Subdiffusion of nonlinear waves in quasiperiodic potentials

19 p.

An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems

This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated.

Nonlinear magnetic vortex dynamics in a circular nanodot excited by spin-polarized current

We investigate analytically and numerically nonlinear vortex spin torque oscillator dynamics in a circular magnetic nanodot induced by a spin-polarized current perpendicular to the dot plane. We use a generalized nonlinear Thiele equation including spin-torque term by Slonczewski for describing the nanosize vortex core transient and steady orbit motions and analyze nonlinear contributions to all forces in this equation. Blue shift of the nano-oscillator frequency increasing the current is explained by a combination of the exchange, magnetostatic, and Zeeman energy contributions to the frequency nonlinear coefficient. Applicability and limitations of the standard nonlinear nano-oscillator model are discussed.

The role of the terms of trade in the trade channel of transmission of oil price shocks

This paper highlights the role of the terms of trade in the trade channel of propagation of oil price shocks both empirically and theoretically. Empirically, I show that oil price shocks have a large, persistent and statistically significant impact on the US terms of trade. Theoretically, I add oil in the model by Corsetti and Pesenti (2005) and analyse under what conditions the terms of trade plays a relevant role in the international transmission of oil price shocks. With nominal price rigidities and full exchange rate pass-through positive oil price shocks depreciate the currency of the oil importing country. The subsequent negative wealth effect adds to the recessive effect of the supply channel and may trongly reduce the consumption in the oil importing country economy. Without exchange rate pass-through oil shocks transmit to the economy only through the supply channel. The model suggests that a change in the exchange rate pass-through might contribute to explain the evidence of a weaker impact of oil price shocks on the macroeconomic activity in recent times.

About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

Permutationally invariant state reconstruction

Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

1 p. -- [Editorial Material]

Sliding Mode Control Strategy for Wind Turbine Power Maximization

The efficiency of the wind power conversions systems can be greatly improved using an appropriate control algorithm. In this work, a sliding mode control for variable speed wind turbine that incorporates a doubly fed induction generator is described. The electrical system incorporates a wound rotor induction machine with back-to-back three phase power converter bridges between its rotor and the grid. In the presented design the so-called vector control theory is applied, in order to simplify the electrical equations. The proposed control scheme uses stator flux-oriented vector control for the rotor side converter bridge control and grid voltage vector control for the grid side converter bridge control. The stability analysis of the proposed sliding mode controller under disturbances and parameter uncertainties is provided using the Lyapunov stability theory. Finally simulated results show, on the one hand, that the proposed controller provides high-performance dynamic characteristics, and on the other hand, that this scheme is robust with respect to the uncertainties that usually appear in the real systems.

Gain Scheduling Control of an Islanded Microgrid Voltage

The aim of this research study has been to design a gain scheduling (GS) digital controller in order to control the voltage of an islanded microgrid in the presence of fast varying loads (FVLs), and to compare it to a robust controller. The inverter which feeds the microgrid is connected to it through an inductance-capacitor-inductance (LCL) filter. The oscillatory and nonlinear behaviour of the plant is analyzed in the whole operating zone. Afterwards, the design of the controllers which contain two loops in cascade are described. The first loop concerns the current control, while the second is linked to the voltage regulation. Two controllers, one defined as Robust and another one as GS controller, are designed for the two loops, emphasizing in their robustness and their ability to damp the oscillatory plant behaviour. To finish, some simulations are carried out to study and compare the two kinds of controllers in different operating points. The results show that both controllers damp the oscillatory behaviour of the plant in closed loop (CL), and that the GS controller ensures a better rejection of current disturbances from FVLs.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Effects of Spring Temperatures on the Strength of Selection on Timing of Reproduction in a Long-Distance Migratory Bird

Climate change has differentially affected the timing of seasonal events for interacting trophic levels, and this has often led to increased selection on seasonal timing. Yet, the environmental variables driving this selection have rarely been identified, limiting our ability to predict future ecological impacts of climate change. Using a dataset spanning 31 years from a natural population of pied flycatchers (Ficedula hypoleuca), we show that directional selection on timing of reproduction intensified in the first two decades (1980-2000) but weakened during the last decade (2001-2010). Against expectation, this pattern could not be explained by the temporal variation in the phenological mismatch with food abundance. We therefore explored an alternative hypothesis that selection on timing was affected by conditions individuals experience when arriving in spring at the breeding grounds: arriving early in cold conditions may reduce survival. First, we show that in female recruits, spring arrival date in the first breeding year correlates positively with hatch date; hence, early-hatched individuals experience colder conditions at arrival than late-hatched individuals. Second, we show that when temperatures at arrival in the recruitment year were high, early-hatched young had a higher recruitment probability than when temperatures were low. We interpret this as a potential cost of arriving early in colder years, and climate warming may have reduced this cost. We thus show that higher temperatures in the arrival year of recruits were associated with stronger selection for early reproduction in the years these birds were born. As arrival temperatures in the beginning of the study increased, but recently declined again, directional selection on timing of reproduction showed a nonlinear change. We demonstrate that environmental conditions with a lag of up to two years can alter selection on phenological traits in natural populations, something that has important implications for our understanding of how climate can alter patterns of selection in natural populations.