952 resultados para Transformed section method


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We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

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We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

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We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

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e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

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Purpose: The aim of this study was to compare the accuracy of fit of three types of implant-supported frameworks cast in Ni-Cr alloy: specifically, a framework cast as one piece compared to frameworks cast separately in sections to the transverse or the diagonal axis, and later laser welded. Materials and Methods: Three sets of similar implant-supported frameworks were constructed. The first group of six 3-unit implant-supported frameworks were cast as one piece, the second group of six were sectioned in the transverse axis of the pontic region prior to casting, and the last group of six were sectioned in the diagonal axis of the pontic region prior to casting. The sectioned frameworks were positioned in the matrix (10 N(.)cm torque) and laser welded. To evaluate passive fit, readings were made with an optical microscope with both screws tightened and with only one-screw tightened. Data were submitted to ANOVA and Tukey-Kramer`s test (p < 0.05). Results: When both screws were tightened, no differences were found between the three groups (p > 0.05). In the single-screw-tightened test, with readings made opposite to the tightened side, the group cast as one piece (57.02 +/- 33.48 mu m) was significantly different (p < 0.05) from the group sectioned diagonally (18.92 +/- 4.75 mu m) but no different (p > 0.05) from the group transversally sectioned (31.42 +/- 20.68 mu m). On the tightened side, no significant differences were found between the groups (p > 0.05). Conclusions: Results of this study showed that casting diagonally sectioned frameworks lowers misfit levels of prosthetic implant-supported frameworks and also improves the levels of passivity to the same frameworks when compared to structures cast as one piece.

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P>This study aimed to verify the effect of modified section method and laser-welding on the accuracy of fit of ill-fitting commercially pure titanium (cp Ti) and Ni-Cr alloy one-piece cast frameworks. Two sets of similar implant-supported frameworks were constructed. Both groups of six 3-unit implant-supported fixed partial dentures were cast as one-piece [I: Ni-Cr (control) and II: cp Ti] and evaluated for passive fitting in an optical microscope with both screws tightened and with only one screw tightened. All frameworks were then sectioned in the diagonal axis at the pontic region (III: Ni-Cr and IV: cp Ti). Sectioned frameworks were positioned in the matrix (10-Ncm torque) and laser-welded. Passive fitting was evaluated for the second time. Data were submitted to anova and Tukey-Kramer honestly significant difference tests (P < 0 center dot 05). With both screws tightened, one-piece cp Ti group II showed significantly higher misfit values (27 center dot 57 +/- 5 center dot 06 mu m) than other groups (I: 11 center dot 19 +/- 2 center dot 54 mu m, III: 12 center dot 88 +/- 2 center dot 93 mu m, IV: 13 center dot 77 +/- 1 center dot 51 mu m) (P < 0 center dot 05). In the single-screw-tightened test, with readings on the opposite side to the tightened side, Ni-Cr cast as one-piece (I: 58 center dot 66 +/- 14 center dot 30 mu m) was significantly different from cp Ti group after diagonal section (IV: 27 center dot 51 +/- 8 center dot 28 mu m) (P < 0 center dot 05). On the tightened side, no significant differences were found between groups (P > 0 center dot 05). Results showed that diagonally sectioning ill-fitting cp Ti frameworks lowers misfit levels of prosthetic implant-supported frameworks and also improves passivity levels of the same frameworks when compared to one-piece cast structures.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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The soft stadium is defined by a monomial potential with exponent α as a parameter, such that α → ∞ corresponds to the billiard. The practical use of the quantum section method depends only on the partial separability of the system on both sides of the section, which holds for all α's. In particular, for α = 1.0, the system becomes globally separable, allowing for a general test of the method. For various values of the parameter, we also tested the use of the asymptotic WKB-type approximation in the construction of Green's functions and asymptotic overlap integrals to obtain higher energy eigenvalues. We show these approximations to be reliable. © 2000 Elsevier Science B.V. All rights reserved.

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PURPOSE. Adequate passive-fitting of one-piece cast 3-element implant-supported frameworks is hard to achieve. This short communication aims to present an alternative method for section of one-piece cast frameworks and for casting implant-supported frameworks. MATERIALS AND METHODS. Three-unit implant-supported nickel-chromium (Ni-Cr) frameworks were tested for vertical misfit (n = 6). The frameworks were cast as one-piece (Group A) and later transversally sectioned through a diagonal axis (Group B) and compared to frameworks that were cast diagonally separated (Group C). All separated frameworks were laser welded. Only one side of the frameworks was screwed. RESULTS. The results on the tightened side were significantly lower in Group C (6.43 +/- 3.24 mu m) when compared to Groups A (16.50 +/- 7.55 mu m) and B (16.27 +/- 1.71 mu m) (P<.05). On the opposite side, the diagonal section of the one-piece castings for laser welding showed significant improvement in the levels of misfit of the frameworks (Group A, 58.66 +/- 14.30 mu m; Group B, 39.4.8 +/- 12.03 mu m; Group C, 23.13 +/- 8.24 mu m) (P<.05). CONCLUSION. Casting diagonally sectioned frameworks lowers the misfit levels. Lower misfit levels for the frameworks can be achieved by diagonally sectioning one-piece frameworks. [J Adv Prosthodont 2012;4:89-92]

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The glued-laminated lumber (glulam) technique is an efficient process for making rational use of wood. Fiber-Reinforced Polymers (FRPs) associated with glulam beams provide significant gains in terms of strength and stiffness, and also alter the mode of rupture of these structural elements. In this context, this paper presents a theoretical model for designing reinforced glulam beams. The model allows for the calculation of the bending moment, the hypothetical distribution of linear strains along the height of the beam, and considers the wood has a linear elastic fragile behavior in tension parallel to the fibers and bilinear in compression parallel to the fibers, initially elastic and subsequently inelastic, with a negative decline in the stress-strain diagram. The stiffness was calculated by the transformed section method. Twelve non-reinforced and fiberglass reinforced glulam beams were evaluated experimentally to validate the proposed theoretical model. The results obtained indicate good congruence between the experimental and theoretical values.

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This work present a study of glulam beams reinforced with FRP. It was developed a theoretical model that calculates strength and stiffness of the beams. The model allows for the calculation of the bending moment, the hypothetical distribution of linear strains along the height of the beam, and considers the wood has a linear elastic fragile behavior in tension parallel to the fibers and bilinear in compression parallel to the fibers, initially elastic and subsequently inelastic, with a negative decline in the stress-strain diagram. The stiffness was calculated by the transformed section method. Twelve non-reinforced and fiberglass reinforced glulam beams were evaluated experimentally to validate the proposed theoretical model. The results obtained indicate good congruence between the experimental and theoretical values.

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Cancado TO, Omais M, Ashmawi HA, Torres MLA - Chronic Pain after Cesarean Section. Influence of Anesthetic/Surgical Technique and Postoperative Analgesia. Background and objectives: Brazil ranks second among countries with the highest rates of cesarean section in the world. Little is known about the future consequences of this procedure on maternal health. This study investigated the influence of anesthetic/surgical technique and postoperative analgesia on the onset of chronic pain after three months of cesarean section. Method: This is a prospective randomized study of 443 patients undergoing cesarean section (elective and emergency), with different doses of hyperbaric bupivacaine 0.5% and opioids in spinal anesthesia. Patients were alocated into five groups as follow: G1 received hyperbaric bupivacaine (8 mg), sufentanil (2.5 mu g), and morphine (100 mu g); G2 received hyperbaric bupivacaine (10 mg), sufentanil (2.5 mu g), and morphine (100 mu g); G3 received hyperbaric bupivacaine (12.5 mg) and morphine (100 mu g); G4 received hyperbaric bupivacaine (15 mg) and morphine (100 mu g); G5 received hyperbaric bupivacaine (12.5 mg) and morphine (100 mu g), without perioperative anti-inflammatory. Pain at rest and in movement were evaluated in the immediate postoperative period. Phone contact was made after three months of surgery for identification of patients with chronic pain. Results: The incidence of chronic pain in the groups was G1 = 20%; G2 = 13%; G3 = 7.1%; G4 = 2.2%, and G5 = 20.3%. Patients who reported higher pain scores in the postoperative period had a higher incidence of chronic pain (p < 0.05). Conclusion: The incidence of chronic pain decreases with higher doses of local anesthetics and use of anti-inflammatory drugs. The higher pain scores in the postoperative period were associated with chronic pain development after three months of cesarean section.

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Um grande desafio da atualidade é a preservação dos recursos hídricos, bem como o correto manejo dos mesmos, frente à expansão das cidades e às atividades humanas. A qualidade de um corpo hídrico é usualmente avaliada através da análise de parâmetros biológicos, físicos e químicos. O comportamento de tais parâmetros pode convenientemente ser simulado através de modelos matemáticos e computacionais, que surgem assim como uma ferramenta bastante útil, por sua capacidade de geração de cenários que possam embasar, por exemplo, tomadas de decisão. Nesta tese são discutidas técnicas de estimação da localização e intensidade de uma fonte de contaminante conservativo, hipoteticamente lançado na região predominantemente fluvial de um estuário. O lançamento aqui considerado se dá de forma pontual e contínua e a região enfocada compreendeu o estuário do Rio Macaé, localizado na costa norte do Rio de Janeiro. O trabalho compreende a solução de um problema direto, que consiste no transporte bidimensional (integrado na vertical) desse contaminante hipotético, bem como a aplicação de técnicas de problemas inversos. Para a solução do transporte do contaminante, aqui modelada pela versão 2D horizontal da equação de advecção-difusão, foram utilizados como métodos de discretização o Método de Elementos Finitos e o Método de Diferenças Finitas. Para o problema hidrodinâmico foram utilizados dados de uma solução já desenvolvida para estuário do Rio Macaé. Analisada a malha de acordo com o método de discretização, foram definidas a geometria do estuário e os parâmetros hidrodinâmicos e de transporte. Para a estimação dos parâmetros propostos foi utilizada a técnica de problemas inversos, com o uso dos métodos Luus-Jaakola, Algoritmo de Colisão de Partículas e Otimização por Colônia de Formigas para a estimação da localização e do método Seção Áurea para a estimação do parâmetro de intensidade da fonte. Para a definição de uma fonte, com o objetivo de propor um cenário experimental idealizado e de coleta de dados de amostragem, foi realizada a análise de sensibilidade quanto aos parâmetros a serem estimados. Como os dados de amostragem de concentração foram sintéticos, o problema inverso foi resolvido utilizando-os com e sem ruído, esse introduzido de forma artificial e aleatória. Sem o uso de ruído, os três métodos mostraram-se igualmente eficientes, com uma estimação precisa em 95% das execuções. Já com o uso de dados de amostragem com ruídos de 5%, o método Luus-Jaakola mostrou-se mais eficiente em esforço e custo computacional, embora todos tenham estimado precisamente a fonte em 80% das execuções. Considerando os resultados alcançados neste trabalho tem-se que é possível estimar uma fonte de constituintes, quanto à sua localização e intensidade, através da técnica de problemas inversos. Além disso, os métodos aplicados mostraram-se eficientes na estimação de tais parâmetros, com estimações precisas para a maioria de suas execuções. Sendo assim, o estudo do comportamento de contaminantes, e principalmente da identificação de fontes externas, torna-se uma importante ferramenta para a gestão dos recursos hídricos, possibilitando, inclusive, a identificação de possíveis responsáveis por passivos ambientais.

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南海北部陆缘深水区(水深>300m)蕴藏着丰富的资源,我国对深水区的地质研究刚刚起步,但相关领域已成为科研热点。深水油气盆地的构造演化是油气勘探中最重要的基础性研究之一,因此针对我国南海北部陆缘深水区开展构造演化及其资源效应的研究具有重要的理论意义和实际意义。 本文利用钻井和地震资料并结合区域地质资料,重点研究了珠江口盆地深水区的结构和构造演化,取得如下创新性成果:1)首次利用半地堑分析方法系统解剖了研究区的结构、各构造单元发育特征,在此基础上指出五个有利油气运聚带;2)采用回剥法并利用最新资料进行校正,得到了研究区更为可靠的构造沉降曲线,重新划分了裂陷期和裂后期的分界,认为32Ma南海海底扩张之后裂陷作用仍在持续,直到23Ma左右才开始大规模裂后热沉降,并进一步解释了裂陷期延迟的形成机制;3)应用非连续拉张模型计算拉张系数的方程计算了研究区的壳幔拉张系数,指出了深水区地幔相对于地壳的优势伸展作用;首次运用平衡剖面技术重建了研究区的构造发育史,计算了各构造期的拉张率和沉积速率,指出研究区新生代整体呈现持续拉张,拉张系数在1.1-1.24之间;4)精细刻画了水合物钻采区的地质构造特征,建立了该区天然气水合物成藏的概念模式;建立了一套根据地震叠加速度计算流体势的方法,为水合物成藏规律的研究提供了新的思路。