1I/`Oumuamua as a Tidal Disruption Fragment From a Binary Star System

1I/`Oumuamua is the first known interstellar small body, probably being only about 100~m in size. Against expectations based on comets, `Oumuamua does not show any activity and has a very elongated figure, and also exhibits undamped rotational tumbling. In contrast, `Oumuamua's trajectory indicates that it was moving with the local stars, as expected from a low-velocity ejection from a relatively nearby system. Here I assume that `Oumuamua is typical of 100-m interstellar objects, and speculate on its origins. I find that giant planets are relatively inefficient at ejecting small bodies from inner solar systems of main-sequence stars, and that binary systems offer a much better opportunity for ejections of non-volatile bodies. I also conclude that `Oumuamua is not a member of a collisional population, which could explain its dramatic difference from small asteroids. I observe that 100-m small bodies are expected to carry little mass in realistic collisional populations, and that occasional events when whole planets are disrupted in catastrophic encounters may dominate interstellar population of 100-m fragments. Unlike the Sun or Jupiter, red dwarf stars are very dense and are capable of thoroughly tidally disrupting terrestrial planets. I conclude that the origin of `Oumuamua as a fragment from a planet that was tidally disrupted and then ejected by a dense member of a binary system could explain its peculiarities.Comment: Revised for ApJ

Planetary Chaos and the (In)stability of Hungaria Asteroids

The Hungaria asteroid group is located interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16-35 degrees. Recently, it has been proposed that Hungaria asteroids are a secularly declining population that may be related to the Late Heavy Bombardment (LHB) impactors (\'Cuk et al. 2012, Bottke et al. 2012). While \'Cuk et al. (2012) and Bottke et al. (2012) have reproduced a Hungaria-like population that declined exponentially, the real Hungarias were never confirmed to be unstable to the same degree. Here we find that the stability of Hungarias is strongly dependent on the evolution of the eccentricity of Mars, which is chaotic and unpredictable on Gyr timescales. We find that the high Martian eccentricity chiefly affects Hungarias through close approaches with Mars, rather than planetary secular modes. However, current minimum perihelia of Hungarias (over Myr timescales) are not diagnostic of their long-term stability due to a number of secular and mean motion resonances affecting the Hungaria region (Milani et al. 2010). We conclude that planetary chaos makes it impossible to determine the effective lifetimes of observed Hungarias. Furthermore, long-term changes of Martian eccentricity could lead to variable Hungaria loss over time. We speculate that some of the most stable Hungarias may have been placed in their present orbit when the eccentricity of Mars was significantly higher than today.Comment: Accepted for Icarus special issue on asteroid

A general approach to synthesis and analysis of quasi-resonant converters

A method for systematic synthesis of quasi-resonant (QR) topologies by addition of resonant elements to a parent pulse-width modulation (PWM) converter network is proposed. It is found that there are six QR classes with two resonant elements, including two novel classes. More complex QR converters can be generated by a recursive application of the synthesis method. Topological definitions of all known and novel QR classes follow directly from the synthesis method and topological properties of PWM parents. The synthesis of QR converters is augmented by a study of possible switch realizations and operating modes. In particular, it is demonstrated that a controllable rectifier can be used to accomplish the constant-frequency control in all QR classes. Links between the QR converters and the underlying PWM networks are extended to general DC and small-signal AC models in which the model of the PWM parent is explicitly exposed. Results of steady-state analyses of selected QR classes and operating modes include boundaries of operating regions, DC characteristics, a comparison of switching transitions and switch stresses, and a discussion of relevant design trade-offs

One-cycle control of switching converters

A new large-signal nonlinear control technique is proposed to control the duty-ratio d of a switch such that in each cycle the average value of a switched variable of the switching converter is exactly equal to or proportional to the control reference in the steady-state or in a transient. One-cycle control rejects power source perturbations in one switching cycle; the average value of the switched variable follows the dynamic reference in one switching cycle; and the controller corrects switching errors in one switching cycle. There is no steady-state error nor dynamic error between the control reference and the average value of the switched variable. Experiments with a constant frequency buck converter have demonstrated the robustness of the control method and verified the theoretical predictions. This new control method is very general and applicable to all types of pulse-width-modulated, resonant-based, or soft-switched switching converters for either voltage or current control in continuous or discontinuous conduction mode. Furthermore, it can be used to control any physical variable or abstract signal that is in the form of a switched variable or can be converted to the form of a switched variable

Switching Flow-Graph nonlinear modeling technique

A unified graphical modeling technique, “Switching Flow-Graph” is developed to study the nonlinear dynamic behavior of pulse-width-modulated (PWM) switching converters. Switching converters are variable structure systems with linear subsystems. Each subsystem can be represented by a flow-graph. The Switching Flow-Graph is obtained by combining the flowgraphs of the subsystems through the use of switching branches. The Switching Flow-Graph model is easy to derive, and it provides a visual representation of a switching converter system. Experiments demonstrate that the Switching Flow-Graph model has very good accuracy

Long-term Stable Equilibria for Synchronous Binary Asteroids

Synchronous binary asteroids may exist in a long-term stable equilibrium, where the opposing torques from mutual body tides and the binary YORP (BYORP) effect cancel. Interior of this equilibrium, mutual body tides are stronger than the BYORP effect and the mutual orbit semi-major axis expands to the equilibrium; outside of the equilibrium, the BYORP effect dominates the evolution and the system semi-major axis will contract to the equilibrium. If the observed population of small (0.1 - 10 km diameter) synchronous binaries are in static configurations that are no longer evolving, then this would be confirmed by a null result in the observational tests for the BYORP effect. The confirmed existence of this equilibrium combined with a shape model of the secondary of the system enables the direct study of asteroid geophysics through the tidal theory. The observed synchronous asteroid population cannot exist in this equilibrium if described by the canonical "monolithic" geophysical model. The "rubble pile" geophysical model proposed by \citet{Goldreich2009} is sufficient, however it predicts a tidal Love number directly proportional to the radius of the asteroid, while the best fit to the data predicts a tidal Love number inversely proportional to the radius. This deviation from the canonical and \citet{Goldreich2009} models motivates future study of asteroid geophysics. Ongoing BYORP detection campaigns will determine whether these systems are in an equilibrium, and future determination of secondary shapes will allow direct determination of asteroid geophysical parameters.Comment: 17 pages, 1 figur

Switching converters with wide DC conversion range

In dc-to-dc conversion applications that require a large range of input and/or output voltages, conventional PWM converter topologies must operate at extremely low duty ratios, which limits the operation to lower switching frequencies because of the minimum ON-time of the transistor switch. This is eliminated in a new class of single-transistor PWM converters featuring voltage conversion ratios with quadratic dependence on duty ratio. Practical circuit examples operating at 0.5 MHz are described

A unified analysis of PWM converters in discontinuous modes

Three discontinuous operating modes of PWM (pulsewidth modulated) converters are considered: the discontinuous inductor current mode (DICM), the discontinuous capacitor voltage mode (DCVM), and a previously unidentified mode called the discontinuous quasi-resonant mode (DQRM). DC and small-signal AC analyses are applicable to all basic PWM converter topologies. Any particular topology is taken into account via its DC conversion ratio in the continuous conduction mode. The small-signal model is of the same order as the state-space averaged model for the continuous mode, and it offers improved predictions of the low-frequency dynamics of PWM converters in the discontinuous modes. It is shown that converters in discontinuous modes exhibit lossless damping similar to the effect of the current-mode programming

General topological properties of switching structures

Investigation of a wide variety of switching converter topologies culminates in the establishment of the most general correlation between the converter topologies--the duality relationships. The recognition of this general law leads to a number of new results: new converter topologies generated by the application of the duality transformation to the existing converter configurations, the discovery of the new mode of converter operation (discontinuous capacitance voltage mode) as well as significantly improved understanding of the existing converters and their equivalent circuit models