C. Pozrikidis · Cambridge University Press eBooks · 1992
In the preceding chapters we developed integral representations of a flow in terms of boundary distributions of Green's functions and their associated stress tensor. Physically, these representations involve boundary distributions of point forces, point sources, and point force dipoles. When we applied the representations at the boundaries of the flow and imposed the required boundary conditions, we obtained Fredholm integral equations of the first or second kind for the unknown boundary functions. Two advantages of solving these equations instead of the primary differential equations are reduction of the dimensionality of the mathematical problem with respect to the physical problem by one unit, and efficient treatment of infinite flows.
Cited by 0
Yi Zhu · 1982
Cited by 0
Ana Vuković, S. Sujecki, P.C. Kendall et al. · IEE Proceedings - Optoelectronics · 1998
The spectral index method (SIM) for analysis of the rib waveguide in air is improved by including the singular behaviour of the principal field component in the vicinity of the re-entrant corners, thereby giving the singular SIM (SSIM). This generally improves the value of the modal propagation constant as compared with more exact solutions. The new approach is successfully extended further to the rib waveguide coupler.
Cited by 5
Isam Ben Soltane, Rémi Colom, Frédéric Dierick et al. · New Journal of Physics · 2023
Abstract Physical systems and signals are characterized by complex functions of the frequency in the harmonic domain. The extension of such functions to the complex frequency plane, and in particular expansions and factorized forms of the harmonic-domain functions in terms of their poles and zeros, is of high interest to describe the physical properties of a system, and study its response dynamics in the temporal and harmonic domains. In this work, we start from a general property of continuity and differentiability of the complex functions to derive the multiple-order singularity expansion method. We rigorously derive the common singularity and zero expansion and factorization expressions, and generalize them to the case of singularities of arbitrary order, while deducing the behavior of these complex frequencies from the simple hypothesis that we are dealing with physically realistic signals.
Cited by 4Open access
2015
eBE rner e ge ldin distribution of singularities on flat triangular and rectangular elements has been developed and used. Here we present the exact expressions proposed for computing the influence of uniform singularity solvin ression al equ all the devices are three-dimensional by definition, useful insight integrals are discussed in [1–7] and the references in these BEM r one milar bove
Cited by 0
Christophe Schinckus, Cinla Akdere · RePEc: Research Papers in Economics
Purpose - How a micro-founded discipline such as economics could deal with the increasing global economic reality? This question has been asked frequently since the last economic crisis that appeared in 2008. In this challenging context, some commentators have turned their attention to a new area of knowledge coming from physics: econophysics which mainly focuses on a macro-analysis of economic systems. By showing that concepts used by econophysicists are consistent with an existing economic knowledge (developed by J.S. Mill), the purpose of this paper is to claim that an interdisciplinary perspective is possible between these two communities. Design/methodology/approach - The authors propose a historical and conceptual analysis of the key concept of emergence to emphasize the potential bridge between econophysics and economics. Findings - Six methodological arguments will be developed in order to show the existence of conceptual bridges as a necessary condition for the elaboration of a common language between economists and econophysics which would not be superfluous, in this challenging context, to clarify the growing complexity of economic phenomena. Originality/value - Although the economics and econophysics study same the complex economic phenomena, very few collaborations exist between them. This paper paves a conceptual/methodological path for more collaboration between the two fields.
Cited by 0
H. Liu, X. -f. Hu, Fields Excited The Probe · 2016
Cited by 0
Marcus Spradlin · 2008
Cited by 0
A.N. Alanssari · 2019 International Russian Automation Conference (RusAutoCon) · 2019
The authors introduce a quick technique based on the singular points for classifying fingerprints. The method detect singular points as (delta and core points), in fingerprints that are obtained from the orientation field. The technique improves the digitized image applying adaptive clustering, image processing, building the flow map by checking the orientations of individual pixels, computes histogram of flow map using overlapping blocks, and recognizing whorl, loop and deltas. The complexity of the technique is on the order of the number of pixels in the fingerprint image. The technique requires iterations without human feedback, and is highly parallel. In this the article, we proposed a new approach to recognize singularity, using cluster method and petal method.
Cited by 0
Antonio Lerario, Michele Stecconi · Arnold Mathematical Journal · 2023
Abstract We explain how to use the probabilistic method to prove the existence of real polynomial singularities with rich topology, i.e., with total Betti number of the maximal possible order. We show how similar ideas can be used to produce real algebraic projective hypersurfaces with a rich structure of umbilical points.
Cited by 1Open access
Michael H. Meylan, Colm Fitzgerald · 2015
Trapped modes are very special solutions to the linear water wave problem in which a solution with finite energy but no decay in time decay exists (McIver, 1996). A near trapped mode
Cited by 0
Zi‐Cai Li · SIAM Journal on Scientific Computing · 1994
A discrete technique of the Schwarz alternating procedure is presented to combine the Ritz–Galerkin and finite element methods. This technique is suited for solving singularity problems in parallel and requires a little more computation for a large overlap of subdomains. The convergence rate of the iterative procedure, which depends upon overlap of subdomains, has also been studied. Additionally, a balance strategy has been proposed to couple the iteration number with the element size used in the finite element method. For a sample of singularity problems, the total CPU time using the technique in this paper proves to be much less than that by the nonconforming combination.
Cited by 4
Carl E. Baum, Lawrence Carin · Elsevier eBooks · 2002
Cited by 9
C. Pozrikidis · Physics of Fluids A Fluid Dynamics · 1989
Oscillatory viscous flow in the presence of particles is considered. The flow is represented in terms of fundamental solutions to the governing unsteady Stokes equation including the oscillating Stokeslet and dipole. It is shown that the force on a particle in arbitrary oscillatory flow is proportional to the total strength of the distributed oscillating Stokeslets necessary to represent the flow. Faxen’s laws for solid and fluid particles are derived in terms of singularity representations and slender-body theory is discussed. The theoretical results are applied in studies of the translational and rotational oscillations of a solid sphere, the translational oscillation of a spherical drop, and the axial and transverse oscillation of a prolate spheroid. It is demonstrated that a spherical drop convected in a uniform streaming flow or moving under the influence of a body force, maintains its shape, independently of surface tension. The force F on a prolate spheroid executing longitudinal or transverse oscillations is computed in an extended range of frequencies ω. The results verify the accuracy of the correlation F(ω) proposed by Lawrence and Weinbaum [J. Fluid Mech. 189, 463 (1988)].
Cited by 112
Mercer, J. E., Lesferd, E. P., Weber, J. A. et al. · The Journal of the Abraham Lincoln Association
Cited by 0Open access
L. Wilson Pearson · 1982
Abstract : This final report summarizes results of the meeting conducted at the University of Kentucky, 19-21 November 1980, entitled Mathematical Foundations of the Singularity Expansion Method. The proceedings of the meeting are being reported as a special issue of the journal Electromagnetics (Vol. 1, No. 4); it should be available in the near future. Included in the final report is a list of titles and authorship which will appear in the above mentioned issue of Electromagnetics. (kr)
Cited by 0
John Mercer, J. Weber, E. LESFERD · 11th Aerospace Sciences Meeting · 1973
A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.
Cited by 11Open access
Carl E. Baum · Electromagnetics · 1981
ABSTRACT The singularity expansion method (SEM) arose from the observation that the transient response of complex electromagnetic scatterers appeared to be dominated by a small number of damped sinusoids. In the complex frequency plane, these damped sinusoids are poles of the Laplace-transformed response. The question is then one of characterizing the object response (time and frequency domains) in terms of all the singularities (poles, branch cuts, entire functions) in the complex frequency plane (hence singularity expansion method). Building on the older concept of natural frequencies, formulae were developed for the pole terms from an integral-equation formulation of the scattering process. The resulting factoring of the pole terms has important application consequences. Later developments include the eigenmode expansion method (EEM) which diagonalizes the integral-equation kernels and which can be used as an intermediate step in ordering the SEM terms. Additional concepts which have appeared include eigenimpedance synthesis and equivalent electrical networks. Of current interest is the use of the theoretical formulae to efficiently analyze and order experimental data. Related to this is the application of SEM results to target identification. This paper does not delve into the mathematical details; it presents an overview of the history and major concepts and results in SEM and EEM and related matters.
Cited by 15
Said Mikki, Abdelelah M. Alzahed, Yahia M. M. Antar · IEEE Access · 2019
We develop a general singularity expansion method (SEM) focused on the spatial structure of electromagnetic fields and currents. In contrast to the traditional temporal SEM, where complex analytical continuation is performed on the forward Green's function of free space, we propose applying the SEM to the reverse Green's function of the electromagnetic device, the recently introduced antenna current Green's function, leading to the discovery of new current and radiation modes. The new spatial SEM turns out to depend only on single-frequency field/current measurement besides completely avoiding the problem of separating early- and late-time responses that have been hindering the traditional approach. The theory is first developed at a very general level and then applied in detail to 1-D wire antennas. We manage to express the far field in terms of the spatial-SEM modes in a closed analytical form. The theory is confirmed by directly comparing with the full-wave method of moment solutions, and excellent agreement between theory and numerical analysis was obtained for generic wire array configurations. The resulting spatial-SEM is expected to stimulate researches into a new generation of frequency-domain RCS target identification technologies and electromagnetic sensing by developing special algorithms relying mainly on the spatial structure of the fields and currents fed by measurements at single frequency instead of the time-domain data usually required in traditional SEM.
Cited by 16Open access
Tan Tai · 2003
It is very important to detect singularities (core and delta) accurately and reliably for classification and matching of fingerprints. In this paper, a method for singularity detection in fingerprint images is presented to improve accuracy of the position and reliability of the singularity. Firstly, the singularities are detected based on block images through shifting position of the whole image time after time at the same block size and the concentrative region of singularities detected under different positions is got and the centroid of the region is computed to gain the accurate position of singularities. Then, the reliability of singularities detected above is determined with multilevel block sizes. In this method, the characteristics of the relative concentration of the position of singularities detected through image shift and of the corresponding relationship of the singularities detected with multilevel block sizes are used and the singularities are detected accurately and reliably. Experimental results show that the method performs well and it is robust to poor quality images.
Cited by 11