scholarly journals Angular Correlation Using Rogers-Szegő-Chaos

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 171
Author(s):  
Christine Schmid ◽  
Kyle J. DeMars
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Probability Density Function ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
One Dimension ◽  
Real Numbers ◽  
The Family ◽  
Heading Angle ◽  
Probability Density Function Pdf

Polynomial chaos expresses a probability density function (pdf) as a linear combination of basis polynomials. If the density and basis polynomials are over the same field, any set of basis polynomials can describe the pdf; however, the most logical choice of polynomials is the family that is orthogonal with respect to the pdf. This problem is well-studied over the field of real numbers and has been shown to be valid for the complex unit circle in one dimension. The current framework for circular polynomial chaos is extended to multiple angular dimensions with the inclusion of correlation terms. Uncertainty propagation of heading angle and angular velocity is investigated using polynomial chaos and compared against Monte Carlo simulation.

Proposition of a New Conformity Criterion for the Assessment of the Concrete Compressive Strength

2017 ◽  
Vol 259 ◽  
pp. 106-110
Author(s):  
Elżbieta Szczygielska ◽  
Viktar V. Tur
Keyword(s):  
Monte Carlo Simulation ◽  
Compressive Strength ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Concrete Strength ◽  
Test Results ◽  
Concrete Compressive Strength ◽  
Strength Assessment ◽  
Probability Density Function Pdf

A new conformity criterion for concrete strength assessment that could be used at the initial production stage, is proposed. As an innovative conformity criterion was evaluated based on Order Statistics Theory, it is independent from the type probability density function (PDF) in population, estimation of the standard deviation, shape of the specimen and the level of autocorrelation of the test results. Proposed criterion was evaluated and positively verified both AOQL-concept using Monte Carlo simulation and the test results obtained under real production.

scholarly journals A CONDITIONAL STOCHASTIC PROJECTION METHOD APPLIED TO A PARAMETRIC VIBRATIONS PROBLEM

2014 ◽  
Vol 20 (6) ◽  
pp. 810-818 ◽  
Author(s):  
Wlodzimierz Brzakala ◽  
Aneta Herbut
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Polynomial Chaos ◽  
Excitation Frequency ◽  
Finite Sequence ◽  
Excitation Amplitude ◽  
Random Excitation ◽  
Parametric Vibrations ◽  
Representative Points ◽  
Cable Stayed Bridges

Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excitation frequency which are two random variables. The excitation frequency ωL is discretized to a finite sequence of representative points, ωL,i Therefore, the problem is (conditionally) formulated and solved as a one-dimensional polynomial chaos expansion generated by the random excitation amplitude. The presented numerical analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben-Ahin bridge). The results obtained by the use of the conditional polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation (truly two-dimensional, not conditional one). The convergence of both methods is discussed. It is found that the conditional polynomial chaos can yield a better convergence then the Monte Carlo simulation, especially if resonant vibrations are probable.

PHASE DIAGRAM OF DOUBLE EXCHANGE MODEL WITH ANTIFERROMAGNETIC COUPLING FOR LOCALIZED t2g SPINS IN ONE DIMENSION REVISITED

2005 ◽  
Vol 19 (24) ◽  
pp. 3731-3743 ◽  
Author(s):  
Q. L. ZHANG
Keyword(s):  
Phase Diagram ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Large Scale ◽  
Double Exchange ◽  
Exchange Model ◽  
One Dimension ◽  
Antiferromagnetic Coupling ◽  
Single Orbit ◽  
Superexchange Coupling

The phase diagram of the single-orbit double exchange model for manganites with ferromagnetic Hund coupling between mobile eg electrons and spins of localized t2g electrons as well as antiferromagnetic superexchange coupling between t2g electrons is investigated with a large scale Monte Carlo simulation in one dimension. The phase boundary is determined based on the internal energy, the electron density and the structure factor. In particular, low-temperature properties at quarter filling are studied in detail.

scholarly journals Topological analysis in Monte Carlo simulation for uncertainty propagation

Solid Earth ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 1663-1684 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Jessell ◽  
Jérémie Giraud ◽  
Mark Lindsay ◽  
Vitaliy Ogarko
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Topological Analysis ◽  
Uncertainty Propagation ◽  
Population Heterogeneity ◽  
Plausible Model ◽  
Uncertainty Index ◽  
Uncertainty Estimates ◽  
Geological Models

Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets' variability and plausible model's variability. Non-linearity is shown to mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUP is introduced. Boolean topological signatures recording lithological unit adjacency are used as n-dimensional points to be considered individually or clustered using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.

Improved MCMC Method for Parameter Estimation Based on Marginal Probability Density Function

2011 ◽  
Author(s):  
Dawn An ◽  
Joo-Ho Choi
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Uncertain Parameters ◽  
Marginal Probability ◽  
Mcmc Method ◽  
Proposal Distribution ◽  
Engineering Problems ◽  
Probability Density Function Pdf

In many engineering problems, sampling is often used to estimate and quantify the probability distribution of uncertain parameters during the course of Bayesian framework, which is to draw proper samples that follow the probabilistic feature of the parameters. Among numerous approaches, Markov Chain Monte Carlo (MCMC) has gained the most popularity due to its efficiency and wide applicability. The MCMC, however, does not work well in the case of increased parameters and/or high correlations due to the difficulty of finding proper proposal distribution. In this paper, a method employing marginal probability density function (PDF) as a proposal distribution is proposed to overcome these problems. Several engineering problems which are formulated by Bayesian approach are addressed to demonstrate the effectiveness of proposed method.

CBED Study of Mn3+ Orbital Ordering in LaMnO3

2000 ◽  
Vol 6 (S2) ◽  
pp. 46-47
Author(s):  
B. Jiang ◽  
J.M. Zuo ◽  
Q. Chen ◽  
S-W Cheong ◽  
J.C.H. Spence
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Parent Compound ◽  
Electronic Configuration ◽  
Antiferromagnetic State ◽  
Orbital Ordering ◽  
The Family ◽  
Jahn Teller ◽  
Octahedral Tilting ◽  
Mn Oxides

Mn oxides of pervoskite-related structure containing Mn ions have attracted considerable interest due to the colossal magnetoresistence (CMR) effect. Doping the family of compounds La1-x Cax MnO3 with divalent Ca ion oxidizes Mn+3 to Mn4+, introducing holes in the 3d bond orbital that give rise to a series of interesting physical properties. The parent compound LaMnO3 (Pbnm) with unit cell of a=5.5367Å b=5.7473Å and c=7.6929Å, is an antiferromagnetic insulator in which orbital ordering is established due to the cooperative Jahn-Teller (JT) effect breaking the degeneracy of the electronic configuration of Mn3+ (t2g3eg1). This particular C-type orbital ordering is responsible for the A-type magnetic structure observed by Wollen and Kohler. Theoretical Monte-Carlo simulation has shown that the A-type antiferromagnetic state is stable in a model based on JT phonons, using coupling values physically reasonable for LaMnO3 and considering the small but important effect of octahedral tilting.

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