3D Fredholm integral equations for scattering by dielectric structures

We consider 3D singular integral equations that describe problems of interaction of an electromagnetic wave with 3D dielectric structures. By using the theory of singular integral equations, we reduce these equations to Fredholm integral equations of the second kind.     

Isogeometric analysis of surface elasticity: a comparison with isoparametric FEM

We report here on the isogeometric treatment of surface-elastic effects and compare the results obtained from Finite Element simulations and Isogeometric Analysis. As expected, the latter delivers smoother solutions than a standard finite element approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Democratic Formulation of D=10 Supersymmetry

We discuss a generalized form of IIA/B supergravity depending on all Ramond–Ramond (R–R) potentials C ^(p), p = 0,1,...,9, as the effective field theory of type-IIA/B superstring theory. For the IIA case, we explicitly break this R–R democracy to either p 3 or p 5, which allows writing a new bulk action that can be coupled to N=1 supersymmetric brane actions.     

Algebraic structures determined by 3 by 3 matrix geometry

Using a ``3 by 3 matrix trick' we show that multiplication (an algebraic structure) in a *-algebra is determined by the geometry of the *-algebra of the 3 by 3 matrices with entries from , . This is an example of an algebra-geometry duality which, we claim, has applications.

     

3D complex structures imaging based on acoustic wave equation

In this paper, a general expression of the 3D hybrid imaging method based on acoustic wavefield extrapolation is presented. Moreover, the planewave synthesization method is given. The numerical results of 3D shot-profile migration and planewave synthesization migration for the SEG/EAEG 3D benchmark model show the good imaging ability of the hybrid imaging method. This method can be applied in field data processing. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Natural almost contact structures and their 3D homogeneous models

We consider a natural condition determining a large class of almost contact metric structures. We study their geometry, emphasizing that this class shares several properties with contact metric manifolds. We then give a complete classification of left‐invariant examples on three‐dimensional Lie groups, and show that any simply connected homogeneous Riemannian three‐manifold admits a natural almost contact structure having g as a compatible metric. Moreover, we investigate left‐invariant CR structures corresponding to natural almost contact metric structures.     

The 3D index of an ideal triangulation and angle structures

The 3D index of Dimofte–Gaiotto–Gukov is a partially defined function on the set of ideal triangulations of 3-manifolds with r tori boundary components. For a fixed 2r tuple of integers, the index takes values in the set of q-series with integer coefficients. Our goal is to give an axiomatic definition of the tetrahedron index and a proof that the domain of the 3D index consists precisely of the set of ideal triangulations that support an index structure. The latter is a generalization of a strict angle structure. We also prove that the 3D index is invariant under 3–2 moves, but not in general under 2–3 moves.     

Numerical analysis of 3D vortical cavity flow

The vortical flows of an incompressible fluid in a rectangular three-dimensional container with a large spanwise aspect ratio driven by a moving solid lid are studied using a combined compact finite difference (CCD) scheme with high accuracy and high resolution. The study focuses on the change of the steady flow structures in the cavity with Reynolds numbers ranging from 100 to 850. The results of the flow in the cavity with a spanwise aspect ratio 6.55 show that several stable closed streamlines localized near the symmetric plane are found at Re ≥500, while a closed stable streamline is found near the side wall at Re ≤300. The change of the flow pattern present in this system affects the diffusion properties in the flow but seems to have no qualitative effect on the global flow properties which include energy dissipation in the cavity. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability analysis of frame structures by bubble-function method

In the stability analysis of frame structures, the results by conventional finite element method (FEM) in which one member is taken as one element are sometimes unavailable. This paper took a new basic function system with bubble functions as the shape function of a bar element to develop a bubble function finite element method (BFEM), in which the bending and the geometric stiffness matrices were derived from the principle of virtual work. Bubble functions are finite element modes that are located entirely within a single element and are zero on boundaries of the element, but are nonzero at the other points. BFEM is as concise as conventional bar FEM but has better accuracy, and is adaptable to the buckling analysis of all kinds of frame structures. The use of bubble functions significantly improves the convergence of finite element analysis, and efficiently reduces the computation cost for the buckling analysis of frame structures. Numerical results show that using bubble functions in finite element for the stability analysis of structures is very efficient, especially for high-rise and large-scale frame structures.     

Linked treemap: a 3D treemap-nodelink layout for visualizing hierarchical structures

Hierarchical structures are present in many different areas of our daily life as well as in sciences. Visualization methods are quite commonly applied to support comprehension of the more complex structures. Nodelinks and treemaps are two widely spread directions of such visualization methods. Visualizations using nodelinks have the advantage of explicitly displaying the hierarchical relations between entities. Visualizations using treemaps, on the other hand, allow for a good global understanding of the present entities and some of their properties. We present a visualization tool for hierarchical structures that combines the advantages of treemaps and nodelinks by naturally incorporating them into a 3D layout. The nodelink is built upon the treemap in a direction orthogonal to the treemap plane. Our visualization tool supports various navigation techniques suitable for different analysis tasks. First, the user interaction allows users to render subtrees of the nodelink transparently. Second, the various levels can be explored separately in an intuitive fashion by sliding its plane through the orthogonal nodelink layout and, thus, moving the treemap to the respective level of the hierarchy. Third, zooming into regions of interest is supported by using a focus+context technique that operates on the combined 3D layout. We demonstrate the efficacy and efficiency of our system for visual exploration purposes in a case study that uses our system as a file explorer. In this context, we perform a user study that evaluates our approach and allows for a comparison to other existing approaches.     

Full 3D finite element Cosserat formulation with application in layered structures

In this paper, a full three-dimensional (3D) finite element Cosserat formulation is developed within the principles of continuum mechanics in the small deformation framework. The developed finite element formulation is general; however, the proposed constitutive laws incorporate the effect of the internal length parameter of 3D layered continua. The extension of the existing two-dimensional (2D) Cosserat formulation to the 3D framework is novel and is consistent with plate theory which can be considered as the 3D version of beam theory. The results demonstrate a high level of consistency with the analytical solutions predicted by plate theory as well as predictions by alternative numerical techniques such as the discrete element method.     

Sources of straight electrostatic flux lines in R 3

It is well known that the point charge, line charge and homogeneously charged plane of infinite extent are sources of electrostatic fields with straight flux lines. It is proved in this note that provided these flux lines occupy all of three-dimensional space, then these charge configurations and appropriate variants of them are the only sources of straight-line electrostatic fields in R ³.     

3D finite element analysis of evaporative laser cutting

A three-dimensional computational model of evaporative laser-cutting process has been developed using a finite element method. Steady heat transfer equation is used to model the laser-cutting process with a moving laser. The laser is assumed continuous wave Gaussian beam. The finite element surfaces on evaporation side are nonplanar and approximated by bilinear polynomial surfaces. Semi-infinite elements are introduced to approximate the semi-infinite domain. An iterative scheme is used to handle the geometric nonlinearity due to the unknown groove shape. The convergence studies are performed for various meshes. Numerical results about groove shapes and temperature distributions are presented and also compared with those by semi-analytical methods.     

2D-3D registration for 3D analysis of lower limb alignment in a weight-bearing condition

X-ray imaging is the conventional method for diagnosing the orthopedic condition of a patient. Computerized Tomography(CT) scanning is another diagnostic method that provides patient’s 3D anatomical information. However, both methods have limitations when diagnosing the whole leg; X-ray imaging does not provide 3D information, and normal CT scanning cannot be performed with a standing posture. Obtaining 3D data regarding the whole leg in a standing posture is clinically important because it enables 3D analysis in the weight bearing condition. Based on these clinical needs, a hardware-based bi-plane X-ray imaging system has been developed; it uses two orthogonal X-ray images. However, such methods have not been made available in general clinics because of the hight cost. Therefore, we proposed a widely adaptive method for 2D X-ray image and 3D CT scan data. By this method, it is possible to threedimensionally analyze the whole leg in standing posture. The optimal position that generates the most similar image is the captured X-ray image. The algorithm verifies the similarity using the performance of the proposed method by simulation-based experiments. Then, we analyzed the internal-external rotation angle of the femur using real patient data. Approximately 10.55 degrees of internal rotations were found relative to the defined anterior-posterior direction. In this paper, we present a useful registration method using the conventional X-ray image and 3D CT scan data to analyze the whole leg in the weight-bearing condition.     

Conservative finite-difference scheme for computer simulation of contrast 3D spatial-temporal structures induced by a laser pulse in a semiconductor

The numerical approach for computer simulation of femtosecond laser pulse interaction with a semiconductor is considered under the formation of 3D contrast time-dependent spatiotemporal structures. The problem is governed by the set of nonlinear partial differential equations describing a semiconductor characteristic evolution and a laser pulse propagation. One of the equations is a Poisson equation concerning electric field potential with Neumann boundary conditions that requires fulfillment of the well-known condition for Neumann problem solvability. The Poisson equation right part depends on free-charged particle concentrations that are governed by nonlinear equations. Therefore, the charge conservation law plays a key role for a finite-difference scheme construction as well as for solvability of the Neumann difference problem. In this connection, the iteration methods for the Poisson equation solution become preferable than using direct methods like the fast Fourier transform. We demonstrate the following: if the finite-difference scheme does not possess the conservatism property, then the problem solvability could be broken, and the numerical solution does not correspond to the differential problem solution. It should be stressed that for providing the computation in a long-time interval, it is crucial to use a numerical method that possessing asymptotic stability property. In this regard, we develop an effective numerical approach—the three-stage iteration process. It has the same economic computing expenses as a widely used split-step method, but, in contrast to the split-step method, our method possesses conservatism and asymptotic stability properties. Computer simulation results are presented.     

Unified analysis of preconditioning methods for saddle point matrices

Short and unified proofs of spectral properties of major preconditioners for saddle point problems are presented. The need to sufficiently accurately construct approximations of the pivot block and Schur complement matrices to obtain real eigenvalues or eigenvalues with positive real parts and non‐dominating imaginary parts are pointed out. The use of augmented Lagrangian methods for more ill‐conditioned problems are discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Generation of assembly graphs by systematic analysis of assembly structures

In assembly line balancing problems, parallel execution of assembly operations is often advocated because of its enhanced flexibility and minimum lead-time. Although the theoretical maximum number of possible assembly sequences combinatorially explodes with the number of components in a product, graphical representations can depict these sequences in a surveyable way. The AND/OR graph representation is an appropriate basis for optimum sequence selection, which can be achieved via heuristic, metaheuristic, and exact methods. The exact method, based on binary linear programming, is described. To arrive at the appropriate model, a novel approach for AND/OR graph generation, based on subassembly detection, is presented. The method is demonstrated with simple cases and next extended to increasingly complex products. A modification of the optimization method is applied, which enables a search for sequences with maximum parallelism.