97 resultados para Lyapunov Exponents
Resumo:
Detailed high-temperature compression creep experiments on a pure 3 mol% yttria-stabilized tetragonal zirconia (3YTZ) and 3YTZ doped with 4.8 wt% TiO2 revealed that both materials exhibit a similar transition in stress exponents from n similar to 1 to n similar to 2 with a decrease in stress. The stress exponent of 1 and the inverse grain size dependence p of similar to 3 are consistent with the Coble diffusion creep at high stresses; the increase in stress exponent at low stresses is attributed to an interface-controlled diffusion creep process. Measurements revealed that grain-boundary sliding contributes to >similar to 50% of the total strain in both regions with n similar to 1 and n similar to 2, indicating the operation of the same fundamental deformation process in both regions. The creep data indicate that doping with TiO2 leads to an increase in the grain-boundary diffusion coefficients. The increase observed in the dihedral angle with doping is also consistent with the increase in grain boundary diffusion coefficient and the reported enhanced ductility in such materials.
Resumo:
The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.
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In this paper, we study the performance of client-Access Point (AP) association policies in IEEE 802.11 based WLANs. In many scenarios, clients have a choice of APs with whom they can associate. We are interested in finding association policies which lead to optimal system performance. More specifically, we study the stability of different association policies as a function of the spatial distribution of arriving clients. We find for each policy the range of client arrival rates for which the system is stable. For small networks, we use Lyapunov function methods to formally establish the stability or instability of certain policies in specific scenarios. The RAT heuristic policy introduced in our prior work is shown to have very good stability properties when compared to several other natural policies. We also validate our analytical results by detailed simulation employing the IEEE 802.11 MAC.
Resumo:
Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.
Resumo:
The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav & Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are shown to be tight for iid, Markov, and unifilar sources, thus recovering some known results. A close relationship between error exponents and correct decoding exponents formfixed rate source compression on the one hand and exponents for guessing moments on the other hand is established.
Resumo:
In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P<0.00001), a decrease in predictability (P<0.00001) and an increase in nonlinearity (P=0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component. (C) 2000 published by Elsevier Science B.V.
Resumo:
High-precision measurement of the electrical resistance of nickel along its critical line, a first attempt of this kind, as a function of pressure to 47.5 kbar is reported. Our analysis yields the values of the critical exponents α=α’=-0.115±0.005 and the amplitude ratios ‖A/A’‖=1.17±0.07 and ‖D/D’‖=1.2±0.1. These values are in close agreement with those predicted by renormalization-group (RG) theory. Moreover, this investigation provides an unambiguous experimental verification to one of the key consequences of RG theory that the critical exponents and amplitudes ratios are insensitive to pressure variation in nickel, a Heisenberg ferromagnet.
Resumo:
Static magnetization for single crystals of insulating Nd0.85Pb0.15MnO3 and marginally conducting Nd0.70Pb0.30MnO3 has been studied around the ferromagnetic to paramagnetic transition temperature T-C. Results of measurements carried out in the critical range vertical bar(T - T-C)/T-C vertical bar <= 0.1 are reported. Critical exponents beta and gamma for the thermal behaviour of magnetization and susceptibility have been obtained both by modified Arrott plots and the Kouvel-Fisher method. The exponent delta independently obtained from the critical isotherm was found to satisfy the Widom scaling relation delta = gamma/beta + 1. For both compositions the values of exponents are consistent with those expected for isotropic magnets belonging to the Heisenberg universality class with short-range exchange in three dimensions. Correspondingly, the specific heat displays only a cusp-like anomaly at the critical temperature of these crystals which is consistent with an exponent alpha < 0. The results show that the ferromagnetic ordering transition in Nd1-xPbxMnO3 in the composition range 0.15 <= x <= 0.40 is continuous. This mixed-valent manganite displays the conventional properties of a Heisenberg-like ferromagnet, irrespective of the differing transport properties and in spite of low ordering temperatures T-C = 109 and 147.2 K for x = 0.15 and 0.30, respectively.
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Cubic pyrochlore Bi1.5Zn1.0Nb1.5O7 thin films were deposited by pulsed laser ablation on Pt(200)/SiO2/Si at 500, 550, 600, and 650 degrees C. The thin films with (222) preferred orientation were found to grow at 650 degrees C with better crystallinity which was established by the lowest full-width half maxima of similar to 0.38. The dielectric response of the thin films grown at 650 degrees C have been characterized within a temperature range of 270-650 K and a frequency window of 0.1-100 kHz. The dielectric dispersion in the thin films shows a Maxwell-Wagner type relaxation with two different kinds of response confirmed by temperature dependent Nyquist plots. The ac conduction of the films showed a varied behavior in two different frequency regions. The power law exponent values of more than 1 at high frequency are explained by a jump-relaxation-model. The possibility of grain boundary related large polaronic hopping, due to two different power law exponents and transformation of double to single response in Nyquist plots at high temperature, has been excluded. The ``attempt jump frequency'' obtained from temperature dependent tangent loss and real part of dielectric constants, has been found to lie in the range of their lattice vibronic frequencies (10(12)-10(13) Hz). The activation energy arising from a large polaronic hopping due to trapped charge at low frequency region has been calculated from the ac conduction behavior. The range of activation energies (0.26-0.59. eV) suggests that the polaronic hopping at low frequency is mostly due to oxygen vacancies. (C) 2010 American Institute of Physics. doi:10.106311.3457335]
Resumo:
The thermodynamics of monodisperse solutions of polymers in the neighborhood of the phase separation temperature is studied by means of Wilson’s recursion relation approach, starting from an effective ϕ4 Hamiltonian derived from a continuum model of a many‐chain system in poor solvents. Details of the chain statistics are contained in the coefficients of the field variables ϕ, so that the parameter space of the Hamiltonian includes the temperature, coupling constant, molecular weight, and excluded volume interaction. The recursion relations are solved under a series of simplifying assumptions, providing the scaling forms of the relevant parameters, which are then used to determine the scaling form of the free energy. The free energy, in turn, is used to calculate the other singular thermodynamic properties of the solution. These are characteristically power laws in the reduced temperature and molecular weight, with the temperature exponents being the same as those of the 3d Ising model. The molecular weight exponents are unique to polymer solutions, and the calculated values compare well with the available experimental data.
Relationship between the controllability grammian and closed-loop eigenvalues: the single input case
Resumo:
The controllability grammian is important in many control applications. Given a set of closed-loop eigenvalues the corresponding controllability grammian can be obtained by computing the controller which assigns the eigenvalues and then by solving the Lyapunov equation that defines the grammian. The relationship between the controllability grammian, resulting from state feedback, and the closed-loop eigenvalues of a single input linear time invariant (LTI) system is obtained. The proposed methodology does not require the computation of the controller that assigns the specified eigenvalues. The closed-loop system matrix is obtained from the knowledge of the open-loop system matrix, control influence matrix and the specified closed-loop eigenvalues. Knowing the closed-loop system matrix, the grammian is then obtained from the solution of the Lyapunov equation that defines it. Finally the proposed idea is extended to find the state covariance matrix for a specified set of closed-loop eigenvalues (without computing the controller), due to impulsive input in the disturbance channel and to solve the eigenvalue assignment problem for the single input case.
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In this paper, we have studied electroencephalogram (EEG) activity of schizophrenia patients, in resting eyes closed condition, with detrended fluctuation analysis (DFA). The DFA gives information about scaling and long-range correlations in time series. We computed DFA exponents from 30 scalp locations of 18 male neuroleptic-naIve, recent-onset schizophrenia (NRS) subjects and 15 healthy male control subjects. Our results have shown two scaling regions in all the scalp locations in all the subjects, with different slopes, corresponding to two scaling exponents. No significant differences between the groups were found with first scaling exponent (short-range). However, the second scaling exponent (long-range) were significantly lower in control subjects at all scalp locations (p<0.05, Kruskal-Wallis test). These findings suggest that the long-range scaling behavior of EEG is sensitive to schizophrenia, and this may provide an additional insight into the brain dysfunction in schizophrenia.
Resumo:
The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav and Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are shown to be tight for i.i.d., Markov, and unifilar sources, thus recovering some known results. A close relationship between error exponents and correct decoding exponents for fixed rate source compression on the one hand and exponents for guessing moments on the other hand is established.
Resumo:
A fatigue crack growth rate study has been carried out on L-72 aluminium alloy plate specimens with and without cold worked holes. The cold worked specimens showed significantly increased fatigue life compared to unworked specimens. Computer software is developed to evaluate the stress intensity factor for non-uniform stress distributions using Green's function approach. The exponents for the Paris equation in the stable crack growth region for cold worked and unworked specimens are 1.26 and 3.15 respectively. The reduction in exponent value indicates the retardation in crack growth rate. An SEM study indicates more plastic deformation at the edge of the hole for unworked samples as compared to the worked samples during the crack initiation period.
Resumo:
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be salved exactly via a simple unitary transformation. Nevertheless, correlation functions exhibit nontrivial interaction-dependent exponents. A similar model defined on a lattice is introduced and solved. Various generalizations, e.g., to the case of internal symmetries of the fermions, are discussed. The present treatment also clarifies certain aspects of Luttinger's original solution of the "Luttinger model."