Tae-Hyuk Ahn¹, Layne T. Watson^1,2, Yang Cao^1,1, Clifford A. Shaffer¹, William T. Baumann³

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 27-52, 2009, DOI:10.3970/cmes.2009.051.027

Abstract For biochemical systems, where some chemical species are represented by small numbers of molecules, discrete and stochastic approaches are more appropriate than continuous and deterministic approaches. The continuous deterministic approach using ordinary differential equations is adequate for understanding the average behavior of cells, while the discrete stochastic approach accurately captures noisy events in the growth-division cycle. Since the emergence of the stochastic simulation algorithm (SSA) by Gillespie, alternative algorithms have been developed whose goal is to improve the computational efficiency of the SSA. This paper explains and empirically compares the performance of some of these SSA alternatives on a realistic… More >

D. L. Young^1,2, C. P. Sun¹, L. H. Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 129-150, 2009, DOI:10.3970/cmes.2009.046.129

Abstract A local differential quadrature (LDQ) method to solve the option-pricing models with stochastic volatilities is proposed. The present LDQ method is a newly developed numerical method which preserves the advantage of high-order numerical solution from the classic differential quadrature (DQ) method. The scheme also overcomes the negative effect of the ill-condition for the resultant full matrix and the sensitivity to the grid distribution. It offers a much better approach for finding the optimal order of polynomial approximation when compared to the conventional DQ method. The option-pricing problem under the stochastic volatilities is an important financial engineering topic governed by the… More >

Raquel R. Pinho¹, João Manuel R. S. Tavares¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.1, pp. 51-76, 2009, DOI:10.3970/cmes.2009.046.051

Abstract This work addresses the problem of tracking feature points along image sequences. In order to analyze the undergoing movement, an approach based on the Kalman filtering technique has been used, which basically carries out the estimation and correction of the features' movement in every image frame. So as to integrate the measurements obtained from each image into the Kalman filter, a data optimization process has been adopted to achieve the best global correspondence set. The proposed criterion minimizes the cost of global matching, which is based on the Mahalanobis distance. A management model is employed to manage the features being… More >

Nagalinga Rajan, Soumyendu Raha¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 91-116, 2008, DOI:10.3970/cmes.2008.023.091

Abstract The article describes a numerical method for time domain integration of noisy dynamical systems originating from engineering applications. The models are second order stochastic differential equations (SDE). The stochastic process forcing the dynamics is treated mainly as multiplicative noise involving a Wiener Process in the Itô sense. The developed numerical integration method is a drift implicit strong order 2.0 method. The method has user-selectable numerical dissipation properties that can be useful in dealing with both multiplicative noise and stiffness in a computationally efficient way. A generalized analysis of the method including the multiplicative noise is presented. Strong order convergence, user-selectable… More >

M. Manjuprasad¹, C. S. Manohar²

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 23-54, 2007, DOI:10.3970/cmes.2007.019.023

Abstract A technique for adaptive random field refinement for stochastic finite element reliability analysis of structures is presented in this paper. Refinement indicator based on global importance measures are proposed and used for carrying out adaptive random field mesh refinements. Reliability index based error indicator is proposed and used for assessing the percentage error in the estimation of notional failure probability. Adaptive mesh refinement is carried out using hierarchical graded mesh obtained through bisection of elements. Spatially varying stochastic system parameters (such as Young's modulus and mass density) and load parameters are modeled in general as non-Gaussian random fields with prescribed… More >

Trenton M. Ricks¹, Thomas E. Lacy, Jr.^1,2, Brett A. Bednarcyk³, Steven M.Arnold³, John W. Hutchins¹

CMC-Computers, Materials & Continua, Vol.40, No.2, pp. 99-130, 2014, DOI:10.3970/cmc.2014.040.099

Abstract A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/ finite element (FE) analyses. A modified twoparameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC… More >

S. Liu¹, X. Liu^2,3, Y. Yuan², P. F. He¹, H. A. Mang^2,4

CMC-Computers, Materials & Continua, Vol.39, No.2, pp. 85-112, 2014, DOI:10.3970/cmc.2014.039.085

Abstract Autogenous shrinkage is defined as the bulk deformation of a closed, isothermal, cement-based material system, which is not subjected to external forces. It is associated with the hydration process of the cement paste. From the viewpoint of engineering practice, autogenous shrinkage deformations result in an increase of tensile stresses, which may lead to cracking of early-age concrete. Since concrete is a multi-phase composite with different material compositions and microscopic configurations at different scales, autogenous shrinkage does not only depend on the hydration of the cement paste, but also on the mechanical properties of the constituents and of their distribution. In… More >

Leiting Dong^1,2, Salah H. Gamal³, Satya N. Atluri^2,4

CMC-Computers, Materials & Continua, Vol.37, No.1, pp. 1-21, 2013, DOI:10.3970/cmc.2013.037.001

Abstract In this paper, a simple and reliable procedure of stochastic computation is combined with the highly accurate and efficient Trefftz Computational Grains (TCG), for a direct numerical simulation (DNS) of heterogeneous materials with microscopic randomness. Material properties of each material phase, and geometrical properties such as particles sizes and distribution, are considered to be stochastic with either a uniform or normal probabilistic distributions. The objective here is to determine how this microscopic randomness propagates to the macroscopic scale, and affects the stochastic characteristics of macroscopic material properties. Four steps are included in this procedure: (1) using the Latin hypercube sampling,… More >

C. Wang¹, W. Gao¹, C.W. Yang¹, C.M. Song¹

CMC-Computers, Materials & Continua, Vol.25, No.1, pp. 19-46, 2011, DOI:10.3970/cmc.2011.025.019

Abstract The random interval response and probabilistic interval reliability of structures with a mixture of random and interval properties are studied in this paper. Structural stiffness matrix is a random interval matrix if some structural parameters and loads are modeled as random variables and the others are considered as interval variables. The perturbation-based stochastic finite element method and random interval moment method are employed to develop the expressions for the mean value and standard deviation of random interval structural displacement and stress responses. The lower bound and upper bound of the mean value and standard deviation of random interval structural responses… More >