The fates of Solar system analogues with one additional distant planet

The potential existence of a distant planet ("Planet Nine") in the Solar system has prompted a re-think about the evolution of planetary systems. As the Sun transitions from a main sequence star into a white dwarf, Jupiter, Saturn, Uranus and Neptune are currently assumed to survive in expanded but otherwise unchanged orbits. However, a sufficiently-distant and sufficiently-massive extra planet would alter this quiescent end scenario through the combined effects of Solar giant branch mass loss and Galactic tides. Here, I estimate bounds for the mass and orbit of a distant extra planet that would incite future instability in systems with a Sun-like star and giant planets with masses and orbits equivalent to those of Jupiter, Saturn, Uranus and Neptune. I find that this boundary is diffuse and strongly dependent on each of the distant planet's orbital parameters. Nevertheless, I claim that instability occurs more often than not when the planet is as massive as Jupiter and harbours a semimajor axis exceeding about 300 au, or has a mass of a super-Earth and a semimajor axis exceeding about 3000 au. These results hold for orbital pericentres ranging from 100 to at least 400 au. This instability scenario might represent a common occurrence, as potentially evidenced by the ubiquity of metal pollution in white dwarf atmospheres throughout the Galaxy.Comment: Accepted for publication in MNRA

Evaporation and Accretion of Extrasolar Comets Following White Dwarf Kicks

Several lines of observational evidence suggest that white dwarfs receive small birth kicks due to anisotropic mass loss. If other stars possess extrasolar analogues to the Solar Oort cloud, the orbits of comets in such clouds will be scrambled by white dwarf natal kicks. Although most comets will be unbound, some will be placed on low angular momentum orbits vulnerable to sublimation or tidal disruption. The dusty debris from these comets will manifest itself as an IR excess temporarily visible around newborn white dwarfs; examples of such disks may already have been seen in the Helix Nebula, and around several other young white dwarfs. Future observations with the James Webb Space Telescope may distinguish this hypothesis from alternatives such as a dynamically excited Kuiper Belt analogue. Although competing hypotheses exist, the observation that $\gtrsim 15\%$ of young white dwarfs possess such disks, if interpreted as indeed being cometary in origin, provides indirect evidence that low mass gas giants (thought necessary to produce an Oort cloud) are common in the outer regions of extrasolar planetary systems. Hydrogen abundances in the atmospheres of older white dwarfs can, if sufficiently low, also be used to place constraints on the joint parameter space of natal kicks and exo-Oort cloud models.Comment: 22 pages, 13 figures, published in MNRAS. Changes made to match published versio

Hamstrings force-length relationships and their implications for angle-specific joint torques: a narrative review

Temporal biomechanical and physiological responses to physical activity vary between individual hamstrings components as well as between exercises, suggesting that hamstring muscles operate differently, and over different lengths, between tasks. Nevertheless, the force-length properties of these muscles have not been thoroughly investigated. The present review examines the factors influencing the hamstrings’ force-length properties and relates them to in vivo function. A search in four databases was performed for studies that examined relations between muscle length and force, torque, activation, or moment arm of hamstring muscles. Evidence was collated in relation to force-length relationships at a sarcomere/fiber level and then moment arm-length, activation-length, and torque-joint angle relations. Five forward simulation models were also used to predict force-length and torque-length relations of hamstring muscles. The results show that, due to architectural differences alone, semitendinosus (ST) produces less peak force and has a flatter active (contractile) fiber force-length relation than both biceps femoris long head (BFlh) and semimembranosus (SM), however BFlh and SM contribute greater forces through much of the hip and knee joint ranges of motion. The hamstrings’ maximum moment arms are greater at the hip than knee, so the muscles tend to act more as force producers at the hip but generate greater joint rotation and angular velocity at the knee for a given muscle shortening length and speed. However, SM moment arm is longer than SM and BFlh, partially alleviating its reduced force capacity but also reducing its otherwise substantial excursion potential. The current evidence, bound by the limitations of electromyography techniques, suggests that joint angle-dependent activation variations have minimal impact on force-length or torque-angle relations. During daily activities such as walking or sitting down, the hamstrings appear to operate on the ascending limbs of their force-length relations while knee flexion exercises performed with hip angles 45 – 90° promote more optimal force generation. Exercises requiring hip flexion at 45 – 120° and knee extension 45 – 0° (e.g. sprint running) may therefore evoke greater muscle forces and, speculatively, provide a more optimum adaptive stimulus. Finally, increases in resistance to stretch during hip flexion beyond 45° result mainly from SM and BFlh muscles

Deep Learning -Powered Computational Intelligence for Cyber-Attacks Detection and Mitigation in 5G-Enabled Electric Vehicle Charging Station

An electric vehicle charging station (EVCS) infrastructure is the backbone of transportation electrification. However, the EVCS has various cyber-attack vulnerabilities in software, hardware, supply chain, and incumbent legacy technologies such as network, communication, and control. Therefore, proactively monitoring, detecting, and defending against these attacks is very important. The state-of-the-art approaches are not agile and intelligent enough to detect, mitigate, and defend against various cyber-physical attacks in the EVCS system. To overcome these limitations, this dissertation primarily designs, develops, implements, and tests the data-driven deep learning-powered computational intelligence to detect and mitigate cyber-physical attacks at the network and physical layers of 5G-enabled EVCS infrastructure. Also, the 5G slicing application to ensure the security and service level agreement (SLA) in the EVCS ecosystem has been studied. Various cyber-attacks such as distributed denial of services (DDoS), False data injection (FDI), advanced persistent threats (APT), and ransomware attacks on the network in a standalone 5G-enabled EVCS environment have been considered. Mathematical models for the mentioned cyber-attacks have been developed. The impact of cyber-attacks on the EVCS operation has been analyzed. Various deep learning-powered intrusion detection systems have been proposed to detect attacks using local electrical and network fingerprints. Furthermore, a novel detection framework has been designed and developed to deal with ransomware threats in high-speed, high-dimensional, multimodal data and assets from eccentric stakeholders of the connected automated vehicle (CAV) ecosystem. To mitigate the adverse effects of cyber-attacks on EVCS controllers, novel data-driven digital clones based on Twin Delayed Deep Deterministic Policy Gradient (TD3) Deep Reinforcement Learning (DRL) has been developed. Also, various Bruteforce, Controller clones-based methods have been devised and tested to aid the defense and mitigation of the impact of the attacks of the EVCS operation. The performance of the proposed mitigation method has been compared with that of a benchmark Deep Deterministic Policy Gradient (DDPG)-based digital clones approach. Simulation results obtained from the Python, Matlab/Simulink, and NetSim software demonstrate that the cyber-attacks are disruptive and detrimental to the operation of EVCS. The proposed detection and mitigation methods are effective and perform better than the conventional and benchmark techniques for the 5G-enabled EVCS

Virtual Structures Based Autonomous Formation Flying Control for Small Satellites

Many space organizations have a growing need to fly several small satellites close together in order to collect and correlate data from different satellite sensors. To do this requires teams of engineers monitoring the satellites orbits and planning maneuvers for the satellites every time the satellite leaves its desired trajectory or formation. This task of maintaining the satellites orbits quickly becomes an arduous and expensive feat for satellite operations centers. This research develops and analyzes algorithms that allow satellites to autonomously control their orbit and formation without human intervention. This goal is accomplished by developing and evaluating a decentralized, optimization-based control that can be used for autonomous formation flight of small satellites. To do this, virtual structures, model predictive control, and switching surfaces are used. An optimized guidance trajectory is also develop to reduce fuel usage of the system. The Hill-Clohessy-Wiltshire equations and the D\u27Amico relative orbital elements are used to describe the relative motion of the satellites. And a performance comparison of the L1, L2, and L∞ norms is completed as part of this work. The virtual structure, MPC based framework combined with the switching surfaces enables a scalable method that allows satellites to maneuver safely within their formation, while also minimizing fuel usage

Definition of Low Earth Orbit slotting architectures using 2D lattice flower constellations

This work proposes the use of 2D Lattice Flower Constellations (2D-LFCs) to facilitate the design of a Low Earth Orbit (LEO) slotting system to avoid collisions between compliant satellites and to optimize the available orbital volume. Specifically, this manuscript proposes the use of concentric orbital shells of admissible “slots” with stacked intersecting orbits that preserve a minimum separation distance between satellites at all times. The problem is formulated in mathematical terms and three approaches are explored: random constellations, single 2D-LFCs, and unions of 2D-LFCs. Each approach is evaluated in terms of several metrics including capacity, Earth coverage, orbits per shell, and symmetries. Additionally, a rough estimate for the capacity of LEO is generated, subject to certain minimum separation and station-keeping assumptions, and several trade-offs are identified to guide policy-makers interested in the adoption of a LEO slotting scheme for space traffic management

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre