A Graph-Theoretic Monte Carlo Framework for Comparing Delta Surface Dynamics and Subsurface Structure in Numerical Models and Physical Experiments

2021 ◽  
Author(s):  
Alex Miltenberger ◽  
Tapan Mukerji ◽  
Jayaram Hariharan ◽  
Paola Passalacqua ◽  
Erik Nesvold
Keyword(s):  
Monte Carlo ◽  
Numerical Models ◽  
Surface Dynamics ◽  
Subsurface Structure ◽  
Graph Theoretic ◽  
Physical Experiments ◽  
Monte Carlo Framework

Probabilistic multiscale modeling of fracture in heterogeneous materials and structures

2020 ◽  
Vol 86 (7) ◽  
pp. 45-54
Author(s):  
A. M. Lepikhin ◽  
N. A. Makhutov ◽  
Yu. I. Shokin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fracture Mechanics ◽  
Multiscale Modeling ◽  
Virtual Work ◽  
Numerical Models ◽  
Heterogeneous Materials ◽  
Heterogeneous Structure ◽  
Generalized Coordinates ◽  
Heterogeneous Structures

The probabilistic aspects of multiscale modeling of the fracture of heterogeneous structures are considered. An approach combining homogenization methods with phenomenological and numerical models of fracture mechanics is proposed to solve the problems of assessing the probabilities of destruction of structurally heterogeneous materials. A model of a generalized heterogeneous structure consisting of heterogeneous materials and regions of different scales containing cracks and crack-like defects is formulated. Linking of scales is carried out using kinematic conditions and multiscale principle of virtual forces. The probability of destruction is formulated as the conditional probability of successive nested fracture events of different scales. Cracks and crack-like defects are considered the main sources of fracture. The distribution of defects is represented in the form of Poisson ensembles. Critical stresses at the tops of cracks are described by the Weibull model. Analytical expressions for the fracture probabilities of multiscale heterogeneous structures with multilevel limit states are obtained. An approach based on a modified Monte Carlo method of statistical modeling is proposed to assess the fracture probabilities taking into account the real morphology of heterogeneous structures. A feature of the proposed method is the use of a three-level fracture scheme with numerical solution of the problems at the micro, meso and macro scales. The main variables are generalized forces of the crack propagation and crack growth resistance. Crack sizes are considered generalized coordinates. To reduce the dimensionality, the problem of fracture mechanics is reformulated into the problem of stability of a heterogeneous structure under load with variations of generalized coordinates and analysis of the virtual work of generalized forces. Expressions for estimating the fracture probabilities using a modified Monte Carlo method for multiscale heterogeneous structures are obtained. The prospects of using the developed approaches to assess the fracture probabilities and address the problems of risk analysis of heterogeneous structures are shown.

Coarse-grained modeling of the nucleation of polycyclic aromatic hydrocarbons into soot precursors

2019 ◽  
Vol 21 (9) ◽  
pp. 5123-5132 ◽  
Author(s):  
J. Hernández-Rojas ◽  
F. Calvo
Keyword(s):  
Monte Carlo ◽  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Physical Growth ◽  
Coarse Grained ◽  
Soot Precursors ◽  
Polycyclic Aromatic ◽  
Hydrocarbon Molecules ◽  
A Minor ◽  
Monte Carlo Framework

The aggregation and physical growth of polycyclic aromatic hydrocarbon molecules was simulated using a coarse-grained potential and a stochastic Monte Carlo framework. In agreement with earlier studies, homomolecular nucleation of pyrene, coronene and circumcoronene is found to be limited at temperatures in the 500–1000 K range. Heteromolecular nucleation is found to occur with a minor spontaneous segregation toward pure and equi concentrations.

scholarly journals A Note on the Numerical Representation of Surface Dynamics in Quasigeostrophic Turbulence: Application to the Nonlinear Eady Model

2009 ◽  
Vol 66 (4) ◽  
pp. 1063-1068 ◽  
Author(s):  
Ross Tulloch ◽  
K. Shafer Smith
Keyword(s):  
Numerical Models ◽  
Buoyancy Frequency ◽  
Complete Suppression ◽  
Numerical Representation ◽  
Vertical Resolution ◽  
Surface Dynamics ◽  
Coriolis Parameter ◽  
Theoretical Predictions ◽  
Vertical Grid ◽  
Similar Restriction

Abstract The quasigeostrophic equations consist of the advection of linearized potential vorticity coupled with advection of temperature at the bounding upper and lower surfaces. Numerical models of quasigeostrophic flow often employ greater (scaled) resolution in the horizontal than in the vertical (the two-layer model is an extreme example). In the interior, this has the effect of suppressing interactions between layers at horizontal scales that are small compared to Nδz/f (where δz is the vertical resolution, N the buoyancy frequency, and f the Coriolis parameter). The nature of the turbulent cascade in the interior is, however, not fundamentally altered because the downscale cascade of potential enstrophy in quasigeostrophic turbulence and the downscale cascade of enstrophy in two-dimensional turbulence (occurring layerwise) both yield energy spectra with slopes of −3. It is shown here that a similar restriction on the vertical resolution applies to the representation of horizontal motions at the surfaces, but the penalty for underresolving in the vertical is complete suppression of the surface temperature cascade at small scales and a corresponding artificial steepening of the surface energy spectrum. This effect is demonstrated in the nonlinear Eady model, using a finite-difference representation in comparison with a model that explicitly advects temperature at the upper and lower surfaces. Theoretical predictions for the spectrum of turbulence in the nonlinear Eady model are reviewed and compared to the simulated flows, showing that the latter model yields an accurate representation of the cascade dynamics. To accurately represent dynamics at horizontal wavenumber K in the vertically finite-differenced model, it is found that the vertical grid spacing must satisfy δz ≲ 0.3f/(NK); at wavenumbers K > 0.3f/(Nδz), the spectrum of temperature variance rolls off rapidly.

RISK ANALYSIS OF OFFSHORE TRANSPORTATION ACCIDENT IN ARCTIC WATERS

2021 ◽  
Vol 159 (A3) ◽  
Author(s):  
R Abbassi ◽  
F Khan ◽  
N Khakzad ◽  
B Veitch ◽  
S Ehlers
Keyword(s):  
Monte Carlo ◽  
Risk Analysis ◽  
Historical Data ◽  
Fault Trees ◽  
Northern Sea Route ◽  
Accident Scenarios ◽  
Oil Tanker ◽  
Harsh Conditions ◽  
Monte Carlo Framework ◽  
Transportation Accident

A methodology for risk analysis applicable to shipping in arctic waters is introduced. This methodology uses the Bowtie relationship to represent an accident causes and consequences. It is further used to quantify the probability of a ship accident and also the related accident consequences during navigation in arctic waters. Detailed fault trees for three possible ship accident scenarios in arctic transits are developed and represented as bowties. Factors related to cold and harsh conditions and their effects on grounding, foundering, and collision are considered as part of this study. To illustrate the application of the methodology, it is applied to a case of an oil-tanker navigating on the Northern Sea Route (NSR). The methodology is implemented in a Markov Chain Monte Carlo framework to assess the uncertainties arisen from historical data and expert judgments involved in the risk analysis.

Introduction — A Monte Carlo Framework

2015 ◽  
pp. 105-106
Author(s):  
Roland Lichters ◽  
Roland Stamm ◽  
Donal Gallagher
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Framework
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