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.

Wireless Sensor Networks for Organizational Network Analysis

Since their emergence, wireless sensor networks (WSNs) have become increasingly popular in the pervasive computing industry. This is particularly true within the past five years, which has seen sensor networks being adapted for wide variety of applications. Most of these applications are restricted to ambience monitoring and military use, however, very few commercial sensor applications have been explored till date. For WSNs to be truly ubiquitous, many more commercial sensor applications are yet to be investigated. As an effort to probe for such an application, we explore the potential of using WSNs in the field of Organizational Network Analysis (ONA). In this short paper, we propose a WSN based framework for analyzing organizational networks. We describe the role of WSNs in learning relationships among the people of an organization and investigate the research challenges involved in realizing the proposed framework.

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).