Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim

Helicopter trim involves solution of nonlinear force equilibrium equations. As in many nonlinear dynamic systems, helicopter trim problem can show chaotic behavior. This chaotic behavior is found in the basin of attraction of the nonlinear trim equations which have to be solved to determine the main rotor control inputs given by the pilot. This study focuses on the boundary of the basin of attraction obtained for a set of control inputs. We analyze the boundary by considering it at different magnification levels. The magnified views reveal intricate geometries. It is also found that the basin boundary exhibits the characteristic of statistical self-similarity, which is an essential property of fractal geometries. These results led the authors to investigate the fractal dimension of the basin boundary. It is found that this dimension is indeed greater than the topological dimension. From all the observations, it is evident that the boundary of the basin of attraction for helicopter trim problem is fractal in nature. (C) 2012 Elsevier Inc. All rights reserved.

Attraction, with boundaries

We study the basin of attraction of static extremal black holes, in the concrete setting of the STU model. By finding a connection to a decoupled Toda-like system and solving it exactly, we find a simple way to characterize the attraction basin via competing behaviors of certain parameters. The boundaries of attraction arise in the various limits where these parameters degenerate to zero. We find that these boundaries are generalizations of the recently introduced (extremal) subtracted geometry: the warp factors still exhibit asymptotic integer power law behaviors, but the powers can be different from one. As we cross over one of these boundaries ('generalized subttractors'), the solutions turn unstable and start blowing up at finite radius and lose their asymptotic region. Our results are fully analytic, but we also solve a simpler theory where the attraction basin is lower dimensional and easy to visualize, and present a simple picture that illustrates many of the basic ideas.

Males and females of the social wasp Ropalidia marginata do not differ in their cuticular hydrocarbon profiles and do not seem to use any long-distance volatile mate attraction cues

Sex pheromones are vital in communication between individuals belonging to opposite sexes and form an integral part of the reproductive biology of various species. Among insects, sexual dimorphism in CHCs has been reported from diverse taxa spanning seven different orders, and thereby CHCs have been implicated as sex pheromones. Because males and females of the primitively eusocial wasp Ropalidia marginata touch each other with their antennae during mating, before engaging in sperm transfer, a sex pheromone that is perceived via contact chemosensation through the antennae can possibly exist in this species. Since CHCs have been implied as sex pheromones in various insects (including hymenopterans), and since sexual dimorphism of CHCs should be an obligatory prerequisite for them to act as sex pheromones, we investigated whether males and females of R. marginata differ in their CHC profiles. We found only nonvolatile CHCs, and our results show absence of sexual dimorphism in CHCs, suggesting that CHCs do not function as sex pheromone in this species. A behavioral assay failed to show presence of mate attraction at a distance, thereby showing the absence of volatile long-distance mate attraction cues (that may originate from sources other than and in addition to CHCs).

Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard-sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially devised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between different minima. We find evidence for the existence of pairs of closely related glassy minima("two-level systems"). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

Perception of ultraviolet light by crab spiders and its role in selection of hunting sites

The perception of ultraviolet (UV) light by spiders has so far been only demonstrated in salticids. Crab spiders (Thomisidae) hunt mostly on flowers and need to find appropriate hunting sites. Previous studies have shown that some crab spiders that reflect UV light use UV contrast to enhance prey capture. The high UV contrast can be obtained either by modulation of body colouration or active selection of appropriate backgrounds for foraging. We show that crab spiders (Thomisus sp.)hunting on Spathiphyllum plants use chromatic contrast, especially UV contrast, to make themselves attractive to hymenopteran prey. Apart from that, they are able to achieve high UV contrast by active selection of non-UV reflecting surfaces when given a choice of UV-reflecting and non-UV reflecting surfaces in the absence of odour cues. Honeybees (Apis cerana) approached Spathiphyllum plants bearing crab spiders on which the spiders were high UV-contrast targets with greater frequency than those plants on which the UV-contrast of the spiders was low. Thus, crab spiders can perceive UV and may use it to choose appropriate backgrounds to enhance prey capture, by exploiting the attraction of prey such as honeybees to UV.

Enhanced ionic conduction in dispersed solid electrolyte systems CaF2---Al2O3 and CaF2---CeO2

Dispersions of Al2O3 as well as CeO2 in CaF2 are found to enhance the conductivity of CaF2. Both these systems are biphasic and the electrical conduction in them is purely ionic in nature. At 650 K the increase in the ionic conductivity of the dispersed solid electrolyte system CaF2---Al2O3 is by about two orders of magnitude in relation to the conductivity of the host electrolyte CaF2, whereas for the CaF2---CeO2 system it is about three orders of magnitude. Some aspects of the increase in the ionic conductivities of CaF2---Al2O3 and CaF2---CeO2 electrolytes can be explained by a recent theoretical model. It is proposed that a substantial enhancement in the vacancy concentration of CaF2, brought about by the attraction of F− ions to the surface of Al2O3 (or CeO2), is responsible for the low temperature increase in the ionic conductivity of CaF2.

L-Arginine L-aspartate

C6HxsN40 +.C4H6NO~-, monoclinic, P2,,a = 5.511 (3), b = 8.438 (4), c = 15.265 (9) A, fl = 97.9 (I) °, D,, -- 1.467 (8) (flotation), D c = 1.452 Mg m -a, Z = 2. The structure has been refined to a final R value of 0.044 for 1226 independent counter-measured reflections. The conformation of the arginine molecule is different from those previously observed, whereas the conformation of the aspartate ion is similar to that found in L-aspartic acid, DL-aspartic acid and L-lysine L-aspartate. The unlike molecules aggregate into separate alternating layers and the a-amino and acarboxylate groups in the arginine layer are periodically brought into close proximity in a 'headto-tail' arrangement. There exist a specific ion-pair interaction involving electrostatic attraction and two nearly parallel N-H...O hydrogen bonds between the guanidyl group and the a-carboxylate group of the aspartate ion.

Mathematical model and rule extraction for tool wear monitoring problem using nature inspired techniques

In this paper, pattern classification problem in tool wear monitoring is solved using nature inspired techniques such as Genetic Programming(GP) and Ant-Miner (AM). The main advantage of GP and AM is their ability to learn the underlying data relationships and express them in the form of mathematical equation or simple rules. The extraction of knowledge from the training data set using GP and AM are in the form of Genetic Programming Classifier Expression (GPCE) and rules respectively. The GPCE and AM extracted rules are then applied to set of data in the testing/validation set to obtain the classification accuracy. A major attraction in GP evolved GPCE and AM based classification is the possibility of obtaining an expert system like rules that can be directly applied subsequently by the user in his/her application. The performance of the data classification using GP and AM is as good as the classification accuracy obtained in the earlier study.

Role of neutrophils in murine salmonellosis

Gastrointestinal infections with Salmonella enterica serovars have different clinical outcomes that range from localized inflammation to a life-threatening systemic disease in the case of typhoid fever. Using a mouse model of systemic salmonellosis, we investigated the contribution of neutrophils to the innate immune defense against Salmonella after oral infection. Neutrophil infiltration was dependent on the bacterial burden in various infected organs (Peyer's patches, mesenteric lymph nodes, spleen, and liver). However, the massive infiltration of neutrophils did not allow clearance of an infection with wild-type Salmonella, presumably due to protection of intracellular Salmonella against neutrophil activities. A Salmonella mutant strain deficient in Salmonella pathogenicity island 2 (SPI2) was able to infect systemic sites, but its replication was highly restricted and it did not cause detectable attraction of neutrophils. Neutrophil depletion by antibody treatment of mice did not restore the virulence of SPI2 or auxotrophic mutant strains, supporting the hypothesis that attenuation of the strains is not due to greater susceptibility to neutrophil killing. Our observations reveal that neutrophils have completely different roles during systemic salmonellosis and localized gastrointestinal infections. In the latter conditions, rapid neutrophil attraction efficiently prevents the spread of the pathogen, whereas the neutrophil influx is delayed during systemic infections and cannot protect against lethal bacteremia.

Free-to-bound and bound exciton transitions at isoelectronic impurities: GaP(Zn,O)

We show, for sufficiently high temperatures and sufficiently weak majority-carrier binding energies, that the dominant radiative transition at an isoelectronic acceptor (donor) in p-type (n-type) material consists of the recombination of singly trapped minority carriers (bound by central-cell forces) with free majority carriers attracted by a Coulomb interaction. There are two reasons why the radiative recombination rate of the free-to-bound process is greater than the bound exciton process, which dominates at lower temperatures: (i) The population of free majority-carrier states greatly exceeds that of exciton states at higher temperatures, and (ii) the oscillator strength of the free-to-bound transition is greatly enhanced by the Coulomb attraction between the free carrier and the charged isoelectronic impurity. This enhancement is important for isoelectronic centers and is easily calculable from existing exciton models. We show that the free carrier attracted by a Coulomb interaction can be viewed as a continuum excited state of the bound exciton. When we apply the results of our calculations to the GaP(Zn, O) system, we find that the major part of the room-temperature luminescence from nearest-neighbor isoelectronic Zn-O complexes results from free-to-bound recombination and not exciton recombination as has been thought previously. Recent experiments on impulse excitation of luminescence in GaP(Zn, O) are reevaluated in the light of our calculations and are shown to be consistent with a strong free-to-bound transition. For deep isoelectronic centers with weakly bound majority carriers, we predict an overwhelming dominance of the free-to-bound process at 300°K.

Contribution of different physical forces to the disjoining pressure of a thin water film being pressed by an oil droplet

With an objective to understand the nature of forces which contribute to the disjoining pressure of a thin water film on a steel substrate being pressed by an oil droplet, two independent sets of experiments were done. (i) A spherical silica probe approaches the three substrates; mica, PTFE and steel, in a 10 mM electrolyte solution at two different pHs (3 and 10). (ii) The silica probe with and without a smeared oil film approaches the same three substrates in water (pH = 6). The surface potential of the oil film/water was measured using a dynamic light scattering experiment. Assuming the capacity of a substrate for ion exchange the total interaction force for each experiment was estimated to include the Derjaguin-Landau-Verwey-Overbeek (DLVO) force, hydration repulsion, hydrophobic attraction and oil-capillary attraction. The best fit of these estimates to the force-displacement characteristics obtained from the two sets of experiment gives the appropriate surface potentials of the substrates. The procedure allows an assessment of the relevance of a specific physical interaction to an experimental configuration. Two of the principal observations of this work are: (i) The presence of a surface at constant charge, as in the presence of an oil film on the probe, significantly enhances the counterion density over what is achieved when both the surfaces allow ion exchange. This raises the corresponding repulsion barrier greatly. (ii) When the substrate surface is wettable by oil, oil-capillary attraction contributes substantially to the total interaction. If it is not wettable the oil film is deformed and squeezed out. (C) 2010 Elsevier Inc. All rights reserved.

Influence of drying on the liquid limit behaviour of a marine clay

The possible mechanisms of particle aggregation and reduction in liquid limit of the Cochin marine clay on drying are investigated. Mineralogical analysis showed the absence of halloysite in the marine specimen. Experimental results also ruled out the possibility of cementitious material being responsible for particle aggregation and reduction in clay plasticity on drying. The presence of calcium and magnesium as the predominant exchangeable ions and of a high pore salt concentration facilitates strong interparticle attraction and small particle separations; the latter leads to development of significant capillary stresses that permits an intimate contact of particles and growth of strong van der Waals' and Coulombic bonds.

Tool wear monitoring using ant behaviour

In this paper we show the applicability of Ant Colony Optimisation (ACO) techniques for pattern classification problem that arises in tool wear monitoring. In an earlier study, artificial neural networks and genetic programming have been successfully applied to tool wear monitoring problem. ACO is a recent addition to evolutionary computation technique that has gained attention for its ability to extract the underlying data relationships and express them in form of simple rules. Rules are extracted for data classification using training set of data points. These rules are then applied to set of data in the testing/validation set to obtain the classification accuracy. A major attraction in ACO based classification is the possibility of obtaining an expert system like rules that can be directly applied subsequently by the user in his/her application. The classification accuracy obtained in ACO based approach is as good as obtained in other biologically inspired techniques.