Time-periodic feedback stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by Bloch equations is considered. This system may be seen as a prototype for infinite dimensional systems with continuous spectrum. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The closed-loop stability analysis is done locally around the equilibrium. The local convergence is shown to be a weak asymptotic convergence for the H1 topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium

Gravitational Collapse of Cylindrical Shells Made of Counter-Rotating Dust Particles

The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles, which emits both gravitational waves and massless particles when it is expanding or collapsing, is studied. It is found that when the models represent a collapsing shell, in some cases the angular momentum of the dust particles is strong enough to halt the collapse, so that a spacetime singularity is prevented from forming, while in other cases it is not, and a line-like spacetime singularity is finally formed on the symmetry axis.Comment: To appear in Phys. Rev.

High-Speed Cylindrical Collapse of Two Perfect Fluids

In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by $c_s, d_s$. It is shown that the high-speed approximation scheme breaks down by non-zero pressures $p_1, p_2$ when $c_s, d_s$ are bounded below by some positive constants. The failure of the high-speed approximation scheme at some particular time of the gravitational collapse suggests the uncertainity on the evolution at and after this time. In the bounded case, the naked singularity formation seems to be impossible for the cylindrical two perfect fluids. For the vanishing case, if a linear equation of state is used, the high-speed collapse does not break down by the effects of the pressures and consequently a naked singularity forms. This work provides the generalisation of the results already given by Nakao and Morisawa [1] for the perfect fluid.Comment: 11 pages, 1 figure, accepted for publication in Gen. Rel. Gra

Coping with salinity in irrigated agriculture: crop evapotranspiration and water management issues

ReviewSoil and water salinity and associated problems are a major challenge for global food production. Strategies to cope with salinity include a better understanding of the impacts of temporal and spatial dynamics of salinity on soil water balances vis-à-vis evapotranspiration (ET) and devising optimal irrigation schedules and efficient methods. Both steady state and transient models are now available for predicting salinity effects on reduction of crop growth and means for its optimization. This paper presents a brief review on the different approaches available, focusing on the FAO56 framework for coping with the effects of soil salinity on crop ET and yields. The FAO56 approach, applied widely in soil water balance models, is commonly used to compute water requirements, including leaching needs. It adopts a daily stress coefficient (Ks) representing both water and salt stresses to adjust the crop coefficient (Kc) when it is multiplied by the grass reference ETo to obtain the actual crop ET values for saline environments (ETc act=Ks Kc ETo). The same concept is also applied to the dual Kc approach, with Ks used to adjust the basal crop coefficient (Kcb). A review on applications of Ks is presented showing that the FAO56 approach may play an interesting role in water balance computations aimed at supporting irrigation scheduling. Transient state models, through alternative formulations, provide additional solutions for quantification of the salinity build-up in the root zone. These include irrigation-induced salinity, upward movement of salts from saline ground water-table, and sodification processes. Regardless of the approach, these models are now very much capable of supporting irrigation water management in saline stress conditions. For maintaining crop growth under salinity environments, soil-crop-water management interventions consistent with site-specific conditions are then discussed. Adequateness of irrigation methods, cyclic uses of multi-salinity waters and proper irrigation scheduling are further analyzed as examples of efficient means to obviate the effects of salinityinfo:eu-repo/semantics/publishedVersio

Anurans Of The Municipality Of Barão De Monte Alto, State Of Minas Gerais, Southeastern Brazil

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)We present a list of the anuran amphibians from municipality of Barão de Monte Alto, state of Minas Gerais, southeastern Brazil. This region is part of the remaining Atlantic Forest and the studied environments are represented by forest patches and open habitats. We recorded 29 anuran species, many of these typical and/or endemic to the Atlantic Forest. None of the species registered was considered under threat of extinction in state, national or international red-lists. It is worth noting, however, the presence of the tree frogs Dendropsophus pseudomeridianus, the first record of this species in the state of Minas Gerais, and D. Bipunctatus, marking its expanded distribution in various locations of Minas Gerais. The present list examines zoogeography and conservation of anurans in the Brazilian southeast and broadens the knowledge of the anuran fauna in this region. © 2016 Check List and Authors.125CAPES, Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES

Naked singularities in cylindrical collapse of counterrotating dust shells

Solutions describing the gravitational collapse of asymptotically flat cylindrical and prolate shells of (null) dust are shown to admit globally naked singularities

Critical Collapse of Cylindrically Symmetric Scalar Field in Four-Dimensional Einstein's Theory of Gravity

Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their local and global properties are investigated and found that they represent gravitational collapse of a massless scalar field. In some cases the collapse forms black holes with cylindrical symmetry, while in the other cases it does not. The linear perturbations of these solutions are also studied and given in closed form. From the spectra of the unstable eigen-modes, it is found that there exists one solution that has precisely one unstable mode, which may represent a critical solution, sitting on a boundary that separates two different basins of attraction in the phase space.Comment: Some typos are corrected. The final version to appear in Phys. Rev.