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Journal articles on the topic 'Irregular integral'

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Published: 9 March 2023
Last updated: 10 March 2023

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1

Collmer, Sabine. "Child Soldiers-An Integral Element in New, Irregular Wars?" Connections: The Quarterly Journal 03, no. 3 (2004): 1–11. http://dx.doi.org/10.11610/connections.03.3.01.

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2

Spada, E., T. Tucciarelli, M. Sinagra, V. Sammartano, and G. Corato. "Uniform flow formulas for irregular sections." Hydrology and Earth System Sciences Discussions 12, no. 2 (February 27, 2015): 2607–55. http://dx.doi.org/10.5194/hessd-12-2607-2015.

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Abstract. Two new methods for uniform flow discharge computation are presented, validated and compared with other available formulas. The first method derives from the well-known Huthoff algorithm, which is first shown to be dependent on the way the river cross-section is discretized into several sub-sections. The second method assumes the vertically averaged longitudinal velocity to be a function only of the friction factor and of the so-called "local hydraulic radius", computed as the ratio between the integral of the elementary areas around a given vertical and the integral of the elementary solid boundaries around the same vertical. Both integrals are weighted with a linear shape function, equal to zero at a distance from the integration variable which is proportional to the water depth according to an empirical coefficient β. Both formulas are validated against (1) laboratory experimental data, (2) discharge hydrographs measured in a real site, where the friction factor is estimated from an unsteady-state analysis of water levels recorded in two different river cross sections, (3) the 3-D solution obtained using the commercial ANSYS CFX code, computing the steady state uniform flow in a short reach of a prismatic channel, with known water level in the downstream section.
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3

Du, Liang Liang, and Xiong Hua Wu. "Natural Boundary Integral Method for Irregular Plate Problems." Applied Mechanics and Materials 138-139 (November 2011): 693–98. http://dx.doi.org/10.4028/www.scientific.net/amm.138-139.693.

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Natural boundary integral method is applied to deal with plate problems defined in irregular domains. We divide the solution into two parts, a particular solution for inhomogeneous biharmonic equation and the general solution for homogeneous biharmonic equation. For the former, the direct expansion method of boundary conditions is used to treat the arbitrary domains, and the processes of natural boundary integral method coupling with finite element method are omitted. Numerical experiments show that the method is very simple and of high accuracy.
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4

Barbuto, Fausto A. A., and Renato Machado Cotta. "Integral transformation of elliptic problems within irregular domains." International Journal of Numerical Methods for Heat & Fluid Flow 7, no. 8 (December 1997): 778–93. http://dx.doi.org/10.1108/09615539710193065.

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5

Besov, Oleg V. "Integral estimates for differentiable functions on irregular domains." Sbornik: Mathematics 201, no. 12 (February 11, 2011): 1777–90. http://dx.doi.org/10.1070/sm2010v201n12abeh004130.

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6

Besov, O. V. "Integral estimates for differentiable functions on irregular domains." Doklady Mathematics 81, no. 1 (February 2010): 87–90. http://dx.doi.org/10.1134/s1064562410010242.

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7

Gao, Honglin, and Sheng Li. "Improved Integral Formulation for Acoustic Radiation Using Integral Equation of Frequency Averaged Quadratic Pressure." Journal of Computational Acoustics 25, no. 01 (March 2017): 1750004. http://dx.doi.org/10.1142/s0218396x17500047.

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This paper is concerned with the problem of obtaining a unique solution for radiation at irregular frequencies when an integral equation of frequency averaged quadratic pressure (FAQP) is used to get robust predictions at medium and high frequencies. It is proved that there is no unique solution of the integral equation of FAQP at irregular frequencies, and existence and uniqueness of solutions under four types of boundary conditions are discussed. A combined energy boundary integral equation formulation (CEBIEF) is presented and proves to be efficient to overcome the nonuniqueness of the integral equation of FAQP. The numerical examples are given to demonstrate the versatility of the CEBIEF method with a proposed function correctly indicating a solution.
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8

T. Shivaram, K., and S. Kiran. "A simple and efficient wavelet approach for evaluating surface integral over curved domain." International Journal of Engineering & Technology 7, no. 4.5 (September 22, 2018): 511. http://dx.doi.org/10.14419/ijet.v7i4.5.21145.

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This paper presents, a simple and efficient wavelet approach for computing the surface integrals over irregular or curved dom ain, the limit of the integrals are nonlinear function are transformed to standard two square by using finite element basis function, Haar wavelet based integration technique is applied to evaluation of surface integral over curved domain, the computational efficiency of the method is illustrated with several numerical examples.
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9

Lyman, John M., and Gregory C. Johnson. "Estimating Annual Global Upper-Ocean Heat Content Anomalies despite Irregular In Situ Ocean Sampling*." Journal of Climate 21, no. 21 (November 1, 2008): 5629–41. http://dx.doi.org/10.1175/2008jcli2259.1.

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Abstract The effects of irregular in situ ocean sampling on estimates of annual globally integrated upper ocean heat content anomalies (OHCA) are investigated for sampling patterns from 1955 to 2006. An analytical method is presented for computing the effective area covered by an objective map for any given in situ sampling distribution. To evaluate the method, appropriately scaled sea surface height (SSH) anomaly maps from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) are used as a proxy for OHCA from 1993 to 2006. Use of these proxy data demonstrates that the simple area integral (SI) of such an objective map for sparse datasets does not agree as well with the actual integral as the weighted integral (WI), defined as the simple integral weighted by the ratio of the total area over the “observed” area. From 1955 to 1966, in situ ocean sampling is inadequate to estimate accurately annual global integrals of the proxy upper OHCA. During this period, the SI for the sampling pattern of any given year underestimates the 13-yr trend in proxy OHCA from 1993 to 2006 by around 70%, and confidence limits for the WI are often very large. From 1967 to 2003 there appear to be sufficient data to estimate annual global integrals. Limited by the constraints of this analysis, the SI for any given year’s sampling pattern still underestimates the 1993–2006 13-yr trend in the proxy by around 30%, but the WI matches the trend well with small confidence limits. For 2004 through 2006 in situ sampling, with near-global in situ Argo data coverage, the 1993–2006 13-yr trend in the proxy is equally well represented by the SI or WI.
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10

Spada, E., T. Tucciarelli, M. Sinagra, V. Sammartano, and G. Corato. "Computation of vertically averaged velocities in irregular sections of straight channels." Hydrology and Earth System Sciences 19, no. 9 (September 14, 2015): 3857–73. http://dx.doi.org/10.5194/hess-19-3857-2015.

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Abstract. Two new methods for vertically averaged velocity computation are presented, validated and compared with other available formulas. The first method derives from the well-known Huthoff algorithm, which is first shown to be dependent on the way the river cross section is discretized into several subsections. The second method assumes the vertically averaged longitudinal velocity to be a function only of the friction factor and of the so-called "local hydraulic radius", computed as the ratio between the integral of the elementary areas around a given vertical and the integral of the elementary solid boundaries around the same vertical. Both integrals are weighted with a linear shape function equal to zero at a distance from the integration variable which is proportional to the water depth according to an empirical coefficient β. Both formulas are validated against (1) laboratory experimental data, (2) discharge hydrographs measured in a real site, where the friction factor is estimated from an unsteady-state analysis of water levels recorded in two different river cross sections, and (3) the 3-D solution obtained using the commercial ANSYS CFX code, computing the steady-state uniform flow in a cross section of the Alzette River.
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11

Chen, Xiao-fei. "Seismogram synthesis for multi-layered media with irregular interfaces by global generalized reflection/transmission matrices method. I. Theory of two-dimensional SH case." Bulletin of the Seismological Society of America 80, no. 6A (December 1, 1990): 1696–724. http://dx.doi.org/10.1785/bssa08006a1696.

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Abstract In this paper, we present a new method of seismogram synthesis for multi-layered media with irregular interfaces due to an arbitrary source. This method can be viewed as either an extension of the T matrix method for an inclusion to multi-layered media by introducing the global generalized R/T matrices, or an extension of the generalized R/T coefficients method for horizontally layered media to irregular layered ones by incorporating the T matrix method. The formulation obtained in this paper is expressed in terms of the global generalized R/T matrices. These global generalized R/T matrices can be determined from integrals along each interface and integral over source area via a recursive relation. This formulation provides an efficient scheme of computation, especially when the number of layers increases. Also, this formulation can be applied to any finite frequency, although for higher frequency it needs more computation time than for lower frequency. As examples, we give solutions of three specific problems, namely, horizontally layered media, irregular topography, and an irregular layer over a half-space.
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12

Paixão, Rodrigo Freitas, and Ana Paula Motta Costa. "A imposição da guarda compartilhada como regra no ordenamento jurídico brasileiro: um paralelo com a Doutrina da Situação Irregular." Revista de Direito de Família e Sucessão 3, no. 1 (June 1, 2017): 14. http://dx.doi.org/10.26668/indexlawjournals/2526-0227/2017.v3i1.1869.

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O artigo busca traçar um paralelo entre a imposição da guarda compartilhada pela Lei 13.058/2014 e a Doutrina da Situação Irregular que estabelecia a forma como os direitos das crianças e dos adolescentes eram tutelados pelo Estado antes da Convenção Internacional sobre os Direitos da Criança. Para tanto, mostrará que, empesar da boa intenção do legislador, a imposição incondicional da guarda compartilhada pode configurar uma afronta à Doutrina da Proteção Integral, em especial ao Princípio do Melhor Interesse da Criança e do Adolescente, e um retorno aos principais pensamentos que embasavam a Doutrina da Situação Irregular.Title: The imposition of joint custody as a rule in the Brazilian legal system: a parallel with the Irregular Situation DoctrineAbstract: The article seeks to draw a parallel between the imposition of shared custody by Law 13.058/2014 and the Irregular Situation Doctrine which established how the rights of children and adolescents were protected by the State prior to the International Convention on the Rights of the Child. This study will demonstrate that, in spite of the good intentions of the legislator, the unconditional imposition of joint custody can constitute an affront to the Integral Protection Doctrine, especially to the Principle of the Best Interests of Children and Adolescents, and a return to the main thoughts that embase the Irregular Situation DoctrineKeywords: human rights of children and adolescents; principle of the best interests of children and adolescents; joint custody; irregular situation docrtine; integral protection doctrine
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13

Lee, C. H., and P. D. Sclavounos. "Removing the irregular frequencies from integral equations in wave-body interactions." Journal of Fluid Mechanics 207 (October 1989): 393–418. http://dx.doi.org/10.1017/s0022112089002636.

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The paper presents a method that removes the effects of all irregular frequencies in boundary-integral equations governing the interaction of regular waves with floating bodies of general geometry. A modified integral equation is obtained by the linear superposition of the classical Green equation and its normal derivative with respect to the field point. The selection of a purely imaginary constant of proportionality ensures the removal of all irregular frequencies in the continuous problem and the appropriate selection of its magnitude eliminates their undesirable effects in its numerical implementation. Computations are presented of the added-mass and damping coefficients and exciting forces on a sphere and a truncated vertical cylinder, illustrating the effectiveness of the method.
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14

L. A. Sphaier, R. M . Cotta. "INTEGRAL TRANSFORM ANALYSIS OF MULTIDIM ENSIONAL EIGENVALUE PROBLEMS WITHIN IRREGULAR DOMAINS." Numerical Heat Transfer, Part B: Fundamentals 38, no. 2 (September 2000): 157–75. http://dx.doi.org/10.1080/104077900750034652.

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15

Cooker, M. J. "A boundary-integral method for water wave motion over irregular beds." Engineering Analysis with Boundary Elements 7, no. 4 (December 1990): 205–13. http://dx.doi.org/10.1016/0955-7997(90)90006-u.

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16

Rath Spivack, Orsola, and Mark Spivack. "Efficient boundary integral solution for acoustic wave scattering by irregular surfaces." Engineering Analysis with Boundary Elements 83 (October 2017): 275–80. http://dx.doi.org/10.1016/j.enganabound.2017.07.024.

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17

Peltoniemi, Jouni I. "Variational volume integral equation method for electromagnetic scattering by irregular grains." Journal of Quantitative Spectroscopy and Radiative Transfer 55, no. 5 (May 1996): 637–47. http://dx.doi.org/10.1016/0022-4073(96)00007-6.

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18

Custodio, Andre. "Teoria da proteção integral: pressuposto para compreensão do direito da criança e do adolescente." Revista do Direito, no. 29 (January 30, 2008): 22–43. http://dx.doi.org/10.17058/rdunisc.v0i29.657.

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O artigo analisa a teoria da proteção integral e o Direito da Criança e do Adolescente. Descreve os princípios da teoria da proteção integral, analisa a doutrina da situação irregular e estuda os fundamentos jurídicos para concretização dos direitos da criança e do adolescente no Brasil contemporâneo.
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19

Seguin, Brian, and Eliot Fried. "Roughening it — evolving irregular domains and transport theorems." Mathematical Models and Methods in Applied Sciences 24, no. 09 (May 20, 2014): 1729–79. http://dx.doi.org/10.1142/s0218202514500067.

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Well-known examples of transport theorems include the Leibniz integral rule and a result established by Reynolds for three-dimensional regions that convect with the motion of a continuum. Here, we prove a generalized transport theorem by relaxing the regularity assumptions on the domain of integration to include domains that may, among other things, develop holes, split into pieces, or whose fractal dimension may evolve with time. Our results are of potential value in continuum physics and the calculus of variations.
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20

Johnson, David A. "The United States Medical Licensing Examination (USMLE): Maintaining the Integrity of the Examination Process." Journal of Medical Regulation 92, no. 3 (September 1, 2006): 16–19. http://dx.doi.org/10.30770/2572-1852-92.3.16.

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ABSTRACT Maintaining the integrity of the USMLE is critical to the state medical boards that rely upon the exam as an integral part of their assessment of physician candidates for licensure. The USMLE program defines irregular behavior as “any action...that subverts or attempts to subvert the examination process.” Program staff routinely monitor compliance with registration and testing protocols. Suspected cases of irregular behavior are referred to a committee for final determination. A finding of irregular behavior carries significant potential implications for the examinee. The USMLE transcript is the primary means for alerting staff at state medical boards to confirmed instances of irregular behavior. The transcript is routinely accompanied by a determination letter summarizing the case and committee’s finding of irregular behavior.
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21

Gurevich, Boris, Shemer Keydar, and Evgeny Landa. "Multifocusing imaging over an irregular topography." GEOPHYSICS 67, no. 2 (March 2002): 639–43. http://dx.doi.org/10.1190/1.1468625.

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If seismic data are acquired over an irregular topography, standard elevation statics methods may be inaccurate because the assumption of vertical raypaths will no longer be valid. An effective solution to the problem of irregular topography can be found through the use of the multifocusing method, in which large supergathers of seismic traces are stacked, each of which can span many common midpoint (CMP) gathers. This can be done by extending the multifocusing moveout formula to explicitly account for nonzero elevations of the source and receiver, as well as their horizontal coordinates. Implementation of this formula into the multifocusing algorithm is straightforward because estimating the necessary raypath information (i.e., emergence angles) is an integral part of the algorithm. The extended multifocusing moveout correction can be applied directly to the data acquired in areas of irregular topography without the need for prior elevation static corrections. Synthetic tests on such data show that the proposed technique results in a better alignment of reflection events.
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22

Takemura, Kouichi. "Euler's integral transformation for systems of linear differential equations with irregular singularities." Banach Center Publications 97 (2012): 141–52. http://dx.doi.org/10.4064/bc97-0-10.

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23

Lomov, I. S. "Integral representations of irregular root functions of loaded second-order differential operators." Differential Equations 52, no. 12 (December 2016): 1563–74. http://dx.doi.org/10.1134/s0012266116120041.

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24

Raevskii, A. S., S. B. Raevskii, A. Yu Sedakov, and A. A. Titarenko. "Integral Equation Method for Calculating Irregular Waveguides Using the Generalized Lorentz Lemma." Journal of Communications Technology and Electronics 64, no. 11 (November 2019): 1188–95. http://dx.doi.org/10.1134/s1064226919110226.

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25

Sidorov, N. A., and D. N. Sidorov. "Solving the hammerstein integral equation in the irregular case by successive approximations." Siberian Mathematical Journal 51, no. 2 (March 2010): 325–29. http://dx.doi.org/10.1007/s11202-010-0033-4.

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26

Pérez Guerrero, J. S., J. N. N. Quaresma, and R. M. Cotta. "Simulation of laminar flow inside ducts of irregular geometry using integral transforms." Computational Mechanics 25, no. 4 (April 20, 2000): 413–20. http://dx.doi.org/10.1007/s004660050488.

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27

Arns, C. H., M. A. Knackstedt, and K. R. Mecke. "Characterisation of irregular spatial structures by parallel sets and integral geometric measures." Colloids and Surfaces A: Physicochemical and Engineering Aspects 241, no. 1-3 (July 2004): 351–72. http://dx.doi.org/10.1016/j.colsurfa.2004.04.034.

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28

Kavehvash, Zahra, Khashayar Mehrany, and Saeed Bagheri. "Improved resolution three-dimensional integral imaging using optimized irregular lens-array structure." Applied Optics 51, no. 25 (August 24, 2012): 6031. http://dx.doi.org/10.1364/ao.51.006031.

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29

Lifanov, I. K., Yu A. Mel’nikov, and A. S. Nenashev. "The Green function for domains of irregular shape and singular integral equations." Doklady Mathematics 74, no. 2 (October 2006): 678–82. http://dx.doi.org/10.1134/s1064562406050164.

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30

Batista, Cláudio G., and Cássio G. Rego. "An integral equation model for radiowave propagation over inhomogeneous smoothly irregular terrain." Microwave and Optical Technology Letters 54, no. 1 (November 22, 2011): 26–31. http://dx.doi.org/10.1002/mop.26473.

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31

Wu, Qinghua, and Meiying Xiang. "A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations." Advances in Mathematical Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/103074.

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A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work. Numerical experiments are conducted to illustrate the performance of the new method and show that in some cases the simpler GMRES method could achieve higher accuracy than GMRES.
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32

Jiang, Wei, Jiancheng Xu, Li Kunpeng, Ye Ouyang, and Jinzhou Yan. "Coupling Heat Conduction and Radiation by an Isogeometric Boundary Element Method in 2-D Structures." Mathematical Problems in Engineering 2022 (September 7, 2022): 1–14. http://dx.doi.org/10.1155/2022/4209720.

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We propose an efficient isogeometric boundary element method to address the coupling of heat conduction and radiation in homogeneous or inhomogeneous materials. The isogeometric boundary element method is used to construct irregular 2D models, which eliminate errors in model construction. The physical unknowns in the governing equations for heat conduction and radiation are discretized using an interpolation approximation, and the integral equations are finally solved by Newton–Raphson iteration; it is noteworthy that we use the radial integration method to convert the domain integrals to boundary integrals, and we combine the numerical schemes for heat conduction and radiation. The results of the three numerical cases show that the adopted algorithm can improve the computational accuracy and efficiency.
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33

Ben Gharbia, Ibtihel, Marcella Bonazzoli, Xavier Claeys, Pierre Marchand, and Pierre-Henri Tournier. "Fast Solution of Boundary Integral Equations for Elasticity Around a Crack Network: A Comparative Study." ESAIM: Proceedings and Surveys 63 (2018): 135–51. http://dx.doi.org/10.1051/proc/201863135.

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Because of the non-local nature of the integral kernels at play, the discretization of boundary integral equations leads to dense matrices, which would imply high computational complexity. Acceleration techniques, such as hierarchical matrix strategies combined with Adaptive Cross Approximation (ACA), are available in literature. Here we apply such a technique to the solution of an elastostatic problem, arising from industrial applications, posed at the surface of highly irregular cracks networks.
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34

Sevastianov, Anton L. "Single-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguides." Discrete and Continuous Models and Applied Computational Science 28, no. 4 (December 15, 2020): 361–77. http://dx.doi.org/10.22363/2658-4670-2020-28-4-361-377.

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This paper investigates the waveguide propagation of polarized electromagnetic radiation in a thin-film integral optical waveguide. To describe this propagation, the adiabatic approximation of solutions of Maxwells equations is used. The construction of a reduced model for adiabatic waveguide modes that retains all the properties of the corresponding approximate solutions of the Maxwell system of equations was carried out by the author in a previous publication in DCM ACS, 2020, No 3. In this work, for a special case when the geometry of the waveguide and the electromagnetic field are invariant in the transverse direction. In this case, there are separate nontrivial TEand TM-polarized solutions of this reduced model. The paper describes the parametrically dependent on longitudinal coordinates solutions of problems for eigenvalues and eigenfunctions - adiabatic waveguide TE and TM polarizations. In this work, we present a statement of the problem of finding solutions to the model of adiabatic waveguide modes that describe the stationary propagation of electromagnetic radiation. The paper presents solutions for the single-mode propagation of TE and TM polarized adiabatic waveguide waves.
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35

Lipachev, E. K. "Integral equations in the wave scattering problem at an irregular interface of domains." Russian Mathematics 51, no. 8 (August 2007): 33–44. http://dx.doi.org/10.3103/s1066369x0708004x.

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36

Huilgol, R. R., M. Panizza, N. Phan-Thien, and R. Zheng. "Application of the boundary integral method to the sedimentation of irregular shaped particles." Journal of Non-Newtonian Fluid Mechanics 57, no. 1 (April 1995): 49–60. http://dx.doi.org/10.1016/0377-0257(94)01295-s.

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37

Pinheiro, I. F., G. Puccetti, G. L. Morini, and L. A. Sphaier. "Integral transform analysis of microchannel fluid flow: Irregular geometry estimation using velocimetry data." Applied Mathematical Modelling 90 (February 2021): 943–54. http://dx.doi.org/10.1016/j.apm.2020.09.035.

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38

LEE, C. H., J. N. NEWMAN, and X. ZHU. "AN EXTENDED BOUNDARY INTEGRAL EQUATION METHOD FOR THE REMOVAL OF IRREGULAR FREQUENCY EFFECTS." International Journal for Numerical Methods in Fluids 23, no. 7 (October 15, 1996): 637–60. http://dx.doi.org/10.1002/(sici)1097-0363(19961015)23:7<637::aid-fld437>3.0.co;2-3.

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39

Zhou, Hong, Xiaofei Chen, and Ying Chang. "Review on localized boundary integral equation: Discrete wavenumber method for 2D irregular layers." Earthquake Science 23, no. 2 (February 10, 2010): 129–37. http://dx.doi.org/10.1007/s11589-009-0070-x.

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40

Chandrawansa, Kumari, Frits H. Ruymgaart, and Arnoud C. M. Van Rooij. "Controlling the Gibbs phenomenon in noisy deconvolution of irregular multivariable input signals." Journal of Applied Mathematics and Stochastic Analysis 13, no. 1 (January 1, 2000): 1–14. http://dx.doi.org/10.1155/s1048953300000010.

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An example of inverse estimation of irregular multivariable signals is provided by picture restoration. Pictures typically have sharp edges and therefore will be modeled by functions with discontinuities, and they could be blurred by motion. Mathematically, this means that we actually observe the convolution of the irregular function representing the picture with a spread function. Since these observations will contain measurement errors, statistical aspects will be pertinent. Traditional recovery is corrupted by the Gibbs phenomenon (i.e., overshooting) near the edges, just as in the case of direct approximations. In order to eliminate these undesirable effects, we introduce an integral Cesàro mean in the inversion procedure, leading to multivariable Fejér kernels. Integral metrics are not sufficiently sensitive to properly assess the quality of the resulting estimators. Therefore, the performance of the estimators is studied in the Hausdorff metric, and a speed of convergence of the Hausdorff distance between the graph of the input signal and its estimator is obtained.
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41

Brito, Leila Maria Torraca de. "Liberdade assistida no horizonte da doutrina de proteção integral." Psicologia: Teoria e Pesquisa 23, no. 2 (June 2007): 133–38. http://dx.doi.org/10.1590/s0102-37722007000200003.

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O trabalho tem como objetivo abordar o significado da medida socioeducativa de liberdade assistida no contexto da doutrina de proteção integral. Por meio de uma revisão crítica da literatura, recordam-se conceitos e práticas utilizados na vigência da antiga doutrina da situação irregular, sustentando-se a importância de ruptura com modelos de atendimento empregados naquela época. Expõe-se, por fim, referenciais e procedimentos indicados aos que atuam com crianças e adolescentes que aportam à justiça da infância e da juventude, com destaque para ações e parcerias que podem ser estabelecidas em programas socioeducativos.
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42

Zhou, Xiaobing. "3D vector gravity potential and line integrals for the gravity anomaly of a rectangular prism with 3D variable density contrast." GEOPHYSICS 74, no. 6 (November 2009): I43—I53. http://dx.doi.org/10.1190/1.3239518.

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Three-dimensional rectangular prisms are building blocks for calculating gravity anomalies from irregular 3D mass bodies with spatially variable density contrasts. A 3D vector gravity potential is defined for a 3D rectangular prism with density contrast varying in depth and horizontally. The vertical component of the gravity anomaly equals the flux of the 3D vector gravity potential through the enclosed surface of the prism. Thus, the 3D integral for the gravity anomaly is reduced to a 2D surface integral. In turn, a 2D vector gravity potential is defined. The vertical component of the gravity anomaly equals the net circulation of the 2D vector gravity potential along the enclosed contour bounding the surfaces of the prism. The 3D integral for the gravity anomaly is reduced to 1D line integrals. Further analytical or numerical solutions can then be obtained from the line integrals, depending on the forms of the density contrast functions. If an analytical solution cannot be obtained, the line-integral method is semianalytical, requiring numerical quadratures to be carried out at the final stages. Singularity and discontinuity exist in the algorithm and the method of exclusive infinitesimal sphere or circle is effective to remove them. Then the vector-potential line-integral method can calculate the gravity anomaly resulting from a rectangular prism with density contrast, varying simply in one direction and sophisticatedly in three directions. The advantage of the method is that the constraint to the form of the density contrast is greatly reduced and the numerical calculation for the gravity anomaly is fast.
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43

Khattab, M. A. A., D. J. Burns, R. J. Pick, and J. C. Thompson. "Opening Mode Stress Intensity Factors for Embedded Rectangular and Irregular Planar Defects." Journal of Pressure Vessel Technology 108, no. 1 (February 1, 1986): 41–49. http://dx.doi.org/10.1115/1.3264750.

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An integral technique has been used to estimate opening mode stress intensity factors, K1, for embedded rectangular and irregular planar defects subjected to uniform tension. These estimates have been confirmed by stress freezing photoelastic techniques. Also K1 estimates for rectangular defects are shown to compare well with theoretical solutions obtained by others.
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44

Tezuka, Kazuhiko, C. H. (Arthur) Cheng, and X. M. Tang. "Modeling of low‐frequency Stoneley‐wave propagation in an irregular borehole." GEOPHYSICS 62, no. 4 (July 1997): 1047–58. http://dx.doi.org/10.1190/1.1444206.

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A fast modeling method is formulated for low‐frequency Stoneley‐wave propagation in an irregular borehole. This fast modeling method provides synthetic waveforms which include the effects of two borehole irregularities, diameter changes (washout), and formation property changes. The essential physics of the low‐frequency Stoneley waves are captured with a simple 1-D model. A mass‐balance boundary condition and a propagator matrix are used to express Stoneley‐wave interactions with the borehole irregularities. The accuracy of the proposed method was confirmed through comparison with existing finite‐difference and boundary integral modeling methods that yielded cross‐correlations greater than 0.98. Comparison of synthetic records calculated for an actual borehole with field records showed qualitative agreement in the major reflections because of the washout zones, but showed some disagreements in the reflections caused by the fractures. Since the synthetic records include only information relating to the borehole geometry and the elastic properties of formation, the reflection caused by the fracture will appear only in the field record. These results suggest the possibility of distinguishing Stoneley‐wave reflections caused by fractures from those caused by borehole irregularities. Further, the fast computational speed of this method—over 300 times faster than either boundary integral or finite‐difference methods—makes it quite suitable for field application.
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45

Haji-Sheikh, A., and M. Mashena. "Integral Solution of Diffusion Equation: Part 1—General Solution." Journal of Heat Transfer 109, no. 3 (August 1, 1987): 551–56. http://dx.doi.org/10.1115/1.3248123.

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A generalized method is presented that accommodates the linear form of the diffusion equation in regions with irregular boundaries. The region of interest many consist of subregions with spatially variable thermal properties. The solution function for the diffusion equation is decomposed into two solutions: one with homogeneous and the other with nonhomogeneous boundary conditions. The Galerkin functions are used to provide a solution for a diffusion problem with homogeneous boundary condition and linear initial condition. Problems with nonhomogeneous boundary conditions can be dealt with by many other schemes, including the standard Galerkin method. The final solution is a combination of these two solutions.
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46

López, Oscar A., and Elizabeth Raven. "An Overall Evaluation of Irregular-Floor-Plan—Shaped Buildings Located in Seismic Areas." Earthquake Spectra 15, no. 1 (February 1999): 105–20. http://dx.doi.org/10.1193/1.1586031.

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This paper aims to identify and analyze the advantages and disadvantages associated with building plan shape considering engineering and architectural needs and to quantify them in terms of the common language of costs and benefits. Parameters that measure the overall seismic response of a given plan shape were defined. Seismic behavior of the irregular shapes can be improved by means of special engineering efforts that provide enough in-plane slab stiffness and a distribution of lateral stiffness and strength so that torsion and distortion can be minimized. The proposed procedure of integral evaluation of buildings was applied to two specific examples, one regular and one irregular building, both with similar characteristics. The irregular building was seismically adequate by means of several dynamic analyses and a careful structural design so that it reached an acceptable level of seismic performance. For this example, the irregular building offers long-term benefits that exceed the initial investment required to improve its seismic behavior.
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47

MARBURG, STEFFEN, and SIA AMINI. "CAT'S EYE RADIATION WITH BOUNDARY ELEMENTS: COMPARATIVE STUDY ON TREATMENT OF IRREGULAR FREQUENCIES." Journal of Computational Acoustics 13, no. 01 (March 2005): 21–45. http://dx.doi.org/10.1142/s0218396x05002566.

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This paper reviews a number of techniques developed to overcome the well-known nonuniqueness problem in boundary integral formulations of acoustic radiation. Although the problem has received much attention, comparative studies are hardly known in this field. Furthermore, the problem has often been studied using an unsuitable example, namely a simple radiating sphere. In this case, often the addition of one collocation point in the centre of the sphere suffices to remove the nonuniqueness problem for a large range of wavenumbers. In contrast to the radiating sphere, the radiating cat's eye structure is considered in this paper. Solution of the discretized ordinary Kirchhoff–Helmholtz integral equation, also known as the Surface Helmholtz Equation, reveals a large number of so-called irregular frequencies, i.e. frequencies where the BEM fails. The paper compares the performance of different methods in alleviating this failure. The CHIEF method and its variation due to Rosen et al. are found to encounter difficulties at high frequencies. A much better performance is obtained by combining the Kirchhoff–Helmholtz integral equation with its normal derivative. In particular the method of Burton and Miller and a modification of it which avoids evaluating the hypersingular operator at nonsmooth points are tested. Both methods seem to provide reliable solutions. The modified method encounters minor failures in the frequency response function at a geometric singularity, although performing surprisingly well in many cases. More tests need to be carried out to assess fully the effectiveness of this method which allows easy use of continuous quadratic elements. However, it is the Burton and Miller formulation which appears to be the most reliable for acoustic radiation analysis. The use of CHIEF and its variations cannot be recommended.
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48

Golovko, A. Yu. "Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains." Proceedings of the Steklov Institute of Mathematics 290, no. 1 (August 2015): 277–87. http://dx.doi.org/10.1134/s0081543815060243.

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49

Pinheiro, I. F., L. A. Sphaier, and D. C. Knupp. "Integral transform solution of eigenvalue problems within irregular geometries: Comparative analysis of different methodologies." Numerical Heat Transfer, Part B: Fundamentals 76, no. 6 (September 18, 2019): 329–50. http://dx.doi.org/10.1080/10407790.2019.1665444.

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50

Ma, H., and Q. H. Qin. "Boundary integral equation supported differential quadrature method to solve problems over general irregular geometries." Computational Mechanics 36, no. 1 (December 10, 2004): 21–33. http://dx.doi.org/10.1007/s00466-004-0639-0.

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