Lyapunov exponents for systems with unbounded coefficients

In this article we propose a generalization of the concept of Lyapunov exponents for discrete linear systems which may be used in the case of unbounded coefficients. We show some simplest properties of this generalization and apply it to define a generalization of regular system. Finally, we discuss the problem of stability by linear approximation.     

Coupled multipolar interactions in small-particle metallic clusters

We propose a new formalism for computing the optical properties of small clusters of particles. It is a generalization of the coupled dipole-dipole particle-interaction model and allows one in principle to take into account all multipolar interactions in the long-wavelength limit. The method is illustrated by computations of the optical properties of N = 6 particle clusters for different multipolar approximations. We examine the effect of separation between particles and compare the optical spectra with the discrete-dipole approximation and the generalized Mie theory.     

Time domain analysis of the weighted distributed order rheological model

This paper presents the fundamental solution and relevant properties of the weighted distributed order rheological model in the time domain. Based on the construction of distributed order damper and the idea of distributed order element networks, this paper studies the weighted distributed order operator of the rheological model, a generalization of distributed order linear rheological model. The inverse Laplace transform on weighted distributed order operators of rheological model has been obtained by cutting the complex plane and computing the complex path integral along the Hankel path, which leads to the asymptotic property and boundary discussions. The relaxation response to weighted distributed order rheological model is analyzed, and it is closely related to many physical phenomena. A number of novel characteristics of weighted distributed order rheological model, such as power-law decay and intermediate phenomenon, have been discovered as well. And meanwhile several illustrated examples play important role in validating these results.     

Endochronic viscoplastic material models for filled PTFE

To describe the nonlinear material behaviour of polytetrafluoroethylene (PTFE), a viscoplastic material model of the overstress type is proposed based on experimental data. The approach starts with a rheological model without an elastic range, using a rate-independent elastoplastic model with an endochronic flow rule and a nonlinear elastic law in parallel connection with a nonlinear Maxwell model. The generalization to three dimensions is possible for both small and finite strains under the assumption that changes of the density are purely elastic. Numerical simulations show that the model can describe the short and long time material behavior of filled PTFE.     

偶极子模型在磁流变液中的使用误差研究

为了提高使用偶极子模型分析磁流变液流变性能的准确性,采用偶极子模型与有限元模型对比的方法,分析了偶极子模型的适用范围,计算了不同体积分数磁流变液偶极子模型表面磁场的误差大小,并进行了实验验证.研究结果表明,磁流变液中软磁性颗粒主要受其相邻颗粒影响;偶极子模型表面磁场最大误差为62%,出现在两颗粒表面距离最近处,在磁流变...     

A simple model of nonlinear viscoelasticity taking into account stress relaxation

We present one of the simplest theory of nonlinear viscoelasticity taking into account stress relaxation. The model is a 3D nonlinear generalization of the standard three-parameter model of 1D classical viscoelasticity. In the framework of this theory, we examine some simple deformations. First of all, we consider a homogeneous deformation as a possible idealization of the usual triaxial test. By this analysis, we show that the model under investigation may be interesting to describe the mechanical behavior of materials like bitumen and hot mix asphalt. Moreover, we investigate the evolution of shearing motions (mainly in the quasi-static approximation) to point out several aspects of the rich mechanical response of constitutive theories in implicit form.     

Exact Solution of the Problem of Flow of a Polymer Solution in a Plane Channel

Onedimensional flow of polymer solutions in a plane channel under the action of the pressure gradient has been considered. To describe the rheological properties of the solutions we have selected: 1) generalization of the Jeffreys phenomenological model with an objective time derivative F _abc with six arbitrary material constants; 2) the differential vector model proposed by Remmelgas, Harrison, and Leal and that is the approximation of the Doi–Edwards–Marrucci–Grizzuti model. Exact analytical solutions of the problem of flow in a plane channel have been obtained for them. In the two cases the problem can have both a unique solution and a nonunique solution. The velocity profiles are either smooth nearly parabolic or have weak tangential discontinuities. Criterial conditions for the appearance of ambiguous flow regimes have been obtained.     

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer‐aided design geometry (for example, given by nonuniform rational B‐splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T‐splines, LR‐splines, (truncated) hierarchical B‐splines, and PHT‐splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer‐aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.     

Superconvergence and the use of the residual as an error estimator in the BEM. II: Collocation,numerical integration and error indicators

We show for a variety of integral equations that the residual can be used as an error estimator provided the Sloan iterate of the approximation superconverges. This generalizes a result given by Geng el al. [J. Acoust. Soc. Am. 100 (1996) 355]. When the solution technique is Galerkin's method we show that the superconvergence of the Sloan iterate can be established under quite general conditions. For collocation this is more difficult and we discuss a generalization of a result of Brunner [J. Comp. Appl. Math. 67 (1996) 185] for doing this. Using ideas of Schulz [Über lokale and globale Fehlergschätzungen für adaptive randelment Methoden, PhD thesis, Mathematisches Institute A, University of Stuttgart, 1997] it is shown how to localize these results to provide asymptotically exact local error indicators. It is also shown that it is important to consider the effect of numerical integration errors, as such errors can destroy superconvergence.     

Breakdown of a gold nanowire between electrodes

Deformation behavior of an atomic Au wire placed between Au electrodes was investigated by using a generalization of the method of linear muffin-tin orbitals (LMTO) within the local-density approximation (LDA). We studied the dynamical motion of the atoms in the wire. Soft phonon modes were studied. It has been found that collective motions are dominated by motions perpendicular to the wire axis. Large displacements which resulted in wire breakage were also studied. The energy barrier associated with this process has been calculated.     

Correcting the diffusion approximation at the boundary

The diffusion approximation to the radiative transport equation applies for light that has propagated deeply into an optically thick medium, such as biological tissue. It does not accurately model light near boundaries where measurements of scattered light are often taken. Here, we compute a correction to the diffusion approximation at the boundary. This correction requires only small modifications to the standard diffusion approximation used in biomedical optics. In particular, one needs only to compute the coefficients in the boundary condition for the diffusion approximation and an additive correction. We give explicit procedures for these computations. Using numerical results for the steady-state plane-parallel slab problem, we show that this corrected diffusion approximation is a much better approximation than the standard diffusion approximation for modeling the reflectance and transmittance.     

Experimental study of the flow behaviour of superplasticized cement paste

The properties of high performance concrete, mainly in the fresh state are governed by the flow behaviour of the paste phase, which is controlled by the dispersion of cement particles by the superplasticizer. In this paper, experimental procedures for evaluating the flow behaviour of cement paste with different types and dosages of superplasticizers are studied. The rheological nature of the paste is represented through the Bingham and Herschel-Bulkley models. It is observed that the Marsh cone flow time, mini-slump spread and the rheological parameters show the same trend with change in dosage of superplasticizer. Also, the rheological parameters increase with time and rate of increase is more significant at dosages less than the saturation dosage, as determined from the Marsh cone test. It is confirmed that the Marsh cone flow time can be predicted using an appropriate model.     

Mathematical models of the VEGF receptor and its role in cancer therapy

We present an analysis of a stochastic model of the vascular endothelial growth factor (VEGF) receptor. This analysis addresses the contribution of ligand-binding-induced oligomerization, activation of src-homology 2 domain-carrying kinases and receptor internalization in the overall behaviour of the VEGF/VEGF receptor (VEGFR) system. The analysis is based upon a generalization of a Wentzel-Kramers-Brillouin (WKB) approximation of the solution of the corresponding master equation. We predict that tumour-mediated overexpression of VEGFRs in the endothelial cells (ECs) of tumour-engulfed vessels leads to an increased sensitivity of the ECs to low concentrations of VEGF, thus endowing the tumour with increased resistance to anti-angiogenic treatment.     

Theory of the universal and nonuniversal quantities of fluids at the critical point

We show that the hierarchical reference theory is an accurate global theory of fluids at least above the critical temperatureT _c. The hierarchy is truncated at the first equation, the one connecting the free energy to the pair correlation function, with an Ornstein-Zernike ansatz. In this approximation the theory can be considered as a sophisticated generalization of the optimized random phase approximation which has genuine nonclassical critical exponents and for which scaling is satisfied. We study the system of hard spheres plus the Lennard-Jones attractive well and find a good agreement with measuredPVT, specific heat, correlation length, and structure factor in rare gases. The accuracy of the theory remains very good up to freezing density.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Wave analysis by Slepian models

Ocean waves exhibit more or less a Gaussian distribution for the instantaneous water surface height, and there is a need to develop simple models for generation of the characteristic non-Gaussian statistics, namely the asymmetric distributions of water surface height and wave slope. We argue that a simple class of non-linear oscillators can reproduce some of the characteristic features of random water wave processes and linear or non-linear response to ocean waves. We describe the Slepian model for the Gaussian case, and explain the use of the regression approximation for level crossing distances and associated variables, such as wave period and amplitude. Finally we speculate about a generalization of the regression technique to the non-linear Markov process case.     

Convex approximation to the likelihood criterion for aperture synthesis imaging

Aperture synthesis allows one to measure visibilities at very high resolutions by coupling telescopes of reasonable diameters. We consider the case where visibility amplitudes and phase are measured separately. It leads to an estimation problem where the noise model yields a nonconvex data-likelihood criterion. We show how to optimally approximate the noise model while keeping the criterion convex. This approximation has been validated both on simulations and on experimental data.     

Temporal autocorrelation function for a diffusing-wave spectroscopy experiment with a point source and backscattering detection

The autocorrelation function of the backscattered intensity in a diffusing-wave spectroscopy experiment that uses a point source is calculated by use of the diffusive-wave model. We show that in this approximation the calculated autocorrelation function decays faster than if the plane-source approximation were used. The design of a probe that implements this geometry is presented together with preliminary results that show the utility of the probe as a sizing tool in concentrated dispersions.     

连续排水边界条件下土体一维流变固结解析解

基于四元件流变模型,通过引入连续排水边界条件研究了单级加载下的土体一维流变固结问题。利用分离变量法和Laplace变换技术得到瞬时荷载下的解析解,进而通过积分的方法得到单级加载下的解析解。随后对排水边界和流变模型进行了退化,得到Terzaghi边界下及三元件流变模型下的一维流变固结解答,通过与现有解答对比初步验证了该文解答的正确性。最后,对不同界面参数、流变参数以及加载速率对土体固结特性的影响进行了分析。结果表明:基于连续排水边界得到的固结解答与基于Terzaghi双面排水得到的固结解答的差异主要在固结前期,且两者的差异随界面参数α、β取值变大而减小。流变固结与线弹性固结差异主要在固结后期,流变固结需要更长时间土体才能完全固结。此外,土体固结速率随加载速率增大而增大。     

Iterative boundary method for diffuse optical tomography

The recent application of tomographic methods to three-dimensional imaging through tissue by use of light often requires modeling of geometrically complex diffuse-nondiffuse boundaries at the tissue-air interface. We have recently investigated analytical methods to model complex boundaries by means of the Kirchhoff approximation. We generalize this approach using an analytical approximation, the N-order diffuse-reflection boundary method, which considers higher orders of interaction between surface elements in an iterative manner. We present the general performance of the method and demonstrate that it can improve the accuracy in modeling complex boundaries compared with the Kirchhoff approximation in the cases of small diffuse volumes or low absorption. Our observations are also contrasted with exact solutions. We furthermore investigate optimal implementation parameters and show that a second-order approximation is appropriate for most in vivo investigations.