973 resultados para finite-state methods
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We develop a simulation based algorithm for finite horizon Markov decision processes with finite state and finite action space. Illustrative numerical experiments with the proposed algorithm are shown for problems in flow control of communication networks and capacity switching in semiconductor fabrication.
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Conformance testing focuses on checking whether an implementation. under test (IUT) behaves according to its specification. Typically, testers are interested it? performing targeted tests that exercise certain features of the IUT This intention is formalized as a test purpose. The tester needs a "strategy" to reach the goal specified by the test purpose. Also, for a particular test case, the strategy should tell the tester whether the IUT has passed, failed. or deviated front the test purpose. In [8] Jeron and Morel show how to compute, for a given finite state machine specification and a test purpose automaton, a complete test graph (CTG) which represents all test strategies. In this paper; we consider the case when the specification is a hierarchical state machine and show how to compute a hierarchical CTG which preserves the hierarchical structure of the specification. We also propose an algorithm for an online test oracle which avoids a space overhead associated with the CTG.
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We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.
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We give a detailed construction of a finite-state transition system for a com-connected Message Sequence Graph. Though this result is well-known in the literature and forms the basis for the solution to several analysis and verification problems concerning MSG specifications, the constructions given in the literature are either not amenable to implementation, or imprecise, or simply incorrect. In contrast we give a detailed construction along with a proof of its correctness. Our transition system is amenable to implementation, and can also be used for a bounded analysis of general (not necessarily com-connected) MSG specifications.
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We develop a simulation based algorithm for finite horizon Markov decision processes with finite state and finite action space. Illustrative numerical experiments with the proposed algorithm are shown for problems in flow control of communication networks and capacity switching in semiconductor fabrication.
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This paper presents a method of partial automation of specification based regression testing, which we call ESSE (Explicit State Space Enumeration). The first step in ESSE method is the extraction of a finite state model of the system making use of an already tested version of the system under test (SUT). Thereafter, the finite state model thus obtained is used to compute good test sequences that can be used to regression test subsequent versions of the system. We present two new algorithms for test sequence computation - both based on our finite state model generated by the above method. We also provide the details and results of the experimental evaluation of ESSE method. Comparison with a practically used random-testing algorithm has shown substantial improvements.
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Bisimulation-based information flow properties were introduced by Focardi and Gorrieri [1] as a way of specifying security properties for transition system models. These properties were shown to be decidable for finite-state systems. In this paper, we study the problem of verifying these properties for some well-known classes of infinite state systems. We show that all the properties are undecidable for each of these classes of systems.
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Finite volume methods traditionally employ dimension by dimension extension of the one-dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured Cartesian mesh in multiple dimensions. This simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution. The resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines. In this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error. Explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions, respectively. It is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next-nearest and next-next-nearest neighbors in three dimensions. Use of these isotropic expressions alone in a standard finite volume framework, however, is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and/or spatially non-uniform. The rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form. Various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms, while preserving the formal order of accuracy and discrete conservation of the original finite volume method, are developed. Numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method. Prominent anisotropic errors, such as spurious asymmetric distortions on a circular reaction-diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization. Furthermore, for a given spatial resolution, a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two-dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization. (C) 2014 Elsevier Inc. All rights reserved.
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We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.
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Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.
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Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.
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In this paper, we develop a novel moving mesh method suitable for solving axisymmetric free-boundary problems, including the Marangoni effect induced by surfactant or temperature variation. This method employs a body-fitted grid system where the gas-liquid interface is one line of the grid system. We model the surfactant equation of state with a non-linear Langmuir law, and, for simplicity, we limit ourselves to the situation of an insoluble surfactant. We solve complicated dynamic boundary conditions accurately on the gas-liquid interface in the framework of finite-volume methods. Our method is used to study the effect of a surfactant on the skin friction of a bubble in a uniaxial flow. For the limiting case where the surface diffusivity is zero, the effect of a tangential stress generated by the surface tension gradient, allows us to explain a new phenomenon in high concentration regimes: larger surface tension, but also larger deformation. Furthermore, this condition leads to the formation of boundary layers and flow separation at high Reynolds numbers. The influence of these complex flow patterns is examined. © 2005 Elsevier SAS. All rights reserved.
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Table of Contents
1 | Introduction | 1 |
1.1 | What is an Adiabatic Shear Band? | 1 |
1.2 | The Importance of Adiabatic Shear Bands | 6 |
1.3 | Where Adiabatic Shear Bands Occur | 10 |
1.4 | Historical Aspects of Shear Bands | 11 |
1.5 | Adiabatic Shear Bands and Fracture Maps | 14 |
1.6 | Scope of the Book | 20 |
2 | Characteristic Aspects of Adiabatic Shear Bands | 24 |
2.1 | General Features | 24 |
2.2 | Deformed Bands | 27 |
2.3 | Transformed Bands | 28 |
2.4 | Variables Relevant to Adiabatic Shear Banding | 35 |
2.5 | Adiabatic Shear Bands in Non-Metals | 44 |
3 | Fracture and Damage Related to Adiabatic Shear Bands | 54 |
3.1 | Adiabatic Shear Band Induced Fracture | 54 |
3.2 | Microscopic Damage in Adiabatic Shear Bands | 57 |
3.3 | Metallurgical Implications | 69 |
3.4 | Effects of Stress State | 73 |
4 | Testing Methods | 76 |
4.1 | General Requirements and Remarks | 76 |
4.2 | Dynamic Torsion Tests | 80 |
4.3 | Dynamic Compression Tests | 91 |
4.4 | Contained Cylinder Tests | 95 |
4.5 | Transient Measurements | 98 |
5 | Constitutive Equations | 104 |
5.1 | Effect of Strain Rate on Stress-Strain Behaviour | 104 |
5.2 | Strain-Rate History Effects | 110 |
5.3 | Effect of Temperature on Stress-Strain Behaviour | 114 |
5.4 | Constitutive Equations for Non-Metals | 124 |
6 | Occurrence of Adiabatic Shear Bands | 125 |
6.1 | Empirical Criteria | 125 |
6.2 | One-Dimensional Equations and Linear Instability Analysis | 134 |
6.3 | Localization Analysis | 140 |
6.4 | Experimental Verification | 146 |
7 | Formation and Evolution of Shear Bands | 155 |
7.1 | Post-Instability Phenomena | 156 |
7.2 | Scaling and Approximations | 162 |
7.3 | Wave Trapping and Viscous Dissipation | 167 |
7.4 | The Intermediate Stage and the Formation of Adiabatic Shear Bands | 171 |
7.5 | Late Stage Behaviour and Post-Mortem Morphology | 179 |
7.6 | Adiabatic Shear Bands in Multi-Dimensional Stress States | 187 |
8 | Numerical Studies of Adiabatic Shear Bands | 194 |
8.1 | Objects, Problems and Techniques Involved in Numerical Simulations | 194 |
8.2 | One-Dimensional Simulation of Adiabatic Shear Banding | 199 |
8.3 | Simulation with Adaptive Finite Element Methods | 213 |
8.4 | Adiabatic Shear Bands in the Plane Strain Stress State | 218 |
9 | Selected Topics in Impact Dynamics | 229 |
9.1 | Planar Impact | 230 |
9.2 | Fragmentation | 237 |
9.3 | Penetration | 244 |
9.4 | Erosion | 255 |
9.5 | Ignition of Explosives | 261 |
9.6 | Explosive Welding | 268 |
10 | Selected Topics in Metalworking | 273 |
10.1 | Classification of Processes | 273 |
10.2 | Upsetting | 276 |
10.3 | Metalcutting | 286 |
10.4 | Blanking | 293 |
Appendices | 297 | |
A | Quick Reference | 298 |
B | Specific Heat and Thermal Conductivity | 301 |
C | Thermal Softening and Related Temperature Dependence | 312 |
D | Materials Showing Adiabatic Shear Bands | 335 |
E | Specification of Selected Materials Showing Adiabatic Shear Bands | 341 |
F | Conversion Factors | 357 |
References | 358 | |
Author Index | 369 | |
Subject Index | 375 |
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Apesar de serem intensamente estudados em muitos países que caminham na vanguarda do conhecimento, os métodos sem malha ainda são pouco explorados pelas universidades brasileiras. De modo a gerar uma maior difusão ou, para a maioria, fazer sua introdução, esta dissertação objetiva efetuar o entendimento dos métodos sem malha baseando-se em aplicações atinentes à mecânica dos sólidos. Para tanto, são apresentados os conceitos primários dos métodos sem malha e o seu desenvolvimento histórico desde sua origem no método smooth particle hydrodynamic até o método da partição da unidade, sua forma mais abrangente. Dentro deste contexto, foi investigada detalhadamente a forma mais tradicional dos métodos sem malha: o método de Galerkin sem elementos, e também um método diferenciado: o método de interpolação de ponto. Assim, por meio de aplicações em análises de barras e chapas em estado plano de tensão, são apresentadas as características, virtudes e deficiências desses métodos em comparação aos métodos tradicionais, como o método dos elementos finitos. É realizado ainda um estudo em uma importante área de aplicação dos métodos sem malha, a mecânica da fratura, buscando compreender como é efetuada a representação computacional da trinca, com especialidade, por meio dos critérios de visibilidade e de difração. Utilizando-se esses critérios e os conceitos da mecânica da fratura, é calculado o fator de intensidade de tensão através do conceito da integral J.