992.     

Analytical method for determining the inverse functions of a system of nonlinear equations describing the static characteristics of a wind-tunnel strain-gauge balance

An analytical method is described for inverting functions in a system of nonlinear equations. The method has successfully passed certification for a system of nonlinear equations describing the static performance characteristics of a wind-tunnel strain-gauge balance. It is well suited to multicomponent instruments in which correlation is observed between the output signals. Translated from Izmeritel'naya Tekhnika, No. 1, pp. 8–10, January, 2000.