General expression of double ellipsoidal heat source model and its error analysis

In order to analyze the maximum power density error with different heat flux distribution parameter values for double ellipsoidal heat source model, a general expression of double ellipsoidal heat source model was derived .front Goldak double ellipsoidal heat source model, and the error of maximum power density was analyzed under this foundation. The calculation error of thermal cycling parameters caused by the maximum power density error was compared quantitatively by numerical simulation. The results show that for guarantee the accuracy of welding numerical simulation, it is better to introduce an error correction coefficient into the Goldak double ellipsoidal heat source model expression. And, heat flux distribution parameter should get higher value for the higher power density welding methods.

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.

A fast ellipsoid model for asteroids inverted from lightcurves

Research about asteroids has recently attracted more and more attention, especially focusing on their physical structures, such as their spin axis, rotation period and shape. The long distance between observers on Earth and asteroids makes it impossible to directly calculate the shape and other parameters of asteroids, with the exception of Near Earth Asteroids and others that have passed by some spacecrafts. Photometric measurements are still generally the main way to obtain research data on asteroids, i.e. the lightcurves recording the brightness and positions of asteroids. Supposing that the shape of the asteroid is a triaxial ellipsoid with a stable spin, a new method is presented in this article to reconstruct the shape models of asteroids from the lightcurves, together with other physical parameters. By applying a special curvature function, the method calculates the brightness integration on a unit sphere and Lebedev quadrature is employed for the discretization. Finally, the method searches for the optimal solution by the Levenberg-Marquardt algorithm to minimize the residual of the brightness. By adopting this method, not only can related physical parameters of asteroids be obtained at a reasonable accuracy, but also a simple shape model of an ellipsoid can be generated for reconstructing a more sophisticated shape model.

Three dimensional numerical simulation of welding temperature fields in stainless steel

Three kinds of mathematical models representing welding heat sources are presented. Among them, Gaussian model and double ellipsoidal model are used to analyze the thermal distributions with finite element method. At the same time, this paper analyzed the influences of the heat source models, the latent heat and the welding parameters on the temperature distributions. The comparisons between the simulated results and the experiments show double ellipsoidal model is good for three-dimensional numerical simulations. Furthermore, the adaptive mesh technique is applied in the three-dimensional model which greatly reduces the number of nodes and elements in the simulation.

Robust facial expression recognition system in higher poses

Facial expression recognition(FER)has numerous applications in computer security,neuroscience,psychology,and engineering.Owing to its non-intrusiveness,it is considered a useful technology for combating crime.However,FER is plagued with several challenges,the most serious of which is its poor prediction accuracy in severe head poses.The aim of this study,therefore,is to improve the recognition accuracy in severe head poses by proposing a robust 3D head-tracking algorithm based on an ellipsoidal model,advanced ensemble of AdaBoost,and saturated vector machine(SVM).The FER features are tracked from one frame to the next using the ellipsoidal tracking model,and the visible expressive facial key points are extracted using Gabor filters.The ensemble algorithm(Ada-AdaSVM)is then used for feature selection and classification.The proposed technique is evaluated using the Bosphorus,BU-3DFE,MMI,CK^(+),and BP4D-Spontaneous facial expression databases.The overall performance is outstanding.

Finite element simulation of three-dimensional temperature field in underwater welding

Mathematical models of three-dimensional temperature fields in underwater welding with moving heat sources are built. Double ellipsoid Gauss model is proposed as heat sources models. Several factors which affect the temperature fields of underwater welding are analyzed. Water has little influence on thermal efftciency. Water convection coefftcient varies with the temperature difference between the water and the workpiece , and water convection makes molten pool freeze quickly. With the increase of water depth, the dimensions of heat sources model should be reduced as arc shrinks. Finite element technology is used to solve mathematical models. ANSYS software is used as finite element tool, and ANSYS Parametric Design Language is used to develop subprograms for loading the moving heat sources and the various convection coefftcients. Experiment results show that computational results by using double ellipsoid Gauss heat sources model accord well with the experimental results.

Analysis of the shape of heavy droplets on flat and spherical surface

In this study,a theoretical model was established for predicting the equilibrium shape of the droplet on flat and spherical surfaces.The theoretical equilibrium shape of heavy droplets could be obtained once contact angle and volume of droplets were given.It showed that the predictions of the theoretical flat model were in good agreement with the shape obtained by Surface Evolver when the contact angle is below 120 and the droplet size is on the order of capillary length.This available range will decrease and increase when the heavy droplet is on convex and concave spherical surface,respectively,in contrast to that on flat surface.The available range will decrease more for higher curvature of convex spherical surfaces.

3D reconstruction of single rising bubble in water using digital image processing and characteristic matrix

Reconstructing the shape of a bubble will lay a firm foundation for further description of the dynamic characteristics of bubbly flow, especially for a single rising bubble or separate bubbles whose interaction could be neglected. In this case, the rising bubble is usually simulated as an ellipsoid consisting of two semi-eUipsoids up and down. Thus the projected image of a bubble consists of two semi-ellipses. In this paper, a method for reconstructing the ellipsoid bubble model is described following digital image processing, using the Hough transform in 2D ellipse parameter extraction which could cover most of the bubble edge points in the image. Then a method based on characteristic symmetric matrix is described to detect 3D bubble ellipsoid model parameters from 2D ellipse parameters of projection planes. This method can be applied to bubbles rising with low-velocity in static flow field much in conformity with the projection theory and the shape variation of the rising bubble. This method does not need to solve nonlinear equation sets and provides an easy way to calculate the characteristic matrix of a space ellipsoid model for deformed bubble. For bubble application, two assumed conditions and a calibration factor are proposed to simplify calculation and detection. Errors of ellipsoid center and three axes are minor. Errors of the three rotation angles have no negative effect on further study on bubbly flow.

Dependence of multiplicity and transverse energy distributions on nuclear geometry at RHIC

We study the dependence of multiplicity and transverse energy on nuclear geometry at RHIC at SNN1/2=19.6,130,and 200 GeV basing on ellipsoidal decay model.It is found that the ellipsoidal decay model can describe the data well.

A Gas-Kinetic Unified Algorithm for Non-Equilibrium Polyatomic Gas Flows Covering Various Flow Regimes

In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.