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Academic literature on the topic 'Neumann expansion'

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Published: 6 September 2023

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Journal articles on the topic "Neumann expansion"

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Exton, Harold. "Generalized Neumann and Kapteyn expansions." Journal of Applied Mathematics and Stochastic Analysis 8, no. 4 (January 1, 1995): 415–21. http://dx.doi.org/10.1155/s1048953395000384.

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Certain formal series of a most general nature are specialized so as to deduce expansions in terms of a class of generalized hypergeometric functions. These series generalize the Neumann and Kapteyn series in the theory of Bessel functions, and their convergence is investigated. An example of a succinct expansion is also given.
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Yang, Q. W. "Model reduction by Neumann series expansion." Applied Mathematical Modelling 33, no. 12 (December 2009): 4431–34. http://dx.doi.org/10.1016/j.apm.2009.02.012.

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Marksteiner, P., E. Badralexe, and A. J. Freeman. "Neumann-Type Expansion of Coulomb Functions." Journal of Computational Physics 111, no. 1 (March 1994): 49–52. http://dx.doi.org/10.1006/jcph.1994.1042.

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Lallemand, B., G. Plessis, T. Tison, and P. Level. "Neumann expansion for fuzzy finite element analysis." Engineering Computations 16, no. 5 (August 1999): 572–83. http://dx.doi.org/10.1108/02644409910277933.

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Yamazaki, Fumio, Associate Member, Masanobu Shinozuka, and Gautam Dasgupta. "Neumann Expansion for Stochastic Finite Element Analysis." Journal of Engineering Mechanics 114, no. 8 (August 1988): 1335–54. http://dx.doi.org/10.1061/(asce)0733-9399(1988)114:8(1335).

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Chakraborty, Subrata, and Santi Sekhar Dey. "Stochastic Finite Element Simulation of Uncertain Structures Subjected to Earthquake." Shock and Vibration 7, no. 5 (2000): 309–20. http://dx.doi.org/10.1155/2000/730364.

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In present study, the stochastic finite element simulation based on the efficient Neumann expansion technique is extended for the analysis of uncertain structures under seismically induced random ground motion. The basic objective is to investigate the possibility of applying the Neumann expansion technique coupled with the Monte Carlo simulation for dynamic stochastic systems upto that extent of parameter variation after which the method is no longer gives accurate results compared to that of the direct Monte carlo simulation. The stochastic structural parameters are discretized by the local averaging method and then simulated by Cholesky decomposition of the respective covariance matrix. The earthquake induced ground motion is treated as stationary random process defined by respective power spectral density function. Finally, the finite element solution has been obtained in frequency domain utilizing the advantage of Neumann expansion technique.
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Marušić, S. "An asymptotic expansion for the Neumann sieve problem." Russian Journal of Mathematical Physics 15, no. 1 (March 2008): 89–97. http://dx.doi.org/10.1134/s106192080801010x.

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López, José L., and Ester Pérez Sinusía. "The Liouville–Neumann expansion in singular eigenvalue problems." Applied Mathematics Letters 25, no. 1 (January 2012): 72–76. http://dx.doi.org/10.1016/j.aml.2011.07.011.

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Wang, Xiangyu, Song Cen, and Chenfeng Li. "Generalized Neumann Expansion and Its Application in Stochastic Finite Element Methods." Mathematical Problems in Engineering 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/325025.

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An acceleration technique, termed generalized Neumann expansion (GNE), is presented for evaluating the responses of uncertain systems. The GNE method, which solves stochastic linear algebraic equations arising in stochastic finite element analysis, is easy to implement and is of high efficiency. The convergence condition of the new method is studied, and a rigorous error estimator is proposed to evaluate the upper bound of the relative error of a given GNE solution. It is found that the third-order GNE solution is sufficient to achieve a good accuracy even when the variation of the source stochastic field is relatively high. The relationship between the GNE method, the perturbation method, and the standard Neumann expansion method is also discussed. Based on the links between these three methods, quantitative error estimations for the perturbation method and the standard Neumann method are obtained for the first time in the probability context.
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Bae, Ha-Rok, and Edwin E. Forster. "Improved Neumann Expansion Method for Stochastic Finite Element Analysis." Journal of Aircraft 54, no. 3 (May 2017): 967–79. http://dx.doi.org/10.2514/1.c033883.

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Dissertations / Theses on the topic "Neumann expansion"

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Hahn, Liljan [Verfasser], Heinz [Akademischer Betreuer] Neumann, Ulf [Akademischer Betreuer] Diederichsen, and Ralf [Akademischer Betreuer] Ficner. "Investigation of Nucleosome Dynamics by Genetic Code Expansion / Liljan Hahn. Betreuer: Heinz Neumann. Gutachter: Heinz Neumann ; Ulf Diederichsen ; Ralf Ficner." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2015. http://d-nb.info/1078150818/34.

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Pillay, Samara. "The narrow escape problem : a matched asymptotic expansion approach." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1428.

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We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.
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"A higher-order energy expansion to two-dimensional singularly perturbed Neumann problems." 2004. http://library.cuhk.edu.hk/record=b5891877.

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Yeung Wai Kong.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.
Includes bibliographical references (leaves 51-55).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.5
Chapter 2 --- Some Preliminaries --- p.13
Chapter 3 --- "Approximate Function we,p" --- p.17
Chapter 4 --- "The Computation Of Je[we,p]" --- p.21
Chapter 5 --- The Signs of c1 And c3 --- p.30
Chapter 6 --- The Asymptotic Behavior of ue and Je[ue] --- p.35
Chapter 7 --- "The Proofs Of Theorem 1.1, Theorem 1.2 And Corol- lary 11" --- p.40
Appendix --- p.43
Bibliography --- p.51
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Gladwin, Jos K. T. "Modeling of Permittivity Variations in Stochastic Computational Electromagnetics." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5718.

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With the evolution of 5G systems offering high data rates, major changes are required in the design approach of the components of communication systems. Furthermore, building complex electromagnetic systems at the terahertz frequency range is of particular interest to the scientific community. Transmitting and receiving electromagnetic (EM) subsystems, including antennas, RF circuits & devices, RF filters, waveguides, etc are essential building blocks of these systems. It has been observed that there is significant uncertainty in the realization of these components due to fabrication tolerance, especially at millimeter wave frequencies and above. In addition to the variations in material properties due to these, the complex nature of antenna hosting environments, excitation function and point of source feeding, affect the performance characteristics of these devices. Incorporating these uncertainties in the EM design of the above advanced systems, both in terms of mathematical formulation and computational implementation is challenging. The tolerance in the fabrication process results in variations of dielectric material properties, which affects the system response. Therefore, a proper quantification of uncertainties using an efficient numerical stochastic EM solver help deliver a robust and optimal design. In this scenario, this thesis explores developing fast and efficient numerical stochastic EM solvers by considering parameters with a statistical variation. Various uncertainty modeling algorithms are formulated, implemented, and their performance is evaluated, validated, and compared by considering different practical stochastic EM problems. Both intrusive and non-intrusive finite element methods (FEM) for uncertainty quantification (UQ) in electromagnetics have been studied extensively in this work. For this analysis, FEM is used due to its versatility in handling complex EM structures with multiple dielectric domains. EM problems are unique due to the special boundary conditions employed, the possibility of resonances due to structural features and the broad frequency range of analysis required. A popular intrusive method for stochastic analysis is the polynomial chaos expansion (PCE) based stochastic spectral finite element (SSFEM) method. SSFEM can capture variations in an EM problem accurately and is shown to be computational efficient when compared with the Monte Carlo (MC) method. But SSFEM computational complexity scales with the number of random variables and results in a curse of dimensionality. Therefore the Neumann expansion (NE) is developed as an intrusive method for solving stochastic EM problems, wherein the matrix obtained by the discretization, can be split into the deterministic and stochastic parts. The Neumann series expansion after appropriate truncation is applied here to obtain the stochastic response. Unlike SSFEM, the computational complexity of NE method is shown to scale marginally with the number of stochastic regions, but is shown to have a limitation of capturing large variations. Another PCE based scheme for uncertainty modeling namely, least square polynomial chaos expansion (LSPCE ) is proposed here, as a non-intrusive method. A non-intrusive scheme is easier to implement and treats the EM solver as a black-box and therefore can be integrated with even commercial EM solvers. LSPCE minimizes the sum of squared error due to PCE truncation, through a system of algebraic equations, to solve the unknown PCE coefficients. This formulation is found to be computationally efficient compared with Monte Carlo and can efficiently handle EM problems with large stochastic dimensionality. Implementation aspects such as the initial number of samples for the proposed method is chosen by analyzing probability distance measures. The number of initial samples is found to be at least twice the number of orthonormal stochastic basis (over-determined system). Furthermore, the computational complexity of LSPCE can be reduced using fewer initial samples, but this results in an under-determined system, which is highly ill-conditioned. It has been shown that, such an ill-posed problem is solved using regularization methods such as regularized steepest descent. Fabrication tolerance can also result in spatial variations in material properties for EM structures and can be modeled as a random field using Karhunen Loeve (KL) expansion for a given covariance kernel and correlation length. KL expansion is truncated for a finite-dimensional representation and analyzed using intrusive methods such as SSFEM and NE. This implementation of stochastic modeling requires several random variables, which is difficult to solve using conventional stochastic algorithms. However, it has been shown that sparse algorithms can be utilized for solving these problems, as PCE coefficients are sparse in this case. Sparse algorithms, namely orthogonal matching pursuit and subspace pursuit, have been applied to enhance computational efficiency. Modern EM systems are expected to be operated over a broad frequency range, which increases the computation cost when frequency domain methods such as FEM is used. Large degree of freedom in complex EM problems increases this further. A formulation involving proper orthogonal decomposition (POD) is attempted, which forms a basis of low dimension and is shown to be efficient and accurate for a single frequency. Extending this to be operated over the frequency range, the intrusive UQ methods, SSFEM and NE are applied to this low dimensional POD basis. It is shown that the use of this modified POD-SSFEM and POD-NE formulations offers significant computational and memory advantages and can be analysed over a broad range of frequency. This new formulation is also shown to be effectively capturing the stochastic response for EM problems with large degree of freedom with limited computational resources. All the above numerical stochastic algorithms are implemented with in-house edge element FEM programs to solve stochastic electromagnetic problems involving variations in the permittivity of dielectric regions. Accuracy of these methods is evaluated by comparing with Monte Carlo simulations and performing statistical tests. Computational constraints have been discussed, and the resulting efficiencies are evaluated. These statistical formulations can be used by the EM designers for developing optimal models, which overcome the impact of fabrication tolerance.
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Books on the topic "Neumann expansion"

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Benedek, Agnes Ilona. Remarks on a theorem of Å. Pleijel and related topics. Bahia Blanca, Argentina: INMABB-CONICET, Universidad Nacional del Sur, 2005.

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Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

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Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.
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Book chapters on the topic "Neumann expansion"

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Yamada, Susumu, Toshiyuki Imamura, and Masahiko Machida. "High Performance LOBPCG Method for Solving Multiple Eigenvalues of Hubbard Model: Efficiency of Communication Avoiding Neumann Expansion Preconditioner." In Supercomputing Frontiers, 243–56. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-69953-0_14.

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Mo, Wenhui. "Mixed Finite Element." In Uncertain Analysis in Finite Elements Models, 147–62. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815079067122010010.

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The parameters of the structure contain random variables and interval variables. The Taylor expansion method and Neumann expansion method of random interval finite element are proposed. The parameters of the structure are random and fuzzy. Taylor expansion method and Neumann expansion method of the random fuzzy finite element are illustrated. The parameters of the structure are random, fuzzy and non-probabilistic. The mixed finite element calculation should be carried out using Taylor expansion and Neumann expansion.
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Mo, Wenhui. "Interval Finite Element for Linear Vibration." In Uncertain Analysis in Finite Elements Models, 79–97. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815079067122010006.

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Interval variables have an effect on linear vibration. The linear vibration is transformed into a static problem by Newmark method. The perturbation method, Neumann expansion method, Taylor expansion method, Sherman Morrison Woodbury expansion method and a new iterative method of interval finite element for linear vibration are proposed. The detailed derivation processes are explored.
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Mo, Wenhui. "Nonlinear Interval Finite Element." In Uncertain Analysis in Finite Elements Models, 98–119. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815079067122010007.

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Nonlinear structures in engineering are affected by uncertain parameters. Firstly, the displacement when the interval variable takes the midpoint value is obtained, and the nonlinear problem is transformed into a linear problem. Five calculation methods of nonlinear interval finite element for general nonlinear problems and elastoplastic problems are proposed. According to the perturbation technique, a perturbation method is proposed. According to Taylor expansion, Taylor expansion method is proposed. Neumann expansion, Sherman Morrison Woodbury expansion and a new iterative method are proposed.
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Mo, Wenhui. "Static Analysis of Interval Finite Element." In Uncertain Analysis in Finite Elements Models, 63–78. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815079067122010005.

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Four methods of interval finite element for static analysis are proposed. Using the second-order and third-order Taylor expansion , interval finite element for static analysis is addressed. Neumann expansion of interval finite element for static analysis is formulated. Interval finite element using Sherman -Morrison-Woodbury expansion is presented. A new iterative method (NIM) is used for interval finite element calculation. Four methods can calculate the upper and lower bounds of node displacement and element stress.
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Ammari, Habib, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab. "Boundary Perturbations due to the Presence of Small Cracks." In Mathematical Methods in Elasticity Imaging. Princeton University Press, 2015. http://dx.doi.org/10.23943/princeton/9780691165318.003.0005.

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This chapter considers the perturbations of the displacement (or traction) vector that are due to the presence of a small crack with homogeneous Neumann boundary conditions in an elastic medium. It derives an asymptotic formula for the boundary perturbations of the displacement as the length of the crack tends to zero. Using analytical results for the finite Hilbert transform, the chapter derives an asymptotic expansion of the effect of a small Neumann crack on the boundary values of the solution. It also derives the topological derivative of the elastic potential energy functional and proves a useful representation formula for the Kelvin matrix of the fundamental solutions of Lamé system. Finally, it gives an asymptotic formula for the effect of a small linear crack in the time-harmonic regime.
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Mo, Wenhui. "Nonlinear Stochastic Finite Element Method." In Uncertain Analysis in Finite Elements Models, 1–22. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815079067122010002.

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Considering the influence of random factors on the structure, three stochastic finite element methods for general nonlinear problems are proposed. They are Taylor expansion method, perturbation method and Neumann expansion method. The mean value of displacement is obtained by the tangent stiffness method or the initial stress method of nonlinear finite elements. Nonlinear stochastic finite element is transformed into linear stochastic finite element. The mean values of displacement and stress are obtained by the incremental tangent stiffness method and the initial stress method of the finite element of elastic-plastic problems. The stochastic finite element of elastic- plastic problems can be calculated by the linear stochastic finite element method.
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"Bessel and Neumann Expansions." In From Bessel to Multi-Index Mittag–Leffler Functions, 51–65. WORLD SCIENTIFIC (EUROPE), 2016. http://dx.doi.org/10.1142/9781786340894_0004.

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Bergo, Bettina. "Epilogue." In Anxiety, 472–78. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780197539712.003.0015.

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Opening to further reflection, the epilogue recalls Franz Neumann’s 1954 arguments that anxiety arises in response to economic and cultural threats to identity and status, often paralyzing political participation. In times of disillusionment and social unrest, anxiety precipitates unreflective responses, including adherence to “caesaristic movements,” grounded on “false concreteness” or social prejudices. Another great observer of the rise of authoritarian movements, Hermann Broch, ties anxiety to our embodied ego’s existence in its world, to its self-enhancement, and to responses to perceived threats. When confronted with dangers to its self-expansion, anxiety, panic, and compensatory behaviors aiming at sadistic “over-satisfactions” (Superbefriedigungen) ensue. These responses can be seen in individuals and in the groups and movements they form. Together, these authors strongly support the book’s argument for abiding with anxiety and approaching it with a certain existential knowledge—of oneself and one’s circumstances.
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Newnham, Robert E. "Introduction." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0003.

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The physical and chemical properties of crystals and textured materials often depend on direction. An understanding of anisotropy requires a mathematical description together with atomistic arguments to quantify the property coefficients in various directions. Tensors and matrices are the mathematics of choice and the atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. These are subjects of this book: tensors, matrices, symmetry, and structure–property relationships. We begin with transformations and tensors and then apply the ideas to the various symmetry elements found in crystals and textured polycrystalline materials. This brings in the 32 crystal classes and the 7 Curie groups. After working out the tensor and matrix operations used to describe symmetry elements, we then apply Neumann’s Law and the Curie Principle of Symmetry Superposition to various classes of physical properties. The first group of properties is the standard topics of classical crystal physics: pyroelectricity, permittivity, piezoelectricity, elasticity, specific heat, and thermal expansion. These are the linear relationships between mechanical, electrical, and thermal variables as laid out in the Heckmann Diagram. These standard properties are all polar tensors ranging in rank from zero to four. Axial tensor properties appear when magnetic phenomena are introduced. Magnetic susceptibility, the relationship between magnetization and magnetic field, is a polar second rank tensor, but the linear relationships between magnetization and thermal, electrical, and mechanical variables are all axial tensors. As shown in Fig. 1.2, magnetization can be added to the Heckmann Diagram converting it into a tetrahedron of linear relationships. Pyromagnetism, magnetoelectricity, and piezomagnetism are the linear relationships between magnetization and temperature change, electric field, and mechanical stress. Examples of tensors of rank zero through four are given in Table 1.1. In this book we will also treat many of the nonlinear relationships such as magnetostriction, electrostriction, and higher order elastic constants. The third group of properties is transport properties that relate flow to a gradient. Three common types of transport properties relate to the movement of charge, heat, and matter. Electrical conductivity, thermal conductivity, and diffusion are all polar second rank tensor properties.
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Conference papers on the topic "Neumann expansion"

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Fu, Zhilin, Satya Chan, and Sooyoung Kim. "Efficient SIC-MMSE Detection Using Neumann Series Expansion." In 2018 International Conference on Information and Communication Technology Convergence (ICTC). IEEE, 2018. http://dx.doi.org/10.1109/ictc.2018.8539491.

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Bae, Ha-rok, and Edwin E. Forster. "Improved Neumann Expansion Method Using Partial Bivariate Subspaces." In 19th AIAA Non-Deterministic Approaches Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2017. http://dx.doi.org/10.2514/6.2017-0365.

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Yuan, Jie, Fabrizio Scarpa, Giuliano Allegri, Sophoclis Patsias, and Ramesh Rajasekaran. "Numerical Assessment of Using Sherman-Morrison, Neumann Expansion Techniques for Stochastic Analysis of Mistuned Bladed Disc System." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-43188.

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The paper presents an assessment about using two classical reduced-order techniques, the Sherman-Morrison-Woodbury (SMW) formula and the Neumann expansion method, to enhance the computational efficiency of the stochastic analysis in mistuned bladed disc systems. The frequency responses of the blades are evaluated for different mistuning patterns via stiffness perturbations. A standard matrix factorization method is used as baseline to benchmark the results obtained from the SMW formula and Neumann expansion methods. The modified SMW algorithm can effectively update the inversion of an uncertainty matrix without the need of separated inversions, however with a limited increase of the computational efficiency. Neumann expansion techniques are shown to significantly decrease the required CPU time, while maintaining a low relative error. The convergence of the Neumann expansion however is not guaranteed when the excitation frequency approaches resonance when the mistuned system has either a low damping or high mistuning level. A scalar-modified Neumann expansion is therefore introduced to improve convergence in the neighbourhood of the resonance frequency.
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Amirkulova, Feruza A., and Andrew N. Norris. "Acoustic Multiple Scattering Using Fast Iterative Techniques." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-72249.

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Acoustic multiple scattering by an arbitrary configuration of cylinders in an acoustic medium is considered. An iteratively computable Neumann series (NS) expansion technique is employed to expedite the MS solution by means of MS theory. The method works if the spectral radius of the interaction matrix is less than one. The spectral properties of this matrix are investigated for different configurations of cylinders, e.g. rigid cylinders, elastic thin shells, etc.; the validity of solution is shown by modifying the frequency ω, the number of scatterers M, and their separation distance d. Fast computation of Neumann series is investigated using renormalized series expansions.
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Bertilsson, Erik, Oscar Gustafsson, Johannes Klasson, and Erik G. Larsson. "Computation limited matrix inversion using Neumann series expansion for massive MIMO." In 2017 51st Asilomar Conference on Signals, Systems, and Computers. IEEE, 2017. http://dx.doi.org/10.1109/acssc.2017.8335382.

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Cho, Maenghyo, and Hyungi Kim. "A Refined Semi-Analytic Sensitivity Based on the Mode Decomposition and Neumann Series Expansion." In 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-1738.

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Minango, Juan, and Celso de Almeida. "Low-complexity MMSE detector based on the first-order Neumann series expansion for massive MIMO systems." In 2017 IEEE 9th Latin-American Conference on Communications (LATINCOM). IEEE, 2017. http://dx.doi.org/10.1109/latincom.2017.8240164.

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Goldman, Daniel, and Paul E. Barbone. "Dirichlet to Neumann Maps for the Representation of Equipment With Weak Nonlinearities." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0511.

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Abstract We consider modeling the presence of a substructure in a dynamical simulation in terms of the force the substructure exerts on the main structure of interest. The reaction force is given in terms of the displacement of the attachment points. We call the map between the displacement of the attachment points and the force at the attachment a Dirichlet to Neumann, or DtN, map. We use a regular perturbation expansion to derive an approximate DtN for the case when the substructure exhibits weakly nonlinear behavior. The representation is accurate to O(ϵ2t2) + O(t2/N2), where ϵ is a measure of the strength of the nonlinearity, N is the number of modes of the subsystem and t is the simulation time. We note that the representation is particularly suited to the situation when ϵ = O(N−1).
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Muscolino, Giuseppe, Roberta Santoro, and Alba Sofi. "Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63482.

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Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.
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Lambert, William, and Stefano Brizzolara. "On the Effect of Non-Linear Boundary Conditions on the Wave Disturbance and Hydrodynamic Forces of Underwater Vehicles Travelling Near the Free-Surface." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18214.

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Abstract This study compares the effect of non-linear free-surface boundary conditions for a high-order non-linear free-surface Rankine-source boundary element method on wave disturbance and hydrodynamic forces acting on an underwater vehicle travelling near a calm free-surface. In particular, simulations for a steady nonaxisymmetric prolate spheroid using different basis flows and linearization techniques were compared to an analytical method achieved by Chatjigeorgiou using a multipole expansion of Green’s functions. It appears that at low Froude numbers, the basis flow used in the formulation contributes significantly to differences in the steady solutions for wave resistance and pitch, whereas for higher Froude numbers the linearization technique becomes a more defining feature. Upon observation of the analytical solution for wave resistance, one can see that it was formed under a Neumann-Kelvin formulation and this is supported by the Neumann-Kelvin simulations converging well to the analytical solution. Further comparisons were made using a wave directional energy spectrum gathered from transverse wave cuts of the free wave pattern. The spectral analysis allows for a higher level of comparison between all of the different cases, establishing a direct relation between the change in wave resistance and the energy content variation of the particular wave spectrum components.
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You might also be interested in the extended bibliographies on the topic 'Neumann expansion' for particular source types:
Journal articles
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