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Efficient computation of the scattering intensity from systems of nonspherical particles

JOURNAL OF APPLIED CRYSTALLOGRAPHY 2016年第5期49卷 1524-1531页

作者： Persson, Rasmus A. X. Bergenholtz, Johan Univ Gothenburg Dept Chem & Mol Biol SE-41296 Gothenburg Sweden Lund Univ Div Phys Chem Ctr Chem & Chem Engn SE-22100 Lund Sweden

The analysis of the angle dependence of the elastic scattering of radiation from a sample is an efficient and non-invasive technique that is used in fundamental science, in medicine and in technical quality control in industry. Precise information on the shape, size, polydispersity and interactions of a colloidal sample is readily obtained provided an underlying scattering model, i.e. form and structure factors, can be computed for the sample. Here, a numerical method that can efficiently compute the form factor amplitude (and thus the scattering intensity) of nonspherical scatterers through an importance sampling algorithm of the Fourier integral of the scattering density is presented. Using the precomputed form factor amplitudes, the calculation of the scattering intensity at any particle concentration then scales linearly with the particle number and linearly with the number of q points for its evaluation. This is illustrated by an example calculation of the scattering by concentrated suspensions of ellipsoidal Janus particles and the numerical accuracy for the computed form factor amplitudes is compared with analytical benchmarks.

关键词： small-angle scattering form factor amplitude numerical algorithms Monte Carlo

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Modeling of forming limit for multilayer sheets based on strain-rate potentials

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 75卷 63-99页

作者： Kim, Daeyong Kim, Hyunki Kim, Ji Hoon Lee, Myoung-Gyu Kim, Kee Joo Barlat, Frederic Lee, Youngseon Chung, Kwansoo Korea Inst Mat Sci Mat Deformat Dept Chang Won 642831 Gyeongnam South Korea Korea Univ Sci & Technol Daejeon 305350 South Korea Seoul Natl Univ Res Inst Adv Mat Engn Res Inst Dept Mat Sci & Engn Seoul 151744 South Korea Pusan Natl Univ Sch Mech Engn Busan 609736 South Korea Korea Univ Dept Mat Sci & Engn Seoul 151744 South Korea Seojeong Coll Dept Automobile Engn Eunhyun Myun 482777 Gyeonggi Do South Korea POSTECII Grad Inst Ferrous Technol Pohang 790784 Gyeongbuk South Korea

In order to evaluate the forming limits of planar anisotropic multilayer sheet materials, the Marciniak-Kuczynski (M-K) model was formulated based on the strain-rate potential. A common practice to predict the forming limits of sheet materials has been based on yield stress potentials defined in the stress field. As an alternative, a method based on plastic stain-rate potentials, which are especially convenient to apply for rigid-viscoplasticity, was considered in this work. The formulation based on the strain-rate potential facilitates the modeling of forming limits for multilayer sheet materials because the number of unknown variables is significantly reduced by assuming the iso-strain condition for each layer without delamination. As for the strain-rate potential, Srp2003-2d, which is the pseudo-conjugate of the yield stress potential Yld2000-2d, was applied along with Hill's 1948 strain-rate potential for comparison. In the approach proposed, rigid-viscoplasticity was formulated according to the incremental deformation theory based on the minimum plastic work path. The rotation of anisotropic symmetry axes in the groove region was also properly accounted for in the formulation. For verification purposes, the predicted forming limit criteria such as the strain-based forming limit diagram (FLD), the stress-based forming limit diagram (FLSD) and the effective strain-based forming limit diagram (x-EPS) were experimentally validated for a monolithic aluminum alloy (AA5182-O) sheet and a three-layer AA5182-O/polypropylene/AA5182-O (AA/PP/AA) sandwich sheet, which confirmed good agreement. In addition, the path-sensitivity of the strain-based FLD and the path-insensitivity of the FLSD and x-EPS were numerically proven based on the M-K model for the three-layer sandwich sheet. Finally, the M K model was compared with a maximum force model most recently developed. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Anisotropic material Ideally plastic material Layered material numerical algorithms Anisotropic plastic strain-rate potential

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EULER CALCULATIONS OF UNSTEADY INTERACTION OF ADVANCING ROTOR WITH A LINE VORTEX

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AIAA JOURNAL 1993年第9期31卷 1659-1666页

作者： SRINIVASAN, GR MCCROSKEY, WJ NASA AMES RES CTRMOFFETT FIELDCA 94035

The unsteady, three-dimensional flowfield of a helicopter rotor blade in forward night encountering a concentrated line vortex is calculated using an implicit, finite difference numerical procedure for the solution of Euler equations. A prescribed vortex method is adopted to preserve the structure of the interacting vortex. The test cases considered for computation correspond to the two-bladed model rotor experimental conditions of Caradonna et al. and consist of parallel and oblique interactions. Comparison of numerical results with the test data show good agreement for the surface pressures for both parallel and oblique interactions at subsonic and transonic flow conditions. The results indicate that the subsonic parallel blade-vortex interaction is nearly two-dimensional-like and the unsteady time-lag effects appear to be negligible. However, both the three-dimensional and unsteady time-lag effects are found to be important under supercritical now conditions and these effects are accentuated in the presence of transonic shocks. In contrast, the oblique blade-vortex interaction is unsteady and three dimensional at both the subsonic and transonic now conditions.

关键词： Vortex Structure Blade Vortex Interaction Supercritical Flow Helicopter Rotor Primitive Variable Freestream Mach Number Rotor Blades Total Energy NACA 64A006 numerical algorithms

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Planar hydraulic fracture growth perpendicular to the isotropy plane in a transversely isotropic material

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2020年 137卷 103878-103878页

作者： Moukhtari, Fatima-Ezzahra Lecampion, Brice Zia, Haseeb Ecole Polytech Fed Lausanne Gaznat Chair Geoenergy Geoenergy Lab ENACGELIIC Stn 18 CH-1015 Lausanne Switzerland

The configuration of a hydraulic fracture (HF) propagating perpendicular to the isotropy plane of a transversely isotropic (TI) material is encountered in most sedimentary basins. We account for both elastic and fracture toughness anisotropy, and investigate fracture growth driven by the injection of a Newtonian fluid at a constant rate from a point source. In addition to the usual dimensionless parameters governing HF growth in isotropy, four dimensionless elastic parameters enter the problem for a TI material: the ratio beta of elastic plane-strain modulus in the two orthogonal directions of the material frame, two Thomsen parameters epsilon,delta and the stiffness ratio C-13/C-11. Moreover, the ratio kappa of fracture toughness in the two orthogonal directions as well as the details of the toughness anisotropy also plays a role on the development of the fracture geometry. We quantify HF growth numerically without any a-priori assumptions on the fracture shape. In doing so, we derive the exact expression for the near-tip elastic modulus as a function of propagation direction and extend to TI an implicit level set algorithm coupling a finite discretization with the near-tip solution for a steadily moving HF. A solution for a toughness dominated elliptical HF in a TI material is derived and used to verify our numerical solver. Importantly, the fracture shape is strictly elliptical only for a very peculiar form of toughness anisotropy. The evolution of the HF from the viscosity dominated regime (early time) to the toughness dominated regime (late time) results in an increase of the fracture elongation. The elongation of the fracture in the viscosity dominated regime scales as 0.76$ beta(-1/3) and increases as the propagation transition to the toughness dominated regime. We confirm the expressions for the transition time-scales in the two orthogonal directions of the material frame obtained from scaling considerations. The exact form of the toughness anisotropy plays

关键词： Fracture Anisotropic material Rock Boundary integral equations numerical algorithms

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Experimental characterization and crystal plasticity modeling of anisotropy, tension-compression asymmetry, and texture evolution of additively manufactured Inconel 718 at room and elevated temperatures

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INTERNATIONAL JOURNAL OF PLASTICITY 2020年第0期125卷 63-79页

作者： Ghorbanpour, Saeede Alam, Md Ershadul Ferreri, Nicholas C. Kumar, Anil McWilliams, Brandon A. Vogel, Sven C. Bicknell, Jonathan Beyerlein, Irene J. Knezevic, Marko Univ New Hampshire Dept Mech Engn 33 Acad WayKingsbury HallW119 Durham NH 03824 USA Univ Calif Santa Barbara Mech Engn Dept Mat Dept Santa Barbara CA 93106 USA Los Alamos Natl Lab Theoret Div Los Alamos NM 87545 USA US Army Res Lab Weap & Mat Res Directorate Aberdeen Proving Ground MD 21005 USA Los Alamos Natl Lab Mat Sci & Technol Div Los Alamos NM 87545 USA Turbocam Int Turbocam Energy Solut Dover NH 03820 USA

In this work, strength and microstructural evolution of superalloy Inconel 718 (IN718) are characterized as a function of the initial microstructure created via direct metal laser melting (DMLM) additive manufacturing (AM) technology along with subsequent hot isostatic pressing (HIP) and heat treatments as well as wrought processing. Stress-strain curves are measured in tension and compression from room temperature to 550 degrees C and crystallographic texture is characterized using neutron diffraction. Furthermore, a recently developed crystal plasticity model incorporating the effects of precipitates is extended to interpret the temperature dependent deformation behavior of the alloy. The model accounts for solid solution, precipitate shearing, and grain size and shape contributions to initial slip resistance, which evolves with a dislocation density-based hardening law considering latent hardening, while non-Schmid effects are taken into account in the activation stress. Part of the experimental data is used for calibration of the model, while the rest is used for experimental validation of the model. It is shown that the model is capable of modeling the data with accuracy. Based on the comparison of the data and model predictions, it is inferred that the grain structure and texture give rise to plastic anisotropy of the alloy, while its tension-compression asymmetry results from non-Schmid effects and latent hardening.

关键词： Microstructures Polycrystalline material Crystal plasticity numerical algorithms Inconel 718

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A variable-step variable-order algorithm for systems of stiff ODEs

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1997年第1-2期63卷 149-157页

作者： VanHecke, T VandenBerghe, G VanDaele, M DeMeyer, H [a] Vakgroep Toegepaste Wiskunde en Informatica Universiteit-Gent Gent Belgium

A variable-step variable-order algorithm for stiff ODEs based on previously derived stabilized extended one-step methods is established. The developed code is tested on certain initial-value problems for systems of OD... 详细信息

关键词： initial-value problems ODEs extended one-step methods A-stability L-stability numerical algorithms

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Improved eigenvectors for Pulliam-Chaussee diagonalized approximate-factorization algorithm

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JOURNAL OF COMPUTATIONAL PHYSICS 2020年 412卷 109443-109443页

作者： Pulliam, Thomas H. Jespersen, Dennis C. Bodony, Daniel J. Bidadi, Shreyas NASA Ames Res Ctr Moffett Field CA 94035 USA Univ Illinois Dept Aerosp Engn Champaign IL USA

The eigensystem of the Pulliam-Chaussee diagonalized form of the approximate-factorization algorithm for the three-dimensional Euler and Navier-Stokes equations is revisited to remove an apparent dimensional inconsistency. The original set of eigenvectors in curvilinear coordinates were derived systematically and has been widely used and referenced. Although mathematically correct, the original eigenvectors for the advected modes appear dimensionally inconsistent and yield a set of matrices with large condition numbers for some flows. A new set of eigenvectors is presented that remove the inconsistency and improves the robustness of the diagonalized scheme. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Computational fluid dynamics numerical algorithms Eigensystems Aeronautics Linear algebra

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Solution of multidimensional inverse heat conduction problem

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HEAT AND MASS TRANSFER 2003年第1-2期40卷 115-122页

作者： Duda, P Cracow Univ Technol Inst Proc & Power Engn PL-31864 Krakow Poland

Calculation of transient temperature distribution in construction elements is the latest topic of interest to engineers today. In many cases, thermal boundary conditions can be applied to only a section of a solid's boundary, while heat transfer coefficients on boundaries exposed to a moving fluid and fluid temperature can be partially or entirely unknown. A method for solving the aforementioned problems is formulated below;its main advantage is that it does not require any knowledge of, or solution to, the fluid field. Furthermore, it works fast enough to be applied in practice in real time. Additionally, temperature measurement points can be positioned within an element or on the element surface and do not have to form a closed surface. Two examples are included to demonstrate the capabilities of the new approach.

关键词： stress monitoring inverse method heating optimization numerical algorithms

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ON THE REPRESENTATION OF OPERATORS IN BASES OF COMPACTLY SUPPORTED WAVELETS

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SIAM JOURNAL ON numerical ANALYSIS 1992年第6期29卷 1716-1740页

作者： BEYLKIN, G SCHLUMBERGER DOLL RES CTR RIDGEFIELDCT 06877

This paper describes exact and explicit representations of the differential operators, d(n)/dx(n), n = 1,2,..., in orthonormal bases of compactly supported wavelets as well as the representations of the Hilbert transform and fractional derivatives. The method of computing these representations is directly applicable to multidimensional convolution operators. Also, sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring O(N log N) operations for computing the wavelet coefficients of all N circulant shifts of a vector of the length N = 2n is constructed. As an example of an application of this algorithm, it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector (see [G. Beylkin, R. R. Coifman, and V. Rokhlin, Comm. Pure. Appl. Math., 44 (1991), pp. 141-183]) may be reduced from O(N) to O(log2 N) significant entries.

关键词： WAVELETS DIFFERENTIAL OPERATORS HILBERT TRANSFORM FRACTIONAL DERIVATIVES PSEUDODIFFERENTIAL OPERATORS SHIFT OPERATORS numerical algorithms

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Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2013年第9期24卷 1852-1862页

作者： Dehnavi, Maryam Mehri Fernandez, David M. Gaudiot, Jean-Luc Giannacopoulos, Dennis D. MIT Cambridge MA 02139 USA McGill Univ Montreal PQ H3A 0E9 Canada Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92697 USA

Accelerating numerical algorithms for solving sparse linear systems on parallel architectures has attracted the attention of many researchers due to their applicability to many engineering and scientific problems. The solution of sparse systems often dominates the overall execution time of such problems and is mainly solved by iterative methods. Preconditioners are used to accelerate the convergence rate of these solvers and reduce the total execution time. Sparse approximate inverse (SAI) preconditioners are a popular class of preconditioners designed to improve the condition number of large sparse matrices. We propose a GPU accelerated SAI preconditioning technique called GSAI, which parallelizes the computation of this preconditioner on NVIDIA graphic cards. The preconditioner is then used to enhance the convergence rate of the BiConjugate Gradient Stabilized (BiCGStab) iterative solver on the GPU. The SAI preconditioner is generated on average 28 and 23 times faster on the NVIDIA GTX480 and TESLA M2070 graphic cards, respectively, compared to ParaSails (a popular implementation of SAI preconditioners on CPU) single processor/core results. The proposed GSAI technique computes the SAI preconditioner in approximately the same time as ParaSails generates the same preconditioner on 16 AMD Opteron 252 processors.

关键词： numerical algorithms parallel algorithms graphics processors parallel programming conditioning

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