Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

Soil Solution as Affected by Plant Residues and Nitrogen Rates

Cation mobility in acidic soils with low organic-matter contents depends not only on sorption intensity but also on the solubility of the species present in soil solution. In general, the following leaching gradient is observed: potassium (K+) magnesium (Mg2+) calcium (Ca2+) aluminum (Al3+). To minimize nutrient losses and ameliorate the subsoil, soil solution must be changed, favoring higher mobility of M2+ (metal ions) forms. This would be theoretically possible if plant residues were kept on the soil surface. An experiment was conducted in pots containing a Distroferric Red Latosol, with soil solution extractors installed at two depths. Pearl millet, black oat, and oilseed radish residues were laid on the soil surface, and nitrogen (as ammonium nitrate) was applied at rates ranging from 0 to 150mgkg-1. Corn was grown for 52 days. Except for K+ and ammonium (NH4 +), nitrogen rates and plant residues had little effect upon the concentrations and forms of the elements in the soil solution. Presence of cover crop residues on soil surface decreased the effect of nitrogen fertilizer on Ca leaching. More than 90% of the Ca2+, Mg2+, and K+ were found as free ions. The Al3+ was almost totally complexed as Al(OH3)0. Nitrogen application increased the concentrations of almost all the ions in soil solution, including Al3+, although there was no modification in the leaching gradient.

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Resonance in Bose-Einstein condensate oscillation from a periodic variation in scattering length

Using the explicit numerical solution of the axially symmetric Gross-Pitaevskii equation, we study the oscillation of the Bose-Einstein condensate (BEC) induced by a periodic variation in the atomic scattering length a. When the frequency of oscillation of a is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with a novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through a maximum and minimum. Such a growth and decay cycle of the amplitude may keep on repeating. Similar behaviour is also observed in a rotating BEC.

A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger's column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger's column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

Solid-state and solution structural study of acetylacetone-modified tin(IV) chloride used as a precursor of SnO2 nanoparticles prepared by a sol-gel route

The effect of addition of different amounts of acetylacetone (acacH) on the species formed at room temperature and after thermohydrolysis at 70 degreesC for 30 and 120 min of ethanolic SnCl4.5H(2)O solutions is followed by EXAFS spectroscopy at the Sn K-edge. We show that thermohydrolyzed solutions are a mixture of SnO2 nanoparticles and soluble tin polynuclear species. The complexation of the tin molecular precursors by acetylacetonate ligands is evidenced by H-1, C-13, and Sn-119 NMR spectroscopy and EXAFS for a acacH/Sn ratio higher than 2. Single crystals are isolated from solution and the structure, determined by X-ray diffraction, is built up from monomeric Cl-3(H2O)Sn(acac)-H2O units bridged together by hydrogen bonding. The acacH/Sn ratio in solution controls the polycondensation of the hydrolyzed species but not the crystallite size of the SnO2 nanoparticles (similar to2 nm). Because of the major presence of chelated tin mono- and dimeric complexes in solution for acacH/Sn > 2, the condensation is almost inhibited, meanwhile the decrease of amount of chelated complexes for the acacH/Sn < 2 gives rise to an increase of the number of nanoparticles.

Magnesium levels in nutrient solution and common bean (Phaseolus vulgaris L cv Carioca) development. Evaluation of the growth relations and assimilate partitioning

The effect of magnesium levels in nutrient solution upon relation between shoot and root, leaf weight ratio and assimilate partitioning of common bean (Phaseolus vulgaris L. cv Carioca) was studied. Bean plants (3 per pot) were grown in 6 l pots containing Hoagland & Arnon n. 2 solution modified to obtain 2.4, 24.3, 48.6, 72.9 and 97.2 ppm of magnesium. The experimental design was a completely randomized factorial replicated 3 times with 5 levels of magnesium and 5 samplings wich were done forthnightly. Therefore, it may be suggested that the 48.6 ppm of magnesium level proposed by Hoagland & Amen (1950) is the best choice for the common bean, according to the conditions of this experiment. Magnesium concentrations over 48.6 ppm didn't show significant alterations of the evaluated parameters. Nutrient solution with 2.4 ppm of magnesium content provides higher efficiency to the common bean plants during almost all its cycle, except the final of the reproductive phase. These results suggest that magnesium concentration increased to 48.6 ppm, in the cycle final perhaps could increase the productivity.

Pb1-xCaxTiO3 solid solution (x=0.0, 0.25, 0.50, and 0.75): A theoretical and experimental approach

In this paper we report an experimental and theoretical study based on a periodic density functional investigation into selected compositions of Pb1-xCaxTiO3 (x=0.0, 0.25, 0.50, and 0.75). Based on our findings, we propose that the pseudocubic structure of these perovskites presents a long-range tendency for cubic symmetry, while the short-range displacements bring the solid solution to a tetragonal symmetry. The results are discussed in terms of x-ray diffraction, structural optimized parameters, Raman spectroscopy, band structure, density of states, Mulliken charge, and overlap population.

Solutions for a class of integro-differential equations with time periodic coefficients

In this work, a series solution is found for the integro-differential equation y″ (t) = -(ω2 c + ω2 f sin2 ωpt)y(t) + ωf (sin ωpt) z′ (0) + ω2 fωp sin ωpt ∫t 0 (cos ωps) y(s)ds, which describes the charged particle motion for certain configurations of oscillating magnetic fields. As an interesting feature, the terms of the solution are related to distinct sequences of prime numbers.

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Light energy management in peach: utilization, photoprotection , photodamage and recovery. Maximizing light absorption in orchard is not always the best solution

The relation between the intercepted light and orchard productivity was considered linear, although this dependence seems to be more subordinate to planting system rather than light intensity. At whole plant level not always the increase of irradiance determines productivity improvement. One of the reasons can be the plant intrinsic un-efficiency in using energy. Generally in full light only the 5 – 10% of the total incoming energy is allocated to net photosynthesis. Therefore preserving or improving this efficiency becomes pivotal for scientist and fruit growers. Even tough a conspicuous energy amount is reflected or transmitted, plants can not avoid to absorb photons in excess. The chlorophyll over-excitation promotes the reactive species production increasing the photoinhibition risks. The dangerous consequences of photoinhibition forced plants to evolve a complex and multilevel machine able to dissipate the energy excess quenching heat (Non Photochemical Quenching), moving electrons (water-water cycle , cyclic transport around PSI, glutathione-ascorbate cycle and photorespiration) and scavenging the generated reactive species. The price plants must pay for this equipment is the use of CO2 and reducing power with a consequent decrease of the photosynthetic efficiency, both because some photons are not used for carboxylation and an effective CO2 and reducing power loss occurs. Net photosynthesis increases with light until the saturation point, additional PPFD doesn’t improve carboxylation but it rises the efficiency of the alternative pathways in energy dissipation but also ROS production and photoinhibition risks. The wide photo-protective apparatus, although is not able to cope with the excessive incoming energy, therefore photodamage occurs. Each event increasing the photon pressure and/or decreasing the efficiency of the described photo-protective mechanisms (i.e. thermal stress, water and nutritional deficiency) can emphasize the photoinhibition. Likely in nature a small amount of not damaged photosystems is found because of the effective, efficient and energy consuming recovery system. Since the damaged PSII is quickly repaired with energy expense, it would be interesting to investigate how much PSII recovery costs to plant productivity. This PhD. dissertation purposes to improve the knowledge about the several strategies accomplished for managing the incoming energy and the light excess implication on photo-damage in peach. The thesis is organized in three scientific units. In the first section a new rapid, non-intrusive, whole tissue and universal technique for functional PSII determination was implemented and validated on different kinds of plants as C3 and C4 species, woody and herbaceous plants, wild type and Chlorophyll b-less mutant and monocot and dicot plants. In the second unit, using a “singular” experimental orchard named “Asymmetric orchard”, the relation between light environment and photosynthetic performance, water use and photoinhibition was investigated in peach at whole plant level, furthermore the effect of photon pressure variation on energy management was considered on single leaf. In the third section the quenching analysis method suggested by Kornyeyev and Hendrickson (2007) was validate on peach. Afterwards it was applied in the field where the influence of moderate light and water reduction on peach photosynthetic performances, water requirements, energy management and photoinhibition was studied. Using solar energy as fuel for life plant is intrinsically suicidal since the high constant photodamage risk. This dissertation would try to highlight the complex relation existing between plant, in particular peach, and light analysing the principal strategies plants developed to manage the incoming light for deriving the maximal benefits as possible minimizing the risks. In the first instance the new method proposed for functional PSII determination based on P700 redox kinetics seems to be a valid, non intrusive, universal and field-applicable technique, even because it is able to measure in deep the whole leaf tissue rather than the first leaf layers as fluorescence. Fluorescence Fv/Fm parameter gives a good estimate of functional PSII but only when data obtained by ad-axial and ab-axial leaf surface are averaged. In addition to this method the energy quenching analysis proposed by Kornyeyev and Hendrickson (2007), combined with the photosynthesis model proposed by von Caemmerer (2000) is a forceful tool to analyse and study, even in the field, the relation between plant and environmental factors such as water, temperature but first of all light. “Asymmetric” training system is a good way to study light energy, photosynthetic performance and water use relations in the field. At whole plant level net carboxylation increases with PPFD reaching a saturating point. Light excess rather than improve photosynthesis may emphasize water and thermal stress leading to stomatal limitation. Furthermore too much light does not promote net carboxylation improvement but PSII damage, in fact in the most light exposed plants about 50-60% of the total PSII is inactivated. At single leaf level, net carboxylation increases till saturation point (1000 – 1200 μmolm-2s-1) and light excess is dissipated by non photochemical quenching and non net carboxylative transports. The latter follows a quite similar pattern of Pn/PPFD curve reaching the saturation point at almost the same photon flux density. At middle-low irradiance NPQ seems to be lumen pH limited because the incoming photon pressure is not enough to generate the optimum lumen pH for violaxanthin de-epoxidase (VDE) full activation. Peach leaves try to cope with the light excess increasing the non net carboxylative transports. While PPFD rises the xanthophyll cycle is more and more activated and the rate of non net carboxylative transports is reduced. Some of these alternative transports, such as the water-water cycle, the cyclic transport around the PSI and the glutathione-ascorbate cycle are able to generate additional H+ in lumen in order to support the VDE activation when light can be limiting. Moreover the alternative transports seems to be involved as an important dissipative way when high temperature and sub-optimal conductance emphasize the photoinhibition risks. In peach, a moderate water and light reduction does not determine net carboxylation decrease but, diminishing the incoming light and the environmental evapo-transpiration request, stomatal conductance decreases, improving water use efficiency. Therefore lowering light intensity till not limiting levels, water could be saved not compromising net photosynthesis. The quenching analysis is able to partition absorbed energy in the several utilization, photoprotection and photo-oxidation pathways. When recovery is permitted only few PSII remained un-repaired, although more net PSII damage is recorded in plants placed in full light. Even in this experiment, in over saturating light the main dissipation pathway is the non photochemical quenching; at middle-low irradiance it seems to be pH limited and other transports, such as photorespiration and alternative transports, are used to support photoprotection and to contribute for creating the optimal trans-thylakoidal ΔpH for violaxanthin de-epoxidase. These alternative pathways become the main quenching mechanisms at very low light environment. Another aspect pointed out by this study is the role of NPQ as dissipative pathway when conductance becomes severely limiting. The evidence that in nature a small amount of damaged PSII is seen indicates the presence of an effective and efficient recovery mechanism that masks the real photodamage occurring during the day. At single leaf level, when repair is not allowed leaves in full light are two fold more photoinhibited than the shaded ones. Therefore light in excess of the photosynthetic optima does not promote net carboxylation but increases water loss and PSII damage. The more is photoinhibition the more must be the photosystems to be repaired and consequently the energy and dry matter to allocate in this essential activity. Since above the saturation point net photosynthesis is constant while photoinhibition increases it would be interesting to investigate how photodamage costs in terms of tree productivity. An other aspect of pivotal importance to be further widened is the combined influence of light and other environmental parameters, like water status, temperature and nutrition on peach light, water and phtosyntate management.

SOLUTE-DERIVED THERMAL STABILITY OF NANOCRYSTALLINE ALUMINUM AND PROCESSING FACTOR INFLUENCE ON THE FORMATION OF AL6MN QUASICRYSTALS IN MELT-SPINNING

Thermal stability of nanograined metals can be difficult to attain due to the large driving force for grain growth that arises from the significant boundary area constituted by the nanostructure. Kinetic approaches for stabilization of the nanostructure effective at low homologous temperatures often fail at higher homologous temperatures. Thermodynamic approaches for thermal stabilization may offer higher temperature stability. In this research, modest alloying of aluminum with solute (1 at.% Sc, Yb, or Sr) was examined as a means to thermodynamically stabilize a bulk nanostructure at elevated temperatures. After using melt-spinning and ball-milling to create an extended solid-solution and nanostructure with average grain size on the order of 30-45 nm, 1 h annealing treatments at 673 K (0.72 Tm) , 773 K (0.83 Tm) , and 873 K (0.94 Tm) were applied. The alloys remain nanocrystalline (<100 nm) as measured by Warren-Averbach Fourier analysis of x-ray diffraction peaks and direct observation of TEM dark field micrographs, with the efficacy of stabilization: Sr>Yb>Sc. Disappearance of intermetallic phases in the Sr and Yb alloys in the x-ray diffraction spectra are observed to occur coincident with the stabilization after annealing, suggesting that precipitates dissolve and the boundaries are enriched with solute. Melt-spinning has also been shown to be an effective process to produce a class of ordered, but non-periodic crystals called quasicrystals. However, many of the factors related to the creation of the quasicrystals through melt-spinning are not optimized for specific chemistries and alloy systems. In a related but separate aspect of this research, meltspinning was utilized to create metastable quasicrystalline Al6Mn in an α-Al matrix through rapid solidification of Al-8Mn (by mol) and Al-10Mn (by mol) alloys. Wheel speed of the melt-spinning wheel and orifice diameter of the tube reservoir were varied to determine their effect on the resulting volume proportions of the resultant phases using integrated areas of collected x-ray diffraction spectra. The data were then used to extrapolate parameters for the Al-10Mn alloy which consistently produced Al6Mn quasicrystal with almost complete suppression of the equilibrium Al6Mn orthorhombic phase.