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The Digital Orrery has been used to perform an integration of the motion of the outer planets for 845 million years. This integration indicates that the long-term motion of the planet Pluto is chaotic. Nearby trajectories diverge exponentially with an e-folding time of only about 20 million years.
We present our temporal and spectral analyses of 29 bursts from SGRJ0501+4516, detected with the Gamma-ray Burst Monitor onboard the Fermi Gamma-ray Space Telescope during the 13 days of the source activation in 2008 (August 22 to September 3). We find that the T(sub 90) durations of the bursts can be fit with a log-normal distribution with a mean value of approx. 123 ms. We also estimate for the first time event durations of Soft Gamma Repeater (SGR) bursts in photon space (i.e., using their deconvolved spectra) and find that these are very similar to the T(sub 90)s estimated in count space (following a log-normal distribution with a mean value of approx. 124 ms). We fit the time-integrated spectra for each burst and the time-resolved spectra of the five brightest bursts with several models. We find that a single power law with an exponential cutoff model fits all 29 bursts well, while 18 of the events can also be fit with two black body functions. We expand on the physical interpretation of these two models and we compare their parameters and discuss their evolution. We show that the time-integrated and time-resolved spectra reveal that E(sub peak) decreases with energy flux (and fluence) to a minimum of approx. 30 keV at F = 8.7 x 10(exp -6)erg/sq cm/s, increasing steadily afterwards. Two more sources exhibit a similar trend: SGRs J1550 - 5418 and 1806 - 20. The isotropic luminosity, L(sub iso), corresponding to these flux values is roughly similar for all sources (0.4 - l.5 x 10(exp 40) erg/s.
Three innovative software inventions from Ames Research Center (NETMARK, Program Management Tool, and Query-Based Document Management) are finding their way into NASA missions as well as industry applications. The first, NETMARK, is a program that enables integrated searching of data stored in a variety of databases and documents, meaning that users no longer have to look in several places for related information. NETMARK allows users to search and query information across all of these sources in one step. This cross-cutting capability in information analysis has exponentially reduced the amount of time needed to mine data from days or weeks to mere seconds. NETMARK has been used widely throughout NASA, enabling this automatic integration of information across many documents and databases. NASA projects that use NETMARK include the internal reporting system and project performance dashboard, Erasmus, NASA s enterprise management tool, which enhances organizational collaboration and information sharing through document routing and review; the Integrated Financial Management Program; International Space Station Knowledge Management; Mishap and Anomaly Information Reporting System; and management of the Mars Exploration Rovers. Approximately $1 billion worth of NASA s projects are currently managed using Program Management Tool (PMT), which is based on NETMARK. PMT is a comprehensive, Web-enabled application tool used to assist program and project managers within NASA enterprises in monitoring, disseminating, and tracking the progress of program and project milestones and other relevant resources. The PMT consists of an integrated knowledge repository built upon advanced enterprise-wide database integration techniques and the latest Web-enabled technologies. The current system is in a pilot operational mode allowing users to automatically manage, track, define, update, and view customizable milestone objectives and goals. The third software invention, Query-Based Document Management (QBDM) is a tool that enables content or context searches, either simple or hierarchical, across a variety of databases. The system enables users to specify notification subscriptions where they associate "contexts of interest" and "events of interest" to one or more documents or collection(s) of documents. Based on these subscriptions, users receive notification when the events of interest occur within the contexts of interest for associated document or collection(s) of documents. Users can also associate at least one notification time as part of the notification subscription, with at least one option for the time period of notifications.
In this work, we analyze the out-of-time-order correlation functions of a solvable model of a large number $\textit{N}$ of $\textit{M}$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. We focus on the growth of commutators of operators at a temperature $\textit{T}$ above the zero temperature quantum critical point separating the spin-glass and paramagnetic phases. In the large $\textit{N, M}$ limit, the squared commutators of the rotor fields do not display any exponential growth of commutators, in spite of the absence of any sharp quasiparticlelike excitations in the disorder-averaged theory. We show that in this limit, the problem is integrable and points out interesting connections to random-matrix theory. At leading order in 1/$\textit{M}$, there are no modifications to the critical behavior but an irrelevant term in the fixed-point action leads to a small exponential growth of the squared commutator. We also introduce and comment on a generalized model involving $\textit{p}$-pair rotor interactions.
The ablation of carbon-phenolic heat shields upon entry into the atmosphere of one of the outer planets leads to the injection of large amounts of C, C2, and C3 into the shock layer. These species must be included in the calculation of transport properties in the shock layer. The kinetic theory of gases has been used to obtain accurate results for the transport properties of monatomic carbon. The Hulburt-Hirschelder potential, the most accurate general purpose atom-atom potential for states with an attractive minimum, was used to represent such states and repulsive states were represented by fitting quantum mechanical potential energy curves with the exponential repulsive potential. These results were orientation averaged according to the peripheral force model to obtain transport collision integrals for the C-C2 and C2-C2 interaction. Results for C3 were obtained by ignoring the presence of the central carbon atom. The thermal conductivity, viscosity, and diffusion coefficients for pure C, C2, and C3, and for mixtures of these gases, were then calculated from 1000 K - 25,000 K.
A simple solution has been developed for the long term behavior of a near-circular orbit in a zonal gravity field. The solution is obtained by linearizing the singly averaged variational equations of motion and eliminating a degree of freedom with an integral of motion. The resulting solution is expressed in semiequinoctial elements (h and k), and has either an exponential or periodic form. The type of solution is dependent upon a stability factor determined by the inclination and the values of the gravity field coefficients. Frozen orbits correspond to the equilibrium solutions of the set of simplified variational equations. An approximate expression for the location of these orbits has been developed and can be useful for certain mission design applications.
Consequence-driven Cybersecurity Analysis for Extreme Fast Charging Electric Vehicle Infrastructure Electric vehicle (EV) development and associated charging infrastructure are expected to advance rapidly. Thirty percent of all global vehicle sales may be EVs and hybrid EVs by 2025, and they will rely on increasingly sophisticated strategies for grid integration. Next-generation EV charging infrastructure is expected to include interconnected renewable resources, such as photovoltaic (PV) arrays and battery storage systems, along with grid-edge devices. Although distributed energy resources (DERs) are useful in several ways, such as peak shaving at high demand times and backup supply for added resilience, the integration of vehicle charging and DERs could create more avenues for cyberattack. Physical and/or remote access to EV charging station components, including charge ports, power electronics, controllers, and local generation (e.g., PV and energy storage) could be paths to cause power fluctuations, leading to altered operations at the charging station, escalated privileges to administrative systems, exfiltration of financial information (including personally identifiable information), and reduced grid stability. One compromised EV supply equipment component can open the door to a variety of exploitable vulnerabilities. Cloud computing and mobile application control have the potential to expand the threat surface to non-repudiation and firmware integrity challenges. Vendor clouds have access to hundreds of chargers, and if compromised, can scale the attack surface exponentially. The high power and voltage levels of xFC infrastructure (e.g., 400 kW at 1000- V DC) increase the hazards and ability to impact the grid and vehicles more than lower-power charging systems. Legacy communications systems and protocols could also put EV infrastructure at risk of cyberattacks requiring a robust patch management process. Communications networks link EVs and chargers to several stakeholders - including charging station operators, grid operators, vendors/manufacturers, and aggregators - who have both physical and network access to share information for control, monitoring, and analytics. Information in these networks that is vulnerable to compromise includes the state of charge, charging duration, payment information, electricity price, and load control. Analyzing and prioritizing these interconnections risks could help address cybersecurity related to data leakage and manipulation.
Viscous flow serves as a significant heating mechanism during the formation of hot spots, but the shear viscosity which determines this response is poorly characterized for most high explosives. Most recently, a model was proposed for the shear viscosity of liquid HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) that was fit to pressures reaching 5 GPa, but this work uncovered uncertainties in the viscosity at 0 GPa and remains untested at higher pressures. We use molecular dynamics (MD) simulations and the Green-Kubo formalism to predict the temperature- and pressure-dependent shear viscosity of HMX over the pressure interval 0 GPa≤P≤40 GPa. Reassessment of the viscosity at 0 GPa rules out several potential explanations for discrepancies between earlier reports; we attribute these differences to details of MD trajectory integration impacting molecular flexibility. The shear viscosity of HMX exhibits an Arrhenius temperature dependence at each pressure considered, with exponential prefactor and activation energy terms that are also strong functions of pressure. An analytic form for the viscosity is developed based on an extension of the well-known Andrade equation that simultaneously captures the temperature and pressure dependencies in the MD data up to 40 GPa. Comparison against a recently developed model for the viscosity of liquid RDX (1,3,5-trinitro-1,3,5-triazinane) shows that both materials exhibit similar functional dependencies with the viscosity of HMX being higher by roughly an order of magnitude at a given temperature-pressure state.
ABSTRACT The spatial distribution of mono-abundance populations (MAPs, selected in [Fe/H] and [Mg/Fe]) reflect the chemical and structural evolution in a galaxy and impose strong constraints on galaxy formation models. In this paper, we use APOGEE data to derive the intrinsic density distribution of MAPs in the Milky Way, after carefully considering the survey selection function. We find that a single exponential profile is not a sufficient description of the Milky Way’s disc. Both the individual MAPs and the integrated disc exhibit a broken radial density distribution; densities are relatively constant with radius in the inner Galaxy and rapidly decrease beyond the break radius. We fit the intrinsic density distribution as a function of radius and vertical height with a 2D density model that considers both a broken radial profile and radial variation of scale height (i.e. flaring). There is a large variety of structural parameters between different MAPs, indicative of strong structure evolution of the Milky Way. One surprising result is that high-α MAPs show the strongest flaring. The young, solar-abundance MAPs present the shortest scale height and least flaring, suggesting recent and ongoing star formation confined to the disc plane. Finally we derive the intrinsic density distribution and corresponding structural parameters of the chemically defined thin and thick discs. The chemical thick and thin discs have local surface mass densities of 5.62 ± 0.08 and 15.69 ± 0.32 M⊙pc−2, respectively, suggesting a massive thick disc with a local surface mass density ratio between thick to thin disc of 36 per cent.
Endfire-tapered slot antennas are suitable for many integrated circuit applications, imaging and phased arrays. An investigation of single elements of such antennas, including slots which are exponentially tapered (Vivaldi), linearly tapered, and constant width. For antennas of all types, a good general agreement is obtained for curves of beamwidth-versus-length, normalized to wavelength, when one compares the data with that for traveling-wave antennas published by Zucker (1961). An important condition for this agreement is that the effective dielectric thickness, defined in the text, is in a certain optimum range. This condition is qualitatively explained in terms of the theory for traveling-wave antennas.
Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.
We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator e -iHt whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion — the Eigenstate Complexity Hypothesis (ECH) — which bounds the overlap between offdiagonal energy eigenstate projectors and the k-local operators of the theory, and use it to argue that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with N = 2 fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE * BQP/poly and PSPACE * BQSUBEXP/subexp, and the “fast-forwarding” of quantum Hamiltonians.
Previous work shows that the mean time from lock to a slipped cycle of a phase-locked loop is given by a certain double integral. Accurate numerical evaluation of this formula for the second-order loop is extremely vexing because the difference between exponentially large quantities is involved. The presented article demonstrates a method in which a much-reduced precision program can be used to obtain the mean first-cycle slip time for a loop of arbitrary degree tracking at a specified SNR and steady-state phase error. It also presents a simple approximate formula that is asymptotically tight at higher loop SNR.
Emerging technology is enabling the design community to consistently expand the amount of functionality that can be implemented within Integrated Circuits (ICs). As the number of gates placed within an FPGA increases, the complexity of the design can grow exponentially. Consequently, the ability to create reliable circuits has become an incredibly difficult task. In order to ease the complexity of design completion, the commercial design community has developed a very rigid (but effective) design methodology based on synchronous circuit techniques. In order to create faster, smaller and lower power circuits, transistor geometries and core voltages have decreased. In environments that contain ionizing energy, such a combination will increase the probability of Single Event Upsets (SEUs) and will consequently affect the state space of a circuit. In order to combat the effects of radiation, the aerospace community has developed several "Hardened by Design" (fault tolerant) design schemes. This paper will address design mitigation schemes targeted for SRAM Based FPGA CMOS devices. Because some mitigation schemes may be over zealous (too much power, area, complexity, etc.. . .), the designer should be conscious that system requirements can ease the amount of mitigation necessary for acceptable operation. Therefore, various degrees of Fault Tolerance will be demonstrated along with an analysis of its effectiveness.
As crewed missions move beyond Low-Earth Orbit, pre-mission planning cannot fully buy down the medical risks of exploration-class missions. Martian missions, where increased hazards exist, (such as long-duration spaceflight, surface-level EVA operations, and communications delays) will require a paradigm shift in the structure of a medical system. An Earth-Independent Medical Operations-based Medical System (EIMO-MS) will need to optimize four critical domains to help provide medical care: utilization of Pre-Mission Planning, augmentation of Acute and Prolonged Medical Decision Making, automated tracking of Resource Management, and assistance in Task Load Balance. The ideal EIMO-MS will be able to accomplish this goal by having an interactive, adaptable interface that will be able to provide real-time medical services. It must respond based on the level of crewmember training, medical situation, and available medical and non-medical resources. To showcase the capabilities and requirements of such a sophisticated automated MS, a series of clinical scenarios of escalating complexity were developed with clinical and systems engineering input. These scenarios describe in clinical detail what a theoretical future medical system, enhanced with multiple information streams (such as a medical database, an AI-based Decision Support System, real-time monitoring, enhanced in-situ laboratory imaging, etc.) can achieve in conjunction with a trained and experienced crew. Scenarios are comprised of: a context section including objectives and applicable spaceflight environment, a highlighted assumptions section, a clinical narrative section, and a systems engineering activity diagram demonstrating the integrated Medical System (MS). The “swim lanes” of the activity diagram act as the logistical core of each scenario and show how the MS will interact with the crew, ground support, and other in-flight systems. The Design Reference Mission that is used for the scenarios is based on existing reference mission profiles [1] with a projected 30-sol stay on the Martian surface. Scenarios span the spectrum from planned evaluations, minor medical care, urgent care, surgical guidance, critical and expectant management, and behavioral health care. Mission complexity will exponentially increase during deep space and Mars exploration-class missions, and medical support for these missions will likewise need to increase in autonomy and adaptability. The integrated system that will support these missions will need to provide assistance in a variety of anticipated and unforeseen scenarios. These medical scenarios, guided by clinician input, are initial steps in crafting the requirements for an EIMO-based medical system. By working in a systems engineering framework, requirements and capabilities can be extracted and mapped while maintaining a clinical core.
We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method first relates the finite-volume spectrum to an infinite-volume short-range quantity, denoted ${\mathcal{M}}_0$, and then relates the latter to the physical scattering amplitudes via known integral equations. The derivation of both relations is performed using all-orders perturbation theory and is exact up to neglected exponentially suppressed volume dependence. The relations hold for arbitrary two-particle systems with any number of coupled channels, non-identical and non-degenerate particles, and any intrinsic spin.
For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.
The present invention discloses systematic methods and apparatus for the design of real time controllers. Real-time control employs adaptive force/position by use of feedforward and feedback controllers, with the feedforward controller being the inverse of the linearized model of robot dynamics and containing only proportional-double-derivative terms is disclosed. The feedback controller, of the proportional-integral-derivative type, ensures that manipulator joints follow reference trajectories and the feedback controller achieves robust tracking of step-plus-exponential trajectories, all in real time. The adaptive controller includes adaptive force and position control within a hybrid control architecture. The adaptive controller, for force control, achieves tracking of desired force setpoints, and the adaptive position controller accomplishes tracking of desired position trajectories. Circuits in the adaptive feedback and feedforward controllers are varied by adaptation laws.