A direct simulation algorithm for a class of beta random fields in modelling material properties

2017 ◽  
Vol 326 ◽  
pp. 642-655 ◽  
Author(s):  
Yong Liu ◽  
Jun Hu ◽  
Hong Wei ◽  
Ay-Lee Saw
Keyword(s):  
Material Properties ◽  
Random Fields ◽  
Simulation Algorithm ◽  
Direct Simulation

scholarly journals A computational modeling approach based on random fields for short fiber-reinforced composites with experimental verification by nanoindentation and tensile tests

2021 ◽  
Author(s):  
Natalie Rauter
Keyword(s):  
Numerical Simulations ◽  
Correlation Functions ◽  
Material Properties ◽  
Random Fields ◽  
Tensile Tests ◽  
Short Fiber ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Component Level

AbstractIn this study a modeling approach for short fiber-reinforced composites is presented which allows one to consider information from the microstructure of the compound while modeling on the component level. The proposed technique is based on the determination of correlation functions by the moving window method. Using these correlation functions random fields are generated by the Karhunen–Loève expansion. Linear elastic numerical simulations are conducted on the mesoscale and component level based on the probabilistic characteristics of the microstructure derived from a two-dimensional micrograph. The experimental validation by nanoindentation on the mesoscale shows good conformity with the numerical simulations. For the numerical modeling on the component level the comparison of experimentally obtained Young’s modulus by tensile tests with numerical simulations indicate that the presented approach requires three-dimensional information of the probabilistic characteristics of the microstructure. Using this information not only the overall material properties are approximated sufficiently, but also the local distribution of the material properties shows the same trend as the results of conducted tensile tests.

Simulation of Homogeneous Two-Dimensional Random Fields: Part II—MA and ARMA Models

1992 ◽  
Vol 59 (2S) ◽  
pp. S270-S277 ◽  
Author(s):  
Pol D. Spanos ◽  
Marc P. Mignolet
Keyword(s):  
Random Fields ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Mathematical Form ◽  
Simulation Algorithm ◽  
Arma Models ◽  
Spectral Matrix ◽  
Target Power ◽  
Ar Models

Alternatively to the autoregressive (AR) models examined in Part I, the determination of moving average (MA) algorithms for simulating realizations of twodimensional random fields with a specified (target) power spectrum is presented. First, the mathematical form of these models is addressed by considering infinitevariate vector processes of an appropriate spectral matrix. Next, the MA parameters are determined by relying on the maximization of an energy-like quantity. Then, a technique is formulated to derive an autoregressive moving average (ARMA) simulation algorithm from a prior MA approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

Simulation of Homogeneous Two-Dimensional Random Fields: Part I—AR and ARMA Models

1992 ◽  
Vol 59 (2S) ◽  
pp. S260-S269 ◽  
Author(s):  
Marc P. Mignolet ◽  
Pol D. Spanos
Keyword(s):  
Power Spectrum ◽  
Random Fields ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Simulation Algorithm ◽  
Two Dimensional ◽  
Arma Models ◽  
Spectral Matrix ◽  
Target Power

The determination of autoregressive (AR) and autoregressive moving average (ARMA) algorithms for simulating realizations of two-dimensional random fields with a specified (target) power spectrum is examined. The form of both of these models is justified first by considering infinite-variate vector processes of appropriate spectral matrix. Next, the AR parameters are selected to achieve the minimum of a positive integral. Then, a technique is formulated to derive an ARM A simulation algorithm from the prior AR approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

scholarly journals Direct simulation of a stochastically driven multi-step birth-death process

2021 ◽  
Author(s):  
Gennady Gorin ◽  
Lior Pachter
Keyword(s):  
Stochastic Process ◽  
Copy Number ◽  
Birth Rate ◽  
Special Function ◽  
Stochastic Simulation Algorithm ◽  
Death Process ◽  
Simulation Algorithm ◽  
Direct Simulation ◽  
Extrinsic Noise ◽  
Time Stepping

1AbstractThe description of transcription as a stochastic process provides a framework for the analysis of intrinsic and extrinsic noise in cells. To better understand the behaviors and possible extensions of existing models, we design an exact stochastic simulation algorithm for a multimolecular transcriptional system with an Ornstein-Uhlenbeck birth rate that is implemented via a special function-based time-stepping algorithm. We demonstrate that its joint copy-number distributions reduce to analytically well-studied cases in several limiting regimes, and suggest avenues for generalizations.

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