Questioning numerical integration methods for microsphere (and microplane) constitutive equations

In the last few years, more and more complex microsphere models have been proposed to predict the mechanical response of various polymers. Similarly than for microplane models, they consist in deriving a one-dimensional force vs. stretch equation and to integrate it over the unit sphere to obtain a three-dimensional constitutive equation. In this context, the focus of authors is laid on the physics of the one-dimensional relationship, but in most of the case the influence of the integration method on the prediction is not investigated.Here we compare three numerical integration schemes: a classical Gaussian scheme, a method based on a regular geometric meshing of the sphere, and an approach based on spherical harmonics. Depending on the method, the number of integration points may vary from 4 to 983,040! Considering simple quantities, i.e. principal (large) strain invariants, it is shown that the integration method must be carefully chosen. Depending on the quantities retained to described the one-dimensional equation and the required error, the performances of the three methods are discussed. Consequences on stress–strain prediction are illustrated with a directional version of the classical Mooney–Rivlin hyperelastic model. Finally, the paper closes with some advices for the development of new microsphere constitutive equations.     

Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

Modeling the effect of deep traps on the capacitance–voltage characteristics of p-type Si-doped GaAs Schottky diodes grown on high index GaAs substrates

Numerical simulation, using SILVACO-TCAD, is carried out to explain experimentally observed effects of different types of deep levels on the capacitance–voltage characteristics of p-type Si-doped GaAs Schottky diodes grown on high index GaAs substrates. Two diodes were grown on (311)A and (211)A oriented GaAs substrates using Molecular Beam Epitaxy (MBE). Although, deep levels were observed in both structures, the measured capacitance–voltage characteristics show a negative differential capacitance (NDC) for the (311)A diodes, while the (211)A devices display a usual behaviour. The NDC is related to the nature and spatial distribution of the deep levels, which are characterized by the Deep Level Transient Spectroscopy (DLTS) technique. In the (311)A structure only majority deep levels (hole traps) were observed while both majority and minority deep levels were present in the (211)A diodes. The simulation, which calculates the capacitance–voltage characteristics in the absence and presence of different types of deep levels, agrees well with the experimentally observed behaviour.     

In vivo evaluation of a mucoadhesive polymeric caplet for intravaginal anti-HIV-1 delivery and development of a molecular mechanistic model for thermochemical characterization

Context and objective: The aim of this study was to develop, characterize and evaluate a mucoadhesive caplet resulting from a polymeric blend (polymeric caplet) for intravaginal anti-HIV-1 delivery.

Materials and methods: Poly(lactic-co-glycolic) acid, ethylcellulose, poly(vinylalcohol), polyacrylic acid and modified polyamide 6, 10 polymers were blended and compressed to a caplet-shaped device, with and without two model drugs 3′-azido-3′-deoxythymidine (AZT) and polystyrene sulfonate (PSS). Thermal analysis, infrared spectroscopy and microscopic analysis were carried out on the caplets employing temperature-modulated DSC (TMDSC), Fourier transform infra-red (FTIR) spectrometer and scanning electron microscope, respectively. In vitro and in vivo drug release analyses as well as the histopathological toxicity studies were carried out on the drug-loaded caplets. Furthermore, molecular mechanics (MM) simulations were carried out on the drug-loaded caplets to corroborate the experimental findings.

Results and discussion: There was a big deviation between the T_g of the polymeric caplet from the T_g's of the constituent polymers indicating a strong interaction between constituent polymers. FTIR spectroscopy confirmed the presence of specific ionic and non-ionic interactions within the caplet. A controlled near zero-order drug release was obtained for AZT (20 d) and PSS (28 d). In vivo results, i.e. the drug concentration in plasma ranged between 0.012–0.332?mg/mL and 0.009–0.256?mg/mL for AZT and PSS over 1–28 d.

Conclusion: The obtained results, which were corroborated by MM simulations, attested that the developed system has the potential for effective delivery of anti-HIV-agents.     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

差分跳频通信系统的特点及性能

文章介绍了一种新型的短波跳频通信技术——差分跳频,分析了差分跳频技术区别于常规跳频技术的主要特点。针对按序列检测的信号接收方法,对差分跳频通信系统在AWGN信道下的性能进行了理论分析,同时做出相应的计算机仿真,证实了差分跳频通信技术和按序列检测方法的结合,使通信系统在AWGN信道下的性能得到了比较显著的提升。     

Mechanical properties of polyethylene mixtures crystallized under high pressure

The mechanical properties of a medium molecular weight polyethylene (MMW‐PE) and an ultrahigh molecular weight PE (UHMW‐PE) binary mixture with different weight fractions crystallized from the melt at 0.1 and 450 MPa were studied. The tensile modulus, yield stress, and strain were obtained as a function of the weight fractions in the PE mixtures at 25 and 85°C. The tensile modulus in the sample crystallized at 0.1 MPa decreased from 1.5 GPa of pure MMW‐PE to about 0.4 GPa of pure UHMW‐PE with the UHMW‐PE content but it did not decrease with the UHMW‐PE in the sample crystallized at 450 MPa in testing at 25°C. A decreasing rate of the storage modulus E′ of UHMW‐PE in a dynamic measurement for the sample crystallized at 0.1 MPa with the temperature is larger than that of the sample crystallized at 450 MPa. These experimental facts are interpreted in relation to the molecular motion and crystallinity of the sample. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1962–1968, 2003     

Moving Least-Squares Differential Quadrature Method for Free Vibration of Antisymmetric Laminates

In this paper, the moving least-squares differential quadrature (MLSDQ) method is employed for free vibration of thick antisymmetric laminates based on the first-order shear deformation theory. The generalized displacements of the laminates are independently approximated with the centered moving least-squares (MLS) technique within each domain of influence. The MLS nodal shape functions and their partial derivatives are computed quickly through back-substitutions after only one LU decomposition. Subsequently, the weighting coefficients in the MLSDQ discretization are determined with the nodal partial derivatives of the MLS shape functions. The MLSDQ method combines the merits of both the differential quadrature and meshless methods which can be conveniently applied to complex domains and irregular discretizations without loss of implementation efficiency and numerical accuracy. The natural frequencies of the laminates with various edge conditions, ply angles, and shapes are calculated and compared with the existing solutions to study the numerical accuracy and stability of the MLSDQ method. Effects of support size, order of completeness of basis functions, and node irregularity on the numerical accuracy are investigated in detail.     

Science in High Magnetic Fields: What Could Be Learned?

High magnetic fields are one of the most powerful tools available to scientists for the study, modification and control of matter. This includes the knowledge on correlations effects, interaction mechanisms, structural information and understanding of mesoscopic effects. In this context, a review of recent scientific achievements at the Grenoble High Magnetic Laboratory is given to illustrate, on specific examples, the power of the Magnetic Field probe.     

带参数的一阶脉冲微分方程边值问题

利用上下解和单调迭代法。讨论了带参数的一阶脉冲微分方程。获得了单边Lipschitz条件下这类方程边值问题的解的存在性。