Double Integral Method Research Articles

A novel explicit solution for twisting control of smart laminated cantilever composite plates/beams using inclined piezoelectric actuators

In the present work, a novel explicit analytical solution is proposed for obtaining twisting deformation and optimal shape control of smart laminated cantilever composite plates/beams using inclined piezoelectric actuators. The linear piezoelectricity and plate theories are adapted for the analysis. A novel double integral multivariable Fourier transformation method and discretised higher order partial differential unit step function equations are employed. For the first time, an exact solution is developed to analyse electro-mechanical twisting moments in smart composite structures. Since there are no published benchmark results for verification, a series of simple, accurate and robust finite element (FE) analysis models and realistic electro-mechanical coupled FE procedures are developed for the effective prediction of the structural behaviour of the smart laminated piezo-composite structures under arbitrary loads. In addition to the novelty of the explicit solution, more comprehensive FE simulations of smart structures and step-by-step guidelines are discussed. The effect of various parameters including electro-mechanical twisting coupling, layup thickness, actuators size, placement, and inclination angle, electrical voltage, stacking sequence, and geometrical dimension are taken into account. The comparison of results shows an excellent agreement. Unlike the earlier studies, the proposed method does not require the characteristic and trial deflection function to be predetermined.

Calculating the reflected radiation error between turbine blades and vanes based on double contour integral method

This paper presents a CFD (Computation Fluid Dynamic) simulation and experimental results for the reflected radiation error from turbine vanes when measuring turbine blade’s temperature using a pyrometer. In the paper, an accurate reflection model based on discrete irregular surfaces is established. Double contour integral method is used to calculate view factor between the irregular surfaces. Calculated reflected radiation error was found to change with relative position between blades and vanes as temperature distribution of vanes and blades was simulated using CFD. Simulation results indicated that when the vanes suction surface temperature ranged from 860K to 1060K and the blades pressure surface average temperature is 805K, pyrometer measurement error can reach up to 6.35%. Experimental results show that the maximum pyrometer absolute error of three different targets on the blade decreases from 6.52%, 4.15% and 1.35% to 0.89%, 0.82% and 0.69% respectively after error correction.

Calculation of Meshing Efficiency of Helical Gear Based on Double Integral Method

The meshing efficiency of helical gear transmission is calculated by using the method of double integral. The external involute helical gear meshing is taken and the model of helical gears is simplified by the idea of differential. The instantaneous efficiency equation of a meshing point is derived, and further more the rectangular coordinate system of meshing zone of helical gears is established. The average meshing efficiency of helical gears is achieved by using double integral method. Then, the influence of design parameters is studied and the efficiency formula is verified by comparing the theoretical results with relevant experimental data, which can provide a theoretical basis for decide the design parameters.

New explicit solution for static shape control of smart laminated cantilever piezo-composite-hybrid plates/beams under thermo-electro-mechanical loads using piezoelectric actuators

In this paper, a new explicit exact analytical solution is proposed for obtaining static deformation and optimal shape control of smart laminated cantilever piezo composite hybrid plates and beams under thermo-electro-mechanical loads using piezoelectric actuators. The linear piezoelectricity and plates theories were adapted for the analysis. A novel double integral multivariable Fourier transformation method combined with discretised higher order partial differential unit step function equations were employed. The effect of various parameters including arbitrary loads such as non-uniform thermal stresses, electrical and mechanical loads, layup thickness, piezoelectric actuators size and placement, stacking sequence, and geometrical dimension were considered. The results were then compared with some published benchmark results and good agreement was observed. Unlike the earlier studies, the proposed method does not require the characteristic and trial deflection function to be predetermined. Both, the embedded and bounded actuators are considered. Until now, the shape control task of reducing mid-plane deformation at free end in smart laminated cantilever plates and beams was unsolvable and approximations were typically employed in numerical analysis Yu et al. (2009). This problem becomes more complicated for wider and longer plates but the method proposed herein successfully resolves this issue.

Double path integral method for obtaining the mobility of the one-dimensional charge transport in molecular chain.

We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in a one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition (A.S. Mishchenko et al., Phys. Rev. Lett. 114, 146401 (2015)) of transport phenomena related to polaron motion in the molecular chain.

The Testimony and Application of Inequality Cauchy-Schwarz

This paper discusses the form of inequality Cauchy-Schwarz in the field of calculus, giving the different methods of proof, which includes Parameter method, variable upper limit integral function method, the double integral and definite integral definition method. What’s more, through a series of examples, it also reflects that the inequality Cauchy-Schwarz can make the process of proving the inequality more simple while certifying the Integral inequality.

Improved Simulation of Double Integrals Based on Monte-Carlo Method

The traditional method of solving double integral by Monte Carlo method is limited with the integral area, it can only be solved the double integral on the rectangular area. To address this limitation, based on the average method of Monte Carlo method,which puts forward that the uniform distribution should be combined with area of the integral region to improve algorithm, the special rectangle integral region is extended to the general integral region.In this way the simulation accuracy and computational efficiency is improved. Practical example shows that improved algorithm simplifies the calculation process, effectively reduces the computational difficulty, Improves the simulation accuracy and computational efficiency.The procedure is simple and easy to debug. The double integral calculation method is simple and effective, so this improved algorithm is more practical.

Cross-stream diffusion under pressure-driven flow in microchannels with arbitrary aspect ratios: a phase diagram study using a three-dimensional analytical model

This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection-diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability.

DISCRETE-TIME RECURRENT NEURAL NETWORKS AND ITS APPLICATION TO COMPRESSION OF INFRA-RED SPECTRUM

We study the discrete-time recurrent neural network that derived from the Leaky-integrator model and its application to compression of infra-red spectrum. Our results show that the discrete-time Leaky-integrator recurrent neural network (RNN) model can be used to approximate the continuous-time model and inherit its dynamical characters if a proper step size is chosen. Moreover, the discrete-time Leaky-integrator RNN model is absolutely stable. By developing the double discrete integral method and employing the state space search algorithm for the discrete-time recurrent neural network model, we demonstrate with quality spectra regenerated from the compressed data how to compress the infra-red spectrum effectively. The information we stored is the parameters of the system and its initial states. The method offers an ideal setting to carry out the recurrent neural network approach to chaotic cases of data compression.

A surface potential based drain current model for asymmetric double gate MOSFETs

In this paper, we present a generic surface potential based current voltage (I–V) model for doped or undoped asymmetric double gate (DG) MOSFET. The model is derived from the 1-D Poisson’s equation with all the charge terms included and the channel potential is solved for the asymmetric operation of DG MOSFET based on the Newton–Raphson iterative method. A noncharge sheet based drain current model based on the Pao-Sah’s double integral method is formulated in terms of front and back gate surface potentials at the source and drain end. The model is able to clearly show the dependence of the front and back surface potential and the drain current on the terminal voltages, gate oxide thicknesses, channel doping concentrations and the Silicon body thickness and a good agreement is observed with the 2-D numerical simulation results.

Precise methods for conducted EMI modeling, analysis, and prediction

Focusing on the state-of-the-art conducted EMI prediction, this paper presents a noise source lumped circuit modeling and identification method, an EMI modeling method based on multiple slope approximation of switching transitions, and double Fourier integral method modeling PWM conversion units to achieve an accurate modeling of EMI noise source. Meanwhile, a new sensitivity analysis method, a general coupling model for steel ground loops, and a partial element equivalent circuit method are proposed to identify and characterize conducted EMI coupling paths. The EMI noise and propagation modeling provide an accurate prediction of conducted EMI in the entire frequency range (0–10 MHz) with good practicability and generality. Finally a new measurement approach is presented to identify the surface current of large dimensional metal shell. The proposed analytical modeling methodology is verified by experimental results.

Synthesis, crystal structure and thermal decomposition kinetics of the complex [Sm(BA) 3bipy] 2

The complex of [Sm(BA) 3bipy] 2 (BA = benzoic acid; bipy = 2,2′-bipyridine) was obtained and characterized by elemental analysis, molar conductance, IR spectra, UV spectra, single crystal X-ray diffraction and TG–DTG techniques. The crystal is monoclinic with space group P2(1)/ n. The unit cell parameters are: a = 14.157(2) Å, b = 15.416(3) Å, c = 26.079(4) Å, β = 103.445(2)°. Two Sm 3+ ions are connected by four carboxylic groups through bridging bidentate mode. Each center Sm 3+ is eight-coordinated with a trigondodecahedron. The thermal decomposition behaviors of the title complex in a static air atmosphere were discussed by TG–DTG and IR techniques. The non-isothermal kinetics was investigated by using double equal-double step method and nonlinear integral isoconversional method. The mechanism function of the first decomposition step was determined. Meanwhile, the thermodynamic parameters (Δ H ≠, Δ G ≠ and Δ S ≠) and kinetic parameters (activation energy E and pre-exponential factor A) were also calculated. The lifetime equation at mass-loss of 10% was deduced as ln τ = −34.56 + 19299.15/ T by isothermal thermogravimetric analysis. The title complex can be used in many areas such as extraction, separation, germicide, catalysis and functional materials and so on.

Synthesis, characterization and thermal decomposition kinetics of Sm(III)complex with 2,4-dichlorobenzoate and 2,2′-bipyridine

The complex of [Sm(2,4-DClBA)3(bipy)]2 (2,4-DClBA, 2,4-dichlorobenzoate; bipy, 2,2′-bipyridine) was synthesized and characterized by elemental analysis, molar conductivity, IR and UV spectra. The thermal decomposition process of the complex was studied by means of TG–DTG and IR techniques. And its thermal decomposition kinetics was investigated via the analysis of the TG–DTG curves by jointly using double equal-double steps method and nonlinear integral isoconversional method. The activation energy E, the pre-exponential factor A and the most probable mechanism functions of the first decomposition stage were obtained. Meanwhile, the thermodynamic parameters (ΔH≠, ΔG≠ and ΔS≠) were also calculated. The lifetime equation at weight-loss of 10% was deduced as ln τ = −35.53 + 20200/T by isothermal thermogravimetric analysis.

Three-dimensional simulations of a platelet-shaped spheroid near a wall in shear flow

We have investigated the three-dimensional motion of an oblate spheroid-shaped particle or “platelet” close to an infinite planar wall in shear flow. The completed double layer-boundary integral equation method modified to include a flat surface boundary was used to compute the effects of the wall on the flow behavior of a platelet of aspect ratio 0.25. Platelet simulations were initiated with the platelet having its axis of symmetry normal to the surface. The platelet is observed to demonstrate three distinct regimes of flow, the dominant regime of flow being dependent on its initial height from the surface. Platelets further than 1.2 platelet radii from the surface display a “modified” Jeffery orbit with periodic rotational motion in the direction of flow (regime I). The presence of the wall retards platelet flow and more importantly introduces periodic lateral motion normal to the wall. When the platelet starts flowing at a height between 1.1 and 0.75 platelet radii from the surface (regime II), it is found to dip down and then “pole vault” off of the surface. Periodic platelet rotation and contact with the surface then ensues with no drift of the platelet away from the surface. In the third regime of flow, a platelet with an initial height of 0.7 platelet radii and below demonstrates wobble motion. The platelet neither rotates nor contacts the surface, but instead, moves laterally in a periodic manner as it translates in the direction of flow. Flow behavior typical of regime III is not observed at all spheroid aspect ratios. The range of initial heights that demonstrate regime III flow diminishes with increasing aspect ratio and regime III disappears completely above an aspect ratio of 0.41. If a platelet located at heights relevant to regime III is given an initial tilt about the y axis or x axis (where x is the flow direction), the resulting flow may either continue in regime III or shift to regime II, depending on the tilt angle. There is a small critical angle of tilt, the magnitude of which depends on the initial platelet height, above which the platelet flow behavior immediately transitions from regime III flow to that of regime II. Tilts about the x axis induce fully three-dimensional flow with rotational motion occurring about all three axes. Therefore, even small tilts about the x axis that are below the critical tilt angles can cause platelet flow to transform from regime III to II eventually at some point downstream. Thus, a platelet flowing close to the surface in linear shear has ample opportunity to contact the surface, an important event for initiating receptor-ligand binding of blood platelets to the injured vascular endothelium during the onset of hemostasis.

Excitation energy flow at 77 K in the photosynthetic apparatus of overwintering evergreens

ABSTRACTThe flow of excitation energy from the antennae to photosynthetic reaction centre complexes at 77 K was studied in leaves of two evergreen species, namely, snow gum (Eucalyptus pauciflora Sieb. ex Spreng.) and a hemiparasitic mistletoe (Amyema miquelii, Lehm. ex Miq.). The leaves that were naturally acclimated to winter conditions of freezing temperatures and high irradiance displayed the recently discovered cold‐hard‐band or CHB feature of the chlorophyll a fluorescence spectra (Gilmore &amp; Ball, Proc. Nat. Acad. Sci. USA 97:11098–11101, 2000). A streak‐camera‐spectrograph was used and the double convolution integral method for global analysis was applied to simultaneously acquire and simulate, respectively, the time‐ and wavelength‐dependence of all major chlorophyll a components (Gilmore et al. Phil. Trans. Roy. Soc. B‐London 355:1371–1384, 2000). The CHB coincided with changed amplitudes and decreased excited state lifetimes for the main F685 nm and F695 nm emission bands from the photosystem II (PSII) core‐inner‐antenna. The CHB dissipates energy as heat separate from PSII while also reducing the PSII quantum yield by competing for both photon absorption and antenna excitation. The CHB did not correlate with changes in the decay kinetics of the PSI antenna F740 nm band. The spectral‐kinetic features of the altered energy flow were similar in the unrelated evergreen species. These results are consistent with a functional association between the CHB, PSII energy dissipation and protective storage of chlorophyll in overwintering evergreens.

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship.

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.

Boundary Element Method, Volume 1: Applications in Thermo-Fluids and Acoustics

Boundary Element Method, Volume 1: Applications in Thermo-Fluids and Acoustics

放射熱伝達解析における形態係数の計算法についての研究

In this paper we examine accuracy and speed of calculating view factors about several geometries using Monte Carlo method, Hemi-cube method, double area integral method and Mitalas-Stephenson method. As a result, the following conclusions are revealed : If there is no obstruct in geometry, Mitalas-Stephenson method has overwhelmingly good performance than other method. Although Hemi-cube method is not good at calculating view factors with very high accuracy, it is faster than Monte Carlo method as far as ordinay precision is required. Monte Carlo method is slower than other method, but it is easy and safe to calculate view factors with high precision using this method.

Three-dimensional radiative transfer in an anisotropically scattering, semi-infinite medium: generalized reflection function

Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large.

Global spectral-kinetic analysis of room temperature chlorophyll a fluorescence from light-harvesting antenna mutants of barley.

This study presents a novel measurement, and simulation, of the time-resolved room temperature chlorophyll a fluorescence emission spectra from leaves of the barley wild-type and chlorophyll-b-deficient chlorina (clo) f2 and f104 mutants. The primary data were collected with a streak-camera-based picosecond-pulsed fluorometer that simultaneously records the spectral distribution and time dependence of the fluorescence decay. A new global spectral-kinetic analysis programme method, termed the double convolution integral (DCI) method, was developed to convolve the exciting laser pulse shape with a multimodal-distributed decay profile function that is again convolved with the spectral emission band amplitude functions. We report several key results obtained by the simultaneous spectral-kinetic acquisition and DCI methods. First, under conditions of dark-level fluorescence, when photosystem II (PS II) photochemistry is at a maximum at room temperature, both the clo f2 and clo f104 mutants exhibit very similar PS II spectral-decay contours as the wild-type (wt), with the main band centred around 685 nm. Second, dark-level fluorescence is strongly influenced beyond 700 nm by broad emission bands from PS I, and its associated antennae proteins, which exhibit much more rapid decay kinetics and strong integrated amplitudes. In particular a 705-720 nm band is present in all three samples, with a 710 nm band predominating in the clo f2 leaves. When the PS II photochemistry becomes inhibited, maximizing the fluorescence yield, both the clo f104 mutant and the wt exhibit lifetime increases for their major distribution modes from the minimal 205-500 ps range to the maximal 1500-2500 ps range for both the 685 nm and 740 nm bands. The clo f2 mutant, however, exhibits several unique spectral-kinetic properties, attributed to its unique PS I antennae and thylakoid structure, indicating changes in both PS II fluorescence reabsorption and PS II to PS I energy transfer pathways compared to the wt and clo f104. Photoprotective energy dissipation mediated by the xanthophyll cycle pigments and the PsbS protein was uninhibited in the clo f104 mutant but, as commonly reported in the literature, significantly inhibited in the clo f2; the inhibited energy dissipation is partly attributed to its thylakoid structure and PS II to PS I energy transfer properties. It is concluded that it is imperative with steady-state fluorometers, especially for in vivo studies of PS II efficiency or photoprotective energy dissipation, to quantify the influence of the PS I spectral emission.