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In this paper,a moving mesh BGK scheme (MMBGK) for multi-material flow computa- tions is proposed. The basic idea of cons- tructing the MMBGK is to couple the Lagran- gian method for the material inter- face with the remapping-free ALE-type kinetic method within each single material region. Numerical examples in one and two dimensional space are presented to illustrate the efficiency and accuracy of the scheme.

An ordering of a two-dimensional matrix assigns consecutive integers to the cells in that matrix. This paper evaluates such orderings by concentrating on the differences between each cell's order key and the keys of its spatial neighbors. In all, ten systematically generated orderings and two hundred random trials from a newly defined class of orderings are compared. The row-by-row (raster) ordering often used in remote sensing and in matrix ordering within computer programs minimizes the mean absolute difference, the root-mean-squared difference (and hence the Geary statistic), and the mean maximum absolute difference for both 8-by-8 and 256-by-256 matrices; of the quadrant-recursive (“quadtree-compatible”) orderings examined, the Morton order had the lowest values for both mean absolute difference measures, whereas the Hilbert order had the lowest root-mean-squared neighbor difference. The Morton order has the overall minimum value for the Moran statistic. Heuristic search procedures applied to the 8-by-8 case found orderings which had considerably “better” values for these statistics (higher for Moran; lower for the others) than did any of the above, suggesting that it will be possible to define new systematic orderings with better scores than any ordering currently in the literature.

The space of integral 3-tensors is Z 2 ⊗Z 2 ⊗Z 2 under the standard action of SL 2 (Z) × SL 2 (Z) × SL 2 (Z). A notion of primitivity is defined in this space and the number of primitive classes of a given discriminant is evaluated in terms of the class number of primitive binary quadratic forms of the same discriminant. Classes containing symmetric 3-tensors are also considered and their number is related to the 3-rank of the class group.

We derive the low-frequency asymptotic expansion of the exterior boundary value problems in two dimensions for second-order elliptic system concerning the theory of elastostatics. As an application of our result, the rate of the local energy decay of solutions of the initial boundary value problem for the corresponding dynamical system is discussed.

Fundamental propositions for mean figures and mean shapes in the plane are proved by using complex numbers. A test of equality of two figure or shape distributions is introduced and applied to data from larvae of mussels and from saurian heads.

Gaps or free space are studied in heptagon patterns. Geometrical features of 2-D nets are investigated. The volume terms of Gibbs energy in corresponding 3-D lattices is estimated. The importance of the research of gaps and space filling is confirmed by the study of the FSCSC (free space crystallography of strange crystals) row of three heptagon patterns with the interesting number (per unit cell) sequences (heptagons: 4, 6, 8; gaps: 2, 3, 4) represented here.

A spanning subgraph S = (V, E′) of a connected simple graph G = (V, E) is a f(x)-spanner if for any pair of nodes u and v, dS(u, v) ≦ f(dG(u, v)), where dG and dS are the usual distance functions in graphs G and S, respectively. We are primarily interested in (t + x)-spanners, which we refer to as additive spanners. We construct low-degree additive spanners for X-trees, pyramids, and multidimensional grids. We prove, for arbitrary t > 0, that to determine whether a given graph G has an additive spanner with no more than m edges is NP-complete. © 1993 by John Wiley & Sons, Inc.

We study the large time behavior of solutions of scalar conservation laws in one and two space dimensions with periodic initial data. Under a very weak nonlinearity condition, we prove that the solutions converge to constants as time goes to infinity. Even in one space dimension our results improve the earlier ones since we only require the fluxes to be nonlinear in a neighborhood of the mean value of the initial data. We then use these results to study the homogenization problem for scalar conservation laws with oscillatory initial data.

This paper presents a review of the rapid developments that have taken place over the last few years for the searching of databases of three-dimensional (3D) molecules. The geometric arrangement of the atoms in a 3D molecule is described by an interatomic distance matrix. This is a form of labelled graph that can thus be searched using the subgraph-isomorphism algorithms that are widely used for searching databases of two-dimensional (2D) molecules. Several in-house and commercial systems have been developed for 3D database searching that are based on such techniques. These systems are reviewed and their effectiveness demonstrated by examples of their use in the discovery of novel, biologically active molecules. Current systems represent a molecule by one or a small number of low-energy conformations and there is hence much interest in the development of representational techniques and searching algorithms that account for the full set of geometric arrangements that can be adopted by a flexible molecule.

SUMMARY An approach based on graph theory is described for detecting clusters of cells in tissue specimens (two-dimensional space). With a set of discrete basic elements (cell nuclei) having several measurable features (area, surface, main and minor axis of best-fitting ellipses) a graph is defined as having attributes associated with edges. Different minimum spanning trees (MSTs) can be constructed using different weight functions on the attributes (attributed MST). Analysis of the MST and of an attributed MST by use of a decomposition function allows detection of image areas with similar local properties. These clusters, which are then clusters of the tree, describe, for example, partial growth in different directions in a case of a human fibrosarcoma assuming that tumour cell nuclei are homogeneous with respect to their configuration and size. The model allows the separation of clusters of tumour cells growing in different directions and the approximation of the different growth angles. This decomposition also allows us to create new (higher) orders of structure (cluster tree).

Automation of finite element mesh generation holds great benefits for mechanical product development and analysis. In addition to freeing engineers from mundane tasks, automation of mesh generation reduces product cycle design and eliminates human-related errors. Most of the existing mesh generation methods are either semi-automatic or require specific topological information. A fully automatic free-form mesh generation method is described in this paper to alleviate some of these problems. The method is capable of meshing singly or multiply connected convex/concave planar regions. These regions can be viewed as crosssectional areas of 2 1/2 D objects analysed as plane stress, plane strain or axisymmetric stress problems. In addition to being fully automatic, the method produces quadrilateral or triangular elements with aspect rations near one. Moreover, it does not require any topological constraints on the regions to be meshed; i.e. it provides free-form mesh generation. The input to the method includes the region's boundary curves, the element size and the mesh grading information. The method begins by decomposing the planar region to be meshed into convex subregions. Each subregion is meshed by first generating nodes on its boundaries using the input element size. The boundary nodes are then offset to mesh the subregion. The resulting meshes are merged together to form the final mesh. The paper describes the method in detail, algorithms developed to implement it and sample numerical examples. Results on parametric studies of the method performance are also discussed.

A hybrid technique for adaptive grid generation using a variety of Poisson grid generators is described. The technique ensures that, when adaptivity functions are weak, the adapted grid reverts to an arbitrary specified base grid rather than to the grid produced by the homogeneous elliptic generator. The hybrid technique also serves to expose the weakness of the claim that elliptic grid generators produce smooth grids.

A general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing funstion. The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite elements meshes of different element sizes zre generated using the available general purpose mesh generators.

Spectroscopic imaging with a one-dimensional phase-encoding gradient and surface-coil reception relies on the restricted range of sensitivity of the surface coil to provide localization in the dimensions transverse to the coil axis and consequently suffers from relatively poor localization in these dimensions. A two-dimensional (2D) cylindrically selective excitation pulse with a large spectral bandwidth is presented here to remedy this problem. The gradient waveforms are derived from multiple spirals in k space which form an overall pinwheel pattern, resulting in a pulse which is much shorter than the equivalent single-spiral trajectory. Nonuniform traversal of the spirals further reduces the pulse width under conditions of gradient slew-rate limitations, yielding overall gains in bandwidth of up to about 30 compared with the equivalent single-spiral trajectory traversed at constant angular rate. The accompanying rf waveform is obtained by weighted 2D Fourier transformation of the desired sensitivity profile. A new weighting factor is introduced into the rf waveform to compensate for nonuniform sampling of k space by the pinwheel near the origin. This factor is independent of the weighting used to account for the rate of traversal of the trajectory and is applicable to 2D pulse design in general. Pulse sequences employing pinwheel excitation in conjunction with either phase-encoding or slice-selective inversion are used to produce multiple-voxel and single-voxel localization in a human heart and a phantom. Pinwheel pulses may be used to advantage on moieties with long spin-lattice relaxation times and short transverse relaxation times and are therefore ideal for applications in phosphorus (31P) NMR.

An approach for automatically and rapidly searching a molecule's conformational space to determine low-energy conformations is described. The method takes a simple 2D description of the molecule (atom types and connectivity), recognizes the presence of conformational units about which it has ‘knowledge’ and generates structures by template joining. Some of the algorithms which can be used to search the conformational space are described, as are methods to manipulate conformational information. Such an approach may be used to generate multiple conformations which may be further refined or stored in some form of 3D database.

This paper proposes a new multiscale segment matching method which is applicable to heavily deformed planar shapes. First, multiscale representations are obtained using curvature scale space filtering. Then inflection point correspondence is developed between consecutive smoothed shapes. The representation in this paper, unlike the well-known curvature scale space image description, ensures that it always satisfies the consistency of hierarchical segment replacement. Moreover, it requires less processing time and memory allocation. Finally, optimum scale segments are matched by a new multiscale segment matching method proposed herein. In this method, the matching problem is formulated as a minimization problem of the total amount of segment dissimilarity. The minimization problem is solved effectively using dynamic programming. The proposed matching method makes it possible to obtain intuitively relevant correspondences even if the shapes have some local heavy deformation.

Recently, attempts have been made regarding automatic learning of models of objects with two-dimensional shapes from their multiple number of images and recognizing objects using pregiven models by partial features of shapes. Both are based on a principle of extracting the local features of a figure and using them as distinctive features for both learning and recognition. This paper proposes a method of feature extraction from a boundary pattern intended to be applied for such purpose. A hinge articulation is considered as a basic component of two-dimensionally shaped objects, and for each one of the hinge representative shapes—a circle, linked bars and crossed bars—a simple but robust detection method is presented. Since extraction of line segments is necessary as a preprocess for detecting linked and crossed bars, a line-segment detection method applying Hough transformation is developed for boundary patterns.

This paper discusses the problem of geometric degeneracies and outlines possible solutions when converting geometric algorithms into practice. It concentrates on the application of one of the suggested solutions, a perturbation technique, to a 2D convex hull program. An outline of the relevant theory and its conversion into practice is given. Experimental results are presented and discussed.

The reconstruction of two-dimensional spatial images with 0.5-mm resolution using radio frequency gradients generated by an NMR coil system rotated about the sample is demonstrated for 23Na. The method retains chemical shift, should be capable of mapping T1 and T2 information, and might offer sensitivity advantages for nuclides with short T2. © 1990 Academic Press, Inc.

This paper describes the development of an automatic, two-dimensional, quadrilateral element mesh generator. The methodology is based on the looping algorithm developed in part by Dr M. L. C. Sluiter. Bezier curves are used to define the boundaries of the parts to be meshed. The required interaction by the user is reduced to specifying the boundary geometry, the preferred element size and the refinement coefficient. Transition elements are automatically generated between regions of varying element sizes. The ability to offset specified boundary curves insures well-conditioned elements along the boundary. Meshes for several sample geometries are presented to illustrate the versatility of the mesh generator.

This paper discusses the generation of unstructured triangular meshes by the advancing front technique. We also employ the technique to discretize surfaces. A simple and effective algorithm for the specification of element sizes is described. A similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable. The isolines are obtained from the FE-calculation based on the previous mesh. In this paper, attention is focused on the Poisson's equation. The optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing. When the estimated error exceeds the tolerance in only a small part of the domain, the adaptive procedure is switched automatically to an adaptive refinement.

This paper provides a method of estimating a rotation center to analyze kinematically the movement of a rigid body moving periodically in a two-dimensional (2-D) space. The rotation center, which is derived from an axis point of the human jaw joint, is defined as a point which moves reciprocally in periodic movement. Accordingly, it is called the reciprocating point. Separating a path of the reciprocating point by its turning point, we can divide the path into two parts—the forward path and the backward path. Both paths are identical and hence it appears that any position in one path has its counterpart in the other path. We show that if we have a function corresponding to a pair of positions mentioned in the foregoing, we can estimate the reciprocating point. Then we derive an algorithm which approximates successively the function and the reciprocating point alternatively. This algorithm is proved to be effective for estimating an axis point of the jaw joint.

This paper describes an orginal method to generate a finite-element mesh in a planar domain of arbitrary shape. The mesh density can be varied arbitrarily, not only on the contour but also inside the domain. The number of elements generated can be imposed approximately.

The method uses techniques from elimination theory to solve the parametric inversion problem for each node on the new, undistorted mesh. These parameter values are then used in the elemental shape functions to transfer the nodal state variables from the distorted mesh to each node in the new mesh by interpolation. The method has been implemented for bilinear and biquadratic elements. The method is based on fundamental finite element approximations, since the interpolation functions which define the element are also used to perform rezoning