Effect of sintering temperature on dielectric properties, vibrational modes and crystal structures of Ba[(Ni0.7Zn0.3)1/3Nb2/3]O3 ceramics

The Ba[(Ni_0.7Zn_0.3)_1/3Nb_2/3]O₃ solid solutions were sintered at 1450, 1500, and 1550 °C for 3 h, respectively, by conventional solid-state sintering method, so as to clarify the effect of the sintering temperatures on vibrational modes, crystal structures, and dielectric properties. Ceramics were characterized by X-ray diffraction (XRD), Raman spectroscopy and Fourier transform far-infrared reflection (FTIR) spectroscopy. Space group and crystal symmetry of Pm[`3]m Pm\bar{3}m were determined by XRD. Lattice vibrational spectra, obtained by Raman and FTIR spectroscopy, show the correlation among polar phonon modes, crystal structures, and dielectric properties of Ba[(Ni_0.7Zn_0.3)_1/3Nb_2/3]O₃ ceramics as a function of the sintering temperatures. The results demonstrate that the dielectric constant e_r \varepsilon_{r} reaches a maximum value of 35.713 at 1500 °C and is related to Raman shifts of the A_1g(O) modes and the FWHM values of the E_g(O) modes, the temperature coefficient of the capacitance t_c \tau_{c} , which gradually increases from −6 × 10⁻⁶/°C to 0, is closely related to the Raman shifts of E_g(O) modes, and the dielectric loss values are closely connected with the full width at half-maximum of E_g(O) active modes and the Raman shifts of of the A_1g(O) modes with the increasing temperatures. FTIR shows that the dielectric properties are closely related to the far-infrared phonon modes. Raman and FTIR active modes were indicated according to the group theory.     

Tables of the Inverse Laplace Transform of the Function [... formula ...]

The inverse transform, g(t) = ?^?1(e^?sβ), 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g(t). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g(t) for a number of values of β between 0.25 and 0.999. In addition, since g(t), regarded as a function of β, is uni-modal with a peak occurring at t = t_max we both tabulate and graph t_max and 1/g(t_max) as a function of β, as well as giving polynomial approximations to 1/g(t_max).     

A Quasi-Boundary Semi-Analytical Method for Backward in Time Advection-Dispersion Equation

In this paper, we take the advantage of an analytical method to solve the advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is employed to calculate the concentration field C(x, t) at any time t< T. Then, we consider a direct regularization by adding an extra term αC(x,0) on the final condition to carry off a second kind Fredholm integral equation. The termwise separable property of the kernel function permits us to transform itinto a two-point boundary value problem. The uniform convergence and error estimate of the regularized solution C^α(x,t) are provided and a strategy to select the regularized parameter is suggested. The solver used in this work can recover the spatial distribution of the groundwater contaminant concentration. Several numerical examples are examined to show that the new approach can retrieve all past data very well and is good enough to cope with heterogeneous parameters’ problems, even though the final data are noised seriously.     

Holographic grating study of mass and thermal diffusion of polystyrene/toluene solutions

The transient grating technique of thermal diffusion forced Rayleigh scattering (TDFRS) has been employed to study translational and thermal diffusion of polystyrene in toluene. Different molar masses and concentrations below or slightly above (lie overlap concentrationc ^* have been investigated. The translational diffusion coefficients agree well with results obtained from photon correlation spectroscopy. Small remaining diferences can be attributed to sample polydispersity. The molar mass independence of the thermal diffusion coefficient is confirmed, and thermal diffusion and Soret coefficients are compared with data obtained from thermal field flow fractionation and diffusion cell experiments.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–34, 1994, Boulder. Colorado, U.S.A.     

An inverse problem of simultaneously estimating contact conductance and heat transfer coefficient of exhaust gases between engine's exhaust valve and seat

The conjugate gradient method using two search step sizes is used to solve the inverse problem of simultaneously estimating the periodic thermal contact conductance, h_c(t), and the heat transfer coefficient of the exhaust gases, h_g(t), between the exhaust valve and seat in an internal combustion engine. The importance of the determination of h_c(t) and h_g(t) lie in that they are the critical factors for designing the cooling system and the insulation of the exhaust valve. The inverse analysis is based on the temperature measurements taken from the sensors placed in both the valve and seat regions during the transient process of operation. In this study two unknown timewise-varying functions h_c(t) and h_g(t) are to be estimated at the same time, thus two search step sizes with each one corresponding to each unknown function are derived. The results show that the CPU time for the inverse solutions using two search step sizes are greatly reduced than using just one search step size¹ for the determination of two unknowns, besides, it also shows that the inverse solutions are reliable even when the measurement errors are considered. The advantage of the conjugate gradient method is that no a priori information is needed on the variation of the unknown quantities, since the solution automatically determines the functional form over the domain specified. The successful development of the present technique can be applied to any kind of two-dimensional periodic contact problems, such as the determination of a two-dimensional contact conductance problem² and the temperature or heat flux behaviour on the inside wall of internal combustion engines³.     

The Analysis of Closed-Loop Dynamic-Stochastic Systems

Certain types of non-linear transformations of stochastic signal processes have proven useful in engineering applications. A form of processing called hard clipping (or hard limiting) has frequently been used in electronic systems which work in “real time” in order to reduce the number of information bits which the system has to process. With hard clipping only one binary digit is used per sample value of an input signal X(t). However, information is lost about X(t) and the spectrum which is calculated from the clipped signal is a distorted form of the original signal spectrum. By a sine transformation of the sample covariance of the clipped process, a consistent estimator is derived for the spectral density of X(t). The asymptotic variance-covariance function is calculated for this estimator.     

Analysis of Survival Data by Regression Techniques

The nature of the process of retirement of groups of industrial properties is so complex that it is difficult to postulate adequate mathematical models such aa those, employed in life-testing, etc. Assuming that there exists a survivor function, M(t), representing the proportion of a group remaining in service at time t, such function is given by exp [–y(t)], where y(t) is the time integral of the retirement rate, r(t) = –d(logM(t))/dt. Rather than to hazard a guess aa to the parametric form of any of these functions, it is the intent of this paper to approximate the integral, y(t), by a polynomial, whereupon M(t) may be graduated by the descending exponential function. For large samples it is found that the covariance structure for the polynomial regression of y(t) on t may be obtained from the multinomial distribution when the data are grouped. Thus the method of weighted least squares may be employed in fitting y(t). “Censored” data in no way vitiate the method.     

On a problem in radiotherapy: Questions of non-negativity

A well-known result is used to show that if g is a non-negative function and the radiation field, f, is its Radon transform, the dose field, f?, is the convolution of g with (1/πr) and is necessarily non-negative. Simple series expansions of f and f? are given, and the series for f is written as a finite Fourier series. Known properties of finite Fourier series are used to seek, fruitlessly, for useful conditions on the coefficients to ensure the non-negativity of f.     

Transport Properties of a Tl-2201 Film Close to the Critical Temperature: The Vortex Glass Transition

We have studied the I-V characteristics of a Tl-2201 film at zero field. In the regime in which flux creep is the dominant dissipation mechanism, the J _c -T curve is divided into two parts at a temperature T _g (about 82 K), close to the critical temperature (84 K). The I-V characteristics around T _g are well described using a flux creep model. For T>T _g , J _c /J _c (0) =0.445x(l-0.525t-0.5t ² ); for T _g , J _c /J _c (0) = 0.9x(1-0.595t-0.44t ² ). Differential resistance (dV/dI) as a function of the measuring current shows a change in curvature close to T _g . The I-V curves collapsed nicely into two branches by plotting (V/I)/|T–T _g | ^v(z-1) vs. (I/T)/|T _g –T| ^2v , indicating a current–reduced vortex glass transition.     

Solvable Brioschi Resolvents

 The Brioschi resolvent y ⁵ −10Zy ³ +45Z ² y−Z ² is a key component of an algorithm for calculating the roots of a general quintic polynomial. It is obtained from the general quintic polynomial by applying two Tschirnhausen transformations. In this paper it is shown that if the quintic polynomial is a solvable polynomial, then its associated parameter Z in the Brioschi resolvent satisfies Z=g(t) where g(t) is a rational function in ℚ(t) and t is chosen from an appropriate field. Received: July 23, 2001; revised version: October 14, 2002 Keywords: Solvable quintic, Brioschi quintic, resolvent sextic, parametrization. The author was supported by a research grant from the Natural Sciences and Engineering Research Council of Canada     

Synthesis and photoluminescence properties of Yb doped Ba5(PO4)3Cl phosphor for white light-emitting diodes

Yb²⁺ ion doped Ba₅(PO₄)₃Cl phosphor was synthesized by solid state reaction. Four distinct absorption bands were observed in the Ultraviolet (UV) light region due to the electronic transitions of Yb²⁺ ion from ¹S₀ ground state to ²F_5/2(t_2g), ²F_5/2(e_g), ²F_7/2(t_2g), and ²F_7/2(e_g) excited states. The main emission wavelength of the phosphor was around 630 nm. The optimized Yb²⁺ ion concentration was 0.2 mol% (λ_exc. = 400 nm). The calculated critical distance was about 8.729 Å and the concentration quenching was observed above 0.2 mol% due to the electric dipole–dipole interaction.     

Evaluating the efficacy of a group of nontraditional plasticizers on the glass transition temperature of ethyl cellulose polymer

Objective: The aim of this study was to investigate the efficiency of a homologous series of esters of dicarboxylic acid on ethyl cellulose polymer in terms of their glass transition temperatures (T_g). Methods: Ethyl cellulose polymer was plasticized with succinates (C-2), glutarates (C-5), adipates (C-6), pimelates (C-7), suberates (C-8), and sebacates (C-10) at different concentration levels. The film formation and physical state of plasticizers within the polymer were investigated and incompatibility of plasticizers was determined by nonhomogeneous system. Results: A decrease in T_g of the plasticized polymer was used as an indicator of plasticizing efficiency. Experimental T_g values were correlated with the theoretical ones predicted by Gordon–Taylor equation. Most of the experimental T_g values did not fit with the predicted ones. For all plasticizers (except succinates) the measured T_g was lower than calculated indicating negative deviation from the ideal behavior. Anti-plasticization was obtained with lower plasticizers concentration. Fourier transform infrared spectroscopy was used to determine the interactions between the polymer and plasticizers on T_g values in predicting the efficiency. Conclusions: The correlation between experimental and calculated T_g values verifies that physiochemical properties are the primary factors influencing the plasticization efficiency. However, further studies are needed to establish the plasticization efficiency.     

Elastodynamic Response of Cracked Orthotropic Strip Under Impact Loading

The paper presents the elastodynamic response of an infinite orthotropic strip of finite width containing a central crack opened by suddenly applied stresses. Integral transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane solved by iterations in the low frequency case. Analytic expressions for the dynamic stress intensity factors are obtained. Numerical results for two particular materials are given. The influence of different orthotropic constants on the magnitude of the overshoots in the stress intensity factors K ₁(t) and K ₂(t) are found.     

New Developments and Applications in Optical Radiometry

The numerical study of the transmission of laser pulses through a two-photon absorber is given for Fourier-limited and chaotic pulses. The light statistics are investigated through a calculation of the second-order correlation function g ⁽²⁾ which is shown to be very sensitive to the experimental conditions.     

Effect of interchain electron transfer on the phase transition of quasi-one-dimensional electron systems

The critical temperatures of phase transitions of quasi-one-dimensional systems are evaluated by assuming electron transfer between chains with intrachain interactions represented by the model of Bychkov, Gor'kov, and Dzyaloshinskii. We examine only the case of g ₁ > 0, where the renormalization group theory for an isolated chain gives reliable results. For small electron transfer energy t, the transition temperature T _c is an increasing function of t. As t gets larger, however, T _c becomes a decreasing function of t due to the tunneling of individual electrons, which destroys the coherent pairing states. A symmetry is found to exist between T _c of the triplet superconductivity and that of the spin density wave state which have the highest critical temperatures in the regions of g ₁ > 2g ₂ and g ₁ < 2g ₂, respectively.Supported in part by the Scientific Research Fund of the Ministry of Education.     

Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

This paper is aimed at exploring the interconversion path between the relaxation modulus E(t) and the corresponding complex modulus E ^?(ω) for linear viscoelastic solid materials. In contrast to other approximate methods, the fast Fourier transform (FFT) algorithm is directly applied on the time-dependent part of the viscoelastic response R(t). Firstly, the method foundations are presented. Then, a theoretical example is performed by means of a generalized Maxwell model, where the influence of sampling conditions and eventual experimental error and data dispersion is analyzed. Finally, an application example using experimental data is carried out to assess the method. As a result, the proposed procedure allows obtaining the complex modulus by means of relaxation tests, and vice versa.     

Radial transport in a porous medium with Dirichlet, Neumann and Robin-type inhomogeneous boundary values and general initial data: analytical solution and evaluation

The analytical solution is presented to the convection–diffusion equation describing the concentration of solutes in a radial velocity field due to extracting groundwater from or injecting water into an aquifer with arbitrary initial concentration data F(r), with r the radial distance, and an inhomogeneous mixed boundary condition G(t), with t the time, at the well radius r = r ₀. The analytical solution is obtained with a generalized Hankel transformation or with a Laplace transformation. The Hankel transformation turns out to be easier for G = 0, F ≠ 0, while the Laplace transformation is easier for F = 0, G ≠ 0. Both techniques can, however, deal with the full problem. The representation found by the generalized Hankel transform can also be found by the Laplace transform, through modification of the contour through the complex plane in the Bromwich integral for the inverse Laplace transform to the real axis. In practice, the numerical evaluation of the integral representation is difficult, due to the oscillating behavior of the integrands. A more appropriate numerical inversion procedure is also suggested, which circumvents the integration of the oscillating integrands, by an alternative modification of the contour in the Bromwich integral such that the new contour follows the steepest descent path starting from a saddle point at the real axis.     

Solution of Certain Problems in the Thermal Diffusion of Binary Gases

Two variants of the experimental method of unique determination of the thermal-diffusion ratio (K _t) of binary gases are described. A formula expressing the temperature and concentration dependence of K _t and obtained by a thermodynamic method is proposed.     

Optical pattern recognition in motion acquired scenes using a binary joint transform correlation

Abstract

The problem of detecting patterns in moved scenes is analysed. The correlation when the input scene presents a relative motion with respect to the recording system image is studied analytically and an original method for detecting patterns by means of a binary joint transform correlator is presented. The method is based on the compensation of the sign errors introduced in the joint power spectrum by the transfer function of the degradation. Two alternatives to determine the sign of the transfer function are demonstrated: the first is based on an algorithm to extract information from the Fourier spectrum of the blurred image and the second method determines the sign errors by post-processing the correlation. Digital simulations and optical results are provided.     

Theoretical and computational modelling of?instrumented indentation of?viscoelastic composites

In this study, we investigate the indentation of viscoelastic composites. The composite is assumed to consist of two phases, i.e., the filler and the matrix, which are linear elastic and linear viscoelastic material, respectively. Two cases are investigated: (1) hard fillers are scattered in a very soft matrix; (2) the matrix is much harder than the fillers. Particular attention is paid to the correlation between the indentation relaxation loads and the material and geometric parameters of the composite system. To this end, we perform a theoretical analysis which is followed by finite element analysis. Our main result is a simple relation correlating the reduced relaxation modulus of the matrix, E _m,r (t), with the indentation relaxation load P(t), i.e., E _m,r (t)=P(t)/P(0), where P(0) represents the indentation load at the starting point of the relaxation test. This result on one hand indicates that for the two cases under study the relaxation feature of the indentation load is determined by the reduced relaxation modulus of the matrix. On the other hand, the result shows that the reduced relaxation modulus of the matrix of the composites may be simply determined from the indentation relaxation load without invoking the knowledge of both the indenter geometry and the profile of indented solids.