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Systems consisting of several maximally charged, nonrotating black holes ('Reissner-Nordstrom' black holes) interacting with one another are studied. An effective action for the system in the slow-motion, fully strong-field regime is presented. An exact calculation of black-hole-black-hole scattering and coalescence in the slow-motion (but strong-field) limit is given.
Abstract Weak form equation learning and surrogate modeling has proven to be computationally efficient and robust to measurement noise in a wide range of applications including ODE, PDE, and SDE discovery, as well as in coarse-graining applications, such as homogenization and mean-field descriptions of interacting particle systems. In this work we extend this coarse-graining capability to the setting of Hamiltonian dynamics which possess approximate symmetries associated with timescale separation. A smooth $$\varepsilon$$ ε -dependent Hamiltonian vector field $$X_\varepsilon$$ X ε possesses an approximate symmetry if the limiting vector field $$X_0=\lim _{\varepsilon \rightarrow 0}X_\varepsilon$$ X 0 = lim ε → 0 X ε possesses an exact symmetry. Such approximate symmetries often lead to the existence of a Hamiltonian system of reduced dimension that may be used to efficiently capture the dynamics of the symmetry-invariant dependent variables. Deriving such reduced systems, or approximating them numerically, is an ongoing challenge. We demonstrate that WSINDy can successfully identify this reduced Hamiltonian system in the presence of large perturbations imparted in the $$\varepsilon >0$$ ε > 0 regime, while remaining robust to extrinsic noise. This is significant in part due to the nontrivial means by which such systems are derived analytically. WSINDy naturally preserves the Hamiltonian structure by restricting to a trial basis of Hamiltonian vector fields. The methodology is computationally efficient, often requiring only a single trajectory to learn the global reduced Hamiltonian, and avoiding forward solves in the learning process. In this way, we argue that weak-form equation learning is particularly well-suited for Hamiltonian coarse-graining. Using nearly-periodic Hamiltonian systems as a prototypical class of systems with approximate symmetries, we show that WSINDy robustly identifies the correct leading-order system, with dimension reduced by at least two, upon observation of the relevant degrees of freedom. While our main contribution is computational, we also provide a contribution to the literature on averaging theory by proving that first-order averaging at the level of vector fields preserves Hamiltonian structure in nearly-periodic Hamiltonian systems. This provides theoretical justification for our approach as WSINDy’s computations occur at the level of Hamiltonian vector fields. We illustrate the efficacy of our proposed method using physically relevant examples, including coupled oscillator dynamics, the Hénon–Heiles system for stellar motion within a galaxy, and the dynamics of charged particles.
Observations undertaken on 12 January 1990 at Darwin (Australia) are used to document the structure of a monsoonal rainband in a low convective available potential energy low-shear tropical environment. Dual-Doppler radar analyses are employed to investigate the structure and kinematics of the convective and stratiform regions. A system with the characteristics of a relatively short-lived squall line in which warm rain processes play a significant role in the production of precipitation is evident. Planetary boundary layer cold-pool production is important in the organization and motion of the system. A trailing stratiform region is evident with a mean updraft-downdraft circulation, but is composed of in situ decaying convective cells. A storm-relative mesoscale cyclonic circulation is also observed within the stratiform cloud. This vortex was maintained by thermodynamically induced midlevel convergence, convectively generated storm-scale circulations, and their interaction with the background monsoon flow.
Angular momentum rate change, rotating gaseous rings, and statistical property of Jacobian constants during particle collision in gaseous flow in closed binary system
Jacobian constants and angular momentum of colliding particles of gaseous streams in close binary stellar system
A motion cue investigation program is reported that deals with human factor aspects of high fidelity vehicle simulation. General data on non-visual motion thresholds and specific threshold values are established for use as washout parameters in vehicle simulation. A general purpose similator is used to test the contradictory cue hypothesis that acceleration sensitivity is reduced during a vehicle control task involving visual feedback. The simulator provides varying acceleration levels. The method of forced choice is based on the theory of signal detect ability.
How vibratory motion can be transmitted from the rotating shaft to the casing and other connecting structures in rotating mechanical equipment is addressed here by developing a new mathematical model of precision rolling element bearings. A new grating stiffness matrix is proposed in order to demonstrate a coupling between the shaft bending motion and the flexural motion of the casing plate. It is shown that the translational bearing stiffness coefficients currently used in rotor dynamic models are a small subset of the proposed matrix. The theory is validated by examples, and the proposed bearing formulation is then extended to demonstrate its superiority over existing models in vibration transmission analyses. It is shown that the model can easily be incorporated into analytical or numerical models typically used for dynamic analyses.
The thrust of the proposed effort under this contract is aimed at improving techniques to track water vapor data in sequences of imagery from geostationary satellites. In regards to this task, significant testing, evaluation, and progress was accomplished during this period. Sets of winds derived from Meteosat data were routinely produced during Atlantic hurricane events in the 1993 season. These wind sets were delivered via Internet in real time to the Hurricane Research Division in Miami for their evaluation in a track forecast model. For eighteen cases in which 72-hour forecasts were produced, thirteen resulted in track forecast improvements (some quite significant). In addition, quality-controlled Meteosat water vapor winds produced by NESDIS were validated against rawinsondes, yielding an 8 m/s RMS. This figure is comparable to upper-level cloud drift wind accuracies. Given the complementary horizontal coverage in cloud-free areas, we believe that water vapor vectors can supplement cloud-drift wind information to provide good full-disk coverage of the upper tropospheric flow. The impact of these winds on numerical analysis and forecasts will be tested in the next reporting period.
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Data from the Fourth Atmospheric Variability Experiment were used to investigate conditions/factors responsible for the development (local time rate-of-change) of convective instability, wind shear, and vertical motion in areas with varying degrees of convective activity. AVE IV sounding data were taken at 3 or 6 h intervals during a 36 h period on 24-25 April 1975 over approximately the eastern half of the United States. An error analysis was performed for each variable studied.
A hybrid robot teleoperation system is presented which makes use of the methodology of motion planning for whole-sensitive robots to assist the operator in generating collision-free motion in a master-slave robot arm manipulator system. The system combines operator commands with data from the sensitive skin to guarantee safe motion for the entire body of the robot arm. The arm avoids obstacles automatically and in real time and moves in a collision-free manner although no prior knowledge of the objects in the environment is available to the motion planning system and no constraints are imposed on the obstacle shapes. The operator is thus relieved of the task of providing safety of the robot arm and surrounding objects.
Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.
Some crustal motions which are precursory to earthquakes are discussed and a system for monitoring such motions is proposed. Studies have shown that the scale of a dilatant region is an indicator both of the magnitude of subsequent earthquake and of the time interval between the earthquake and the precursory phenomena. Monitoring may be accomplished by the use of corner reflectors at sites situated in an array over a given region, such as California, for example, the sites being tracked by means of a laser system operating in the Geopause satellite.
Typically, before constructing an object with an additive manufacturing system, the 3D object must be sent through a process called slicing. Slicing converts a 3D object commonly in the form of an STL file into a set of layers by horizontally intersecting a plane with the object at various heights. At each height, called a layer, multiple 2D polygons can be generated. Each polygon represents a boundary for solid geometry and is called an island. Each island is then comprised of multiple path types in an attempt to optimally fill the polygon. To move between each island and each islands’ paths, travels are inserted. Travels are simply motion by the system to move from one area of construction to another. Travels do not contribute to the construction of the object, and so, are considered wasted motion. In large-scale additive manufacturing, objects can be quite large and the distance between islands can be large as well. As a result, these travels can waste a significant amount of time. Ideally, travels would be as short as possible, however, computing global minimal travel paths is computationally expensive. To combat this problem, researchers at Oak Ridge National Lab developed a GPU-based approach to travel insertion based on a unique factoradic representation. This representation was then utilized by the GPU to solve the Traveling Salesman Problem (TSP). This algorithm was able to compute global minimal travel paths quickly resulting in faster object construction. A general investigation was also carried out to determine when a GPU vs CPU implementation would be beneficial.
The retrograde system of a space vehicle is described which permits motion in space without the projection of gas by rotor or jet engine. It is composed of masses, which accelerate, decelerate and guide the center of gravity in space in an ordered actuation. The invention may be used to replace rotors and jet engines of our present space vehicles. In space, it may use electrical solar energy and develop indefinitely in the solar system.
The consistent formulation of the governing nonlinear equations of motion for a coupled rotor/support system is presented. Rotor/support coupling is clearly documented by enforcing dynamic equilibrium between the rotor and the moving flexible support. The nonlinear periodic coefficient equations of motion are applicable to both coupled rotor/fuselage aeroelastic problems of helicopters in hover or forward flight and coupled rotor/tower dynamics of a large horizontal axis wind turbine (HAWT). Finally, the equations of motion are used to study the influence of flexible supports and nonlinear terms on rotor aeroelastic stability and response of a large two-bladed HAWT.
The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.
Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing dual-spacecraft precision formation flying (PFF) to enable a 'virtual' telescope (VT). Using precision dual-spacecraft alignment, very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Proposed science missions include astrophysics concepts for X-ray imaging and exo-planet observation with large spacecraft separations (1000 km to 80,000 km), and heliophysics concepts for X-ray or extreme ultra-violet (EUV) imaging or solar coronagraphs with smaller separations (50m - 500m). These proposed missions require advances in guidance, navigation, and control (GN&C) for PFF to enable high resolution science imaging. For many applications, the dual-spacecraft dynamics are coupled through the GN&C system when the relative ranging and position alignment sensor components are not co-located with their respective spacecraft mass centers. We develop a model-based PFF system design approach for the VT application, considering the coupling inherent in precision dual-spacecraft inertial alignment. These systems employ a variety of GN&C sensors and actuators, including laser-based alignment and ranging systems, camera-based imaging sensors, inertial measurement units (IMU), as well as microthruster systems and image motion compensation platforms. Results of a GN&C performance assessment reveal how data from relative position sensors can be employed in a Kalman filter framework to significantly improve alignment estimation performance. The assessment provides a comparison of two different GN&C formation flying architectures, illustrating the performance trades inherent in the choice of PFF system architecture in the VT application.