On physics-based crystal plasticity models: Application to virtual material testing of sheet metals

It is possible to pursue a multi-scale modeling approach for sheet forming simulations by applying the concept of virtual material testing to determine the yield surface from the microstructure of a given material. Full-field simulations with phenomenological crystal plasticity models are widely used for this kind of investigations. However, recent developments focus on incorporating physical quantities like dislocation density into these models. In this work, a dislocation density based crystal plasticity model is used to investigate the plastic anisotropy of the deep drawing steel DC04. In particular, we focus on the prediction of R-values, which can be used to calibrate macroscopic plasticity models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large deviations in testing fractional Ornstein–Uhlenbeck models

The paper obtains the explicit form of fine large deviation theorems for the log-likelihood ratio in testing models with fractional Ornstein–Uhlenbeck processes with Hurst parameter bigger than half and obtains the explicit rates of decrease of the error probabilities of Neyman–Pearson, Bayes and minimax tests.     

Parameter identification based on FE‐models by genetic algorithms

A realistic and reliable model is an important precondition for the simulation of revitalization tasks as well as for the estimation of properties of existing buildings. Within one theory the parameters of the model should be approximated best by gradually performed experiments and their analysis. Usually this kind of optimization problems leads into non‐convex non‐differentiable objective function spaces with high dimensions. Normally ore complex structures are modeled using finite element method. We present a method of identifying Young's modulus for a beam and a plate by using FE‐models and genetic optimization algorithms for parameter identification.     

Derivation of macroscopic equations for individual cell‐based models: a formal approach

In this paper we review the theory of cells (particles) that evolve according to a dynamics determined by friction and that interact between themselves by means of suitable potentials. We derive by means of elementary arguments several macroscopic equations that describe the evolution of cell density. Some new results are also obtained—a formal derivation of a limit equation in the case of attractive potential as well as in the case of repulsive potential with a hard‐core part are presented. Finally we discuss the possible relevance of those results within the framework of individual cell‐based models. Several classes of potentials, including hard‐core, repulsive and potentials with attractive parts are discussed. The effect of noise terms in the equation is also considered. Copyright © 2005 John Wiley & Sons, Ltd.     

On the parameter identification of visco-hyperelastic material models for adhesive tapes

In this work we investigate the performance of a visco-hyperelastic material model to predict the time-dependent deformation behaviour of highly elastic adhesives. The model is based on the hyperelastic Arruda-Boyce model with a Prony series approach. The parameter identification is conducted for fixed relaxations times which are predicted via evaluating an integral ansatz for the shear modulus. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Applications of bulk queues to group testing models with incomplete identification

A population of items is said to be “group-testable”, (i) if the items can be classified as “good” and “bad”, and (ii) if it is possible to carry out a simultaneous test on a batch of items with two possible outcomes: “Success” (indicating that all items in the batch are good) or “failure” (indicating a contaminated batch). In this paper, we assume that the items to be tested arrive at the group-testing centre according to a Poisson process and are served (i.e., group-tested) in batches by one server. The service time distribution is general but it depends on the batch size being tested. These assumptions give rise to the bulk queueing model M/G^(m,M)/1, where m and M(>m) are the decision variables where each batch size can be between m and M. We develop the generating function for the steady-state probabilities of the embedded Markov chain. We then consider a more realistic finite state version of the problem where the testing centre has a finite capacity and present an expected profit objective function. We compute the optimal values of the decision variables (m, M) that maximize the expected profit. For a special case of the problem, we determine the optimal decision explicitly in terms of the Lambert function.     

Interpolation approximations based on Gauss–Lobatto–Legendre–Birkhoff quadrature

We derive in this paper the asymptotic estimates of the nodes and weights of the Gauss–Lobatto–Legendre–Birkhoff (GLLB) quadrature formula, and obtain optimal error estimates for the associated GLLB interpolation in Jacobi weighted Sobolev spaces. We also present a user-oriented implementation of the pseudospectral methods based on the GLLB quadrature nodes for Neumann problems. This approach allows an exact imposition of Neumann boundary conditions, and is as efficient as the pseudospectral methods based on Gauss–Lobatto quadrature for PDEs with Dirichlet boundary conditions.     

A semiparametric Wald statistic for testing logistic regression models based on case-control data

We propose a semiparametric Wald statistic to test the validity of logistic regression models based on case-control data. The test statistic is constructed using a semiparametric ROC curve estimator and a nonparametric ROC curve estimator. The statistic has an asymptotic chisquared distribution and is an alternative to the Kolmogorov-Smirnov-type statistic proposed by Qin and Zhang in 1997, the chi-squared-type statistic proposed by Zhang in 1999 and the information matrix test statistic proposed by Zhang in 2001. The statistic is easy to compute in the sense that it requires none of the following methods: using a bootstrap method to find its critical values, partitioning the sample data or inverting a high-dimensional matrix. We present some results on simulation and on analysis of two real examples. Moreover, we discuss how to extend our statistic to a family of statistics and how to construct its Kolmogorov-Smirnov counterpart. This work was supported by the 11.5 Natural Scientific Plan (Grant No. 2006BAD09A04) and Nanjing University Start Fund (Grant No. 020822410110)     

Unit root testing in the presence of ARFIMA–GARCH errors

We consider asymptotic behavior of self‐normalized sums of autoregressive fractionally integrated moving average (ARFIMA) processes whose innovations are GARCH errors. The asymptotic distribution of the sums is derived under very mild conditions. Applications to unit root tests with ARFIMA–GARCH errors are discussed. It is shown that even when the errors exhibit both long‐range dependence and heavy‐tailed conditional heteroscedasticity, the asymptotic distributions of the Dickey–Fuller ρ‐type tests are functionals of standard Brownian motion rather than those of fractional Brownian motions. Some Monte Carlo simulations are provided to illustrate the finite sample properties of two of the tests. Copyright © 2010 John Wiley & Sons, Ltd.     

From the mathematical kinetic theory for active particles on the derivation of hyperbolic macroscopic tissue models

This paper deals with the derivation of macroscopic equations from the underlying kinetic model delivered by the kinetic theory of active particles with discrete microscopic states. Hyperbolic models for local density and mean velocity are obtained with the aim at adding further knowledge to mathematical methods for modelling living matter.     

Qualitative analysis of second-order models of tumor–immune system competition

This paper deals with the qualitative analysis, existence of equilibria and asymptotic behavior of some second-order models of the competition between tumor and immune cells. The background model belongs to d’Onofrio [A. d’Onofrio, A general framework for modeling tumor–immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235; A. d’Onofrio, Tumor–immune system interaction: Modelig the tumor-stimulated proliferation of effectors and immunotherapy, Math. Models Methods Appl. Sci. 16 (2006) 1375–1401]. Various developments proposed in this paper are focussed on the hiding–learning dynamics, followed by the qualitative analysis.     

Elastic–plastic buckling of annular circular plate with linear material hardening

The contribution treats the buckling problem of a circular annular plate where the unstable state and the buckling process occurs when the stress state in the most loaded points of the plate is already in the elastic–plastic region. It is supposed that the plate buckles axisymmetrically (m = 0) or nonaxisymmetrically with m > 0, m ∈ ℕ waves in the circumferential direction. Using the equilibrium method, the critical buckling loads are calculated. The results show the influence of the material hardening coefficient 0 ≤ f ≤ 1 on the buckling load. The comparison between calculations with the consideration of flow and deformation theory of plasticity is given.     

Numerical and theoretical discussions for solving nonlinear generalized Benjamin–Bona–Mahony–Burgers equation based on the Legendre spectral element method

This article is devoted to solving numerically the nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation that has several applications in physics and applied sciences. First, the time derivative is approximated by using a finite difference formula. Afterward, the stability and convergence analyses of the obtained time semi‐discrete are proven by applying the energy method. Also, it has been demonstrated that the convergence order in the temporal direction is O(dt) . Second, a fully discrete formula is acquired by approximating the spatial derivatives via Legendre spectral element method. This method uses Lagrange polynomial based on Gauss–Legendre–Lobatto points. An error estimation is also given in detail for full discretization scheme. Ultimately, the GBBMB equation in the one‐ and two‐dimension is solved by using the proposed method. Also, the calculated solutions are compared with theoretical solutions and results obtained from other techniques in the literature. The accuracy and efficiency of the mentioned procedure are revealed by numerical samples.     

A note on the initial identification of scalar component models

This paper solves an open theoretical question in the identification stage of Scalar Component Models, posed initially by Tiao and Tsay and noted by several researchers, specifically as it refers to the choice of a certain parameter present in the process and which they denote h. The theoretical concept of sure overall orders, instead of the so-called overall orders, is useful in addressing this issue. Using simple examples, we justify the need for our theoretical results. Moreover, we use a Ranks Table and its properties to complement the SCM identification stage with interesting theoretical information without adding significant calculations to the procedure initially proposed by Tiao and Tsay.     

A Björck–Pereyra-type algorithm for Szegö–Vandermonde matrices based on properties of unitary Hessenberg matrices

In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems V_Φ(x), i.e., polynomial-Vandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O(n²) computational procedure. We present numerical experiments that indicate that for ill-conditioned matrices the new algorithm yields better forward accuracy than Gaussian elimination.     

Large time behaviour of solutions to Penrose–Fife phase change models

A non‐conserved phase transition model of Penrose–Fife type is considered where Dirichlet boundary conditions for the temperature are taken. A sketch of the proof of existence and uniqueness of the solution is given. Then, the large time behaviour of such a solution is studied. By using the Simon–?ojasiewicz inequality it is shown that the whole solution trajectory converges to a single stationary state. Due to the non‐coercive character of the energy functional, the main difficulty in the proof is to control the large values of the temperature. This is achieved by means of non‐standard a priori estimates. Copyright © 2005 John Wiley & Sons, Ltd.     

Goal‐oriented error estimation for Cahn–Hilliard models of binary phase transition

A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn–Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward‐in‐time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one‐ and two‐dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Numerical solution of the Rosenau–KdV–RLW equation by operator splitting techniques based on B‐spline collocation method

In the present study, the operator splitting techniques based on the quintic B‐spline collocation finite element method are presented for calculating the numerical solutions of the Rosenau–KdV–RLW equation. Two test problems having exact solutions have been considered. To demonstrate the efficiency and accuracy of the present methods, the error norms L₂ and L_∞ with the discrete mass Q and energy E conservative properties have been calculated. The results obtained by the method have been compared with the exact solution of each problem and other numerical results in the literature, and also found to be in good agreement with each other. A Fourier stability analysis of each presented method is also investigated.     

A nearly optimal preconditioning based on recursive red–black orderings

Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ${}^{\text{½ log}{}_{\text{2}}\text{(√(5) −1)}}$ ) where n is the total number of unknowns (½ log₂(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n^1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log² n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd.