Flux density calibration in diffuse optical tomographic systems

The solution of the forward equation that models the transport of light through a highly scattering tissue material in diffuse optical tomography (DOT) using the finite element method gives flux density (Phi) at the nodal points of the mesh. The experimentally measured flux (U-measured) on the boundary over a finite surface area in a DOT system has to be corrected to account for the system transfer functions (R) of various building blocks of the measurement system. We present two methods to compensate for the perturbations caused by R and estimate true flux density (Phi) from U-measured(cal). In the first approach, the measurement data with a homogeneous phantom (U-measured(homo)) is used to calibrate the measurement system. The second scheme estimates the homogeneous phantom measurement using only the measurement from a heterogeneous phantom, thereby eliminating the necessity of a homogeneous phantom. This is done by statistically averaging the data (U-measured(hetero)) and redistributing it to the corresponding detector positions. The experiments carried out on tissue mimicking phantom with single and multiple inhomogeneities, human hand, and a pork tissue phantom demonstrate the robustness of the approach. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE) DOI: 10.1117/1.JBO.18.2.026023]

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part II: comparison and validation

The analytical solutions for the coupled diffusion equations that are encountered in diffuse fluorescence spectroscopy/ imaging for regular geometries were compared with the well-established numerical models, which are based on the finite element method. Comparison among the analytical solutions obtained using zero boundary conditions and extrapolated boundary conditions (EBCs) was also performed. The results reveal that the analytical solutions are in close agreement with the numerical solutions, and solutions obtained using EBCs are more accurate in obtaining the mean time of flight data compared to their counterpart. The analytical solutions were also shown to be capable of providing bulk optical properties through a numerical experiment using a realistic breast model. (C) 2013 Optical Society of America

Friction Welding of Thixocast A356 Aluminium Alloy

In this paper, a numerical model for friction welding of thixo-cast materials is developed, which includes a coupling of thermal effect and plastic deformation using a finite element method (FEM). As the constitutive equations for flow behavior of materials for a thixo-cast material are expected to be different from those of conventionally cast material of the same alloy, the necessary material data are experimentally determined from isothermal hot compression tests of the A356 thixocast alloy. The Johnson-Cook model has been employed to represent the flow behavior of the thixocast A356 alloy. The purpose of this FEM analysis is to provide better understanding of the friction welding process of thixo-cast material, and to obtain optimized process parameters before an actual welding is carried out.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

Non-rotating beams isospectral to a given rotating uniform beam

In this paper, we seek to find non-rotating beams with continuous mass and flexural stiffness distributions, that are isospectral to a given uniform rotating beam. The Barcilon-Gottlieb transformation is used to convert the fourth order governing equation of a non-rotating beam, to a canonical fourth order eigenvalue problem. If the coefficients in this canonical equation match with the coefficients of the uniform rotating beam equation, then the non-rotating beam is isospectral to the given rotating beam. The conditions on matching the coefficients leads to a pair of coupled differential equations. We solve these coupled differential equations for a particular case, and thereby obtain a class of non-rotating beams that are isospectral to a uniform rotating beam. However, to obtain isospectral beams, the transformation must leave the boundary conditions invariant. We show that the clamped end boundary condition is always invariant, and for the free end boundary condition to be invariant, we impose certain conditions on the beam characteristics. We also verify numerically that the frequencies of the non-rotating beam obtained using the finite element method (FEM) are the exact frequencies of the uniform rotating beam. Finally, the example of beams having a rectangular cross-section is presented to show the application of our analysis. Since experimental determination of rotating beam frequencies is a difficult task, experiments can be easily conducted on these rectangular non-rotating beams, to calculate the frequencies of the rotating beam. (c) 2012 Elsevier Ltd. All rights reserved.

Synthesis and application of weight function for edge cracked semicircular disk (ECSD)

We analyze the utility of edge cracked semicircular disk (ECSD) for rapid assessment of fracture toughness using compressive loading. Continuing our earlier work on ECSD, a theoretical examination here leads to a novel way for synthesizing weight functions using two distinct form factors. The efficacy of ECSD mode-I weight function synthesized using displacement and form factor methods is demonstrated by comparing with finite element results. Theory of elasticity in conjunction with finite element method is utilized to analyze crack opening potency of ECSD under eccentric compression to explore newer configurations of ECSD for fracture testing.

Constraining complex aquifer geometry with geophysics (2-D ERT and MRS measurements) for stochastic modelling of groundwater flow

Stochastic modelling is a useful way of simulating complex hard-rock aquifers as hydrological properties (permeability, porosity etc.) can be described using random variables with known statistics. However, very few studies have assessed the influence of topological uncertainty (i.e. the variability of thickness of conductive zones in the aquifer), probably because it is not easy to retrieve accurate statistics of the aquifer geometry, especially in hard rock context. In this paper, we assessed the potential of using geophysical surveys to describe the geometry of a hard rock-aquifer in a stochastic modelling framework. The study site was a small experimental watershed in South India, where the aquifer consisted of a clayey to loamy-sandy zone (regolith) underlain by a conductive fissured rock layer (protolith) and the unweathered gneiss (bedrock) at the bottom. The spatial variability of the thickness of the regolith and fissured layers was estimated by electrical resistivity tomography (ERT) profiles, which were performed along a few cross sections in the watershed. For stochastic analysis using Monte Carlo simulation, the generated random layer thickness was made conditional to the available data from the geophysics. In order to simulate steady state flow in the irregular domain with variable geometry, we used an isoparametric finite element method to discretize the flow equation over an unstructured grid with irregular hexahedral elements. The results indicated that the spatial variability of the layer thickness had a significant effect on reducing the simulated effective steady seepage flux and that using the conditional simulations reduced the uncertainty of the simulated seepage flux. As a conclusion, combining information on the aquifer geometry obtained from geophysical surveys with stochastic modelling is a promising methodology to improve the simulation of groundwater flow in complex hard-rock aquifers. (C) 2013 Elsevier B.V. All rights reserved.

Detailed investigation of contact deformation in ZrN/Zr multiplayer-understanding the role of volume fraction, bilayer spacing, and morphology of interfaces

A systematic study was done to understand the influence of volume fractions and bilayer spacings for metal/nitride multilayer coating using finite element method (FEM). An axisymmetric model was chosen to model the real situation by incorporating metal and substrate plasticity. Combinations of volume fractions and bilayer spacings were chosen for FEM analysis consistent with experimental results. The model was able to predict trends in cracking with respect to layer spacing and volume fraction. Metal layer plasticity is seen to greatly influence the stress field inside nitride. It is seen that the thicker metal induces higher tensile stresses inside nitride and hence leads to lower cracking loads. Thin metal layers < 10 nm were seen to have curved interfaces, and hence, the deformation mode was interfacial delamination in combination with edge cracking. There is an optimum seen with respect to volume fraction similar to 13% and metal layer thickness similar to 30 nm, which give maximum crack resistance.

A POSTERIORI ERROR CONTROL OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC OBSTACLE PROBLEMS

In this article, we derive an a posteriori error estimator for various discontinuous Galerkin (DG) methods that are proposed in (Wang, Han and Cheng, SIAM J. Numer. Anal., 48: 708-733, 2010) for an elliptic obstacle problem. Using a key property of DG methods, we perform the analysis in a general framework. The error estimator we have obtained for DG methods is comparable with the estimator for the conforming Galerkin (CG) finite element method. In the analysis, we construct a non-linear smoothing function mapping DG finite element space to CG finite element space and use it as a key tool. The error estimator consists of a discrete Lagrange multiplier associated with the obstacle constraint. It is shown for non-over-penalized DG methods that the discrete Lagrange multiplier is uniformly stable on non-uniform meshes. Finally, numerical results demonstrating the performance of the error estimator are presented.

Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion

Adhesion can cause energy losses in asperities or particles coming into dynamic contact resulting in frictional dissipation, even if the deformation occurring is purely elastic. Such losses are of special significance in impact of nanoparticles and friction between surfaces under low contact pressure to hardness ratio. The objective of this work is to study the effect of adhesion during the normal impact of elastic spheres on a rigid half-space, with an emphasis on understanding the mechanism of energy loss. We use finite element method for modeling the impact phenomenon, with the adhesion due to van der Waals force and the short-range repulsion included as body forces distributed over the volume of the sphere. This approach, in contrast with commonly used surface force approximation, helps to model the interactions in a more precise way. We find that the energy loss in impact of elastic spheres is negligible unless there are adhesion-induced instabilities. Significant energy loss through elastic stress waves occurs due to jump-to-contact and jump-out-of-contact instabilities and can even result in capture of the elastic sphere on the half-space.

Note on modelling directionality in piezoresistivity

When computing the change in electrical resistivity of a piezoresistive cubic material embedded in a deforming structure, the piezoresistive and the stress tensors should be in the same coordinate system. While the stress tensor is usually calculated in a coordinate system aligned with the principal axes of a regular structure, the specified piezoresistive coefficients may not be in that coordinate system. For instance, piezoresistive coefficients are usually given in an orthogonal cartesian coordinate system aligned with the <100> crystallographic directions and designers sometimes deliberately orient a crystallographic direction other than <100> along the principal directions of the structure to increase the gauge factor. In such structures, it is advantageous to calculate the piezoresistivity tensor in the coordinate system along which the stress tensors are known rather than the other way around. This is because the transformation of stress will have to be done at every point in the structure but piezoresistivity tensor needs to be transformed only once. Here, using tensor transformation relations, we show how to calculate the piezoresistive tensor along any arbitrary Cartesian coordinate system from the piezoresistive coefficients for the <100> coordinate system. Some of the software packages that simulate the piezoresistive effect do not have interfaces for calculation of the entire piezoresistive tensor for arbitrary directions. This warrants additional work for the user because not considering the complete piezoresisitive tensor can lead to large errors. This is illustrated with an example where the error is as high as 33%. Additionally, for elastic analysis, we used hybrid finite element formulation that estimates stresses more accurately than displacement-based formulation. Therefore, as shown in an example where the change in resistance can be calculated analytically, the percentage error of our piezoresistive program is an order of magnitude lower relative to displacement-based finite element method.

Evolution of Surface Roughness During Electropolishing

The characteristics of surface roughness span a range of length scales determined by the nature of the surface generation process. The mechanism by which material is removed at a length scale determines the roughness at that scale. Electropolishing preferentially reduces the peaks of surface protuberances at sub-micron length scales to produce smooth surfaces. The material removal in electropolishing occurs by two different mechanisms of anodic leveling and microsmoothing. Due to insufficient lateral resolution, individual contribution of these two mechanisms could not be measured by conventional roughness measurement techniques and parameters. In this work, we utilize the high lateral resolution offered by Atomic force microscopy along with the power spectral density method of characterization, to study the evolution of roughness during electropolishing. The power spectral density show two corner frequencies indicating the length scales over which the two mechanisms operate. These characteristic frequencies are found to be a function of the electropolishing time and hence can be used to optimize the electropolishing process.

Crack stability in edge-notched clamped beam specimens: modeling and experiments

Stability of a fracture toughness testing geometry is important to determine the crack trajectory and R-curve behavior of the specimen. Few configurations provide for inherent geometric stability, especially when the specimen being tested is brittle. We propose a new geometrical construction called the single edge notched clamped bend specimen (SENCB), a modified form of three point bending, yielding stable cracking under load control. It is shown to be particularly suitable for small-scale structures which cannot be made free-standing, (e.g., thin films, coatings). The SENCB is elastically clamped at the two ends to its parent material. A notch is inserted at the bottom center and loaded in bending, to fracture. Numerical simulations are carried out through extended finite element method to derive the geometrical factor f(a/W) and for different beam dimensions. Experimental corroborations of the FEM results are carried out on both micro-scale and macro-scale brittle specimens. A plot of vs a/W, is shown to rise initially and fall off, beyond a critical a/W ratio. The difference between conventional SENB and SENCB is highlighted in terms of and FEM simulated stress contours across the beam cross-section. The `s of bulk NiAl and Si determined experimentally are shown to match closely with literature values. Crack stability and R-curve effect is demonstrated in a PtNiAl bond coat sample and compared with predicted crack trajectories from the simulations. The stability of SENCB is shown for a critical range of a/W ratios, proving that it can be used to get controlled crack growth even in brittle samples under load control.

Effect of Process Deviations on Performance of Piezoresistive Pressure Sensors

Diaphragm thickness and the corresponding piezoresistor locations change due to over or under etching in bulk micromachined piezoresistive pressure sensor which intern influences the device performance. In the present work, variation of sensitivity and nonlinearity of a micro electro mechanical system low pressure sensor is investigated. The sensor is modeled using finite element method to analyze the variation of sensitivity and nonlinearity with diaphragm thickness. To verify the simulated results, the sensors with different diaphragm thicknesses are fabricated. The models are verified by comparing the calculated results with experimental data. This study is potentially useful for the researchers as most of the times the diaphragm is either over-etched or under-etched due to inherent variation in wafer thickness and involving manual operations.

Numerical modeling of the non-isothermal liquid droplet impact on a hot solid substrate

The heat transfer from a solid phase to an impinging non-isothermal liquid droplet is studied numerically. A new approach based on an arbitrary Lagrangian-Eulerian (ALE) finite element method for solving the incompressible Navier Stokes equations in the liquid and the energy equation within the solid and the liquid is presented. The novelty of the method consists in using the ALE-formulation also in the solid phase to guarantee matching grids along the liquid solid interface. Moreover, a new technique is developed to compute the heat flux without differentiating the numerical solution. The free surface and the liquid solid interface of the droplet are represented by a moving mesh which can handle jumps in the material parameter and a temperature dependent surface tension. Further, the application of the Laplace-Beltrami operator technique for the curvature approximation allows a natural inclusion of the contact angle. Numerical simulation for varying Reynold, Weber, Peclet and Biot numbers are performed to demonstrate the capabilities of the new approach. (C) 2014 Elsevier Ltd. All rights reserved.