New Concepts for Three-Dimensional Shape Analysis

A new approach to machine representation and analysis of three-dimensional objects is presented. The representation, based on the notion of "skeleton" of an object leads to a scheme for comparing two given object views for shape relations. The objects are composed of long, thin, rectangular prisms joined at their ends. The input picture to the program is the digitized line drawing portraying the three-dimensional object. To compare two object views, two characteristic vertices called "cardinal point" and "end-cardinal point," occurring consistently at the bends and open ends of the object are detected. The skeletons are then obtained as a connected path passing through these points. The shape relationships between the objects are then obtained from the matching characteristics of their skeletons. The method explores the possibility of a more detailed and finer analysis leading to detection of features like symmetry, asymmetry and other shape properties of an object.

Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory

The eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2ϵ, are shown to converge (in a specific sense) to the eigenvalues and eigenfunctions of the well-known two-dimensional biharmonic operator of plate theory, as ϵ approaches zero. In the process, it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature. It is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three-dimensional solutions, in terms of powers of ϵ. The method presented here applies equally well to the stationary problem of linear plate theory, as shown elsewhere by P. Destuynder.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

On an Integrated Transfer Matrix method for multiply connected mufflers

The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency. (C) 2011 Elsevier Ltd. All rights reserved.

Treatment of NOx from Diesel Engine Exhaust by Dielectric Barrier Discharge Method

This paper reports improved performance of advantages when compared to its counterpart as it is cost discharge plasma in filtered engine exhaust treatment. Our effective, low capital and operation costs, salable by- paper deals about the removal of NOX emissions from the diesel products, and integration with the existing systems. In this exhaust by electric discharge plasma. For the treatment of diesel paper we describe an alternate reactor geometry referred to exhaust a new type of reactor referred to as cross-flow dielectric as cross-flow DBD reactor, where the exhaust gas flow barrier discharge reactor has been used, where the gas flow is perpendicular to the wire-cylinder reaction chamber. This perpendicular to the corona electrode. Experiments were reactor is used to treat the actual exhaust of a 3.75 kW diesel- conducted at different flow rates ranging from 2 l/min to 10 l/ generator set. The main emphasis is laid on the NOX treatment min. The discharge plasma assisted barrier discharge reactor of diesel engine exhaust. Experiments were carried out at has shown promising results in NOX removal at high flow rates.

Partition function for hindered, one-and multi-dimensional rotors

Writing the hindered rotor (hr) partition function as the trace of (rho) over cap = e(-beta(H) over cap hr), we approximate it by the sum of contributions from a set of points in position space. The contribution of the density matrix from each point is approximated by performing a local harmonic expansion around it. The highlight of this method is that it can be easily extended to multidimensional systems. Local harmonic expansion leads to a breakdown of the method a low temperatures. In order to calculate the partition function at low temperatures, we suggest a matrix multiplication procedure. The results obtained using these methods closely agree with the exact partition function at all temperature ranges. Our method bypasses the evaluation of eigenvalues and eigenfunctions and evaluates the density matrix for internal rotation directly. We also suggest a procedure to account for the antisymmetry of the total wavefunction in the same. (C) 2012 Elsevier B.V. All rights reserved.

Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier-Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant. (C) 2012 Elsevier Inc. All rights reserved.

Numerical Investigation of Heat Transfer from a Two-Dimensional Sudden Expansion Flow Using Nanofluids

Laminar forced convection heat transfer from two-dimensional sudden expansion flow of different nanofluids is studied numerically. The governing equations are solved using the unsteady stream function-vorticity method. The effect of volume fraction of the nanoparticles and type of nanoparticles on heat transfer is examined and found to have a significant impact. Local and average Nusselt numbers are reported in connection with various nanoparticle, volume fraction, and Reynolds number for expansion ratio 2. The Nusselt number reaches peak values near the reattachment point and reaches asymptotic value in the downstream. Bottom wall eddy and volume fraction shows a significant impact on the average Nusselt number.

A Numerical Scheme for Three-Dimensional Front Propagation and Control of Jordan Mode

As an example of a front propagation, we study the propagation of a three-dimensional nonlinear wavefront into a polytropic gas in a uniform state and at rest. The successive positions and geometry of the wavefront are obtained by solving the conservation form of equations of a weakly nonlinear ray theory. The proposed set of equations forms a weakly hyperbolic system of seven conservation laws with an additional vector constraint, each of whose components is a divergence-free condition. This constraint is an involution for the system of conservation laws, and it is termed a geometric solenoidal constraint. The analysis of a Cauchy problem for the linearized system shows that when this constraint is satisfied initially, the solution does not exhibit any Jordan mode. For the numerical simulation of the conservation laws we employ a high resolution central scheme. The second order accuracy of the scheme is achieved by using MUSCL-type reconstructions and Runge-Kutta time discretizations. A constrained transport-type technique is used to enforce the geometric solenoidal constraint. The results of several numerical experiments are presented, which confirm the efficiency and robustness of the proposed numerical method and the control of the Jordan mode.

Synthesis of one-dimensional N-doped Ga2O3 nanostructures: different morphologies and different mechanisms

N-doped monoclinic Ga2O3 nanostructures of different morphologies have been synthesized by heating Ga metal in ambient air at 1150 degrees C to 1350 degrees C for 1 to 5 h duration. Neither catalyst nor any gas flow has been used for the synthesis of N-doped Ga2O3 nanostructures. The morphology was controlled by monitoring the curvature of the Ga droplet. Plausible growth mechanisms are discussed to explain the different morphology of the nanostructures. Elemental mapping by electron energy loss spectroscopy of the nanostructures indicate uniform distribution of Ga, O and N. It is interesting to note that we have used neither nitride source nor any gas flow but the synthesis was carried out in ambient air. We believe that ambient nitrogen acts as the source of nitrogen. Unintentional nitrogen doping of the Ga2O3 nanostructures is a straightforward method and such nanostructures could be promising candidates for white light emission.

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN. (c) 2012 Elsevier Ltd. All rights reserved.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

Photoresist functionalisation method for high-density protein microarrays using photolithography

Since the last decade, there is a growing need for patterned biomolecules for various applications ranging from diagnostic devices to enabling fundamental biological studies with high throughput. Protein arrays facilitate the study of protein-protein, protein-drug or protein-DNA interactions as well as highly multiplexed immunosensors based on antibody-antigen recognition. Protein microarrays are typically fabricated using piezoelectric inkjet printing with resolution limit of similar to 70-100 mu m limiting the array density. A considerable amount of research has been done on patterning biomolecules using customised biocompatible photoresists. Here, a simple photolithographic process for fabricating protein microarrays on a commercially available diazo-naphthoquinone-novolac-positive tone photoresist functionalised with 3-aminopropyltriethoxysilane is presented. The authors demonstrate that proteins immobilised using this procedure retain their activity and therefore form functional microarrays with the array density limited only by the resolution of lithography, which is more than an order of magnitude compared with inkjet printing. The process described here may be useful in the integration of conventional semiconductor manufacturing processes with biomaterials relevant for the creation of next-generation bio-chips.

Geometrically non-linear dynamics of composite four-bar mechanisms

This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). (C) 2012 Elsevier Ltd. All rights reserved.

VAM applied to dimensional reduction of non-linear hyperelastic plates

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.