Strong Form (strong + form)

Distribution by Scientific Domains


Selected Abstracts


Is Dialetheism an Idealism?

DIALECTICA, Issue 2 2007
The Russellian Fallacy, the Dialetheist's Dilemma
In his famous work on vagueness, Russell named ,fallacy of verbalism' the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories , the non-adjunctive and relevant approaches ,, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of their underlying semantics. The meaning of ,intuitive reading' is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense , therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency , and this could be a welcome result for a dialetheist. [source]


Ascending visceral regulation of cortical affective information processing

EUROPEAN JOURNAL OF NEUROSCIENCE, Issue 8 2003
Gary G. Berntson
Abstract Over a century ago, William James proposed that strong emotions represent the perceptual consequences of somato-visceral feedback. Although the strong form of this conception is no longer viable, considerable evidence has accumulated indicating a range of visceral influences on higher neurobehavioural processes. This literature has only recently begun to consolidate, because earlier reports generally remained at the demonstration level, and pathways and mechanisms for such influences were uncertain. Recently, specific effects of visceral feedback have become apparent on cortical activity, cerebral auditory-evoked responses, anxiety, memory and behavioural aspects of immunological sickness. Moreover, considerable progress has been made recently in determining the specific neural pathways and systems underlying these actions, especially the role of noradrenergic projections from the nucleus of the tractus solitarius and the locus coeruleus to the amygdala in memory processes, and to the basal forebrain in the processing of anxiety-related information. The present paper highlights selected recent findings in this area, and outlines relevant structures and pathways involved in the ascending visceral influence on higher neurobehavioural processes. [source]


A variational multiscale model for the advection,diffusion,reaction equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009
Guillaume 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]


A CBS-type stabilizing algorithm for the consolidation of saturated porous media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005
V. A. Salomoni
Abstract The presented method stems from the works by Zienkiewicz and co-workers for coupled fluid/thermal problems starting from the early 1990s. They propose algorithms to overcome the difficulties connected to the application of the FEM to the area of fluid mechanics, which include the problems of singular behaviour in incompressibility and the problems connected to convective terms. The major step forward was to introduce the concept of characteristic lines (the particle paths in a simple convection situation): for a class of problems with a single scalar variable, the equations in the characteristic co-ordinates regain self-adjointness. The procedure is called characteristic based split algorithm (CBS). We use here a CBS-type procedure for a saturated deformable elastic porous medium, in which the fluid velocity is governed by Darcy's equation (which comes directly from Navier,Stokes ones). The physical,mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains. The power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual ,u,p' problem into a ,u,v,p' one, where u generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid, respectively. Attention is focused on the expression of Darcy's velocity which is considered as the starting point of the algorithm. The accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u,p solutions. A good fitting among different results has been obtained. It is further shown that the procedure eliminates the oscillations at the onset of consolidation, typical for many schemes. The FEM code Ed-Multifield has been used for implementing and testing the procedure. Copyright © 2005 John Wiley & Sons, Ltd. [source]


Moving least-square interpolants in the hybrid particle method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005
H. Huang
Abstract The hybrid particle method (HPM) is a particle-based method for the solution of high-speed dynamic structural problems. In the current formulation of the HPM, a moving least-squares (MLS) interpolant is used to compute the derivatives of stress and velocity components. Compared with the use of the MLS interpolant at interior particles, the boundary particles require two additional treatments in order to compute the derivatives accurately. These are the rotation of the local co-ordinate system and the imposition of boundary constraints, respectively. In this paper, it is first shown that the derivatives found by the MLS interpolant based on a complete polynomial are indifferent to the orientation of the co-ordinate system. Secondly, it is shown that imposing boundary constraints is equivalent to employing ghost particles with proper values assigned at these particles. The latter can further be viewed as placing the boundary particle in the centre of a neighbourhood that is formed jointly by the original neighbouring particles and the ghost particles. The benefit of providing a symmetric or a full circle of neighbouring points is revealed by examining the error terms generated in approximating the derivatives of a Taylor polynomial by using a linear-polynomial-based MLS interpolant. Symmetric boundaries have mostly been treated by using ghost particles in various versions of the available particle methods that are based on the strong form of the conservation equations. In light of the equivalence of the respective treatments of imposing boundary constraints and adding ghost particles, an alternative treatment for symmetry boundaries is proposed that involves imposing only the symmetry boundary constraints for the HPM. Numerical results are presented to demonstrate the validity of the proposed approach for symmetric boundaries in an axisymmetric impact problem. Copyright © 2005 John Wiley & Sons, Ltd. [source]


A triangular hybrid equilibrium plate element of general degree

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
E. A. W. Maunder
Abstract Hybrid stress-based finite elements with side displacement fields have been used to generate equilibrium models having the property of equilibrium in a strong form. This paper establishes the static and kinematic characteristics of a flat triangular hybrid equilibrium element with both membrane and plate bending actions of general polynomial degree p. The principal characteristics concern the existence of hyperstatic stress fields and spurious kinematic modes. The former are shown to exist for p>3, and their significance to finite element analysis is reviewed. Knowledge of the latter is crucial to the determination of the stability of a mesh of triangular elements, and to the choice of procedure adopted for the solution of the system of equations. Both types of characteristic are dependent on p, and are established as regards their numbers and general algebraic forms. Graphical illustrations of these forms are included in the paper. Copyright © 2005 John Wiley & Sons, Ltd. [source]


A gradient smoothing method (GSM) for fluid dynamics problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2008
G. R. Liu
Abstract A novel gradient smoothing method (GSM) based on irregular cells and strong form of governing equations is presented for fluid dynamics problems with arbitrary geometries. Upon the analyses about the compactness and the positivity of coefficients of influence of their stencils for approximating a derivative, four favorable schemes (II, VI, VII and VIII) with second-order accuracy are selected among the total eight proposed discretization schemes. These four schemes are successively verified and carefully examined in solving Poisson's equations, subjected to changes in the number of nodes, the shapes of cells and the irregularity of triangular cells, respectively. Numerical results imply us that all the four schemes give very good results: Schemes VI and VIII produce a slightly better accuracy than the other two schemes on irregular cells, but at a higher cost in computation. Schemes VII and VIII that consistently rely on gradient smoothing operations are more accurate than Schemes II and VI in which directional correction is imposed. It is interestingly found that GSM is insensitive to the irregularity of meshes, indicating the robustness of the presented GSM. Among the four schemes of GSM, Scheme VII outperforms the other three schemes, for its outstanding overall performance in terms of numerical accuracy, stability and efficiency. Finally, GSM solutions with Scheme VII to some benchmarked compressible flows including inviscid flow over NACA0012 airfoil, laminar flow over flat plate and turbulent flow over an RAE2822 airfoil are presented, respectively. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Meshfree weak,strong (MWS) form method and its application to incompressible flow problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2004
G. 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]


A projection scheme for incompressible multiphase flow using adaptive Eulerian grid

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004
T. Chen
Abstract This paper presents a finite element method for incompressible multiphase flows with capillary interfaces based on a (formally) second-order projection scheme. The discretization is on a fixed Eulerian grid. The fluid phases are identified and advected using a level set function. The grid is temporarily adapted around the interfaces in order to maintain optimal interpolations accounting for the pressure jump and the discontinuity of the normal velocity derivatives. The least-squares method for computing the curvature is used, combined with piecewise linear approximation to the interface. The time integration is based on a formally second order splitting scheme. The convection substep is integrated over an Eulerian grid using an explicit scheme. The remaining generalized Stokes problem is solved by means of a formally second order pressure-stabilized projection scheme. The pressure boundary condition on the free interface is imposed in a strong form (pointwise) at the pressure-computation substep. This allows capturing significant pressure jumps across the interface without creating spurious instabilities. This method is simple and efficient, as demonstrated by the numerical experiments on a wide range of free-surface problems. Copyright © 2004 John Wiley & Sons, Ltd. [source]


The sequential sum problem and performance bounds on the greedy algorithm for the on-line Steiner problem

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2005
Zevi Miller
Abstract This article is motivated by versions of the dynamic or "on-line" Steiner tree problem (OST) introduced by Imase and Waxman [4]. In this problem one is given an edge-weighted graph G and a sequence , = (x1,,,xn) of distinct vertices of G. The requirement is to construct for each i , n a tree Ti spanning the first i vertices of , subject to the condition that Ti,1,Ti for all i, where Ti is constructed without knowledge of the remaining vertices xj, j > i. The goal of the on-line Steiner problem is to minimize the performance ratio; that is, the maximum (over 1 , i , n) of the ratio of the weight of Ti to the weight of the minimum weight tree in G spanning the first i vertices (the latter tree is called the "Steiner tree" for these vertices). In [4] a lower bound of 1 + ˝, log2(n,1), was proved for this ratio. The authors further made the interesting conjecture that there is some on-line algorithm for the OST whose performance ratio achieves this lower bound. We show that a strong form of the greedy algorithm achieves a ratio that converges to the conjectured ˝log2(k) + O(1) as the proportion of degree 2 vertices in the instance graph grows. Our results also imply improvements in certain cases on the known upper bound ,log2(n), for the performance ratio of the greedy algorithm. Our approach is to study a related graph parameter. For each sequence , as above, define the associated cost where c(i,,) = min1 , t < idist(xi, xt). Then let Opt(n, G) be the maximum of L(,) over all such sequences , of length n. The problem of, given n and G, determining Opt(n, G) we call the Sequential Sum Problem (SSP). In this article we analyze the SSP, obtaining exact values and bounds on Opt(n, G) and relating these bounds to the greedy algorithm for the OST. For example, we calculate Opt(n, P) for the path P, and obtain a surprising characterization of all length n sequences , which realize Opt(n, P). By analyzing Opt(n, P) for the "continuous" path, we derive upper bounds on the performance ratio of the greedy algorithm for the OST in arbitrary graphs. On the other hand, generalizing the lower bound argument of [4] we show that there are instances of OST, which can significantly "fool" any on-line algorithm for OST. Specifically, given any tree T normalized to have total edge weight 1, we construct a graph G and a length k , |V(T)| sequence , of vertices of G for which the performance ratio of any on-line algorithm for the OST with input , is lower bounded by Opt(k, T). Finally, we show that the SSP for arbitrary G is NP-complete. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(3), 143,164 2005 [source]


Asymptotic equivalence and contiguity of some random graphs

RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2010
Svante Janson
Abstract We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple proof of a recent result by van den Esker, van der Hofstad, and Hooghiemstra on the equivalence between graph distances for some random graph models. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source]


Inter-Firm Training Co-ordination in Britain

BRITISH JOURNAL OF INDUSTRIAL RELATIONS, Issue 2 2006
Howard Gospel
This paper examines employer co-operation in the provision of training. Such collective action has a long history in Britain, but has varied over time in extent and strength. It exists in a strong form in the German-speaking countries, where employers' organizations and chambers of commerce are a fundamental part of the training system. On the basis of new data, we argue that this form of training is important in the UK and has a positive effect on the quantity and quality of training. Case studies are presented on several examples of collective action , a local chamber of commerce, an industry-wide employers' organization, a group training association, a network of firms in a large company's supply chain and a local consortium of big employers. Although such forms of organization have much to commend them, in the UK coverage is uneven and stability is fragile. [source]


Parametric enrichment adaptivity by the extended finite element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2008
Haim Waisman
Abstract An adaptive method within the extended finite element method (XFEM) framework which adapts the enrichment function locally to the physics of a problem, as opposed to polynomial or mesh refinement, is presented. The method minimizes a local residual and determines the parameters of the enrichment function. We consider an energy form and a ,strong' form of the residual as error measures to drive the algorithm. Numerical examples for boundary layers and solid mechanics problems illustrate that the procedure converges. Moreover, when only the character of the solution is known, a good approximation is obtained in the area of interest. It is also shown that the method can be used to determine the order of singularities in solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source]