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Interior Nodes (interior + node)
Selected AbstractsBIOGEOGRAPHY OF MARINE RED ALGAE: MYTHS AND REALITIESJOURNAL OF PHYCOLOGY, Issue 2001Article first published online: 24 SEP 200 Hommersand, M. H. Department of Biology, Coker Hall, University of North Carolina, Chapel Hill, NC 27599-3280 USA Theories about the geographical distribution of marine algae fall roughly into two categories: (1) a concept of biogeographical regions in which algal distribution is determined primarily by growth, reproductive and lethal temperature boundaries (Setchell, van den Hoek, Breeman, Lüning) and (2) an historical perspective in which distribution is determined primarily by patterns of dispersal and the establishment of barriers to dispersal (vicariance biogeography) (Svedelius, Garbary, Lindstrom, Hommersand). Setchell proposed the 5° isotherm rule in 1920, and in 1924 Svedelius advocated a worldwide distribution for tropical and subtropical groups followed by discontinuous distribution upon closure of the connection between the Indian Ocean and Mediterranean Sea and, later, between North and South America (Wegener's theory). Transarctic dispersal routes have received special attention in recent years (Lindstrom, Lüning, van Oppen, Olsen, Stam), as have special relationships between Australasia, South Africa and South America (Hommersand). Less well understood are the climatic changes that have taken place in the Cenozoic which are strategic to an understanding vicariant biogeography. The advent of molecular methods combined with the tools of phylogenetic systematics now make it possible to identify ancestral taxa, test the consistency of tree topologies, and calculate mean branch lengths between sister lineages diverging from an interior node of a tree. With such methods it may be possible to infer ancestral areas, identify dispersal pathways, determine the chronology of isolating events, assess the impact of multiple invasions, and generally relate dispersal and vicariance models to phylogenetic hypotheses for red, brown and green algal taxa. [source] A variational multiscale model for the advection,diffusion,reaction equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009Guillaume Houzeaux Abstract The variational multiscale (VMS) method sets a general framework for stabilization methods. By splitting the exact solution into coarse (grid) and fine (subgrid) scales, one can obtain a system of two equations for these unknowns. The grid scale equation is solved using the Galerkin method and contains an additional term involving the subgrid scale. At this stage, several options are usually considered to deal with the subgrid scale equation: this includes the choice of the space where the subgrid scale would be defined as well as the simplifications leading to compute the subgrid scale analytically or numerically. The present study proposes to develop a two-scale variational method for the advection,diffusion,reaction equation. On the one hand, a family of weak forms are obtained by integrating by parts a fraction of the advection term. On the other hand, the solution of the subgrid scale equation is found using the following. First, a two-scale variational method is applied to the one-dimensional problem. Then, a series of approximations are assumed to solve the subgrid space equation analytically. This allows to devise expressions for the ,stabilization parameter' ,, in the context of VMS (two-scale) method. The proposed method is equivalent to the traditional Green's method used in the literature to solve residual-free bubbles, although it offers another point of view, as the strong form of the subgrid scale equation is solved explicitly. In addition, the authors apply the methodology to high-order elements, namely quadratic and cubic elements. The proposed model consists in assuming that the subgrid scale vanishes also on interior nodes of the element and applying the strategy used for linear element in the segment between these interior nodes. The proposed scheme is compared with existing ones through the solution of a one-dimensional numerical example for linear, quadratic and cubic elements. In addition, the mesh convergence is checked for high-order elements through the solution of an exact solution in two dimensions. Copyright © 2008 John Wiley & Sons, Ltd. [source] Shape functions for polygonal domains with interior nodesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004Elisabeth Anna Malsch Abstract The presented formulation follows in a series of publications which outline a method for constructing test functions which satisfy essential edge conditions exactly. The method promises a complete solution, satisfying all of the requirements of a Ritz coordinate function. The influence of interior points on the domain solution is included in this construction. Similar to conformal bubble functions, the test functions are zero along the boundary and single valued only at the points they describe. Unlike the bubble function construction, the interior points can be located at any desired point in the domain. The resulting set of trial functions can satisfy the required global conditions including the exact reproduction of constant and linear fields. Copyright © 2004 John Wiley & Sons, Ltd. [source] Unequally spaced non-periodic B-spline finite strip methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Chang-Koon Choi Abstract The unequally spaced non-periodic B-spline finite strip method (FSM) is presented. The motivation to investigate the irregularly spaced interior nodes in the longitudinal direction of strip is to generalize the concept of non-periodic B-spline FSM and to improve the general accuracy of the stress evaluation in the region of high stress gradients. In the present paper, the unequally spaced non-periodic B3-spline series with multiple knots at the boundary are introduced for the interpolation of displacement and description of geometry in the formulation of isoparametric spline FSM. The use of multiple knots at the boundary makes the shape function satisfy the Kronecker delta properties at the boundary. The unequally spaced B-spline FSM is applied to the stress-reduced shell problem with six degrees of freedom per node. The main purpose of this study is to find a way of ensuring that the geometry of strip is appropriately approximated when the interior nodes of the strip are not regularly spaced along the longitudinal direction. Some numerical results have been compared with those of the previous studies to evaluate the accuracy and efficiency of this method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Meshfree weak,strong (MWS) form method and its application to incompressible flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2004G. R. Liu Abstract A meshfree weak,strong (MWS) form method has been proposed by the authors' group for linear solid mechanics problems based on a combined weak and strong form of governing equations. This paper formulates the MWS method for the incompressible Navier,Stokes equations that is non-linear in nature. In this method, the meshfree collocation method based on strong form equations is applied to the interior nodes and the nodes on the essential boundaries; the local Petrov,Galerkin weak form is applied only to the nodes on the natural boundaries of the problem domain. The MWS method is then applied to simulate the steady problem of natural convection in an enclosed domain and the unsteady problem of viscous flow around a circular cylinder using both regular and irregular nodal distributions. The simulation results are validated by comparing with those of other numerical methods as well as experimental data. It is demonstrated that the MWS method has very good efficiency and accuracy for fluid flow problems. It works perfectly well for irregular nodes using only local quadrature cells for nodes on the natural boundary, which can be generated without any difficulty. Copyright © 2004 John Wiley & Sons, Ltd. [source] Minimal regularity of the solutions of some transmission problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2003D. Mercier We consider some transmission problems for the Laplace operator in two-dimensional domains. Our goal is to give minimal regularity of the solutions, better than H1, with or without conditions on the (positive) material constants. Under a monotonicity or quasi-monotonicity condition on the constants (or on the inverses according to the boundary conditions), we study the behaviour of the solution near vertex and near interior nodes and show in each case that the given regularity is sharp. Without condition we prove that the regularity near a corner is of the form H1+,, where , is a given bound depending on the material constants. Numerical examples are presented which confirm the sharpness of our lower bounds. Copyright © 2003 John Wiley & Sons, Ltd. [source] Phylogeny and biogeography of Crinum L. (Amaryllidaceae) inferred from nuclear and limited plastid non-coding DNA sequencesBOTANICAL JOURNAL OF THE LINNEAN SOCIETY, Issue 3 2003ALAN W. MEEROW The genus Crinum L. is the only pantropical genus of the Amaryllidaceae. Phylogenetic and biogeographical analyses of nrDNA ITS and plastid trnL-F sequences for all continental groups of the genus Crinum and related African genera are presented, with the genus Amaryllis used as outgroup. ITS indicates that C. baumii is more closely related to Ammocharis and Cybistetes than to Crinum sensu stricto. Three clades are resolved in Crinum s.s. One unites a monophyletic American group with tropical and North African species. The second includes all southern African species and the Australian endemic C. flaccidum. The third includes monophyletic Madagascar, Australasian and Sino-Himalayan clades, with southern African species. The trnL-F phylogeny resolves an American and an Asian/Madagscar clade, and confirms the relationship of C. flaccidum with species endemic to southern Africa. The salverform, actinomorphic perianths of subg. Crinum appear to have evolved several times in the genus from ancestors with zygomorphic perianths (subg. Codonocrinum), thus neither subgenus is monophyletic. Biogeographical analyses place the origin of Crinum in southern Africa, as the region is optimized at all ancestral nodes in the tree topology, and in basal interior nodes of all but one of the major clades. The genus underwent three major waves of radiation corresponding to the three main clades resolved in our trees. Two entries into Australia for the genus are indicated, as are separate Sino-Himalayan and Australasian dispersal events. © 2003 The Linnean Society of London, Botanical Journal of the Linnean Society, 2003, 141, 349,363. [source] | |||||||||||||