The Equations of Equilibrium in Orthogonal Curvilinear Reference Coordinates

Analytical solutions to problems in finite elasticity are most often derived using the semi-inverse approach along with the spatial form of the equations of motion involving the Cauchy stress tensor. This procedure is somewhat indirect since the spatial equations involve derivatives with respect to spatial coordinates while the unknown functions are in terms of material coordinates, thus necessitating the use of the chain rule. In this classroom note, we derive compact expressions for the components of the divergence, with respect to orthogonal material coordinates, of the first Piola-Kirchhoff stress tensor. The spatial coordinate system is also assumed to be an orthogonal curvilinear one, although, not necessarily of the same type as the material coordinate system. We show by means of some example applications how analytical solutions can be derived more directly using the derived results.

Mean field lattice model for adsorption isotherms in zeolite NaA

Using a lattice model for adsorption in microporous materials, pure component adsorption isotherms are obtained within a mean field approximation for methane at 300 K and xenon at 300 and 360 K in zeolite NaA. It is argued that the increased repulsive adsorbate-adsorbate interactions at high coverages must play an important role in determining the adsorption behavior. Therefore, this feature is incorporated through a "coverage-dependent interaction'' model, which introduces a free, adjustable parameter. Another important feature, the site volume reduction, has been treated in two ways: a van der Waal model and a 1D hard-rod theory [van Tassel et al., AIChE J. 40, 925 (1994)]; we have also generalized the latter to include all possible adsorbate overlap scenarios. In particular, the 1D hard-rod model, with our coverage-dependent interaction model, is shown to be in best quantitative agreement with the previous grand canonical Monte Carlo isotherms. The expressions for the isosteric heats of adsorption indicate that attractive and repulsive adsorbate-adsorbate interactions increase and decrease the heats of adsorption, respectively. It is concluded that within the mean field approximation, our simple model for repulsive interactions and the 1D hard-rod model for site volume reduction are able to capture most of the important features of adsorption in confined regions. (C) 1999 American Institute of Physics. [S0021-9606(99)70515-5].

Performance analysis of a modified spatial smoothing technique for direction estimation

The statistical performance analysis of ESPRIT, root-MUSIC, minimum-norm methods for direction estimation, due to finite data perturbations, using the modified spatially smoothed covariance matrix, is developed. Expressions for the mean-squared error in the direction estimates are derived based on a common framework. Based on the analysis, the use of the modified smoothed covariance matrix improves the performance of the methods when the sources are fully correlated. Also, the performance is better even when the number of subarrays is large unlike in the case of the conventionally smoothed covariance matrix. However, the performance for uncorrelated sources deteriorates due to an artificial correlation introduced by the modified smoothing. The theoretical expressions are validated using extensive simulations. (C) 1999 Elsevier Science B.V. All rights reserved.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

Sensing of delaminations in composite laminates using embedded magnetostrictive particle layers

This is an exploratory study to illustrate the feasibility of detecting delamination type of damage in polymeric laminates with one layer of magnetostrictive particles. One such beam encircled with excitation and sensing coils is used for this study. The change in stress gradient of the magnetostrictive layer in the vicinity of delamination shows up as a change in induced voltage in the sensing coil, and therefore provides a means to sense the presence of delamination. Recognizing the constitutive behavior of the Terfenol-D material is highly nonlinear, analytical expressions for the constitutive relations are developed by using curve fitting techniques to the experimental data. Analytical expressions that relate the applied excitation field with the stress and magnetic flux densities induced in the magnetostrictive layer are developed. Numerical methods are used to find the relative change in the induced voltage in the sensing coil due to the presence of delamination. A typical example of unidirectional laminate, with embedded delaminations, is used for the simulation purposes. This exploratory study illustrates that the open-circuit voltage induced in the sensing coil changes significantly (as large of 68 millivolts) with the occurrence of delamination. This feature can be exploited for device off-line inspection techniques and/or linking monitoring procedures for practical applications.

Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions

The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate-adsorbate interactions in the Brag-Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with epsilon(aa) as the adsorbate-adsorbate interaction parameter, the comparisons for different values of epsilon(aa)(*)=epsilon(aa)z/2kT, and number of sites per cage, n, illustrate that for -1 0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent epsilon(aa)) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages. (C) 1999 American Institute of Physics. [S0021-9606(99)70333-8].

Theory of combined AM and high-harmonic FM mode locked laser

Closed form solutions for a simultaneously AM and high-harmonic FM mode locked laser system is presented. Analytical expressions for the pulsewidth and pulsewidth-bandwidth products are derived in terms of the system parameters. The analysis predicts production of 17 ps duration pulses in a Nd:YAG laser mode locked with AM and FM modulators driven at 80 MHz and 1.76 GHz for 1 W modulator input power. The predicted values of the pulsewidth-bandwidth product lie between the values corresponding to the pure AM and FM mode locking values.

Performance analysis of single-symbol maximum likelihood decodable linear STBCs

Performance of space-time block codes can be improved using the coordinate interleaving of the input symbols from rotated M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) constellations. This paper is on the performance analysis of coordinate-interleaved space-time codes, which are a subset of single-symbol maximum likelihood decodable linear space-time block codes, for wireless multiple antenna terminals. The analytical and simulation results show that full diversity is achievable. Using the equivalent single-input single-output model, simple expressions for the average bit error rates are derived over flat uncorrelated Rayleigh fading channels. Optimum rotation angles are found by finding the minimum of the average bit error rate curves.

Receiver-only optimized Vector Quantization for fading channels

This paper considers the design and analysis of a filter at the receiver of a source coding system to mitigate the excess distortion caused due to channel errors. The index output by the source encoder is sent over a fading discrete binary symmetric channel and the possibly incorrect received index is mapped to the corresponding codeword by a Vector Quantization (VQ) decoder at the receiver. The output of the VQ decoder is then processed by a receive filter to obtain an estimate of the source instantiation. The distortion performance is analyzed for weighted mean square error (WMSE) and the optimum receive filter that minimizes the expected distortion is derived for two different cases of fading. It is shown that the performance of the system with the receive filter is strictly better than that of a conventional VQ and the difference becomes more significant as the number of bits transmitted increases. Theoretical expressions for an upper and lower bound on the WMSE performance of the system with the receive filter and a Rayleigh flat fading channel are derived. The design of a receive filter in the presence of channel mismatch is also studied and it is shown that a minimax solution is the one obtained by designing the receive filter for the worst possible channel. Simulation results are presented to validate the theoretical expressions and illustrate the benefits of receive filtering.

Implications of the half-duplex constraint on relay-aided cooperation using rateless codes

The half-duplex constraint, which mandates that a cooperative relay cannot transmit and receive simultaneously, considerably simplifies the demands made on the hardware and signal processing capabilities of a relay. However, the very inability of a relay to transmit and receive simultaneously leads to a potential under-utilization of time and bandwidth resources available to the system. We analyze the impact of the half-duplex constraint on the throughput of a cooperative relay system that uses rateless codes to harness spatial diversity and efficiently transmit information from a source to a destination. We derive closed-form expressions for the throughput of the system, and show that as the number of relays increases, the throughput approaches that of a system that uses more sophisticated full-duplex nodes. Thus, half-duplex nodes are well suited for cooperation using rateless codes despite the simplicity of both the cooperation protocol and the relays.

Enhanced lithium-ion transport in PEG-based composite polymer electrolyte with Mn0.03Zn0.97Al2O4 nanoparticles

The ion conduction and thermal properties of composite solid polymer electrolyte (SPE) comprising Poly(ethylene) Glycol (PEG, mol wt. 2000), lithium perchlorate (LiClO4) and insulating Mn0.03Zn0.97Al2O4 nanoparticle fillers were studied by complex impedance analysis and DSC techniques. The average size of the nanoparticles was determined by powder X-ray diffraction (XRD) using Scherrer's equation and was found to be similar to 8 nm. The same was also determined by TEM imaging and found to be similar to 12 nm. The glass transition temperature T, as measured by differential scanning calorimeter (DSC), showed a minimum at 5 mol% of narroparticles. Fractional crystallinity was determined using DSC. NMR was used to deter-mine crystallinity of a pure PEG sample, which was then used as the standard. Fractional crystallinity X. was the lowest for 5 mol% and beyond. The ionic conductivity of the composite polymer electrolyte containing 5 mol% Mn0.03Zn0.97Al2O4 nanoparticles was found to be 1.82 x 10(-5) S/cm, while for the pristine one, it was 7.27 x 10(-7) S/cm at room temperature. As a function of nanoparticle content, conductivity was observed to go through two maxima, one at around 5 mol% and another shallower one at around 12 mol%. The temperature dependence of conductivity could be divided into two regions, one consistent with Arrhenius behaviour and the other with VTF. We conclude that the enhancement of ionic conductivity on the addition of Mn0.03Zn0.97Al2O4 nanoparticles is a result of reduction in both the T, and the crystallinity. (C) 2002 Elsevier Science B.V. All rights reserved.

Large eddy simulation of a premixed flame with approximate deconvolution modeling

Approximate deconvolution modeling is a very recent approach to large eddy simulation of turbulent flows. It has been applied to compressible flows with success. Here, a premixed flame which forms in the wake of a flameholder has been selected to examine the subgrid-scale modeling of reaction rate by this new method because a previous plane two-dimensional simulation of this wake flame, using a wrinkling function and artificial flame thickening, had revealed discrepancies when compared with experiment. The present simulation is of the temporal evolution of a round wakelike flow at two Reynolds numbers, Re = 2000 and 10,000, based on wake defect velocity and wake diameter. A Fourier-spectral code has been used. The reaction is single-step and irreversible, and the rate follows an Arrhenius law. The reference simulation at the lower Reynolds number is fully resolved. At Re = 10,000, subgrid-scale contributions are significant. It was found that subgrid-scale modeling in the present simulation agrees more closely with unresolved subgrid-scale effects observed in experiment. Specifically, the highest contributions appeared in thin folded regions created by vortex convection. The wrinkling function approach had not selected subgrid-scale effects in these regions.

On using peak amplitude and rise time for AE source characterization

Acoustic Emission (AE) signals, which are electrical version of acoustic emissions, are usually analysed using a set of signal parameters. The major objective of signal analysis is to study the characteristics of the sources of emissions. Peak amplitude (P-a) and rise time (R-t) are two such parameters used for source characterization. In this paper, we theoretically investigate the efficiency of P-a and R-t to classify and characterize AE sources by modelling the input stress pulse and transducer. Analytical expressions obtained for P-a and R-t clearly indicate their use and efficiency for source characterization. It is believed that these results may be of use to investigators in areas like control systems and signal processing also.

A chemical approach to understand fragilities of glass-forming liquids

Fragility is viewed as a measure of the loss of rigidity of a glass structure above its glass transition temperature. It is attributed to the weakness of directional bonding and to the presence of a high density of low-energy configurational states. An a priori fragility function of electronegativities and bond distances is proposed which quite remarkably reproduces the entire range of reported fragilities and demonstrates that the fragility of a melt is indeed encrypted in the chemistry of the parent material. It has also been shown that the use of fragility-modified activation barriers in the Arrhenius function account for the whole gamut of viscosity behavior of liquids. It is shown that fragility can be a universal scaling parameter to collapse all viscosity curves on to a master plot.

System Dy-Fe-O: thermodynamic properties of ternary oxides using Calvet calorimetry and solid-state electrochemical cell

The enthalpy increments and the standard molar Gibbs energies of formation-of DyFeO3(s) and Dy3Fe5O12(s) have been measured using a Calvet micro-calorimeter and a solid oxide galvanic cell, respectively. A co-operative phase transition, related to anti-ferromagnetic to paramagnetic transformation, is apparent. from the heat capacity data for DyFeO3 at similar to 648 K. A similar type of phase transition has been observed for Dy3Fe5O12 at similar to 560 K which is related to ferrimagnetic to paramagnetic transformation. Enthalpy increment data for DyFeO3(s) and Dy3Fe5O12(s), except in the vicinity of the second-order transition, can be represented by the following polynomial expressions:{H(0)m(T) - H(0)m(298.15 K)) (Jmol(-1)) (+/-1.1%) = -52754 + 142.9 x (T (K)) + 2.48 x 10(-3) x (T (K))(2) + 2.951 x 10(6) x (T (K))(-1); (298.15 less than or equal to T (K) less than or equal to 1000) for DyFeO3(s), and {H(0)m(T) - H(0)m(298.15 K)} (Jmol(-1)) (+/-1.2%) = -191048 + 545.0 x (T - (K)) + 2.0 x 10(-5) x (T (K))(2) + 8.513 x 10(6) x (T (K))(-1); (208.15 less than or equal to T (K) less than or equal to 1000)for Dy3Fe5O12(s). The reversible emfs of the solid-state electrochemical cells: (-)Pt/{DyFeO3(s) + Dy2O3(s) + Fe(s)}/YDT/CSZ//{Fe(s) + Fe0.95O(s)}/Pt(+) and (-)Pt/{Fe(s) + Fe0.95O(s)}//CSZ//{DyFeO3(s) + Dy3Fe5O12(s) + Fe3O4(s)}/Pt(+), were measured in the temperature range from 1021 to 1250 K and 1035 to 1250 K, respectively. The standard Gibbs energies of formation of solid DyFeO3 and Dy3Fe5O12 calculated by the least squares regression analysis of the data obtained in the present study, and data for Fe0.95O and Dy2O3 from the literature, are given by Delta(f)G(0)m(DyFeO3,s)(kJmol(-1))(+/-3.2)= -1339.9 + 0.2473 x (T(K)); (1021 less than or equal to T (K) less than or equal to 1548)and D(f)G(0)m(Dy3Fe5O12,s) (kJmol(-1)) (+/-3.5) = -4850.4 + 0.9846 x (T (K)); (1035 less than or equal to T (K) less than or equal to 1250) The uncertainty estimates for Delta(f)G(0)m include the standard deviation in the emf and uncertainty in the data taken from the literature. Based on the thermodynamic information, oxygen potential diagram and chemical potential diagrams for the system Dy-Fe-O were developed at 1250 K. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.