Fractal Measures and Nonlinear Dynamics of Overcontact Binaries

Overcontact binary stars are systems of two stars where the component stars are in contact with each other. This implies that they share a common envelope of gas. In this work we seek signatures of nonlinearity and chaos in these stars by using time series analysis techniques. We use three main techniques, namely the correlation dimension,f (\alpha) spectrum and the bicoherence. The former two are calculated from the reconstructed dynamics, while the latter is calculated from the Fourier transforms of the time series of intensity variations(light curves) of these stars. Our dataset consists of data from 463 overcontact binary stars in the Kepler field of view [1]. Our analysis indicates nonlinearity and signatures of chaos in almost all the light curves. We also explore whether the underlying nonlinear properties of the stars are related to their physical properties like fill-out-factor, a measure of the extend of contact between the components of an overcontact binary system . We observe that significant correlations exist between the fill out factor and the nonlinear quantifiers. This correlation is more pronounced in specific subcategories constructed based on the mass ratios and effective temperatures of the binaries. The correlations observed can be indicative of variations in the nonlinear properties of the star as it ages. We believe that this study relating nonlinear and astrophysical properties of binary stars is the first of its kind and is an important starting point for such studies in other astrophysical objects displaying nonlinear dynamical behaviour.Comment: 17 pages, 12 figures, submitted to Communications in Nonlinear Science and Numerical Simulatio

Quaternion-based complexity study of human postural sway time series

A multidimensional approach for the study of the center of pressure (CoP) was selected. During the work the dataset was characterized recurring to algorithms taken from Chaotic and Stochastic time series analysis. The effects of the visual and cognitive components were addressed to allow a proper modelization of the data in the complex and quaternion domains

Chaotic coyote algorithm applied to truss optimization problems

The optimization of truss structures is a complex computing problem with many local minima, while metaheuristics are naturally suited to deal with multimodal problems without the need of gradient information. The Coyote Optimization Algorithm (COA) is a population-based nature-inspired metaheuristic of the swarm intelligence field for global optimization that considers the social relations of the coyote proposed to single-objective optimization. Unlike most widespread algorithms, its population is subdivided in packs and the internal social influences are designed. The COA requires a few control hyperparameters including the number of packs, the population size, and the number maximum of generations. In this paper, a modified COA (MCOA) approach based on chaotic sequences generated by Tinkerbell map to scatter and association probabilities tuning and an adaptive procedure of updating parameters related to social condition is proposed. It is then validated by four benchmark problems of structures optimization including planar 52-bar truss, spatial 72-bar truss, 120-bar dome truss and planar 200 bar-truss with discrete design variables and focus in minimization of the structure weight under the required constraints. Simulation results collected in the mentioned problems demonstrate that the proposed MCOA presented competitive solutions when compared with other state-of-the-art metaheuristic algorithms in terms of results quality

Stochasticity & Predictability in Terrestrial Planet Formation

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array of final planetary configurations. This is a result of the chaotic evolution of trajectories which are highly sensitive to minuscule displacements. We determine that differences between systems evolved from virtually identical initial conditions can be larger than the differences between systems evolved from very different initial conditions. This implies that individual simulations lack predictive power. For example, there is not a reproducible mapping between the initial and final surface density profiles. However, some key global properties can still be extracted if the statistical spread across many simulations is considered. Based on these spreads, we explore the collisional growth and orbital properties of terrestrial planets which assemble from different initial conditions (we vary the initial planetesimal distribution, planetesimal masses, and giant planet orbits). Confirming past work, we find that the resulting planetary systems are sculpted by sweeping secular resonances. Configurations with giant planets on eccentric orbits produce fewer and more massive terrestrial planets on tighter orbits than those with giants on circular orbits. This is further enhanced if the initial mass distribution is biased to the inner regions. In all cases, the outer edge of the system is set by the final location of the $\nu_6$ resonance and we find that the mass distribution peaks at the $\nu_5$ resonance. Using existing observations, we find that extrasolar systems follow similar trends. Although differences between our numerical modelling and exoplanetary systems remain, we suggest that CoRoT-7, HD 20003, and HD 20781 may host undetected giant planets.Comment: replaced to match published version, 20 pages, 11 figures, published in MNRAS, simulation outputs available at https://cheleb.net/astro/sp15

Crosshair Optimizer

Metaheuristic optimization algorithms are heuristics that are capable of creating a good enough\u27\u27 solution to a computationally complex problem. Algorithms in this area of study are focused on the process of exploration and exploitation: exploration of the solution space and exploitation of the results that have been found during that exploration, with most resources going toward the former half of the process. The novel Crosshair optimizer developed in this thesis seeks to take advantage of the latter, exploiting the best possible result as much as possible by directly searching the area around that best result with a stochastic approach. This research seeks to prove that the Crosshair Optimizer is comparable, if not better in some aspects, to current established metaheuristics optimization algorithms, not only in obtaining optimal results, but usability in high performance computing, and versatility through the use of multiple randomizers and parameter tuning