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An effective numerical algorithm for intra-granular fission gas release during non-equilibrium trapping and resolution

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JOURNAL OF NUCLEAR MATERIALS 2018年 509卷 687-699页

作者： Pastore, G. Pizzocri, D. Rabiti, C. Barani, T. Van Uffelen, P. Luzzi, L. Idaho Natl Lab POB 1625 Idaho Falls ID 83415 USA MIT Dept Nucl Sci & Engn 77 Massachusetts Ave Cambridge MA 02139 USA Politecn Milan Dept Energy Nucl Engn Div Via La Masa 34 I-20156 Milan Italy European Commiss Joint Res Ctr Directorate Nucl Safety & Secur POB 2340 D-76125 Karlsruhe Germany

Fission gas release and gaseous swelling in nuclear fuel are driven by the transport of fission gas from within the fuel grains to grain boundaries (intra-granular fission gas release). The process involves gas atom diffusion in conjunction with trapping in and resolution from intra-granular bubbles, and is described mathematically by a system of two partial differential equations (PDE). Under the assumption of equilibrium between trapping and resolution (quasi-stationary approximation) the system can be reduced to a single diffusion equation with an effective diffusion coefficient. numerical solutions used in engineering fuel performance calculations invariably rely on this simplification. First, we investigate the validity of the quasi-stationary approximation compared to the solution of the general system of PDEs. Results demonstrate that the approximation is valid under most conditions of practical interest, but is inadequate to describe intra-granular fission gas release during rapid transients to relatively high temperatures such as postulated reactivity-initiated accidents (RIA). Then, we develop a novel numerical algorithm for the solution of the general PDE system in time-varying conditions. We verify the PolyPole-2 algorithm against a reference finite difference solution for a large number of randomly generated operation histories including prototypical RIA transients. Results demonstrate that PolyPole-2 captures the solution of the general system with a high accuracy and a low computational cost. The PolyPole-2 algorithm overcomes the quasi-stationary approximation and the concept of an effective diffusion coefficient for the solution of the intra-granular fission gas release problem in nuclear fuel analysis. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Fission gas Diffusion Trapping Resolution Nuclear fuel modeling Intra-granular fission gas release Quasi-stationary approximation Effective diffusion coefficient numerical algorithms Modal methods PolyPole

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Robust Incentive Stackelberg Strategy for Markov Jump Delay Stochastic Systems via Static Output Feedback ⁎

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IFAC-PapersOnLine 2020年第2期53卷 6709-6714页

作者： Hiroaki Mukaidani Saravanakumar Ramasamy Hua Xu Weihua Zhuang Hiroshima University 1-7-1 Kagamiyama Higashi-Hiroshima 739-8521 Japan The University of Tsukuba 3-29-1 Otsuka Bunkyo-ku Tokyo 112-0012 Japan University of Waterloo 200 University Avenue West Waterloo ON N2L3G1 Canada

A static output feedback (SOF) incentive Stackelberg game (ISG) for a continuous-time Markov jump delay stochastic system (MJDSS) is discussed. The existence conditions on the SOF incentive Stackelberg strategy set are established in terms of the solvability of a set of higher-order cross-coupled stochastic algebraic Lyapunov-type equations (CCSALTEs). A classical Lagrange-multiplier technique is used to derive the CCSALTEs, thereby avoiding having to solve the bilinear matrix inequalities (BMIs), a well-known NP-hard problem in designing the SOF strategy. A heuristic algorithm is proposed to solve CCSALTEs such that convergence is attained by applying the Krasnoselskii-Mann (KM) iterative algorithm. A simple numerical example demonstrates the efficiency of the SOF incentive Stackelberg strategy.

关键词： Stackelberg games H ∞ control stochastic systems numerical algorithms

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Robust Stackelberg Games via Static Output Feedback Strategy for Uncertain Stochastic Systems with State Delay ⁎

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IFAC-PapersOnLine 2020年第2期53卷 7154-7159页

In this paper, a robust Stackelberg game for a class of uncertain stochastic systems with state delay is investigated. After introducing some definitions and preliminaries, we derive the conditions for the existence of the robust static output feedback (SOF) Stackelberg strategy set such that the upper bounds of leader’s cost function and the weighted cost function of the followers are minimized respectively. In order to obtain the robust SOF Stackelberg strategy set, a heuristic algorithm is proposed based on the stochastic Lyapunov type matrix equations (SLMEs) and the linear matrix inequalities (LMIs). In particular, it is shown that robust convergence is guaranteed by applying the Krasnoselskii-Mann (KM) iterative algorithm. An academic numerical example is presented to demonstrate the effectiveness of the proposed method.

关键词： Stackelberg games H ∞ control stochastic systems numerical algorithms

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A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling

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COMPUTATIONAL MECHANICS 2018年第4期62卷 815-833页

作者： Aldakheel, Fadi Wriggers, Peter Miehe, Christian Leibniz Univ Hannover Inst Continuum Mech Appelstr 11 D-30167 Hannover Germany Univ Stuttgart Inst Appl Mech CE Chair 1 D-70569 Stuttgart Germany

The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2-15, 1977). Within a top-down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic-plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486-522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic-plastic solids under finite strain deformation. It combines modified structures of Gurson-Tvergaard-Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157-169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1-17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit-Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup-cone failure mechanism.

关键词： Ductile fracture Porous plasticity GTN model numerical algorithms Phase-field modeling

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Landmarks and new frontiers of computational fluid dynamics

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Advances in Aerodynamics 2019年第1期1卷 96-131页

作者： Joseph J.S.Shang Wright State University 3640 Colonel Glenn HighwayDaytonOH 45435-0001USA

A narrative of landmarks in computational fluid dynamics(CFD)is presented to highlight the cornerstone *** accomplishments starting from the very beginning of the coherent development until the most recent progress will be elucidated over the span over more than six ***,the cuttingedge scientific innovations will also be discussed for their lasting impacts to fluid dynamics and the physics-based modeling and simulation *** traverse such a vast domain over time by a single presentation,numerous and excellent contributions to CFD will be unavoidably *** it is my ardent hope that the present discussion will be able to reaffirm excellence in research and to identify new frontiers for scientific ***,the challenges to future innovations will also be delineated to recommend for potential and fertile research areas for the modeling and simulation science.

关键词： Computational fluid dynamics numerical algorithms Turbulence Interdisciplinary computational fluid dynamics

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numerical study of the stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids

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PHYSICS OF FLUIDS 2019年第9期31卷 093101-093101页

作者： Evans, J. D. Cuminato, J. A. Palhares Junior, I. L. Oishi, C. M. Univ Bath Dept Math Sci Bath BA2 7AY Avon England Univ Sao Paulo Inst Ciencias Matemat & Comp Dept Matemat Aplicada & Estat BR-13566590 Sao Carlos SP Brazil Univ Estadual Paulista Fac Ciencias & Tecnol Dept Matemat & Comp BR-19060900 Presidente Prudente SP Brazil

Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien-Tanner (PTT) and Giesekus fluids, investigating the polymer stress behavior around the stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. ["Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity," Phys. Fluids 29, 1-33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and natural stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The natural stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.

关键词： Central processing unit Computational rheology Stick-slip transition Computational methods Vector fields Rarefied gas dynamics Coordinate system numerical algorithms Viscoelastic flows Newtonian flow

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A Comparison of Implicit and Explicit Simulations of Vortex Breakdown

A Comparison of Implicit and Explicit Simulations of Vortex ...

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AIAA Science and Technology (SciTech) Forum and Exposition

作者： Zhang, Xiao Chung, Joseph D. Kaplan, Carolyn R. Oran, Elaine S. Univ Maryland Dept Aerosp Engn 3202 James M Patterson Bldg College Pk MD 20742 USA Univ Maryland Dept Aerosp Engn 3232 Jeong H Kim Engn Bldg College Pk MD 20742 USA

ISBN: (数字)9781624105784

ISBN: (纸本)9781624105784

Vortex breakdown is an instability which occurs in swirling flows and is seen in both incompressible and compressible flow regimes. The choice of numerical algorithm to compute this flow is critical to resolving the relevant physical phenomena. In previous work, we described the procedure of combining a Barely Implicit Correction (BIC) algorithm with a fourth-order Flux-Corrected Transport (FCT) algorithm to eliminate the sound speed limit for explicit calculations of low-speed flows, and showed that BIC-FCT could predict the three major vortex breakdown modes (spiral, bubble and double-helix). Here, we show a direct comparison of the implicit BIC and explicit FCT algorithms by using the same time step within the explicit stability limit. The comparison is conducted on simulations of a three-dimensional, swirling jet flow with vortex breakdown, by examining the flow structures and examining the property fields. Differences are observed in the phase of the downstream spiral and double-helix modes. Based on a pressure wave analysis, we attribute this phase shift to the difference of how the explicit FCT and implicit BIC treat an open outflow boundary.

关键词： Vortex Breakdown Flux Corrected Transport Compressible Flow numerical algorithms Adverse Pressure Gradient Flow Characteristics Mach Number Ideal Gas Navier Stokes Equations numerical Stability

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A Low-Complexity Parallelizable numerical Algorithm for Sparse Semidefinite Programming

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2018年第4期5卷 1898-1909页

作者： Madani, Ramtin Kalbat, Abdulrahman Lavaei, Javad Univ Texas Arlington Dept Elect Engn Arlington TX 76019 USA United Arab Emirates Univ Dept Elect Engn Abu Dhabi 15551 U Arab Emirates Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA Tsinghua Berkeley Shenzhen Inst Berkeley CA 94704 USA

In the past two decades, the semidefinite programming (SDP) technique has been proven to be extremely successful in the convexification of hard optimization problems appearing in graph theory, control theory, polynomial optimization theory, and many areas in engineering. In particular, major power optimization problems, such as optimal power flow, state estimation, and unit commitment, can be formulated or well approximated as SDPs. However, the inability to efficiently solve large-scale SDPs is an impediment to the deployment of such formulations in practice. Motivated by the significant role of SDPs in revolutionizing the decision-making process for real-world systems, this paper designs a low-complexity numerical algorithm for solving sparse SDPs, using the alternating direction method of multipliers and the notion of tree decomposition in graph theory. The iterations of the designed algorithm are highly parallelizable and enjoy closed-form solutions, whose most expensive computation amounts to eigenvalue decompositions over certain submatrices of the SDP matrix. The proposed algorithm is a general-purpose parallelizable SDP solver for sparse SDPs, and its performance is demonstrated on the SDP relaxation of the optimal power flow problem for real-world benchmark systems with more than 13 600 nodes.

关键词： Large-scale optimization numerical algorithms power systems semidefinite programming tree decomposition

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A scalable algorithm of numerical real-time path integral for quantum dissipative systems

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JOURNAL OF CHEMICAL PHYSICS 2019年第22期150卷 224108-224108页

作者： Sato, Yoshihiro Gettysburg Coll Dept Phys Gettysburg PA 17325 USA

numerical real-time path integration has been a practical method to study a quantum system under the influence of its environment. Performing the path integral computations, however, is a resource-demanding task in general, and implementing it is less straightforward with modern hardware architectures of massively parallel platforms. In this article, a numerical algorithm based on the quasiadiabatic propagator path integral scheme is proposed and shown to scale for systems with large size. As a case study of performance, the quantum dynamics of excitation energy transfer in the Fenna-Matthews-Olson complex is discussed, employing a vibronic model in which the system size can be varied simply by adding vibrational excitations.

关键词： Protein complexes Density-matrix Quantum dissipation Electronic excitation Excitation energy transfer Quantum mechanical systems and processes Fenna-Matthews-Olson complex numerical algorithms Vibrational spectra Quantum mechanical principles

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Propagation of Detonation Waves in a Premixed Mach 5 Crossflow

Propagation of Detonation Waves in a Premixed Mach 5 Crossfl...

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AIAA Science and Technology (SciTech) Forum and Exposition

作者： Goodwin, Gabriel B. Bachman, Christian L. Oran, Elaine S. Kaplan, Carolyn R. Sosa, Jonathan Ahmed, Kareem A. Naval Res Lab Naval Ctr Space Technol Code 8221 Washington DC 20375 USA Univ Maryland Dept Aerosp Engn College Pk MD 20742 USA Univ Cent Florida Dept Mech & Aerosp Engn Orlando FL 32816 USA

ISBN: (数字)9781624105784

ISBN: (纸本)9781624105784

Detonation waves are an extremely efficient mechanism for burning fuel-air mixtures to release their chemical energy and generate thrust in high-speed airbreathing engines. In standing detonation wave engines, one of the major challenges is sustaining a stable, standing detonation wave within the combustor. Experiments at the University of Central Florida (UCF) have studied the propagation of detonation waves injected orthogonally into Mach 5 flows of premixed hydrogen and air. This paper focuses on numerical simulations of detonation propagation in the experimental facility with fuel equivalence ratios of 0.85 and 0.70. The compressible reactive Navier-Stokes equations are solved by a high-order numerical algorithm on a locally adapting mesh. In the range of conditions studied, the overdriven detonations injected into the crossflow decoupled into shocks and flames. Subsequent detonations occurred through shock reflections and shock-flame interactions. The survivability of the subsequent detonations was observed to be highly dependent on the fuel equivalence ratio and wall boundary conditions.

关键词： Detonation Waves Deflagration to Detonation Transition Chemical Energy Combustors Navier Stokes Equations numerical Simulation Detonation Wave Engines High Speed Airbreathing Engines numerical algorithms Flow Conditions

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