80 resultados para Linear equation with two unknowns
Resumo:
In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces art assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density,function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically, and using a numerical Laplace inversion technique, the dynamic stress intensity factors art obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.
Resumo:
The temperature and stress field in a thin plate with collinear cracks interrupting an electric current field are determined. This is accomplished by using a complex function method that allows a direct means of finding the distribution of the electric current, the temperature and stress field. Temperature dependency for the heat-transfer coefficient, coefficient of linear expansion and the elastic modulus are considered. As an example, temperature distribution is calculated for an alloy (No. GH2132) plate with two collinear cracks under high temperature. Relationships between the stress, temperature, electric density and crack length are obtained. Crack trajectories emanating from existing crack are predicted by application of the strain energy density criterion which can also be used for finding the load carrying capacity of the cracked plate. (C) 2003 Elsevier Ltd. All rights reserved.
Resumo:
In this paper, we studied the role of vertical component Of Surface tension of a water droplet on the deformation of membranes and microcantilevers (MCLs) widely used in lab-on-a-chip and micro-and nano-electromechanical system (MEMS/NEMS). Firstly, a membrane made of a rubber-like material, poly(dimethylsiloxane) (PDMS), was considered. The deformation was investigated using the Mooney-Rivlin (MR) model and the linear elastic constitutive relation, respectively. By comparison between the numerical solutions with two different models, we found that the simple linear elastic model is accurate enough to describe such kind of problem, which would be quite convenient for engineering applications. Furthermore, based on small-deflection beam theory, the effect of a liquid droplet on the deflection of a MCL was also studied. The free-end deflection of the MCL was investigated by considering different cases like a cylindrical droplet, a spherical droplet centered on the MCL and a spherical droplet arbitrarily positioned on the MCL. Numerical simulations demonstrated that the deflection might not be neglected, and showed good agreement with our theoretical analyses. (C) 2008 Elsevier Inc. All rights reserved.
Resumo:
The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.
Resumo:
A new calibration method for a photoelastic modulator is proposed. The calibration includes a coarse calibration and a fine calibration. In the coarse calibration, the peak retardation of the photoelastic modulator is set near 1.841 rad. In the fine calibration, the value of the zeroth Bessel function is obtained. The zeroth Bessel function is approximated as a linear equation to directly calculate the peak retardation. In experiments, the usefulness of the calibration method is verified and the calibration error is less than 0.014 rad. The calibration is immune to the intensity fluctuation of the light source and independent of the circuit parameters. The method specially suits the calibration of a photoelastic modulator with a peak retardation of less than a half-wavelength. (c) 2007 Optical Society of America.
Resumo:
Ultrasonic solvent extraction combined with solid-phase microextraction (SPME) with calix[4]arene/hydroxy-terminated silicone (C[4]/OHTSO) oil coated fiber was used to extract phthalate acid esters (PAEs) plasticizers in plastic, such as blood bags, transfusion tubing, food packaging bag, and mineral water bottle for analysis by gas chromatography (GC). Both extraction parameters (i.e. extraction time, extraction temperature, ionic strength) and conditions of the thermal desorption in a GC injector were optimized by analysis of eight phthalates. The fiber shows wonderful sensitivity and selectivity to the tested compounds. Owing to its high thermal stability (380 degreesC), the carryover effect that often encountered when using conventional fibers can be reduced by appropriately enhancing the injector temperature. The method showed linear response over two to four orders of magnitude with correlation coefficients (r) better than 0.996, and limits of detection (LOD) ranged between 0.006 and 0.084 mug l(-1). The relative standard deviation values obtained were less than or equal to 10%. bis-2-Ethylhexyl phthalate (DEHP) was the sole analyte detected in these plastics and recoveries were in the ranges 95.5-101.4% in all the samples. (C) 2004 Elsevier B.V. All rights reserved.
Resumo:
We derive the modified rate equations for an Aharonov-Bohm (AB) ring with two transversely coupled quantum dots (QD's) embedded in two arms in the presence of a magnetic field. We find that the interdot coupling between the two QD's can cause a temporal oscillation in electron occupation at the initial stage of the quantum dynamics, while the source-drain current decays monotonically to a stationary value. On the other hand, the interdot coupling equivalently divides the AB ring into two coupled subrings. That also destroys the normal AB oscillations with a period of 2pi, and generates new and complex periodic oscillations with their periods varying in a linear manner as the ratio between two magnetic fluxes (each penetrates one AB subring) increases. Furthermore, the interference between two subrings is also evident from the observation of the perturbed fundamental AB oscillation.
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The influence of lateral propagating modes on the threshold current and the spontaneous emission factor in selectively oxidized vertical cavity surface-emitting lasers (VCSELs) is investigated based on the mode behaviors of lateral propagating modes and the rate equation model. The numerical results show that the lateral propagating modes may be trapped in the aperture region for the selectively oxidized VCSEL with two oxide layers, one above and one below the active region. The output characteristics of VCSELs can be affected due to the reabsorption of the quasitrapped lateral propagating modes. A lower threshold current can be expected for a VCSEL with double oxide layers than that with a single oxide layer. The numerical results of rate equations also show that a larger spontaneous emission factor can be obtained by fitting the output-input curves for the VCSEL with double oxide layers. (C) 1999 American Institute of Physics. [S0021-8979(99)07919-0].
Resumo:
A series of new titanium complexes with two asymmetric bidentate beta-enaminoketonato (N,O) ligands (4b-t), [RN=CCF3)CHC(t-BU)O](2)TiCl2 (4b, R = -C6H4F(o); 4c, R = -C6H4F(m);4d, R = -C6H4F(p); 4e, R = - C6H3F2(2,3); 4f, R = -C6H3F2(2,4); 4g, R = -C6H3F2(2,5); 4h, R = -C6H3F2(2,6); 4i, R = -C6H3F2(3,4); 4j, R = -C6H3F2(3,5); 4k, R = -C6H2F3(2,3,4); 4l, R = -C6H2F3(3,4,5); 4m, R = -C6H4CF3(o); 4n, R =-C6H4CF3(m); 4o, R = -C6H4CF3(p); 4p, R = -C6H4Cl(p); 4q, R = -C6H4I(p); 4r, R = -C6H4NO2(P); 4s, R = -CH2C6H5; 4t, R = -C6H11), have been synthesized and characterized.
Resumo:
Copolymers of linear low-density polyethylene (LLDPE) grafted with two novel nonionic surfactants, acrylic glycerol monostearate ester (AGMS) and acrylic polyoxyethylenesorbitan monooleate ester (ATW-EEN80), containing hydrophilic and hydrophobic groups and 1-olefin double bond were prepared by using a plasticorder at 190 degrees C. To evaluate the grafting degree, two different approaches based on H-1-NMR data were proposed, and FTIR calibration was showed to validate these methods. The rheological response of the molten polymers, determined under dynamic shear flow at small-amplitude oscillations, indicated that crosslinking formation of the chains could be decreased with increasing the monomer concentration. Their thermal behavior was studied by DSC and polarization microscope (PLM): The crystallization temperature (T-C) of grafted LLDPE shifted to higher temperature compared with neat LLDPE because the grafted chains acted as nucleating agents. Water and glycerol were used to calculate the surface free energy of grafted LLDPE films.
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The non-covalent complexes between three flavonoid glycosides (quercitrin, hyperoside and rutin) and heptakis(2,6-di-O-methyl)-beta-cyclodextrin (DM-beta-CD) were investigated by electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICR-MS). The 1:1 complexation of each flavonoid glycoside (guest) to the DM-beta-CD (host) was monitored in the negative ion mode by mixing each guest with an up to 30-fold molar excess of the host. The binding constants for all complexes were calculated by a linear equation in the order: DM-beta-CD:quercitrin > DM-beta-CD:rutin > DM-beta-CD:hyperoside. A binding model for the complexes has also been proposed based on the binding constants and tandem mass spectrometric data of these complexes.
Resumo:
Four single polymers with two kinds of attachment of orange chromophore to blue polymer host for white electroluminescence (EL) were designed. The effect of the side-chain attachment and main-chain attachment on the EL efficiencies of the resulting polymers was compared. The side-chain-type single polymers are found to exhibit more efficient white EL than that of the main-chain-type single polymers. Based on the side-chain-type white single polymer with 4-(4-alkyloxy-phenyl)-7-(4-diphenylamino-phenyl)-2,1,3-benzothiadiazoles as the orange-dopant unit and polyfluorene as the blue polymer host, white EL with simultaneous orange (lambda(max) = 545 nm) and blue emission (lambda(max) = 432 nm/460 nm) is realised. A single-layer device (indium tin oxide/poly(3,4-ethylenedioxythiophene)/polymer/Ca/Al) made of these polymers emits white light with the Commission Internationale de l'Eclairage coordinates of (0.30,0.40), possesses a turn-on voltage of 3.5 V, luminous efficiency of 10.66 cd A(-1), power efficiency of 6.68 lm W-1, and a maximum brightness of 21240 cd m(-2).
Resumo:
Two heterometallic chain coordination polymers with the chemical formula {[Cu2Mn2L2(CH3OH)(H2O)] center dot 0.5CH(3)OH center dot 0.5CH(3)CH(2)OH}(n) (1) and {[Cu2Co2L2(H2O)(2)] center dot H2O}(n) (2) have been synthesized and characterized by IR, UV spectroscopy and single-crystal X-ray structural analysis, where H4L = 2-hydroxy-3-[(E)-({2-[(2-hydroxybetizoyl)amino]ethyl}imino)methyl] benzoic acid. Magnetic measurements showed that the two compounds exhibit antiferromagnetic coupling exchange interactions, and satisfactory fittings to the observed magnetic susceptibility data were obtained by assuming a linear four-spin arrangement with two isotropic magnetic exchange interactions.
Resumo:
The molecular structural parameters of indophenol and its derivatives were calculated by semi-empirical molecular orbital quantum chemical method,The relation between molecular structural parameters and formal potentials was analyzed by principal factor analysis and multiple Linear regression method. It was found that the formal potential of indophenols has a good relation with two-center electron exchange energy, E-ex (2), resonance energy of O-C bond, E-ex (C-1-O), and molecular ionization potential, I-p, among 19 moleclular structural parameters. The regression equation is E-0' = 1. 47 x 10 (-3) E-ex (two) - 5. 74 x 10 (-2) E-ex (C-1 - O) - 1. 41 x 10 (-2) I-p with RC = 0. 9999 and SD = 0. 00424. It was confirmed by the relation between structure parameters and formal potentials, and the thermodynamic stability of its intermediate products that the H (+) ionization is prior to the electron transfer step in the oxidation mechanism.
Resumo:
Promethazine and thioridazine were separated and detected by capillary electrophoresis with end-column amperometric detection. The influence of pH Value on oxidation potential, the peak current and the resolution were studied and the following conditions was selected: 0.03 M Na2HPO4 and 0.015 M citric acid at pH 3.0, detection potential at 1.10 V. The detection limits of these two substances were in the range of 10(-8) mol/l. The linear range spanned two to three orders of magnitude. This method was applied to the detection of promethazine and thioridazine spiked in urine. (C) 1999 Elsevier Science B.V. All rights reserved.