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Monte Carlo sampling

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Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
..., and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
..., the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential...
Image
Published: 15 December 2019
Fig. 6 Monte Carlo electron trajectory simulations for 20 kV primary beam energy. (a) Simulations of the backscattered electron energy distributions for normal (black curve) and tilted (blue curve) incidence of the electron beam. Note that the energy distribution for the tilted sample More
Image
Published: 01 December 1998
Fig. 2 Monte Carlo simulations of the interaction volume of a 20 keV primary electron beam in an iron sample. (a) Electron trajectories. (b) Sites of K-shell ionizations and production of characteristic x-rays. Source: Ref 1 More
Image
Published: 15 December 2019
Fig. 6 Monte Carlo simulations of a focusing guide performance. (a) Unfocused beam at the sample position. (b) Incident beam through a 2.4 m (7.9 ft) focusing square guide with logarithmic spiral curvature. Note that the color scale at right is much higher (500 versus 200 counts). More
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005534
EISBN: 978-1-62708-197-9
... experiments in which there is a large sample size ( Ref 38 ). Additional recommendations for experimental designs for use in computer-based experimentation are given here. Monte Carlo Sampling The Monte Carlo sampling method is popular in industry. Because it involves repeated sampling of the output...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005401
EISBN: 978-1-62708-196-2
... with a strong initial texture showing periods of rapid and slow growth. Source: Ref 22 Texture-controlled grain growth during beta annealing of titanium alloys has been simulated using both the Monte Carlo (Potts) and phase-field modeling approaches. In the work of Ivasishin et al. ( Ref 24 , 25...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004027
EISBN: 978-1-62708-185-6
... the grayness. These involve probabilistic methods such as Monte Carlo-Potts (MC-P) or cellular automata (CA) in which the consequences of using certain selection rules for the evolution of a microstructure can be computed and pictorially represented for comparison with observed microstructures. Local...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005428
EISBN: 978-1-62708-196-2
... with the total boundary area. H may represent stored energies that arise in the case of deformed structures and so provide a driving force for recrystallization. Dynamics Microstructural evolution is simulated by using a Monte Carlo method to sample different states of the system. The method...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006770
EISBN: 978-1-62708-295-2
... accelerating voltages and lower atomic number compositions, the interaction area can be substantially larger. Fig. 8 Monte-Carlo-predicted interaction volume Often it is not possible in failure investigations to polish the sample. Many times, the desire is to examine the surface of a sample...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002369
EISBN: 978-1-62708-193-1
.... If the values are selected at random from the distribution of possible values, the approach is called “Monte Carlo analysis” ( Ref 57 , 58 ). The probability of failure is equal to the fraction of outcomes that have shorter than desired lifetimes. Monte Carlo methods have become quite popular due to the ready...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005505
EISBN: 978-1-62708-197-9
... design quality (reliability and robustness). Many methods have been developed for stochastic sampling, including Monte Carlo methods ( Ref 31 , 32 ), structural reliability analysis methods ( Ref 33 , Ref 34 , Ref 35 ), sensitivity-based methods, based on Taylor's expansion ( Ref 36 , 37...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005432
EISBN: 978-1-62708-196-2
... that distinguish CA simulations (and other representational simulations such as Monte Carlo simulations) from mean field analytical models and models employing a homogeneous effective medium. This article examines how CA can be applied to the simulation of static and dynamic recrystallization. It describes...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005169
EISBN: 978-1-62708-186-3
...; radius of curvature after HT hot isostatic pressing MDOL maximum HV Knoop hardness Monte Carlo R springback; reduction; plastic horsepower MDRX Monte Carlo step Hz Rockwell hardness; requires mg multidisciplinary optimization R0 strain anisotropy ratio; thermal Mg multidisciplinary design I scale...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006637
EISBN: 978-1-62708-213-6
... the critical angle, those particles have transverse kinetic energy exceeding the collective string potential; the collective steering effect subsequently disappears. Channeling was first predicted in 1912 ( Ref 11 ). In 1963, channeling was accidently observed through Monte Carlo simulations ( Ref 12 , 13...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005410
EISBN: 978-1-62708-196-2
.... Fig. 4 Dependence on the nominal concentration x Zr 0 of the cluster size distribution of an aluminum solid solution at 500 °C. At this temperature, the solubility limit is x Zr e = 0.0548 % . Symbols correspond to atomic simulations (kinetic Monte Carlo) ( Ref 18...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006660
EISBN: 978-1-62708-213-6
... that have lost very little energy. These electrons have been shown to exit the sample very close to the initial beam position, resulting in spatial resolutions in typical transition metals to be better than 0.1 μm for beam voltages up to 20 kV ( Ref 10 ). Monte Carlo electron trajectory simulations...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006668
EISBN: 978-1-62708-213-6
... of the SEM compared with other common microscopy and microanalysis techniques. The following sections cover the critical issues regarding sample preparation, the physical principles regarding electron beam-sample interaction, and the mechanisms for many types of image contrast. The article also presents...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005434
EISBN: 978-1-62708-196-2
.... The article mainly focuses on phenomena and modeling approaches that are specific to VPP; however, most of the complementary information needed on general or specialized topics of interest (nucleation, microstructure evolution, Monte Carlo methods, etc.) is found in the cited references or in other articles...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005422
EISBN: 978-1-62708-196-2
... of boundary junctions on grain growth. Various models have been used for the simulation of grain-boundary migration and related phenomena, in particular, grain growth and recrystallization, notably Monte Carlo ( Ref 1 , Ref 2 , Ref 3 , Ref 4 ), phase field ( Ref 5 , 6 ), and network models ( Ref 7...