We deploy the theory of the generalized three-body problem to describe an exosystem composed of a host star, a transiting Jupiter-sized exoplanet, and an Earth-sized exoplanet. By performing a thorough and systematic orbit classification we map a large section of the phase space and determine the final states of the Earth-sized exoplanet. In particular, we manage to classify the initial conditions of the perturber into several categories such as bounded regular or chaotic motion, collision, and escaping motion. Bounded regular motion corresponds to regions of the phase space in which the orbit of the Earth-sized planet would be stable. In our computations, we use realistic values of the involved parameters and initial conditions corresponding to real observable exosystems. Our analysis provides important information on how the mass of the host star as well as the mass of the Jupiter size affects the orbital dynamics of the Earth-sized exoplanet.
Plasma actuators generated by surface dielectric barrier discharge are developed for controlling flow in aeronautics applications. This research studies the simulation of cold plasma discharge at atmospheric pressure coupled with compressible fluid dynamics using COMSOL Multiphysics 5.4. Modeling of dielectric barrier discharge in air at high voltages is carried out in two dimensions. The development of electric field and space charge density are discussed in several cases to determine the discharge regime. Non-thermal plasma generates tangential ionic winds at the surface during corona discharge. The results are validated by the experimental results of the literature. The maximum electric wind velocity above the actuator grows linearly with the applied voltage, and simultaneously, the horizontal extension of the discharge grows with the applied voltage. The induced electrohydrodynamic force augments with the applied voltage amplitude, reaching saturation at higher voltages. Moreover, as the voltage rises, the discharge becomes filamentary, inducing a higher number of streamer pulses. Hence, the power consumption discharge increases abruptly as the voltage rises. In addition, the efficiency increases at higher voltage amplitudes and with the dielectric thickness. Our findings give a clear description of physical atmospheric plasma parameters in the surface discharge mechanism and the efficiency of the actuator plasma.
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