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Singular Points (singular + point)
Selected AbstractsOn singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems with cornersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004A. Dimitrov Abstract In this paper, a numerical procedure is presented for the computation of corner singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems near corners of various shape. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of this problem is approximated using a mixed u, p Galerkin,Petrov finite element method. Additionally, a separation of variables is used to reduce the dimension of the original problem. As a result, the quadratic eigenvalue problem (P+,Q+,2R)d=0 is obtained, where the saddle-point-type matrices P, Q, R are defined explicitly. For a numerical solution of the algebraic eigenvalue problem an iterative technique based on the Arnoldi method in combination with an Uzawa-like scheme is used. This technique needs only one direct matrix factorization as well as few matrix,vector products for finding all eigenvalues in the interval ,,(,) , (,0.5, 1.0), as well as the corresponding eigenvectors. Some benchmark tests show that this technique is robust and very accurate. Problems from practical importance are also analysed, for instance the surface-breaking crack in an incompressible elastic material and the three-dimensional viscous flow of a Newtonian fluid past a trihedral corner. Copyright © 2004 John Wiley & Sons, Ltd. [source] Efficient computation of order and mode of corner singularities in 3D-elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2001A. Dimitrov Abstract A general numerical procedure is presented for the efficient computation of corner singularities, which appear in the case of non-smooth domains in three-dimensional linear elasticity. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of the problem is approximated by a Galerkin,Petrov finite element method. A quadratic eigenvalue problem (P+,Q+,2R) u=0 is obtained, with explicitly analytically defined matrices P,Q,R. Moreover, the three matrices are found to have optimal structure, so that P,R are symmetric and Q is skew symmetric, which can serve as an advantage in the following solution process. On this foundation a powerful iterative solution technique based on the Arnoldi method is submitted. For not too large systems this technique needs only one direct factorization of the banded matrix P for finding all eigenvalues in the interval ,e(,),(,0.5,1.0) (no eigenpairs can be ,lost') as well as the corresponding eigenvectors, which is a great improvement in comparison with the normally used determinant method. For large systems a variant of the algorithm with an incomplete factorization of P is implemented to avoid the appearance of too much fill-in. To illustrate the effectiveness of the present method several new numerical results are presented. In general, they show the dependence of the singular exponent on different geometrical parameters and the material properties. Copyright © 2001 John Wiley & Sons, Ltd. [source] A qualitative study of mental health nurse identities: Many roles, one professionINTERNATIONAL JOURNAL OF MENTAL HEALTH NURSING, Issue 6 2009John Hurley ABSTRACT The aim of the study was to clarify and build upon current understandings of mental health nurse (MHN) identity. The study adopted a framework of social constructionism and qualitative methodology. Semistructured interviews were conducted, which were thematically analyzed using Nvivo software. Twenty-five MHN were recruited across three geographical sites in the UK. Participants constructed a cluster of seven MHN identity characteristics that constituted a unique contribution to talk-based therapies. These themes of characteristics are: (i) the MHN as generic specialist; (ii) the MHN as adopting a service-user focus; (iii) the MHN as positioning and utilizing the personal self; (iv) the MHN as spending time with the service user; (v) the MHN as delivering talk-based therapies in versatile ways; (vi) the MHN as having an everyday attitude; and (vii) the MHN as having transferable skills. The distinctiveness, and thus, professional identity of mental health nursing, must be understood as a cluster of capabilities rather than a search for a singular point of difference. The breadth of capabilities employed by MHN highlights the value and worth of their contribution to service-user care. [source] Experimental study of feasibility in kinetically-controlled reactive distillationAICHE JOURNAL, Issue 2 2005Madhura Chiplunkar Abstract Bifurcation studies predict limited ranges of feasibility for products in certain reactive distillations. These are closely related to the bifurcations in the singular points of dynamic models for simple reactive distillation (isobaric open evaporation with liquid phase reaction). A new dynamic model is described with constant vapor rate together with an experimental study for the reactive distillation of acetic acid with isopropanol to produce isopropyl acetate, catalyzed by Amberlyst-15 ion-exchange resin. An experimental apparatus with real-time measurement of liquid compositions based on Fourier transform infrared (FTIR) spectroscopy is described, and used to follow the composition dynamics at several initial conditions and Damköhler numbers (Da). The experimental results match model predictions that show four regions of behavior. For Da , 1, these show a stable node at acetic acid and several other fixed points as saddles. However, near Da , 2, both isopropanol and acetic acid are stable nodes and a quaternary singular point appears. The presence of two stable nodes requires the presence of a distillation boundary and, therefore, a limited feasibility for the bottom product compositions from continuous reactive distillation. For the reaction rates studied, the model predictions are closely consistent with the experimental findings, and are robust to variations in the vapor rate. These experiments are among the first to analyze the dynamics and feasibility in a kinetically-controlled reactive distillation and are consistent with previous studies for the reaction equilibrium limit, indicating the formation of a reactive azeotrope. © 2005 American Institute of Chemical Engineers AIChE J, 51: 464,479, 2005 [source] Eigenfunctions and Hardy inequalities for a magnetic Schrödinger operator in ,2MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2003Bénédicte Alziary Abstract The zero set {z,,2:,(z)=0} of an eigenfunction , of the Schrödinger operator ,V=(i,+A)2+V on L2(,2) with an Aharonov,Bohm-type magnetic potential is investigated. It is shown that, for the first eigenvalue ,1 (the ground state energy), the following two statements are equivalent: (I) the magnetic flux through each singular point of the magnetic potential A is a half-integer; and (II) a suitable eigenfunction , associated with ,1 (a ground state) may be chosen in such a way that the zero set of , is the union of a finite number of nodal lines (curves of class C2) which emanate from the singular points of the magnetic potential A and slit the two-dimensional plane ,2. As an auxiliary result, a Hardy-type inequality near the singular points of A is proved. The C2 differentiability of nodal lines is obtained from an asymptotic analysis combined with the implicit function theorem. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the BIEM solution for a half-space by Neumann seriesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2007M. Y. Antes Abstract This paper presents an approach which allows the solution of elastic problems concerning a half-space (half-plane) with cavities by the boundary integral equation methods using Neumann's series. To evaluate the series terms at singular points, the regular representations of singular integrals for the external problems were proven and the regular recurrent relationships for the series terms, which can be calculated by any known quadrature rule, are obtained. The numerical proposed procedure was tested by comparison with known theoretical solution and the method convergence was studied for various depths of a buried cavity. Copyright © 2006 John Wiley & Sons, Ltd. [source] Lower bound limit analysis with adaptive remeshingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005Andrei V. Lyamin Abstract The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field. Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707,1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented. The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut. Copyright © 2005 John Wiley & Sons, Ltd. [source] Simulation of lid-driven cavity flows by parallel lattice Boltzmann method using multi-relaxation-time schemeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2004J.-S. Wu Abstract Two-dimensional near-incompressible steady lid-driven cavity flows (Re = 100,7,500) are simulated using multi-relaxation-time (MRT) model in the parallel lattice Boltzmann BGK Bhatnager,Gross,Krook method (LBGK). Results are compared with those using single-relaxation-time (SRT) model in the LBGK method and previous simulation data using Navier,Stokes equations for the same flow conditions. Effects of variation of relaxation parameters in the MRT model, effects of number of the lattice points, improved computational convergence and reduced spatial oscillations of solution near geometrically singular points in the flow field using LBGK method due to MRT model are highlighted in the study. In summary, lattice Boltzmann method using MRT model introduces much less spatial oscillations near geometrical singular points, which is important for the successful simulation of higher Reynolds number flows. Copyright © 2004 John Wiley & Sons, Ltd. [source] Potential flow around obstacles using the scaled boundary finite-element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003Andrew J. Deeks Abstract The scaled boundary finite-element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one co-ordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) co-ordinate direction. These co-ordinate directions are defined by the geometry of the domain and a scaling centre. The method can be employed for both bounded and unbounded domains. This paper applies the method to problems of potential flow around streamlined and bluff obstacles in an infinite domain. The method is derived using a weighted residual approach and extended to include the necessary velocity boundary conditions at infinity. The ability of the method to model unbounded problems is demonstrated, together with its ability to model singular points in the near field in the case of bluff obstacles. Flow fields around circular and square cylinders are computed, graphically illustrating the accuracy of the technique, and two further practical examples are also presented. Comparisons are made with boundary element and finite difference solutions. Copyright © 2003 John Wiley & Sons, Ltd. [source] Experimental study of feasibility in kinetically-controlled reactive distillationAICHE JOURNAL, Issue 2 2005Madhura Chiplunkar Abstract Bifurcation studies predict limited ranges of feasibility for products in certain reactive distillations. These are closely related to the bifurcations in the singular points of dynamic models for simple reactive distillation (isobaric open evaporation with liquid phase reaction). A new dynamic model is described with constant vapor rate together with an experimental study for the reactive distillation of acetic acid with isopropanol to produce isopropyl acetate, catalyzed by Amberlyst-15 ion-exchange resin. An experimental apparatus with real-time measurement of liquid compositions based on Fourier transform infrared (FTIR) spectroscopy is described, and used to follow the composition dynamics at several initial conditions and Damköhler numbers (Da). The experimental results match model predictions that show four regions of behavior. For Da , 1, these show a stable node at acetic acid and several other fixed points as saddles. However, near Da , 2, both isopropanol and acetic acid are stable nodes and a quaternary singular point appears. The presence of two stable nodes requires the presence of a distillation boundary and, therefore, a limited feasibility for the bottom product compositions from continuous reactive distillation. For the reaction rates studied, the model predictions are closely consistent with the experimental findings, and are robust to variations in the vapor rate. These experiments are among the first to analyze the dynamics and feasibility in a kinetically-controlled reactive distillation and are consistent with previous studies for the reaction equilibrium limit, indicating the formation of a reactive azeotrope. © 2005 American Institute of Chemical Engineers AIChE J, 51: 464,479, 2005 [source] Eigenfunctions and Hardy inequalities for a magnetic Schrödinger operator in ,2MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2003Bénédicte Alziary Abstract The zero set {z,,2:,(z)=0} of an eigenfunction , of the Schrödinger operator ,V=(i,+A)2+V on L2(,2) with an Aharonov,Bohm-type magnetic potential is investigated. It is shown that, for the first eigenvalue ,1 (the ground state energy), the following two statements are equivalent: (I) the magnetic flux through each singular point of the magnetic potential A is a half-integer; and (II) a suitable eigenfunction , associated with ,1 (a ground state) may be chosen in such a way that the zero set of , is the union of a finite number of nodal lines (curves of class C2) which emanate from the singular points of the magnetic potential A and slit the two-dimensional plane ,2. As an auxiliary result, a Hardy-type inequality near the singular points of A is proved. The C2 differentiability of nodal lines is obtained from an asymptotic analysis combined with the implicit function theorem. Copyright © 2003 John Wiley & Sons, Ltd. [source] The local theory of the cosmic skeletonMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2009D. Pogosyan ABSTRACT The local theory of the critical lines of two- and three-dimensional random fields that underline the cosmic structures is presented. In the context of cosmological matter distribution, the subset of critical lines of the three-dimensional density field serves to delineate the skeleton of the observed filamentary structure at large scales. A stiff approximation used to quantitatively describe the filamentary skeleton shows that the flux of the skeleton lines is related to the average Gaussian curvature of the (N , 1) dimensional sections of the field. The distribution of the length of the critical lines with threshold is analysed in detail, while the extended descriptors of the skeleton , its curvature and singular points , are introduced and briefly described. Theoretical predictions are compared to measurements of the skeleton in realizations of Gaussian random fields in two and three dimensions. It is found that the stiff approximation accurately predicts the shape of the differential length, allows for analytical insight and explicit closed form solutions. Finally, it provides a simple classification of the singular points of the critical lines: (i) critical points; (ii) bifurcation points and (iii) slopping plateaux. [source] Ridge directional singular points for fingerprint recognition and matchingAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 1 2006Issam Dagher Abstract In this paper, a new approach to extract singular points in a fingerprint image is presented. It is usually difficult to locate the exact position of a core or a delta due to the noisy nature of fingerprint images. These points are the most widely used for fingerprint classification and matching. Image enhancement, thinning, cropping, and alignment are used for minutiae extraction. Based on the Poincaré curve obtained from the directional image, our algorithm extracts the singular points in a fingerprint with high accuracy. It examines ridge directions when singular points are missing. The algorithm has been tested for classification performance on the NIST-4 fingerprint database and found to give better results than the neural networks algorithm. Copyright © 2005 John Wiley & Sons, Ltd. [source] On the number of singular points of weak solutions to the Navier-Stokes equationsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2001Gregory A. Seregin We consider a suitable weak solution to the three-dimensional Navier-Stokes equations in the space-time cylinder , × ]0, T[. Let , be the set of singular points for this solution and , (t) , {(x, t) , ,}. For a given open subset , , , and for a given moment of time t ,]0, T[, we obtain an upper bound for the number of points of the set ,(t) , ,. © 2001 John Wiley & Sons, Inc. [source] | |||||||||||||