A coupling cutting stock-lot sizing problem in the paper industry

An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.     

A Lagrangian representation of tangles

We construct a functor from the category of oriented tangles in R³ to the category of Hermitian modules and Lagrangian relations over Z[t,t^-1]. This functor extends the Burau representations of the braid groups and its generalization to string links due to Le Dimet.     

线性互补问题的一类新的带参数价值函数的阻尼牛顿法

本文给出了线性互补问题LCP(q ,M)的一类新的带参数光滑价值函数 ,基此价值函数提出了一种阻尼牛顿类算法 ,并证明了当M为P 矩阵时 ,该算法全局收敛且有限步终止 .通过数值实验说明了该算法高效可靠 .与互补问题的磨光方程组中所采用的带参数价值函数不同 ,这里的参数最终并不趋向于零 ,而是趋向于被称作解的乘子向量 (与凸非线性极小极大问题的Lagrange乘子完全一致 ) ,这一思想是本文作者首次提出来的 ,同时本文中所采用的阻尼牛顿类方法也有其独到之处 ,在互补问题的研究中有进一步发展的潜力     

Singularity-free augmented Lagrangian algorithms for constrained multibody dynamics

After a general review of the methods currently available for the dynamics of constrained multibody systems in the context of numerical efficiency and ability to solve the differential equations of motion in singular positions, we examine the acceleration based augmented Lagrangian formulations, and propose a new one for holonomic and non-holonomic systems that is based on the canonical equations of Hamilton. This new one proves to be more stable and accurate that the acceleration based counterpart under repetitive singular positions. The proposed algorithms are numerically efficient, can use standard conditionally stable numerical integrators and do not fail in singular positions, as the classical formulations do. The reason for the numerical efficiency and better behavior under singularities relies on the fact that the leading matrix of the resultant system of ODEs is sparse, symmetric, positive definite, and its rank is independent of that of the Jacobian of the constraint equations. The latter fact makes the proposed method particularly suitable for singular configurations.     

EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS

An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, from the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

平面ISODYNE法及其在复合材料力学中的应用

由J. T. Pindera提出的平面isodyne法是散光法的一种发展。具有非破坏性直接测取受力物体内部应力的特点。不需要大功率的激光器,条纹清晰,无畸变,对于平面应力问题可以得到应力分量的全部信息。在复合材料力学、断裂力学和接触问题等领域有广泛的应用前景。文章闸述了该方法的原理和技术,并应用它得到一受三点弯曲荷载的有裂纹的复合材料梁粘结层的应力分布。     

Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system

Semi-Lagrangian (SL) methods have been very popular in the Vlasov simulation community , , , , , ,  and . In this paper, we propose a new Strang split SL discontinuous Galerkin (DG) method for solving the Vlasov equation. Specifically, we apply the Strang splitting for the Vlasov equation [6], as a way to decouple the nonlinear Vlasov system into a sequence of 1-D advection equations, each of which has an advection velocity that only depends on coordinates that are transverse to the direction of propagation. To evolve the decoupled linear equations, we propose to couple the SL framework with the semi-discrete DG formulation. The proposed SL DG method is free of time step restriction compared with the Runge–Kutta DG method, which is known to suffer from numerical time step limitation with relatively small CFL numbers according to linear stability analysis. We apply the recently developed positivity preserving (PP) limiter [37], which is a low-cost black box procedure, to our scheme to ensure the positivity of the unknown probability density function without affecting the high order accuracy of the base SL DG scheme. We analyze the stability and accuracy properties of the SL DG scheme by establishing its connection with the direct and weak formulations of the characteristics/Lagrangian Galerkin method [23]. The quality of the proposed method is demonstrated via basic test problems, such as linear advection and rigid body rotation, and via classical plasma problems, such as Landau damping and the two stream instability.     

Theoretical and analytical Radial Distribution Function for non-polar mixtures

The theoretical and analytical Radial Distribution Function (RDF) for non-polar mixtures is presented, and the estimation methods of model parameters (such as the minimum molecular diameter d_ii, mean calibration factor of volume β_V and mean free path of relative motion λ_r,ij) are discussed. The calculated thermodynamic properties for H_e-H₂ fluid mixtures by this RDF fit well with that of MC simulations and classical results from the Yukawa-type EOS, in which the Double Yukawa (DY) potential was used and the quantum effect was considered. Compared with the semi-empirical RDF expressions in references, the advantage of this theoretical and analytical RDF is that it can be used for all kinds of potential functions of non-polar molecules, and it covers a very wide range of temperatures and densities. The extensive practical application of this RDF for chemistry, physics and technology needs further investigation.     

Fixed-point algorithms for constrained ICA and their applications in fMRI data analysis

Constrained independent component analysis (CICA) eliminates the order ambiguity of standard ICA by incorporating prior information into the learning process to sort the components intrinsically. However, the original CICA (OCICA) and its variants depend on a learning rate, which is not easy to be tuned for various applications. To solve this problem, two learning-rate-free CICA algorithms were derived in this paper using the fixed-point learning concept. A complete stability analysis was provided for the proposed methods, which also made a correction to the stability analysis given to OCICA. Variations for adding constraints either to the components or to the associated time courses were derived too. Using synthetic data, the proposed methods yielded a better stability and a better source separation quality in terms of higher signal-to-noise-ratio and smaller performance index than OCICA. For the artificially generated brain activations, the new CICAs demonstrated a better sensitivity/specificity performance than standard univariate general linear model (GLM) and standard ICA. Original CICA showed a similar sensitivity/specificity gain but failed to converge for several times. Using functional magnetic resonance imaging (fMRI) data acquired with a well-characterized sensorimotor task, the proposed CICAs yielded better sensitivity than OCICA, standard ICA and GLM in all the target functional regions in terms of either higher t values or larger suprathreshold cluster extensions using the same significance threshold. In addition, they were more stable than OCICA and standard ICA for analyzing the sensorimotor fMRI data.