Diffusion in Heterogenous Media and Sorption—Desorption Processes

We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., K(x) = D|x|−η, with −1 < η and D = const, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells.

A Gravity Assist Mapping Based on Gaussian Process Regression

We develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR). This work is inspired by the Keplerian Map and Flyby Map. The flyby is allowed to occur anywhere above 300 km altitude at the Earth in the system of Sun-(Earth+Moon)-spacecraft, whereas the Keplerian map is typically restricted to the cases outside the Hill sphere only. The performance of the GPR model and the influence of training samples (number and distribution) on the quality of the prediction of post-flyby orbital states are investigated. The information provided by this training set is used to optimize the hyper-parameters in the GPR model. The trained model can make predictions of the post-flyby state of an object with an arbitrary initial condition and is demonstrated to be efficient and accurate when evaluated against the results of numerical integration. The method can be attractive for space mission design.

Optimal Tuning of Single-Axis Satellite Attitude Control Parameters Using Genetic Algorithm

This paper studies the optimization of control parameters for single-axis attitude control of a rigid satellite using thrusters. It is desired to tune the control parameters to minimize the number of thruster firings. The motion task is defined as an attitude pointing maneuver from arbitrary initial condition to the rest. To this end, a control loop with pulse-width pulse-frequency modulator is suggested. The control actuators are pairs of identical non-ideal thrusters which each one produces torque in one direction around the control axis. A novel approach is proposed to model the dynamics of thruster with a design parameter which shapes the response of the actuator. Nine parameters of the control loop, e.g. feedback gains, modulator parameters, and thruster dynamics, are selected as decision variables. Genetic algorithm is used to find the optimal values of the variables such that the firing is minimized. It is shown that firing minimization requires a sluggish thruster. Moreover, to study the effect of deviation from optimal value on number of thruster firings and fuel consumption, a sensitivity analysis is performed. Based on sensitivity analysis, an optimal range is suggested for each parameter where both number of firing and fuel consumption are minimized.

Machine Learning for Turbulence Modeling and Predictions

A stand-alone machine learned turbulence model is applied for the solution of integral boundary layer equations, and issues and constraints associated with the model are discussed. The results demonstrate that grouping flow variables into a problem relevant parameter for input during machine learning is desirable to improve accuracy of the model. Further, the accuracy of the model can be improved significantly by incorporation of physics-based constraints during training. Data driven machine learning training requires trial-and-error approach, shows oscillations in a posteriori predictions, and shows unphysical results when used with arbitrary initial condition, as the query is essentially extrapolations. Physics informed machine learning addresses the above limitations, and is identified to be a viable approach for development of machine learned turbulence model.

Global stability in a nonlocal reaction-diffusion equation

We study stability of stationary solutions for a class of nonlocal semilinear parabolic equations. To this end, we prove the Feynman–Kac formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation arising in population ecology. For this equation, we find conditions which imply that its positive stationary solution is asymptotically stable. We consider also the case when the initial condition is given by a random field.

Evolving Network Model That Almost Regenerates Epileptic Data

In many realistic networks, the edges representing the interactions between nodes are time varying. Evidence is growing that the complex network that models the dynamics of the human brain has time-varying interconnections, that is, the network is evolving. Based on this evidence, we construct a patient- and data-specific evolving network model (comprising discrete-time dynamical systems) in which epileptic seizures or their terminations in the brain are also determined by the nature of the time-varying interconnections between the nodes. A novel and unique feature of our methodology is that the evolving network model remembers the data from which it was conceived from, in the sense that it evolves to almost regenerate the patient data even on presenting an arbitrary initial condition to it. We illustrate a potential utility of our methodology by constructing an evolving network from clinical data that aids in identifying an approximate seizure focus; nodes in such a theoretically determined seizure focus are outgoing hubs that apparently act as spreaders of seizures. We also point out the efficacy of removal of such spreaders in limiting seizures.