Optimal operation of hydrothermal systems with Hydrological Scenario Generation through Bootstrap and Periodic Autoregressive Models

In electrical power systems with strong hydro generation, the use of adequate techniques to generate synthetic hydrological scenarios is extremely important for the evaluation of the ways the system behaves in order to meet the forecast energy demand. This paper proposes a new model to generate natural inflow energy scenarios in the long-term operation planning of large-sized hydrothermal systems. This model is based on the Periodic Autoregressive Model, PAR (p), where the identification of the p orders is based on the significance of the Partial Autocorrelation Function (PACF) estimated via Bootstrap, an intensive computational technique. The scenarios generated through this new technique were applied to the operation planning of the Brazilian Electrical System (BES), using the previously developed methodology of Stochastic Dynamic Programming based on Convex Hull algorithm (SDP-CHull). The results show that identification via Bootstrap is considerably more parsimonious, leading to the identification of lower orders models in most cases which retains the statistical characteristics of the original series. Additionally it presents a closer total mean operation cost when compared to the cost obtained via historic series.     

Stabilizing periodic orbits of fractional order chaotic systems via linear feedback theory

In this paper stabilizing unstable periodic orbits (UPO) in a chaotic fractional order system is studied. Firstly, a technique for finding unstable periodic orbits in chaotic fractional order systems is stated. Then by applying this technique to the fractional van der Pol and fractional Duffing systems as two demonstrative examples, their unstable periodic orbits are found. After that, a method is presented for stabilization of the discovered UPOs based on the theories of stability of linear integer order and fractional order systems. Finally, based on the proposed idea a linear feedback controller is applied to the systems and simulations are done for demonstration of controller performance.     

Perfect tuning of spin-polarization in a ring-shaped multiple-quantum-dot nanostructure in the presence of Rashba spin–orbit coupling

Spin-dependent electronic transport through an open multiple-quantum-dot ring threaded by a magnetic flux is theoretically investigated by using the single particle Green?s function method. By introducing local Rashba spin–orbit interaction on an individual quantum dot and local magnetic moments on two of other quantum dots, we calculate the spin-polarization in the output lead. We find the spin-polarization can be tuned by manipulating magnetic moments, adjusting magnetic flux and setting the Rashba spin–orbit strength. It is also shown the system can operate as an efficient spin-inverter when the structure is adjusted properly. The analysis can be utilized in designing optimized nanodevices.     

Generation and control of electronic hybrid entanglement via a two-dimensional Rashba anisotropic nanodot

In the present article we report the dynamics of electronic spin–subbands, as well as subband–subband, hybrid entanglements in a two-dimensional anisotropic quantum dot. The dot is under the influence of Rashba effect and an external magnetic field. To study the hybrid entanglements, we partition the system into two categories in which either spatial degrees of freedom, subbands, entangle with the spin or the subbands become entangled amongst themselves. For the first case we calculate the von Neumann entropy, while for the latter the negativity is calculated. Our calculations show that for both cases information is periodically distributed between the corresponding subspaces. Effects of Rashba parameter and magnetic field on the characteristics of such oscillatory behavior are also discussed. For spin–subband entanglement the oscillations include dips, surrounded by plateaus of maximal entanglement. The subband–subband entanglement shows vanishingly small plateaus. The duration of plateaus is controlled by Rashba coupling and the external field.     

Vibration band gap analysis of a new periodic beam model using GDQR method

In this study, a new periodic beam model is introduced. This beam consists of the concentrated rigid masses and tapered beam elements with linearly variable width. The theoretical equations are derived by employing the Euler-Bernoulli beam and the Bloch–Floquet theorem and then solved using the generalized differential quadrature rule method to calculate the first two band gaps. The effects of the mass, mass moment of inertia and taper ratio on the widths and central frequencies of the first two band gaps are investigated. Results show that the wide band gaps at low frequency ranges can be obtained by changing the geometrical parameters. This is of interest for different applications of the band gap phenomenon such as broadband piezoelectric energy harvesting. Finally, the finite element simulation (ANSYS software) is used to validate the analytical method and good agreement is found.     

Chaotic attitude motion of gyrostat statellites in a central force field

The nonlinear attitude motion of gyrostat satellites in a central force field is investigated, with particular emphasis on their long-time dynamic behavior for a wide range of parameters. The numbers of equilibrium solutions, as well as their stability, vary with the rotor speed, and bifurcation diagrams have been obtained. Various dynamic behaviors of gyrostat satcllites, e.g. periodic, quasiperiodic, and chaotic, are studied via the Poincaré map technique. It is shown that the rotor speed has a significant effect on the dynamic behavior of gyrostat satellites.     

Melnikov's method for rigid bodies subject to small perturbation torques

Summary In this paper, the global motion of rigid bodies subjected to small perturbation torques, either conservative or dissipative, is investigated by means of Melnikov's method. Deprit's variables are introduced to transform the equations of motion into a standard form which is rendered suitable for the application of Melnikov's method. The Melnikov method is used to predict the transversal intersections of stable and unstable manifolds for the pertubed rigid-body motion. The chosen examples are a self-excited rigid body subject to a small periodic torque in a viscous medium, and the heavy rigid body. It is shown in both cases that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.     

Periodic Solutions of Symmetric Perturbations of Gravitational Potentials

It is shown that for certain symmetric perturbations of gravitational potentials in the space, which admit two first integrals of motion, a circular solution of the unperturbed system with inclination different from 0 and π gives rise to a periodic solution of the reduced dynamics which is defined in the quotient space of the action by the subgroup that fixes the symmetry axis. In the planar case, if we assume that the system admits a first integral of motion which is also symmetric with respect to the origin, then it is shown that each circular solution of the unperturbed problem gives rise to a periodic solution of the perturbed system.     

SMALE HORSESHOES AND CHAOS IN DISCRETIZED PERTURBED NLS SYSTEMS(Ⅱ)-SMALE HORSESHOES

The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger(NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set Λ on which the dynamics is topologically conjugate to a shift on four symbols.     

Formation around planetary displaced orbit

The paper investigates the relative motion around the planetary displaced orbit. Several kinds of displaced orbits for geocentric and martian cases were discussed. First, the relative motion was linearized around the displaced orbits. Then, two semi-natural control laws were investigated for each kind of orbit and the stable regions were obtained for each case. One of the two control laws is the passive control law that is very attractive for engineering practice. However, the two control laws are not very suitable for the Martian mission. Another special semi-natural control law is designed based on the requirement of the Martian mission. The results show that large stable regions exist for the control law.