线性矩阵方程的埃尔米特广义反汉密尔顿半正定解

利用埃尔米特广义反汉密尔顿半正定矩阵的表示定理,作者建立了线性矩阵方程在埃尔米特广义反汉密尔顿半正定矩阵集合中可解的充分必要条件,得到了解的一般表达式.对于逆特征值问题,也得到了可解的充分必要条件.对于任意一个 n 阶复矩阵,得到了相关最佳逼近问题解的表达式.     

The Method of Fundamental Solution for a Radially Symmetric Heat Conduction Problem with Variable Coefficient

We consider an inverse heat conduction problem with variable coefficient on an annulus domain. In many practice applications, we cannot know the initial temperature during heat process, therefore we consider a non-characteristic Cauchy problem for the heat equation. The method of fundamental solutions is applied to solve this problem. Due to ill-posedness of this problem, we first discretize the problem and then regularize it in the form of discrete equation. Numerical tests are conducted for showing the effectiveness of the proposed method.     

Modal Model Identification with Unknown Nonstationary Base Motion

Techniques developed for structural identification are typically devoted to obtaining a model, parametrical or not, on the basis of information on the structural response and on the forcing action, both assumed as known from experimental tests. In many situations, however, it may be necessary, or simply useful, to refer only to the measured response. In this paper we describe the theoretical aspects of a technique we have recently developed to identify the modal model in the frequency domain when the input is unknown. To simplify, we refer to unknown nonstationary base motion, but many of our conclusions can be extended to different situations. We show that, from a theoretical point of view, the identification problem has a unique solution, for this kind of input, when at least three time histories are known, and this circumstance had never been pointed out before. Because the theoretical analysis furnishes only necessary conditions for the existence of a unique solution, an extensive numerical analysis is reported in the second part of the paper, which also shows the sensitivity of the identification procedure.     

Direct determination of the concentration dependence of diffusivities using combined model-based Raman and NMR experiments

Diffusion in liquids can still be predicted only with high uncertainty due to a lack of sufficient experimental data. Diffusion experiments are complex and time-consuming. Furthermore, the determination of the concentration dependence of the diffusion coefficients requires usually several experiments even for binary mixtures. A powerful model identification framework based on two fast experimental techniques is presented here. Raman inter-diffusion experiments in combination with a novel incremental identification technique establish the concentration dependence directly from the data without requiring a priori specification of the model structure. In regions where this technique is sensitive to error noise, it is complemented with NMR intra-diffusion measurements. Models describing the concentration dependence are identified in two steps. Based on the combined data suitable model candidates are proposed and initialized through basic curve fitting in the first identification step. A statistically sound dynamic optimization step yields the final model parameters. The methodology is exemplarily used to determine the diffusion coefficient in the mixture ethyl acetate–cyclohexane in the full concentration space.     

Notes on Groundwater Age in Forward and Inverse Modeling

Several example applications of the groundwater age equation are used to derive some basic results about age in aquifers and to draw linkages among published results involving temporal moments and aquifer–aquitard diffusive mass transfer. We then describe a brief numerical study of an inverse problem in which hydraulic conductivities are identified using both piezometric head and groundwater age data where inclusion of age data helps to reduce evidential nonuniqueness. This reflects the global representation of flow process contained in age data, and that the value of age data in inverse identification of flow properties depends on the paths taken by the sampled groundwater. Paper presented at PORO2007, the 7th North American Workshop on Applications of the Physics of Porous Media, Puerto Vallarta, Mexico, 2–6 November, 2007.     

Aerodynamic characteristics of a two-dimensional supersonic biplane, covering its take-off to cruise conditions

Supersonic biplanes can possibly achieve low-boom and low-drag supersonic flights. In the present study, aerodynamic analysis and design of two-dimensional (2-D) biplanes were investigated with the help of computational fluid dynamics (CFD) tools. By utilizing an inverse-design method, a 2-D biplane configuration with lower wave drag than the single flat-plate airfoil at sufficient lift conditions (C _l > 0.14) was designed at its design Mach number (M _∞ = 1.7). In general, although, supersonic biplanes show superior aerodynamic characteristics at their design Mach numbers, unfortunately, they are characterized by poor performances under their off-design conditions. Flow choking occurs at high subsonic speeds, and continues to Mach numbers greater than the design Mach number in the acceleration stage due to flow hysteresis. Hinged slats and flaps were applied as high-lift devices to avoid the flow choking and concomitant hysteresis problems, and were also used as actual high-lift devices under take-off and landing conditions. As further improvement, morphing and Fowler motion were considered. Finally, a series of 2-D biplane configurations from take-off (and landing) to cruise conditions were studied by applying the slats and flaps, as well as morphing mechanisms, to our inversely designed biplane.      

Mechanical Characterization of Biological Membranes with Moiré Techniques and Multi-Point Simulated Annealing

This paper describes an hybrid procedure for mechanical characterization of biological membranes. The in-plane displacement field of a glutaraldehyde treated bovine pericardium patch obtained with an equi-biaxial tension test is measured with intrinsic moiré and then compared with finite element predictions. Preliminary analysis of moiré patterns observed in the experiments justifies the assumption of the constitutive model based on transversely isotropic hyperelasticity. In order to determine the 16 hyperelastic constants included in the constitutive model and the fiber orientation, the difference Ω between displacement values measured with moiré and their counterpart determined numerically is minimized by means of multi-level and multi-point simulated annealing. Results clearly demonstrate the efficiency of the identification procedure presented in this research: in fact, residual difference between experimental data and numerical values of in-plane displacements is less than 2%. In order to validate the entire identification process, another experimental test is conducted by inflating the same specimen. Out-of-plane displacements, now measured with projection moiré, are compared with predictions of a new finite element model reproducing the experimental test. The 16 hyper-elastic constants previously determined are given in input to the inflation test FE model. Remarkably, experimental and numerical results are again in excellent agreement: maximum percent error on w-displacement is less than 3%.     

Stress Reconstruction and Constitutive Parameter Identification in Plane-Stress Elasto-plastic Problems Using Surface Measurements of Deformation Fields

This paper deals with the identification of elasto-plastic constitutive parameters from deformation fields measured over the surface of thin flat specimens with the grid method. The approach for recovering the constitutive parameters is the virtual fields method. A dedicated algorithm is used for deriving the distribution of the 2D stress components from the measured deformation fields. A state of plane stress is assumed. Guesses of the constitutive parameters are input in the algorithm and updated until the stresses satisfy the principle of virtual work in the least squares sense. The advantage of this approach is that it can handle very heterogeneous plastic flows and it is much faster than classical finite element model updating approaches. An experimental application is provided to demonstrate it. Six mild steel double-notched specimens have been tested in a configuration combining tension and in-plane bending. The identified parameters are in good agreement with their reference counterparts. Stress fields are eventually reconstructed across the specimen all along the test for analyzing the evolution of the plastic flow.     

抑制HMQC实验中与碳-12相连质子的信号

建议了一个新的HMQC实验的脉冲序列,其准备期和混合期分别为90°_x(¹H)-τ/2-180°^x(¹H,¹³C)-τ/2-90°_x(¹H,¹³C)和90°_x(¹³C)-τ/2-180°_x(¹H,¹³C)-τ/2-,以及τ=(2J_CH)^-1(J_CH为C-H偶合常数).在这个新的HMQC实验中,与碳-12相连质子的信号被有效地抑制,其抑制的机理与脉冲的相位循环无关.从而,它可以用于有效地抑制HMQC谱的噪音.特别是,在没有脉冲梯度场装置时,该方法显得非常实用     

Diagnostics of the medium structure by long wave of finite amplitude

The averaged systems of hydrodynamic equations for a structured medium in the Lagrangian and the Eulerian coordinates are discussed. In the general case, the equations cannot be reduced to the average hydrodynamic terms. Under propagation of long waves in media with structure, the non-linear effects appear and they are analyzed in the framework of the asymptotic averaged model. The heterogeneity in a medium structure always increases the non-linear effects for the long-wave perturbations. A new method for diagnostics of the properties of medium components by long non-linear waves is suggested (inverse problem). The mass contents of components in the media can be determined by this diagnostic method.