929 resultados para Lyapunov Exponent


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This article focusses on the two libel cases arising from Brian Penton's review of Vivian Crockett's novel Mezzomorto for the Bulletin in 1934, viewing them as points of entry into Australian literary politics in the 1930s, and as windows on to one of the most enduring and interesting feuds in Australian literary culture, that between P.R. 'Inky' Stephensen, self-styled 'Bunyip Critic,' and Brian Penton, arch exponent of 'destructive criticism' and scourge of parochial pretension. The cases are particularly interesting for what they reveal about the evolving positions of two influential figures in Australian writing of the 1930s and 1940s. They also play in to contemporary debates about the state and status of 'literature' in Australia. And while Penton's biographer Patrick Buckridge avers that the cases did not impact on any of the larger contemporary literary issues (meaning censorship and free speech), a case may be made for the significance of the libel actions in the context of attempts to establish an industrial and cultural presence for a diverse range of Australian writing.

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This paper presents a trajectory-tracking control strategy for a class of mechanical systems in Hamiltonian form. The class is characterised by a simplectic interconnection arising from the use of generalised coordinates and full actuation. The tracking error dynamic is modelled as a port-Hamiltonian Systems (PHS). The control action is designed to take the error dynamics into a desired closed-loop PHS characterised by a constant mass matrix and a potential energy with a minimum at the origin. A transformation of the momentum and a feedback control is exploited to obtain a constant generalised mass matrix in closed loop. The stability of the close-loop system is shown using the close-loop Hamiltonian as a Lyapunov function. The paper also considers the addition of integral action to design a robust controller that ensures tracking in spite of disturbances. As a case study, the proposed control design methodology is applied to a fully actuated robotic manipulator.

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The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K(q)K(q) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter HH from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h(2)h(2) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K(2)K(2) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

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Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal properties of their converted horizontal visibility graphs (HVGs). The energy parameters of protein dynamics we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. The shape of the h(q)h(q) curves from MF-DFA indicates that these time series are multifractal. The numerical values of the exponent h(2)h(2) of MF-DFA show that the series of total energy and potential energy are non-stationary and anti-persistent; the other time series are stationary and persistent apart from series of pressure (with H≈0.5H≈0.5 indicating the absence of long-range correlation). The degree distributions of their converted HVGs show that these networks are exponential. The results of fractal analysis show that fractality exists in these converted HVGs. For each energy, pressure or volume parameter, it is found that the values of h(2)h(2) of MF-DFA on the time series, exponent λλ of the exponential degree distribution and fractal dimension dBdB of their converted HVGs do not change much for different proteins (indicating some universality). We also found that after taking average over all proteins, there is a linear relationship between 〈h(2)〉〈h(2)〉 (from MF-DFA on time series) and 〈dB〉〈dB〉 of the converted HVGs for different energy, pressure and volume.

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Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

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Lithium silicophosphate glasses have been prepared by a sol-gel route over a wide range of compositions. Their structural and electrical properties have been investigated. Infrared spectroscopic studies show the presence of hydroxyl groups attached to Si and P. MAS NMR investigations provide evidence for the presence of different phosphatic units in the structure. The variations of de conductivities at 423 K and activation energies have been studied as a function of composition, and both exhibit an increasing trend with the ratio of nonbridging oxygen to bridging oxygen in the structure. Ac conductivity behavior shows that the power law exponent, s, is temperature dependent and exhibits a minimum. Relaxation behavior has been examined in detail using an electrical modulus formalism, and modulus data were fitted to Kohlraush-William-Watts stretched exponential function. A structural model has been proposed and the unusual properties exhibited by this unique system of glasses have been rationalized using this model. Ion transport in these glasses appears to be confined to unidimensional conduits defined by modified phosphate chains and interspersed with unmodified silica units.

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Pinning by second phase particles offers a potent means for limiting grain growth and enhancing superplasticity in alumina-based ceramics. In the present study, a colloidal technique was used to produce green bodies of alumina-yttria composites; at elevated temperatures, the yttria particles react with alumina to produce YAG particles. The densification and high temperature deformation characteristics of alumina-YAG composites were studied using conventional free sintering and sinter-forging, which involves the application of a compressive stress without any lateral constraints. It is shown that the YAG particles retard both densification and grain growth. The experiments indicate also that the presence of YAG particles does not significantly alter the stress exponent for creep deformation.

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Isotope-shift exponent (cu) and the pressure coefficient of superconducting transition temperature (beta) have been studied in the nonadiabatic limit. We have considered the effect of nonadiabaticity in both within and beyond the Migdal-Eliashberg formalism. It reveals from our study that the pressure coefficient of superconducting transition is high for the low-T-c region and low for the high-T-c region and the minimum value of alpha is obtained where the transition temperature is maximum. Lowest value of isotope-shift exponent is obtained for small momentum exchange between the electrons and the bosonic field. Qualitative variation of beta with temperature is consistent with the experimental results of the hole doped superconductors for small momentum exchange.

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A detailed study was undertaken to characterize the deformation behavior of a superplastic 3 mol% yttria-stabilized tetragonal zirconia (3YTZ) over a wide range of strain rates, temperatures and grain sizes. The experimental data were analyzed in terms of the following equation for high temperature deformation: Image Full-size image ∞ σn d−pexp(−Q/RT), where Image Full-size image is the strain rate, σ is the flow stress, d is the grain size, Q is the activation energy, R is the gas constant, T is the absolute temperature, and n and p are constants termed the stress exponent and the inverse grain size exponent, respectively. The experimental data over a wide range of stresses revealed a transition in stress exponent. Deformation in the low and high stress regions was associated with n not, vert, similar 3 and p not, vert, similar 1, and n not, vert, similar 2 and p not, vert, similar 3, respectively. The transition stress between the two regions decreased with increasing grain size. The activation energy was similar for both regions with a value of not, vert, similar 550 kJ mol−1. Microstructural measurements revealed that grains remained essentially equiaxed after the accumulation of large strains, and very limited concurrent grain growths occurred in most experiments. Assessment of possible rate controlling creep mechanisms and comparison with previous studied indicate that in the n not, vert, similar 2 region, deformation occurs by a grain boundary sliding process whose rate is independent of impurity content. Deformation in the n not, vert, similar 3 region is controlled by an interface reaction that is highly sensitive to impurity content. It is concluded that an increase in impurity content increases yttrium segregation to grain boundaries, which enhances the rate of the interface reaction, thereby decreasing the apparent transition stress between the n not, vert, similar 2 and n not, vert, similar 3 regions. This unified approach incorporating two sequential mechanisms can rationalize many of the apparently dissimilar results that have been reported previously for deformation of 3YTZ.

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In contrast to metallic alloys, the mechanical characteristics of superplastic ceramics are very sensitive to minor changes in levels of trace impurities. In the present study, the mechanical behavior of a 2 mol% yttria stabilized tetragonal zirconia was studied in tension and compression in two batches of material, with small variations in levels of trace impurities, to examine the influence of stress axis and impurity content on the deformation behavior. The mechanical properties of the material were characterized in terms of the expression: (epsilon)over dot proportional to sigma(n) where (epsilon)over dot is the strain rate, sigma is the stress and n is termed the stress exponent. The mechanical behavior of the ceramic was identical in tension and compression, for a material with a given level of impurity. The high purity specimens exhibited a transition from a stress exponent of similar to 3 to similar to 2 with an increase in stress, whereas the low purity material displayed only n similar to 2 behavior over the entire stress range studied. Detailed high resolution and analytical electron microscopy studies revealed that there was no amorphous phase at interfaces in both batches of material; however, segregation of Al at interfaces was detected only in the low purity material. The observed transition in stress exponents can be rationalized in terms of two sequential mechanisms: grain boundary sliding with n similar to 2 and interface reaction controlled grain boundary sliding with n similar to 3. The transition from n similar to 3 to similar to 2 occurred at lower stresses with an increase in the grain size and a decrease in the purity level.

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Detailed molecular dynamics simulations of Lennard-Jones ellipsoids have been carried out to investigate the emergence of criticality in the single-particle orientational relaxation near the isotropic-nematic (IN) phase transition. The simulations show a sudden appearance of a power-law behavior in the decay of the second-rank orientational relaxation as the IN transition is approached. The simulated value of the power-law exponent is 0.56, which is larger than the mean-field value (0.5) but less than the observed value (0.63) and may be due to the finite size of the simulated system. The decay of the first-rank orientational time correlation function, on the other hand, is nearly exponential but its decay becomes very slow near the isotropic-nematic transition, The zero-frequency rotational friction, calculated from the simulated angular Velocity correlation function, shows a marked increase near the IN transition.

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The near-critical behavior of the susceptibility deduced from light-scattering measurements in a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide has been determined. The measurements have been performed in the one-phase region near the lower consolute points of samples with different concentrations of sodium bromide. A crossover from Ising asymptotic behavior to mean-field behavior has been observed. As the concentration of sodium bromide increases, the crossover becomes more pronounced, and the crossover temperature shifts closer to the critical temperature. The data are well described by a model that contains two independent crossover parameters. The crossover of the susceptibility critical exponent γ from its Ising value γ=1.24 to the mean-field value γ=1 is sharp and nonmonotonic. We conclude that there exists an additional length scale in the system due to the presence of the electrolyte which competes with the correlation length of the concentration fluctuations. An analogy with crossover phenomena in polymer solutions and a possible connection with multicritical phenomena is discussed.

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We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as t/tau, where tau is the characteristic timescale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects (n) in the final state is not necessarily given by the Kibble-Zurek scaling form n similar to 1/tau(d nu)/((z nu+1)), where d is the spatial dimension, and. and z are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by n similar to 1/(tau d/(2z2)), where the exponent z(2) determines the behavior of the off-diagonal term of the 2 x 2 Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point.

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The present work focuses on simulation of nonlinear mechanical behaviors of adhesively bonded DLS (double lap shear) joints for variable extension rates and temperatures using the implicit ABAQUS solver. Load-displacement curves of DLS joints at nine combinations of extension rates and environmental temperatures are initially obtained by conducting tensile tests in a UTM. The joint specimens are made from dual phase (DP) steel coupons bonded with a rubber-toughened adhesive. It is shown that the shell-solid model of a DLS joint, in which substrates are modeled with shell elements and adhesive with solid elements, can effectively predict the mechanical behavior of the joint. Exponent Drucker-Prager or Von Mises yield criterion together with nonlinear isotropic hardening is used for the simulation of DLS joint tests. It has been found that at a low temperature (-20 degrees C), both Von Mises and exponent Drucker-Prager criteria give close prediction of experimental load-extension curves. However. at a high temperature (82 degrees C), Von Mises condition tends to yield a perceptibly softer joint behavior, while the corresponding response obtained using exponent Drucker-Prager criterion is much closer to the experimental load-displacement curve.

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This paper presents an off-line (finite time interval) and on-line learning direct adaptive neural controller for an unstable helicopter. The neural controller is designed to track pitch rate command signal generated using the reference model. A helicopter having a soft inplane four-bladed hingeless main rotor and a four-bladed tail rotor with conventional mechanical controls is used for the simulation studies. For the simulation study, a linearized helicopter model at different straight and level flight conditions is considered. A neural network with a linear filter architecture trained using backpropagation through time is used to approximate the control law. The controller network parameters are adapted using updated rules Lyapunov synthesis. The off-line trained (for finite time interval) network provides the necessary stability and tracking performance. The on-line learning is used to adapt the network under varying flight conditions. The on-line learning ability is demonstrated through parameter uncertainties. The performance of the proposed direct adaptive neural controller (DANC) is compared with feedback error learning neural controller (FENC).