A fixed-grid finite element based enthalpy formulation for generalized phase change problems: role of superficial mushy region

The enthalpy method is primarily developed for studying phase change in a multicomponent material, characterized by a continuous liquid volume fraction (phi(1)) vs temperature (T) relationship. Using the Galerkin finite element method we obtain solutions to the enthalpy formulation for phase change in 1D slabs of pure material, by assuming a superficial phase change region (linear (phi(1) vs T) around the discontinuity at the melting point. Errors between the computed and analytical solutions are evaluated for the fluxes at, and positions of, the freezing front, for different widths of the superficial phase change region and spatial discretizations with linear and quadratic basis functions. For Stefan number (St) varying between 0.1 and 10 the method is relatively insensitive to spatial discretization and widths of the superficial phase change region. Greater sensitivity is observed at St = 0.01, where the variation in the enthalpy is large. In general the width of the superficial phase change region should span at least 2-3 Gauss quadrature points for the enthalpy to be computed accurately. The method is applied to study conventional melting of slabs of frozen brine and ice. Regardless of the forms for the phi(1) vs T relationships, the thawing times were found to scale as the square of the slab thickness. The ability of the method to efficiently capture multiple thawing fronts which may originate at any spatial location within the sample, is illustrated with the microwave thawing of slabs and 2D cylinders. (C) 2002 Elsevier Science Ltd. All rights reserved.

Water quality parameter estimation in steady-state distribution system

The maintenance of chlorine residual is needed at all the points in the distribution system supplied with chlorine as a disinfectant. The propagation and level of chlorine in a distribution system is affected by both bulk and pipe wall reactions. It is well known that the field determination of wall reaction parameter is difficult. The source strength of chlorine to maintain a specified chlorine residual at a target node is also an important parameter. The inverse model presented in the paper determines these water quality parameters, which are associated with different reaction kinetics, either in single or in groups of pipes. The weighted-least-squares method based on the Gauss-Newton minimization technique is used for the estimation of these parameters. The validation and application of the inverse model is illustrated with an example pipe distribution system under steady state. A generalized procedure to handle noisy and bad (abnormal) data is suggested, which can be used to estimate these parameters more accurately. The developed inverse model is useful for water supply agencies to calibrate their water distribution system and to improve their operational strategies to maintain water quality.

On a Novel Geometric Representation of Rotation

This paper presents a novel method of representing rotation and its application to representing the ranges of motion of coupled joints in the human body, using planar maps. The present work focuses on the viability of this representation for situations that relied on maps on a unit sphere. Maps on a unit sphere have been used in diverse applications such as Gauss map, visibility maps, axis-angle and Euler-angle representations of rotation etc. Computations on a spherical surface are difficult and computationally expensive; all the above applications suffer from problems associated with singularities at the poles. There are methods to represent the ranges of motion of such joints using two-dimensional spherical polygons. The present work proposes to use multiple planar domain “cube” instead of a single spherical domain, to achieve the above objective. The parameterization on the planar domains is easy to obtain and convert to spherical coordinates. Further, there is no localized and extreme distortion of the parameter space and it gives robustness to the computations. The representation has been compared with the spherical representation in terms of computational ease and issues related to singularities. Methods have been proposed to represent joint range of motion and coupled degrees of freedom for various joints in digital human models (such as shoulder, wrist and fingers). A novel method has been proposed to represent twist in addition to the existing swing-swivel representation.

Electrical Breakdown of Gases Between Coaxial Cylindrical Electrodes in Crossed Electric and Magnetic Fields

Sparking potentials have been measured in nitrogen and dry air between coaxial cylindrical electrodes for values of n = R2/R1 = approximately 1 to 30 (R1 = inner electrode radius, R2 = outer electrode radius) in the presence of crossed uniform magnetic fields. The magnetic flux density was varied from 0 to 3000 Gauss. It has been shown that the minimum sparking potentials in the presence of the crossed magnetic field can be evaluated on the basis of the equivalent pressure concept when the secondary ionization coefficient does not vary appreciably with B/p (B = magnetic flux density, p = gas pressure). The values of secondary ionization coefficients �¿B in nitrogen in crossed fields calculated from measured values of sparking potentials and Townsend ionization coefficients taken from the literature, have been reported. The calculated values of collision frequencies in nitrogen from minimum sparking potentials in crossed fields are found to increase with increasing B/p at constant E/pe (pe = equivalent pressure). Studies on the similarity relationship in crossed fields has shown that the similarity theorem is obeyed in dry air for both polarities of the central electrode in crossed fields.

Fracture analysis of cracked plate panels using NI-MVCCI technique

The objective of this paper is to propose a numerically integrated modified virtual crack closure integral (NI-MVCCI) technique for fracture analysis of cracked plate panels. NI-MVCCI technique is generalized one and the expressions for computing the strain energy release rate (SERR) are independent of the finite element employed. NI-MVCCI technique has been demonstrated for 4-noded, 8-noded (regular and quarter-point) and 9-noded isoparametric finite elements. Numerical studies on fracture analysis of 2-D crack (mode-I and mode-II) problems have been conducted employing these elements. SERR and stress intensity factors (SIF) have been computed for these problems and found to be in good agreement with the respective analytical solutions available in the literature. The appropriate Gauss numerical integration order to be employed for each of these elements for accurate computation of SERR and SIF has been recommended based on the studies.

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography

We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss-Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant. (c) 2012 Optical Society of America

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.

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data

We develop iterative diffraction tomography algorithms, which are similar to the distorted Born algorithms, for inverting scattered intensity data. Within the Born approximation, the unknown scattered field is expressed as a multiplicative perturbation to the incident field. With this, the forward equation becomes stable, which helps us compute nearly oscillation-free solutions that have immediate bearing on the accuracy of the Jacobian computed for use in a deterministic Gauss-Newton (GN) reconstruction. However, since the data are inherently noisy and the sensitivity of measurement to refractive index away from the detectors is poor, we report a derivative-free evolutionary stochastic scheme, providing strictly additive updates in order to bridge the measurement-prediction misfit, to arrive at the refractive index distribution from intensity transport data. The superiority of the stochastic algorithm over the GN scheme for similar settings is demonstrated by the reconstruction of the refractive index profile from simulated and experimentally acquired intensity data. (C) 2014 Optical Society of America

Ultrasound-modulated optical tomography: direct recovery of elasticity distribution from experimentally measured intensity autocorrelation

Based on an ultrasound-modulated optical tomography experiment, a direct, quantitative recovery of Young's modulus (E) is achieved from the modulation depth (M) in the intensity autocorrelation. The number of detector locations is limited to two in orthogonal directions, reducing the complexity of the data gathering step whilst ensuring against an impoverishment of the measurement, by employing ultrasound frequency as a parameter to vary during data collection. The M and E are related via two partial differential equations. The first one connects M to the amplitude of vibration of the scattering centers in the focal volume and the other, this amplitude to E. A (composite) sensitivity matrix is arrived at mapping the variation of M with that of E and used in a (barely regularized) Gauss-Newton algorithm to iteratively recover E. The reconstruction results showing the variation of E are presented. (C) 2015 Optical Society of America

A New Successive Displacement Type Load Flow Algorithm and its Application to Radial Systems

A new successive displacement type load flow method is developed in this paper. This algorithm differs from the conventional Y-Bus based Gauss Seidel load flow in that the voltages at each bus is updated in every iteration based on the exact solution of the power balance equation at that node instead of an approximate solution used by the Gauss Seidel method. It turns out that this modified implementation translates into only a marginal improvement in convergence behaviour for obtaining load flow solutions of interconnected systems. However it is demonstrated that the new approach can be adapted with some additional refinements in order to develop an effective load flow solution technique for radial systems. Numerical results considering a number of systems-both interconnected and radial, are provided to validate the proposed approach.

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.

Saltation in wind blown sand

The Boltzmann equation of the sand particle velocity distribution function in wind-blown sand two-phase flow is established based on the motion equation of single particle in air. And then, the generalized balance law of particle property in single phase granular flow is extended to gas-particle two-phase flow. The velocity distribution function of particle phase is expanded into an infinite series by means of Grad's method and the Gauss distribution is used to replace Maxwell distribution. In the case of truncation at the third-order terms, a closed third-order moment dynamical equation system is constructed. The theory is further simplified according to the measurement results obtained by stroboscopic photography in wind tunnel tests.

风沙两相流中的跃移运动

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Ｂoltzmann方程；并以此将单相颗粒流理论中的广义平衡方程推广到气固两相流的情形。提出用Grad方法将粒子相速度分布函数展成无穷级数，并引入Gauss分布取代单相颗粒流中传统的Maxwell分布。在保留到3次项的情况下，建立了气体－颗粒两相湍流边界层三阶矩封闭理论的动力学方程组。并在风洞频闪摄影实验的基础上，对理论进行简化，得到便于工程应用的简化方程。

一个推广Virial定理的数学方法和应用

本文在提出广义Gauss定理的思路下,提出了广义Stokes定理和一个推广Virial定理的新方法,后者应用于天体磁流体力学和引力平衡问题时得到的结果有:(1)气体具有运动时的平衡系统的判据,(2)磁场对气团形态的影响。应用于实验室等离子体平衡问题时,其结果有:(1)包围在气体中孤立磁场的特性,(2)发现内包无力场必须外包一有力场,(3)无力场的形态,应用于Tokmak等离子体环时的结果有:(1)环的胖瘦对环表面磁压的影响,(2)两个外加磁场分量分别和气压、环的胖瘦,截面形态、环电流分布和逆磁或顺磁的平衡关系,搞清楚了外加磁场约束等离子体总体平衡的物理机制。