Slow peaking and low-gain designs for global stabilization of nonlinear systems

This paper presents an analysis of the slow-peaking phenomenon, a pitfall of low-gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems. The phenomenon is best understood on a chain of integrators perturbed by a vector field up(x, u) that satisfies p(x, 0) = 0. Because small controls (or low-gain designs) are sufficient to stabilize the unperturbed chain of integrators, it may seem that smaller controls, which attenuate the perturbation up(x, u) in a large compact set, can be employed to achieve larger regions of attraction. This intuition is false, however, and peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p(x, u). These growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system. When this higher order condition is satisfied, an explicit control law is derived that achieves global asymptotic stability of x = 0. This stabilization result is extended to more general cascade nonlinear systems in which the perturbation p(x, v) v, v = (ξ, u) T, contains the state ξ and the control u of a stabilizable subsystem ξ = a(ξ, u). As an illustration, a control law is derived that achieves global stabilization of the frictionless ball-and-beam model.

Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria

This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since - after establishing the invariance of observability under output injection - this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.

An analysis of competing toughening mechanisms in layered and particulate solids

The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus 90 ° symmetric kinking is considered for an isotropic, homogeneous solid with weak interfaces. Each interface is treated as a cohesive zone of finite strength and toughness. Third, the degree of toughening associated with crack multiplication is assessed for a particulate solid comprising isotropic elastic grains of hexagonal shape, bonded by cohesive zones of finite strength and toughness. The study concludes with the prediction of R-curves for a mode I crack in a multi-layer stack of elastic and elastic-plastic solids. A detailed comparison of the potency of the above mechanisms and their practical application are given. In broad terms, crack tip kinking can be highly potent, whereas multiple cracking is difficult to activate under quasi-static conditions. Plastic dissipation can give a significant toughening in multi-layers especially at the nanoscale. © 2013 Springer Science+Business Media Dordrecht.

Nonylphenol, bisphenol-A and DDTs in Lake Donghu, China

A preliminary survey was carried out in April 2003 to estimate the levels of nonylphenol (NP), bisphenol-A (BPA) and residual DDTs in Lake Donghu. After then, the sediments of some areas of the lake were moved out for clearing the lake by the local government. Therefore, the variance of NP and BPA after the clearance of sediment in the surface water was determined from December 2003 to May 2004. Sediments, surface water and fish were collected from four sub-lake areas and the analytes were qualified by GC/MS in SIM mode after concentration onto an Oasis solid phase extraction cartridge. NP and BPA values ranged between 5.46-119.10 and 0.9913.42 mg/kg dw, respectively, in sediments, 75.2-179.6 and 15.1-62.5 mu g/L in surface water. Meanwhile, the bioaccumulation factors (BCFs) of NP and BPA were calculated in fish livers. Plasma vitellogenin (VTG), a sensitive biomarker showing oestrogenicity was detected in the captured male Wuchang bream (Megalobrama amblycephala Yih) and common carp (Cyprinus carpio). After sediment clearance, the concentrations of NP and BPA decreased to 0.65-25.04 and 0.04-21.32 mu g/L. The results indicate the presence of high-dose xenoestrogenic NP and BPA, probably major contributors which associate with VTG induction in Lake Donghu male fish.

Interband and intraband photocurrent of self-assembled InAs/InAlAs/InP nanostructures

The interband and intraband photocurrent properties of InAs/InAlAs/InP nanostructures have been studied. The doping effect on the photoluminescence properties of the quantum dots and the anisotropy of the quantum wire interband photocurrent properties are presented and discussed. With the help of interband excitation, an intraband photocurrent signal of the InAs nanostructures is observed. With the increase of the interband excitation power, the intraband photocurrent signal first increases and then decreases, which can be explained by the variance of the ground state occupation of the InAs nanostructures and the change of the mobility and lifetime of the electrons. The temperature dependence of the intraband photocurrent signal of the InAs nanostructures is also investigated.

The enhancement of diffusion by strain of InAs quantum dots in a GaAs matrix

We investigate the annealing behavior of Photoluminescence (PL) from self-assembled InAs quantum dots (QDs) with different thicknesses GaAs cap layers. The diffusion introduced by annealing treatment results in a blue-shift of the QD PL peak, and a decrease in the integrated intensity. The strain present in QDs enhances the diffusion, and the QDs with the cap layers of different thicknesses will experience a strain of different strength. This can lend to a, better understanding of the larger blue-shift of the PL peak of the deeper buried QDs, and the different variance of the full width at half maximum of the luminescence from QDs with the cap layers of different thicknesses.

Characterization and analysis of two-dimensional GaAs-based photonic crystal nanocavities at room temperature

This paper describes the design and fabrication process of a two-dimensional GaAs-based photonic crystal nanocavity and analyzes the optical characterization of cavity modes at room temperature. Single InAs/InGaAs quantum dots (QDs) layer was embedded in a GaAs waveguide layer grown on an Al0.7Ga0.3As layer and GaAs substrate. The patterning of the structure and the membrane release were achieved by using electron-beam lithography, reaction ion etching, inductively coupled plasma etching and selective wet etching. The micro-luminescence spectrum is recorded from the fabricated nanocavities, and it is found that some high-order cavity modes are clearly observed besides the lowest-order resonant mode is exhibited in spite of much high rate of nonradiative recombination. The variance of resonant modes is also discussed as a function of r/a ratio and will be used in techniques aimed to improve the probability of achieving spectral coupling of a single QD to a cavity mode.

The enhancement of diffusion by strain of InAs quantum dots in a GaAs matrix

We investigate the annealing behavior of Photoluminescence (PL) from self-assembled InAs quantum dots (QDs) with different thicknesses GaAs cap layers. The diffusion introduced by annealing treatment results in a blue-shift of the QD PL peak, and a decrease in the integrated intensity. The strain present in QDs enhances the diffusion, and the QDs with the cap layers of different thicknesses will experience a strain of different strength. This can lend to a, better understanding of the larger blue-shift of the PL peak of the deeper buried QDs, and the different variance of the full width at half maximum of the luminescence from QDs with the cap layers of different thicknesses.

Fabrication and luminescence characterization of two-dimensional GaAs-based photonic crystal nanocavities

This paper describes the design and fabrication process of a two-dimensional GaAs-based photonic crystal nanocavity with InAs quantum dots (QDs) emitters and analyzes the optical characteristics of cavity modes at room temperature. The micro-luminescence spectrum recorded from the nanocavities exhibits a narrow optical transition at the lowest order resonance wavelength of about 1137 nm with about 1 nm emission linewidth. In addition, the spectra of photonic crystal nanocavities processed under different etching conditions show that the verticality of air hole sidewall is an important factor determing the luminescence characteristics of photonic crystal nanocaivties. Finally,,the variance of resonant modes is also discussed as a function of r/a ratio and will be used in techniques aimed at improving the probability of achieving spectral coupling of a single QD to a cavity mode.

Thermocapillary migrations of drops and bubbles

The transport phenomenon of drops or bubbles is a very important topic in fundamental hydrodynamics research and practical applications such as material processing and the chemical engineering. In microgravity environment, if drops or bubbles stay in a continuous phase with non-uniform temperature ¯eld, they will start to move as a result of the variance of the interface tension. This kind of movement is called the Marangoni migration. This review tries to sum up the main results in this ¯eld on theoretical analysis, numerical simulations and experiments. So far the theoretical analysis is still limited to the linear or weak nonlinear steady questions, while the current numerical simulations can already obtain the time- dependent process of the bubble/drop migration when the e®ect of heat convection is small. For strong heat convection problem, or when the Marangoni number is bigger than 100, no numerical result is in consistence with those of experiments so far. Some of the lastest numerical results are shown when heat convection is strong, and the main di®erence between strong and weak heat convection is analyzed. Finally, we also discuss the main unresolved problems in this ¯eld and some possible directions in the future.

Period-doubling bifurcations of the thermocapillary convection in a floating half zone

This study experimentally explored the fine structures of the successive period-doubling bifurcations of the time-dependent thermocapillary convection in a floating half zone of 10 cSt silicone oil with the diameter d (0)=3.00 mm and the aspect ratio A=l/d (0)=0.72 in terrestrial conditions. The onset of time-dependent thermocapillary convection predominated in this experimental configuration and its subsequent evolution were experimentally detected through the local temperature measurements. The experimental results revealed a sequence of period-doubling bifurcations of the time-dependent thermocapillary convection, similar in some way to one of the routes to chaos for buoyant natural convection. The critical frequencies and the corresponding fractal frequencies were extracted through the real-time analysis of the frequency spectra by Fast-Fourier-Transformation (FFT). The projections of the trajectory onto the reconstructed phase-space were also provided. Furthermore, the experimentally predicted Feigenbaum constants were quite close to the theoretical asymptotic value of 4.669 [Feigenbaum M J. Phys Lett A, 1979, 74: 375-378].

Isocaling and the symmetry energy in the multifragmentation regime of heavy-ion collisions

The ratio of the symmetry energy coefficient to temperature, a(sym)/T, in Fermi energy heavy-ion collisions, was experimentally extracted as a function of the fragment atomic number using isoscaling parameters and the variance of the isotope distributions. The extracted values were compared to the results of calculations made with an antisymmetrized molecular dynamics (AMD) model employing a statistical decay code to account for deexcitation of excited primary fragments. The experimental values are in good agreement with the values calculated from the final ground-state products but are significantly different from those characterizing the yields of the primary AMD fragments.

Comparison of steroid substrates and inhibitors of P-glycoprotein by 3D-QSAR analysis

Steroid derivatives show a complex interaction with P-glycoprotein (Pgp). To determine the essential structural requirements of a series of structurally related and functionally diverse steroids for Pgp-mediated transport or inhibition, a three-dimensional quantitative structure activity relationship study was performed by comparative similarity index analysis modeling. Twelve models have been explored to well correlate the physiochemical features with their biological functions with Pgp on basis of substrate and inhibitor datasets, in which the best predictive model for substrate gave cross-validated q(2) = 0.720, non-cross-validated r(2) = 0.998, standard error of estimate SEE = 0.012, F = 257.955, and the best predictive model for inhibitor gave q(2) = 0.536, r(2) = 0.950, SEE = 1.761 and F = 45.800. The predictive ability of all models was validated by a set of compounds that were not included in the training set. The physiochemical similarities and differences of steroids as Pgp substrate and inhibitor, respectively, were analyzed to be helpful in developing new steroid-like compounds. (C) 2004 Elsevier B.V. All rights reserved.

The effects of sediment transport on grain-size distributions

Changes in statistics (mean, sorting, and skewness) describing grain-size distributions have long been used to speculate on the direction of sediment transport. We present a simple model whereby the distributions of sediment in transport are related to their source by a sediment transfer function which defines the relative probability that a grain within each particular class interval will be eroded and transported. A variety of empirically derived transfer functions exhibit negatively skewed distributions (on a phi scale). Thus, when a sediment is being eroded, the probability of any grain going into transport increases with diminishing grain size throughout more than half of its size range. This causes the sediment in transport to be finer and more negatively skewed than its source, whereas the remaining sediment (a lag) must become relatively coarser and more positively skewed. Flume experiments show that the distributions of transfer functions change from having a highly negative skewness to being nearly symmetrical (although still negatively skewed) as the energy of the transporting process increases. We call the two extremes low-energy and high-energy transfer functions , respectively. In an expanded sediment-transport model, successive deposits in the direction of transport are related by a combination of two transfer functions. If energy is decreasing and the transfer functions have low-energy distributions, successive deposits will become finer and more negatively skewed. If, however, energy is decreasing, but the initial transfer function has a high-energy distribution, successive deposits will become coarser and more positively skewed. The variance of the distributions of lags, sediment in transport, and successive deposits in the down-current direction must eventually decrease (i.e., the sediments will become better sorted). We demonstrate that it is possible for variance first to increase, but suggest that, in reality, an increasing variance in the direction of transport will seldom be observed, particularly when grain-size distributions are described in phi units. This model describing changes in sediment distributions was tested in a variety of environments where the transport direction was known. The results indicate that the model has real-world validity and can provide a method to predict the directions of sediment transport

Energy landscape theory, funnels, specificity, and optimal criterion of biomolecular binding

We study the nature of biomolecular binding. We found that in general there exists several thermodynamic phases: a native binding phase, a non-native phase, and a glass or local trapping phase. The quantitative optimal criterion for the binding specificity is found to be the maximization of the ratio of the binding transition temperature versus the trapping transition temperature, or equivalently the ratio of the energy gap of binding between the native state and the average non-native states versus the dispersion or variance of the non-native states. This leads to a funneled binding energy landscape.