Two-parameter estimation with three-mode NOON state in a symmetric triple-well potential

We propose a scheme to realize two-parameter estimation via Bose–Einstein condensates confined in a symmetric triple-well potential. The three-mode NOON state is prepared adiabatically as the initial state. The two parameters to be estimated are the phase differences between the wells. The sensitivity of this estimation scheme is studied by comparing quantum and classical Fisher information matrices. As a result, we find an optimal particle number measurement method. Moreover, the precision of this estimation scheme means that the Heisenberg scaling behaves under the optimal measurement.     

Analysis of plasma sheath propagation attenuation based on ray tracing

Based on the complex Snell's law of lossy media, a ray tracing method is proposed to study the propagation attenuation characteristics of electromagnetic (EM) waves in plasma sheaths. The plasma sheath is modelled as layered media. This method considers the complex ray characteristics of inhomogeneous plane EM waves, tracks the propagation rays of EM waves in each layer of media, and calculates the propagation attenuation of EM waves in each layer of media according to the propagation direction of the complex rays. The attenuation during numerical cumulative propagation is the total attenuation of EM waves through the plasma sheath. By comparing the results with that obtained from the WKB method, the accuracy of the ray tracing algorithm is proved. The results of the propagation attenuation of a blunt cone model are calculated by the proposed method, and the effects of different parameters on the EM wave propagation attenuation in the plasma sheath are analysed at different heights, velocities, incident angles, and incident positions. Studying the propagation characteristics of EM waves in the plasma sheath is of importance in application for radar target tracking, blackout communication, and other issues.     

Long-term correlations in hourly wind speed records in Pernambuco, Brazil

We study the statistical properties of hourly wind speed time series detected at four weather stations in the state of Pernambuco, Brazil, in the period 2008-2009. We find that the average and maximum hourly wind speeds deviate from a mutual linear relationship, and that they may be well explained individually by a Weibull distribution, however, with different shape parameter values. On the other hand, the long-term correlations of both of these observables obey the same power-law behavior, with two distinct scaling regimes. Our results agree with previous studies on wind speed series correlations in other regions of the world, which is suggestive of universal behavior.     

Directed transport in equilibrium: A model study

It is generally believed that sustained directed transport in mechanical systems is not achievable under equilibrium conditions. In this article, by analyzing a simple model, we will show that directed motion under equilibrium conditions can take place and is not inconsistent with conservation of energy and the second law of thermodynamics. Our model demonstrates a novel symmetry breaking mechanism sustainable under equilibrium conditions and average uniform motion of the center of mass is a consequence of the sustained broken symmetry. The most important consequence of our results is that, no current condition for mechanical equilibrium is possibly non-universal.     

Evolutionary model of the growth and size of firms

The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat’s law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms, the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size–variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.     

The diminishing segment process

Let Ξ₀=[−1,1], and define the segments Ξ_n recursively in the following manner: for every n=0,1,…, let Ξ_n+1=Ξ_n∩[a_n+1−1,a_n+1+1], where the point a_n+1 is chosen randomly on the segment Ξ_n with uniform distribution. For the radius ρ_n of Ξ_n, we prove that n(ρ_n−1/2) converges in distribution to an exponential law, and we show that the centre of the limiting unit interval has arcsine distribution.     

Decay property of Timoshenko system in thermoelasticity

We investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay property of the regularity‐loss type. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We derive L² decay estimates of solutions and observe that for the Fourier law the decay structure of solutions is of the regularity‐loss type if the wave speeds of the first and the second equations in the system are different. For the Cattaneo law, decay property of the regularity‐loss type occurs no matter what the wave speeds are. In addition, by restricting the initial data to with a suitably large s and γ ∈ [0,1], we can derive faster decay estimates with the decay rate improvement by a factor of t^?γ/2. Copyright © 2011 John Wiley & Sons, Ltd.     

Indirect adaptive fuzzy observer and controller design based on interval type-2 T-S fuzzy model

This paper presents the design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T-S fuzzy model. The nonlinear systems can be well approximated by IT2 T-S fuzzy model, in which the fuzzy rules’ antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The proposed IT2 T-S fuzzy model is a combination of IT2 fuzzy system and T-S fuzzy model, and also inherits the benefits of type-2 fuzzy logic systems, which is able to directly handle uncertainties and can minimize the effects of uncertainties in rule-based fuzzy system. These characteristics can improve the accuracy of the system modeling and reduce the number of system rules. The proposed method using feedback control, adaptive laws, and on-line object parameters are adjusted to ensure observation error bounded. In addition, using Lyapunov synthesis approach and Lipschitz condition, the stability analysis is conducted. The simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.     

有重弹性体形变与质量分布规律的简明推导

依据胡克定律与串联弹性体的劲度系数计算公式,直观简便地导出了弹性体在重力场中的形变规律、质量分布规律及其质心位置.