Effective response of a non-linear composite in external AC electric field

A general effective response is proposed for nonlinear composite media, which obey a current field relation of the form J = sigmaE + chi\E\(2) E when an external alternating current (AC) electrical field is applied. For a sinusoidal applied field with finite frequency omega, the effective constitutive relation between the current density and electric field can be defined as, = sigma(e) + chi(e) <\E(x, omega, t)\(2) E(x, omega, t)> + (. . .), where sigma(e) and chi(e) are the general effective linear and nonlinear conductive responses, respectively. The angled brackets <(. . .)> denotes the ensemble average. As two examples, we have investigated the cylindrical and spherical inclusions embedded in a host and also derived the formulae of the general effective linear and nonlinear conductive responses in dilute limit. For higher volume fraction of inclusions, we have proposed a nonlinear effective medium approximation (EMA) method to estimate the general effective response of nonlinear composites in external AC field. Furthermore, the effective nonlinear responses at harmonics are predicted by using the general effective response. (C) 2002 Elsevier Science B.V. All rights reserved.

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV (Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.

Comparison of nonlinear and linear PCA on surface wind, surface height, and SST in the South China Sea

We compared nonlinear principal component analysis (NLPCA) with linear principal component analysis (LPCA) with the data of sea surface wind anomalies (SWA), surface height anomalies (SSHA), and sea surface temperature anomalies (SSTA), taken in the South China Sea (SCS) between 1993 and 2003. The SCS monthly data for SWA, SSHA and SSTA (i.e., the anomalies with climatological seasonal cycle removed) were pre-filtered by LPCA, with only three leading modes retained. The first three modes of SWA, SSHA, and SSTA of LPCA explained 86%, 71%, and 94% of the total variance in the original data, respectively. Thus, the three associated time coefficient functions (TCFs) were used as the input data for NLPCA network. The NLPCA was made based on feed-forward neural network models. Compared with classical linear PCA, the first NLPCA mode could explain more variance than linear PCA for the above data. The nonlinearity of SWA and SSHA were stronger in most areas of the SCS. The first mode of the NLPCA on the SWA and SSHA accounted for 67.26% of the variance versus 54.7%, and 60.24% versus 50.43%, respectively for the first LPCA mode. Conversely, the nonlinear SSTA, localized in the northern SCS and southern continental shelf region, resulted in little improvement in the explanation of the variance for the first NLPCA.

Study on system identification of linear and non-linear liquid chromatography separation

The paper proposes the identification method of linear and non-linear chromatographic system. The non-linear isotherms and lumped mass transfer coefficients of chromatography separating sorbitol and mannitol are determined. And the theoretical elution curves calculated by non-linear chromatographic model are more accurate than those calculated by linear chromatographic model.

Linear solvation energy relationships regarding sorption and retention properties of hydrophobic organic compounds in soil leaching column chromatography

The capacity factors of a series of hydrophobic organic compounds (HOCs) were measured in soil leaching column chromatography (SLCC) on a soil column, and in reversed-phase liquid chromatography on a C-18 column with different volumetric fractions (phi) of methanol in methanol-water mixtures. A general equation of linear solvation energy relationships, log(XYZ) = XYZ(0) + mV(1)/100 + spi* + bbeta(m) + aalpha(m), was applied to analyze capacity factors (k'), soil organic partition coefficients (K-oc) and octanol-water partition coefficients (P). The analyses exhibited high accuracy. The chief solute factors that control log K-oc, log P, and log k' (on soil and on C-18) are the solute size (V-1/100) and hydrogen-bond basicity (beta(m)). Less important solute factors are the dipolarity/polarizability (pi*) and hydrogen-bond acidity (alpha(m)). Log k' on soil and log K-oc have similar signs in four fitting coefficients (m, s, b and a) and similar ratios (m:s:b:a), while log k' on C-18 and log P have similar signs in coefficients (m, s, b and a) and similar ratios (m:s:b:a). Consequently, log k' values on C-18 have good correlations with log P (r > 0.97), while log k' values on soil have good correlations with log K-oc (r > 0.98). Two K-oc estimation methods were developed, one through solute solvatochromic parameters, and the other through correlations with k' on soil. For HOCs, a linear relationship between logarithmic capacity factor and methanol composition in methanol-water mixtures could also be derived in SLCC. (C) 2002 Elsevier Science Ltd. All rights reserved.

Recognition by Linear Combinations of Models

Visual object recognition requires the matching of an image with a set of models stored in memory. In this paper we propose an approach to recognition in which a 3-D object is represented by the linear combination of 2-D images of the object. If M = {M1,...Mk} is the set of pictures representing a given object, and P is the 2-D image of an object to be recognized, then P is considered an instance of M if P = Eki=aiMi for some constants ai. We show that this approach handles correctly rigid 3-D transformations of objects with sharp as well as smooth boundaries, and can also handle non-rigid transformations. The paper is divided into two parts. In the first part we show that the variety of views depicting the same object under different transformations can often be expressed as the linear combinations of a small number of views. In the second part we suggest how this linear combinatino property may be used in the recognition process.

Linear Object Classes and Image Synthesis from a Single Example Image

The need to generate new views of a 3D object from a single real image arises in several fields, including graphics and object recognition. While the traditional approach relies on the use of 3D models, we have recently introduced techniques that are applicable under restricted conditions but simpler. The approach exploits image transformations that are specific to the relevant object class and learnable from example views of other "prototypical" objects of the same class. In this paper, we introduce such a new technique by extending the notion of linear class first proposed by Poggio and Vetter. For linear object classes it is shown that linear transformations can be learned exactly from a basis set of 2D prototypical views. We demonstrate the approach on artificial objects and then show preliminary evidence that the technique can effectively "rotate" high- resolution face images from a single 2D view.

Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

Human plasma proteome analysis by multidimensional chromatography prefractionation and linear ion trap mass spectrometry identification

A resurgence of interest in the human plasma proteome has occurred in recent years because it holds great promise of revolution in disease diagnosis and therapeutic monitoring. As one of the most powerful separation techniques, multidimensional liquid chromatography has attracted extensive attention, but most published works have focused on the fractionation of tryptic peptides. In this study, proteins from human plasma were prefractionated by online sequential strong cation exchange chromatography and reversed-phase chromatography. The resulting 30 samples were individually digested by trypsin, and analyzed by capillary reversed-phase liquid chromatography coupled with linear ion trap mass spectrometry. After meeting stringent criteria, a total of 1292 distinct proteins were successfully identified in our work, among which, some proteins known to be present in serum in < 10 ng/mL were detected. Compared with other works in published literatures, this analysis offered a more full-scale list of the plasma proteome. Considering our strategy allows high throughput of protein identification in serum, the prefractionation of proteins before MS analysis is a simple and effective method to facilitate human plasma proteome research.

Characteristics of elution profile in radial chromatography under linear conditions

Based on the mass balance equations of solute transfer in the radial chromatographic column, the theoretical expression to describe the column efficiency and shape of elution profile is obtained under linear isotherm case. Moreover, the tendency for the variation of column efficiency and symmetry of peak profile is systematically discussed. The results showed that in radial chromatography the relationship between the column efficiency and volumetric flow rate is similar with that relationship in axial chromatography; relatively high column efficiency still can be obtained under high flow rate in radial chromatography. Accompanying the increase of retention factor of solutes and injection time, the column efficiency decreases monotonously. The effect of column diameter and column length on the column efficiency interfere with each other. It is more advantageous to increase the column efficiency by applying columns with larger column diameter and shorter column length. According to the discussion of the effect of diffusion on the column efficiency, radial chromatography is proved to be suitable for the separation of samples with relatively high diffusion coefficient, which predicts its obvious advantage in the preparative separation of samples such as proteins and DNA.