A numerical approach to determine the sufficiency of given boundary data sets for uniquely estimating interior elastic properties

We consider an inverse elasticity problem in which forces and displacements are known on the boundary and the material property distribution inside the body is to be found. In other words, we need to estimate the distribution of constitutive properties using the finite boundary data sets. Uniqueness of the solution to this problem is proved in the literature only under certain assumptions for a given complete Dirichlet-to-Neumann map. Another complication in the numerical solution of this problem is that the number of boundary data sets needed to establish uniqueness is not known even under the restricted cases where uniqueness is proved theoretically. In this paper, we present a numerical technique that can assess the sufficiency of given boundary data sets by computing the rank of a sensitivity matrix that arises in the Gauss-Newton method used to solve the problem. Numerical experiments are presented to illustrate the method.

Methodology for Pavement Design Reliability and Back Analysis Using Markov Chain Monte Carlo Simulation

Given the increasing cost of designing and building new highway pavements, reliability analysis has become vital to ensure that a given pavement performs as expected in the field. Recognizing the importance of failure analysis to safety, reliability, performance, and economy, back analysis has been employed in various engineering applications to evaluate the inherent uncertainties of the design and analysis. The probabilistic back analysis method formulated on Bayes' theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis-Hastings algorithm has proved to be highly efficient to address this issue. It is also quite flexible and is applicable to any type of prior information. In this paper, this method has been used to back-analyze the parameters that influence the pavement life and to consider the uncertainty of the mechanistic-empirical pavement design model. The load-induced pavement structural responses (e.g., stresses, strains, and deflections) used to predict the pavement life are estimated using the response surface methodology model developed based on the results of linear elastic analysis. The failure criteria adopted for the analysis were based on the factor of safety (FOS), and the study was carried out for different sample sizes and jumping distributions to estimate the most robust posterior statistics. From the posterior statistics of the case considered, it was observed that after approximately 150 million standard axle load repetitions, the mean values of the pavement properties decrease as expected, with a significant decrease in the values of the elastic moduli of the expected layers. An analysis of the posterior statistics indicated that the parameters that contribute significantly to the pavement failure were the moduli of the base and surface layer, which is consistent with the findings from other studies. After the back analysis, the base modulus parameters show a significant decrease of 15.8% and the surface layer modulus a decrease of 3.12% in the mean value. The usefulness of the back analysis methodology is further highlighted by estimating the design parameters for specified values of the factor of safety. The analysis revealed that for the pavement section considered, a reliability of 89% and 94% can be achieved by adopting FOS values of 1.5 and 2, respectively. The methodology proposed can therefore be effectively used to identify the parameters that are critical to pavement failure in the design of pavements for specified levels of reliability. DOI: 10.1061/(ASCE)TE.1943-5436.0000455. (C) 2013 American Society of Civil Engineers.

Evaluation of Fracture Parameters by Double-G, Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (4), unstable fracture toughness (K-Ic(c)), unstable fracture toughness (K-Ic(un)) and initiation fracture toughness (K-Ic(ini)) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K-Ic(un) of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.

Cramer-Rao-Type Bounds for Sparse Bayesian Learning

In this paper, we derive Hybrid, Bayesian and Marginalized Cramer-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. We find that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. We also illustrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.

Application of a modified jogged-screw model for creep of titanium aluminides: evaluation of the key substructural parameters

A modification of the jogged-screw model has been adopted recently by the authors to explain observations of 1/2[110]-type jogged-screw dislocations in equiaxed Ti-48Al under creep conditions. The aim of this study has been to verify and validate the parameters and functional dependencies that have been assumed in this previous work. The original solution has been reformulated to take into account the finite length of the moving jog. This is a better approximation of the tall jog. The substructural model parameters have been further investigated in light of the Finite Length Moving Line (FLML) source approximation. The original model assumes that the critical jog height (beyond which the jog is not dragged) is inversely proportional to the applied stress. By accounting for the fact that there are three competing mechanisms (jog dragging, dipole dragging, dipole bypass) possible, we can arrive at a modified critical jog height. The critical jog height was found to be more strongly stress dependent than assumed previously. The original model assumes the jog spacing to be invariant over the stress range. However, dynamic simulation using a line tension model has shown that the jog spacing is inversely proportional to the applied stress. This has also been confirmed by TEM measurements of jog spacings over a range of stresses. Taylor's expression assumed previously to provide the dependence of dislocation density on the applied stress, has now been confirmed by actual dislocation density measurements. Combining all of these parameters and dependencies, derived both from experiment and theory, leads to an excellent prediction of creep rates and stress exponents. The further application of this model to other materials, and the important role of atomistic and dislocation dynamics simulations in its continued development is also discussed.

A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

We develop a unified model to explain the dynamics of driven one dimensional ribbon for materials with strain and magnetic order parameters. We show that the model equations in their most general form explain several results on driven magnetostrictive metallic glass ribbons such as the period doubling route to chaos as a function of a dc magnetic field in the presence of a sinusoidal field, the quasiperiodic route to chaos as a function of the sinusoidal field for a fixed dc field, and induced and suppressed chaos in the presence of an additional low amplitude near resonant sinusoidal field. We also investigate the influence of a low amplitude near resonant field on the period doubling route. The model equations also exhibit symmetry restoring crisis with an exponent close to unity. The model can be adopted to explain certain results on magnetoelastic beam and martensitic ribbon under sinusoidal driving conditions. In the latter case, we find interesting dynamics of a periodic one orbit switching between two equivalent wells as a function of an ac magnetic field that eventually makes a direct transition to chaos under resonant driving condition. The model is also applicable to magnetomartensites and materials with two order parameters. (C) 2013 American Institute of Physics. http://dx.doi.org/10.1063/1.4790845]

Estimating wind stress at the ocean surface from scatterometer observations

Wind stress is the most important ocean forcing for driving tropical surface currents. Stress can be estimated from scatterometer-reported wind measurements at 10 m that have been extrapolated to the surface, assuming a neutrally stable atmosphere and no surface current. Scatterometer calibration is designed to account for the assumption of neutral stability; however, the assumption of a particular sea state and negligible current often introduces an error in wind stress estimations. Since the fundamental scatterometer measurement is of the surface radar backscatter (sigma-0) which is related to surface roughness and, thus, stress, we develop a method to estimate wind stress directly from the scatterometer measurements of sigma-0 and their associated azimuth angle and incidence angle using a neural network approach. We compare the results with in situ estimations and observe that the wind stress estimations from this approach are more accurate compared with those obtained from the conventional estimations using 10-m-height wind measurements.

Delineation of seismic source zones based on seismicity parameters and probabilistic evaluation of seismic hazard using logic tree approach

The delineation of seismic source zones plays an important role in the evaluation of seismic hazard. In most of the studies the seismic source delineation is done based on geological features. In the present study, an attempt has been made to delineate seismic source zones in the study area (south India) based on the seismicity parameters. Seismicity parameters and the maximum probable earthquake for these source zones were evaluated and were used in the hazard evaluation. The probabilistic evaluation of seismic hazard for south India was carried out using a logic tree approach. Two different types of seismic sources, linear and areal, were considered in the present study to model the seismic sources in the region more precisely. In order to properly account for the attenuation characteristics of the region, three different attenuation relations were used with different weightage factors. Seismic hazard evaluation was done for the probability of exceedance (PE) of 10% and 2% in 50 years. The spatial variation of rock level peak horizontal acceleration (PHA) and spectral acceleration (Sa) values corresponding to return periods of 475 and 2500 years for the entire study area are presented in this work. The peak ground acceleration (PGA) values at ground surface level were estimated based on different NEHRP site classes by considering local site effects.

Influence of crack parameters on wavelet energy correlated damage index

This paper illustrates a Wavelet Coefficient based approach using experiments to understand the sensitivity of ultrasonic signals due to parametric variation of a crack configuration in a metal plate. A PZT patch sensor/actuator system integrated to a metal plate with through-thickness crack is used. The proposed approach uses piezoelectric patches, which can be used to both actuate and sense the ultrasonic signals. While this approach leads to more flexibility and reduced cost for larger scalability of the sensor/actuator network, the complexity of the signals increases as compared to what is encountered in conventional ultrasonic NDE problems using selective wave modes. A Damage Index (DI) has been introduced, which is function of wavelet coefficient. Experiments have been carried out for various crack sizes, crack orientations and band-limited tone-burst signal through FIR filter. For a 1 cm long crack interrogated with 20 kHz tone-burst signal, the Damage Index (DI) for the horizontal crack orientation increases by about 70% with respect to that for 135 degrees oriented crack and it increases by about 33% with respect to the vertically oriented crack. The detailed results reported in this paper is a step forward to developing computational schemes for parametric identification of damage using sensor/actuator network and ultrasonic wave.

Study on important diffusion parameters of binary Ni3Sn4 phase

Important diffusion parameters, such as-parabolic growth constant, integrated diffusivity, ratio of intrinsic diffusivities of species Ni and Sn, Kirkendall marker velocity and the activation energy for diffusion kinetics of binary Ni3Sn4 phase have been investigated with the help of incremental diffusion couple technique (Sn/Ni0.57Sn0.43) in the temperature range 200-150 degrees C. Low activation energy extracted from Arrhenius plot indicates grain boundary controlled diffusion process. The species Sn is three times faster than Ni at 200 degrees C. Further, the activation energy of Sn tracer diffusivity is greater than that of Ni.

Antioxidant and oxidative stress parameters in brain of Heteropneustes fossilis under air exposure condition; role of mitochondrial electron transport chain

Many fishes are exposed to air in their natural habitat or during their commercial handling. In natural habitat or during commercial handling, the cat fish Heteropneustes fossilis is exposed to air for > 24 h. Data on its oxidative metabolism in the above condition are not available. Oxidative stress (OS) indices (lipid and protein oxidation), toxic reactive oxygen species (ROS: H2O2) generation, antioxidative status (levels of superoxide dismutase, catalase, glutathione peroxidase and reductase, ascorbic acid and nonprotein sulfhydryl) and activities of electron transport chain (ETC) enzymes (complex I-IV) were investigated in brain tissue of H. fossilis under air exposure condition (0, 3, 6, 12 and 18 h at 25 degrees C). Decreased activities of antioxidant (except catalase) and ETC enzymes (except complex II) with increased H2O2 and OS levels were observed in the tissue under water deprivation condition. Positive correlation was observed for complex II activity and non-protein thiol groups with time period of air exposure. The critical time period to induce OS and to reduce most of the studied antioxidant level in brain was found to be 3-6 h air exposure. The data can be useful to minimize the stress generated during commercial handling of the live fishes those exposed to air in general and H. fossilis in particular. (C) 2013 Elsevier Inc. All rights reserved.

Influence of operational and geometrical parameters on the performance of twin thermoacoustic prime mover

Thermoacoustics is the interaction between heat and sound, which are useful in designing heat engines and heat pumps. Research in the field of thermoacoustics focuses on the demand to improve the performance which is achieved by altering operational, geometrical and fluid parameters. The present study deals with improving the performance of twin thermoacoustic prime mover, which has gained the significant importance in the recent years for the production of high amplitude sound waves. The performance of twin thermoacoustic prime mover is evaluated in terms of onset temperature difference, resonance frequency and pressure amplitude of the acoustic waves by varying the resonator length and charge pressures of fluid medium nitrogen. DeltaEC, the free simulation software developed by LANL, USA is employed in the present study to simulate the performance of twin thermoacoustic prime mover. Experimental and simulated results are compared and the deviation is found to be within 10%.

Parametrisation-free determination of the shape parameters for the pion electromagnetic form factor

Recent data from high-statistics experiments that have measured the modulus of the pion electromagnetic form factor from threshold to relatively high energies are used as input in a suitable mathematical framework of analytic continuation to find stringent constraints on the shape parameters of the form factor at t = 0. The method uses also as input a precise description of the phase of the form factor in the elastic region based on Fermi-Watson theorem and the analysis of the pi pi scattering amplitude with dispersive Roy equations, and some information on the spacelike region coming from recent high precision experiments. Our analysis confirms the inconsistencies of several data on the modulus, especially from low energies, with analyticity and the input phase, noted in our earlier work. Using the data on the modulus from energies above 0.65 GeV, we obtain, with no specific parametrisation, the prediction < r(pi)(2)> is an element of (0.42, 0.44) fm(2) for the charge radius. The same formalism leads also to very narrow allowed ranges for the higher-order shape parameters at t = 0, with a strong correlation among them.

Electrical switching in amorphous Si-Te-Ge thin films: Impact of input energy on crystallization process and switching parameters

Electrical switching studies on amorphous Si15Te74Ge11 thin film devices show interesting changes in the switching behavior with changes in the input energy supplied; the input energy determines the extent of crystallization in the active volume, which is reflected in the value of SET resistances. This in turn, determines the trend exhibited by switching voltage (V-t) for different input conditions. The results obtained are analyzed on the basis of the amount of Joule heat generated, which determines the temperature of the active volume. Depending on the final temperature, devices are rendered either in the intermediate state with a resistance of 5*10(2) Omega or the ON state with a resistance of 5*10(1) Omega. (C) 2013 Elsevier B.V. All rights reserved.

SEP-Optimal Transmit Power Policy for Peak Power and Interference Outage Probability Constrained Underlay Cognitive Radios

In underlay cognitive radio (CR), a secondary user (SU) can transmit concurrently with a primary user (PU) provided that it does not cause excessive interference at the primary receiver (PRx). The interference constraint fundamentally changes how the SU transmits, and makes link adaptation in underlay CR systems different from that in conventional wireless systems. In this paper, we develop a novel, symbol error probability (SEP)-optimal transmit power adaptation policy for an underlay CR system that is subject to two practically motivated constraints, namely, a peak transmit power constraint and an interference outage probability constraint. For the optimal policy, we derive its SEP and a tight upper bound for MPSK and MQAM constellations when the links from the secondary transmitter (STx) to its receiver and to the PRx follow the versatile Nakagami-m fading model. We also characterize the impact of imperfectly estimating the STx-PRx link on the SEP and the interference. Extensive simulation results are presented to validate the analysis and evaluate the impact of the constraints, fading parameters, and imperfect estimates.