Lagrangian models of particle-laden flows with stochastic forcing: Monte Carlo, moment equations, and method of distributions analyses

2021 ◽  
Vol 33 (3) ◽  
pp. 033326
Author(s):  
Daniel Domínguez-Vázquez ◽  
Gustaaf B. Jacobs ◽  
Daniel M. Tartakovsky
Keyword(s):  
Monte Carlo ◽  
Moment Equations ◽  
Stochastic Forcing ◽  
Lagrangian Models ◽  
Particle Laden Flows

Human-Induced Loads on Grandstands as Non-Stationary Gaussian Processes

2016 ◽  
Vol 837 ◽  
pp. 191-197 ◽  
Author(s):  
Ondrej Rokos ◽  
Jiří Maca
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Gaussian Processes ◽  
Gaussian Noise ◽  
Mean Value ◽  
Moment Equations ◽  
Overall Performance ◽  
Stationary Gaussian Processes ◽  
Stationary Approximation ◽  
Transition Stages

In this contribution, we employ non-stationary filtered Gaussian processes as an enrichment of a periodic mean value in order to approximate crowd loads on grandstands. Our work generalizes previous considerations where the superposition of a mean value and a stationary filtered Gaussian noise was used, and helps therefore to better predict the response of a structure mainly in the transition stages. We specify general theory of stochastic differential equations within the context of grandstands by recalling particular moment equations, and demonstrate its benefits or drawbacks on two simple examples. Overall performance is measured in terms of the second moment evolutions in time and in terms of the total up-crossings of the system's response compared to previously developed stationary approximation and Monte Carlo simulation. Throughout, only an active part of a crowd is considered.

scholarly journals Uncertainty propagation for deterministic models of biochemical networks using moment equations and the extended Kalman filter

2021 ◽  
Vol 18 (181) ◽  
pp. 20210331
Author(s):  
Tamara Kurdyaeva ◽  
Andreas Milias-Argeitis
Keyword(s):  
Monte Carlo ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Biochemical Networks ◽  
Moment Closure ◽  
Moment Equations ◽  
Deterministic Models ◽  
Model Predictions ◽  
The Impact ◽  
Low Order

Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.

scholarly journals Integration of moment equations in a reduced-order modeling strategy for Monte Carlo simulations of groundwater flow

2020 ◽  
Vol 590 ◽  
pp. 125257
Author(s):  
Chuan-An Xia ◽  
Damiano Pasetto ◽  
Bill X. Hu ◽  
Mario Putti ◽  
Alberto Guadagnini
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Groundwater Flow ◽  
Reduced Order Modeling ◽  
Moment Equations ◽  
Reduced Order ◽  
Modeling Strategy

Development of Closure Relations in Kinetic Theory

1975 ◽  
Vol 53 (13) ◽  
pp. 1301-1303 ◽  
Author(s):  
Donald Baganoff ◽  
James P. Elliott
Keyword(s):  
Shock Wave ◽  
Monte Carlo ◽  
Kinetic Theory ◽  
Fourth Order ◽  
Strong Shock ◽  
Strong Shock Wave ◽  
Moment Equations ◽  
Systematic Method ◽  
Truncation Level ◽  
Closure Relations

A systematic method of obtaining closure relations for Maxwell's moment equations is developed, and shown, by application to the problem of an infinitely strong shock wave, to lead to results at the fourth order truncation level which agree with Mott–Smith and Monte Carlo predictions.

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

Sign in / Sign up

Export Citation Format

Share Document