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Real time estimation and prediction of ship motions using Kalman filtering techniques
A landing scheme for landing V/STOL aircraft on rolling ships was sought using computerized simulations. The equations of motion as derived from hydrodynamics, their form and the physical mechanisms involved and the general form of the approximation are discussed. The modeling of the sea is discussed. The derivation of the state-space equations for the DD-963 destroyer is described. Kalman filter studies are presented and the influence of the various parameters is assessed. The effect of various modeling parameters on the rms error is assessed and simplifying conclusions are drawn. An upper bound for prediction time of about five seconds is established, with the exception of roll, which can be predicted up to ten seconds ahead.
Ion-chain sympathetic cooling and gate dynamics
Sympathetic cooling is a technique often employed to mitigate motional heating in trapped-ion quantum computers. However, choosing system parameters such as number of coolants and cooling duty cycle for optimal gate performance requires evaluating trade-offs between motional errors and other slower errors such as qubit dephasing. The optimal parameters depend on cooling power, heating rate, and ion spacing in a particular system. In this study, we aim to analyze best practices for sympathetic cooling of long chains of trapped ions using analytical and computational methods. We use a case study to show that optimal cooling performance is achieved when coolants are placed at the center of the chain and provide a perturbative upper bound on the cooling limit of a mode given a particular set of cooling parameters. In addition, using computational tools, we analyze the trade-off between the number of coolant ions in a chain and the center-of-mass mode heating rate. We also show that cooling as often as possible when running a circuit is optimal when the qubit coherence time is otherwise long. These results provide a roadmap for how to choose sympathetic cooling parameters to maximize circuit performance in trapped-ion quantum computers using long chains of ions.
Acoustic wave propagation in the solar atmosphere 1. Rediscussion of the linearized theory including nonstationary solutions
The normal dispersion analysis for linear adiabatic wave propagation in stratified atmospheres adopts a real frequency and solves for the complex vertical wavenumber. We show that an exponentially stratified atmosphere does not have any spatially bounded normal modes for real frequencies. The usual treatment involves a representation where the imaginary part of the vertical wavenumber yields a rho(sup -1/2) dependence of the velocity amplitude which diverges as the absolute value of z approaches infinity. This solution includes a cutoff frequency below which acoustic modes cannot propagate. The standard dispersion analysis is a local representation of the wave behavior in both space and time but which is assumed to represent the motion throughout - infinity is less than t is less than infinity and 0 is less than infinity. However, any solution which has a purely sinusoidal time dependence extends through this full domain and is divergent due to the rho(sup -1/2) dependence. We show that a proper description is in terms of a near field of a boundary piston which is driven arbitrarily as a function of space and time. The atmosphere which responds to this piston is a semi-infinite layer which has an initially constant sound speed but which has the usual gravitational stratification. In a restricted domain of space and time above this boundary, the wavelike behavior of the medium may be described by frequencies and vertical wavenumbers which are both complex. When both parameters are allowed to have imaginary components, a new range of solutions is found for which there is virtually no cutoff frequency. We show that vertical energy propagation can take place through the solar atmosphere as a result of oscillations below the nominal cutoff frequency. Previously, the largest amplitude oscillations which generally have low frequencies were dropped from the calculation of energy flux becuase their frequencies are below the cutoff frequency. This new family of near-field waves permits these modes to carry energy vertically outward and raises the possibility that the largest amplitude 5 minute oscillations play a substantial role in the transport of acoustic energy to the chromosphere.
Use of satellite data in a diagnostic parameterization of convective heating
Heating estimates derived from a diagnostic technique using observed rainfall and GOES IR digital imagery were completed and evaluated for accuracy. A sensitivity analysis was done to examine assumptions regarding shape of the normalized mass flux profile, cloud precipitation efficiency, and existence of convective scale downdrafts. The results, which were derived using what are felt to be bounding limits of the assumptions, indicate that the heating estimates are reliable for use in diagnostic available potential energy (APE) budgets. Comparison to heating estimates derived as residuals in the thermodynamic equation show the level of maximum heating (near 300 mb) to be the same on a time averaged basis. Heating estimates were used to study the response of the large scale environment to the cumulus scale thermodynamic forcing. An analysis of the thermally forced component of vertical motion through the omega equation showed that a significant fraction of the total grid scale upward motion results from the heating provided by the condensation and vertical eddy heat transport in the convective cells.
Deuteron off-resonance rotating frame relaxation for the characterization of slow motions in rotating and static solid-state proteins
Here, we demonstrate the feasibility of deuterium solid-state NMR off-resonance rotating frame relaxation measurements for studies of slow motions in biomolecular solids. The pulse sequence, which includes adiabatic pulses for magnetization alignment, is illustrated for static and magic-angle spinning conditions away from rotary resonances. We apply the measurements for three systems with selective deuterium labels at methyl groups: a) a model compound, Fluorenylmethyloxycarbonyl methionine-D 3 amino acid, for which the principles of the measurements and corresponding motional modeling based on rotameric interconversions are demonstrated; b) amyloid-β 1-40 fibrils labeled at a single alanine methyl group located in the disordered N-terminal domain. This system has been extensively studied in prior work and here serves as a test of the method for complex biological systems. The essential features of the dynamics consist of large-scale rearrangements of the disordered N-terminal domain and the conformational exchange between the free and bound forms of the domain, the latter one due to transient interactions with the structured core of the fibrils. and c) a 15-residue helical peptide which belongs to the predicted α-helical domain near the N-terminus of apolipoprotein B. The peptide is solvated with triolein and incorporates a selectively labeled leucine methyl groups. The method permits model refinement, indicating rotameric interconversions with a distribution of rate constants.
Convective effects in float-zone and Czochralski melts
The hydrodynamics of crystal-growth melts is a relatively new research area. Numerical modeling of these processes is necessary. The work discussed herein is in two parts: numerical simulations of the flow in a Czochralski melt, and also of that in a float zone. In addition, for the float-zone case, energy stability theory will be used to determine stability bounds for the onset of oscillatory thermo-capillary flow. Convective effects in crystal-growth melts arise from a variety of mechanisms. Temperature gradients both in the direction of gravity and normal to it give rise to convection due to buoyancy effects. Rotation of the crucible and/or crystal causes a forced convection which may augment or oppose the buoyancy-driven flow. Finally, thermo-capillary forces (due to the variation of surface tension with temperature) drive surface motions which in turn generate convection in the bulk fluid. All of these mechanisms are present in either Czochralski or float-zone growth. The objective of the Czochralski modeling is to develop an accurate numerical simulation of the flow in a Czochralski silicon melt and to investigate the effects of various parameters on the flow properties. Like some earlier investigations, the intent is to simulate the effects of buoyancy, forced and thermo-capillary convection, including unsteady effects. Unlike earlier work, the aim is to include the effects of a variable free surface and freezing interface and, possibly incorporate nonaxisymmetric effects.
Collision detection for spacecraft proximity operations
Collision Detection for Spacecraft Proximity Operations This thesis describes the development of a new collision detection algorithm to be used when two spacecraft are operating in the same vicinity. The two spacecraft are modelled as unions of convex polyhedra, where the polyhedron resulting from the union may be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. The algorithm determines if a collision is possible and, if so, predicts the time when the collision will take place. The theoretical basis for the new collision detection algorithm is the C-function formulation of the configuration space approach recently introduced by researchers in robotics. Three different types of C-functions are defined that model the contacts between the vertices, edges, and faces of the polyhedra representing the two spacecraft. These C-functions are used to formulate three "collision" conditions. The first of these conditions limits the points representing potential collisions to the zeros of the C-functions. The new algorithm is fundamentally a search for the smallest zero of any C-function that satisfies the second and third collision conditions. The C-functions are shown to be transcendental functions of time for the assumed trajectory of the moving spacecraft. The zeros of these functions cannot be expressed in dosed form. Therefore, numerical search procedures are developed to find aLl of the zeros of a C-function in specified bounded intervals of time. These bounded intervals of time are found by examining the second and third collision conditions. The capabilities of the new algorithm are demonstrated for several example cases. These include examples of collisions determined by zeros of each of the three different types of C-functions. In addition to predicting the time of first contact of the polyhedra, the algorithm identifies the features of the two polyhedra that are touching at this time. The new collision detection algorithm is the first such algorithm that is capable of solving the collision detection problem exactly for the case where the moving object has constant linear and angular velocities. This is a significant improvement on previous collision detection algorithms described in the literature. In particular, the ability to handle constant angular velocity represents a more realistic type of rotational motion than those which have been used in other algorithms.
Newton versus the machine: solving the chaotic three-body problem using deep neural networks
ABSTRACT Since its formulation by Sir Isaac Newton, the problem of solving the equations of motion for three bodies under their own gravitational force has remained practically unsolved. Currently, the solution for a given initialization can only be found by performing laborious iterative calculations that have unpredictable and potentially infinite computational cost, due to the system’s chaotic nature. We show that an ensemble of converged solutions for the planar chaotic three-body problem obtained using an arbitrarily precise numerical integrator can be used to train a deep artificial neural network (ANN) that, over a bounded time interval, provides accurate solutions at a fixed computational cost and up to 100 million times faster than the numerical integrator. In addition, we demonstrate the importance of training an ANN using converged solutions from an arbitrary precise integrator, relative to solutions computed by a conventional fixed precision integrator, which can introduce errors in the training data, due to numerical round-off and time discretization, that are learned by the ANN. Our results provide evidence that, for computationally challenging regions of phase space, a trained ANN can replace existing numerical solvers, enabling fast and scalable simulations of many-body systems to shed light on outstanding phenomena such as the formation of black hole binary systems or the origin of the core collapse in dense star clusters.
Coupled loads analysis of a novel shared-mooring floating wind farm
Shared mooring lines are a method to reduce the stationkeeping cost of floating offshore wind farms; however, their impacts on floating array dynamics are not yet well understood. Here this article presents advancements to floating wind farm simulation capabilities that allow the dynamic modeling of shared-mooring floating wind arrays - specifically, platform coupling through shared lines and proper phasing of wave loads across the array. These capabilities are demonstrated on a 10-turbine shared-mooring array featuring two staggered rows of wind turbines. A baseline array design with individually moored turbines is used as a basis for comparison. Coupled analysis using FAST.Farm shows that the shared-mooring design has smaller fluctuations in surge when compared to the baseline design. The mean and maximum platform offsets are highest in normal operating conditions, but the maximum mooring line tensions are highest in 50-year storm conditions. Power spectral density analysis of platform surge and sway motions shows that the shared mooring configuration does not introduce any significant inter-platform resonances. The tower-base bending moment statistics and the line tension damage equivalent loads indicate no consequential differences in turbine loading or mooring fatigue life. Anchor load analysis shows that the total required anchor capacity for the shared-mooring array is decreased by approximately 25% when shared anchors are used. Dynamic simulations of the shared mooring system under line failures show that remaining line tensions stay within bounds and that offsets are significantly smaller when compared to the baseline design. Overall, the results show that shared moorings do not introduce any dynamic response concerns in this floating wind array design.
Some new results on spherical dynamos
Small-scale motions in the earth's liquid core are likely to be highly anisotropic because of the effects of rotation. Guided by physical considerations, the 'alpha-effect' described by an anisotropic tensor alpha sub ik is formulated and the corresponding boundary value problem for a sphere is solved for a variety of boundary conditions. A converged solution has been obtained only in the case of the Fermi condition of an infinitely conducting exterior of the sphere. Some remarks are made on the hypothetical upper bound on magnetic field strengths in planetary cores originally proposed by Busse (1976).
Trompe L'Oeil 'binary' pulsars
A freely precessing pulsar produces pulse phase residuals which can mimic those of a pulsar in a binary orbit. In particular, discrete sets of phase residuals due to precessional motion of an isolated pulsar are sampled; it is shown that this data is well fit by residuals from a binary pulsar in a sufficiently tight orbit. Analytic and numerical relationships between the projected orbital size, a(p) sin i, and the orbital eccentricity, e, of a misidentified binary pulsar; are found the observations that would distinguish between these models are discussed. Regardless of the mechanism that causes the precession, the maximum amplitude of the phase residual is pi/2: consequently, a(p)sin i is (approximately) bounded by cP(puls)/4. The newly discovered 'binary' millisecond pulsars in the globular cluster 47 Tuc is discussed, and it is shown that the periodic frequency modulation reported cannot be explained by free precession.
Time Dependence of Collision Probabilities During Satellite Conjunctions
The NASA Conjunction Assessment Risk Analysis (CARA) team has recently implemented updated software to calculate the probability of collision (P (sub c)) for Earth-orbiting satellites. The algorithm can employ complex dynamical models for orbital motion, and account for the effects of non-linear trajectories as well as both position and velocity uncertainties. This “3D P (sub c)” method entails computing a 3-dimensional numerical integral for each estimated probability. Our analysis indicates that the 3D method provides several new insights over the traditional “2D P (sub c)” method, even when approximating the orbital motion using the relatively simple Keplerian two-body dynamical model. First, the formulation provides the means to estimate variations in the time derivative of the collision probability, or the probability rate, R (sub c). For close-proximity satellites, such as those orbiting in formations or clusters, R (sub c) variations can show multiple peaks that repeat or blend with one another, providing insight into the ongoing temporal distribution of risk. For single, isolated conjunctions, R (sub c) analysis provides the means to identify and bound the times of peak collision risk. Additionally, analysis of multiple actual archived conjunctions demonstrates that the commonly used “2D P (sub c)” approximation can occasionally provide inaccurate estimates. These include cases in which the 2D method yields negligibly small probabilities (e.g., P (sub c)) is greater than 10 (sup -10)), but the 3D estimates are sufficiently large to prompt increased monitoring or collision mitigation (e.g., P (sub c) is greater than or equal to 10 (sup -5)). Finally, the archive analysis indicates that a relatively efficient calculation can be used to identify which conjunctions will have negligibly small probabilities. This small-P (sub c) screening test can significantly speed the overall risk analysis computation for large numbers of conjunctions.
Study of Magnetic Motions in the Solar Photosphere and their Implications for Heating the Solar Atmosphere
We continued our program of CO observations with the McMath-Pierce facility at Kitt Peak National Solar Observatory. Uitenbroek has developed a two-and three dimensional radiative transfer code that now includes chemical equilibrium calculations. This code allows us to compute a CO spectrum from for instance a snapshot of a solar granulation simulation (e.g. Stein & Nordlund 1989, Apj 342, L95) and compare these theoretical spectra with our spatially resolved CO spectroscopy. Van Ballegooijen and Uitenbroek have started calculations of two-dimensional fluxtube models that account consistently for hydrogen ionization in the calculation of the electron density. To this end we solve radiative transfer for hydrogen (bound-bound and bound-free transitions) in the two-dimensional models, including the effect of partial frequency redistribution (PRD) in the Lyman (alpha) and (beta) lines. From our internally consistent models we will calculate emergent spectra and the way these vary with location of some well-known spectral diagnostics and compare our results with observed line profiles. We can readily compare theoretical CO profiles from out models with our spatially resolved CO observations. Also we can compare with spatially resolved Ca II (ground based) and Mg II (we have observations done with the UVSP/SMM instrument), and Lyman (alpha) observations that should be available from SUMER/SOHO.
Uncertainty in Synthetic Tropical Cyclone Hazard and Risk Estimates: Insights from RAFT, CHAZ, MIT, STORM, and CLIMADA
We synthesize five complementary tropical cyclone (TC) hazard frameworks—RAFT (physics-based machine learning), CHAZ and MIT (statistical–dynamical), STORM (fully statistical), and CLIMADA (observation-driven resampling)—to characterize uncertainty in wind-related TC metrics relevant to energy applications. All datasets and the IBTrACS observational record are harmonized to a common 6-hourly, 2.5° grid. We compare basin-wide and coastal properties using consistent definitions for TC frequency, mean and maximum intensity, 24-hour intensification, and 6-hour translation speed, and quantify agreement with Pearson r, RMSE, and Kling–Gupta efficiency (KGE) alongside resampling-based confidence intervals. CLIMADA is included for basin context but excluded from coastal skill scoring because it resamples historical IBTrACS; if supplied with projected future tracks from an external hazard model, CLIMADA can be used to simulate future TC scenarios. Results show robust, cross-model signals: (i) a corridor of activity from the tropical Atlantic through the Caribbean into the Bahamas and western subtropical Atlantic; (ii) a meridional dipole in 24-hour intensification (low-latitude strengthening, subtropical weakening); and (iii) a transition from slower tropical motion to faster midlatitude translation. Coastal winds (mean and maximum) consistently cluster from the eastern Gulf into the Bahamas–western Atlantic transition. The largest structural spread occurs in the amplitude and footprint of lifetime maximum intensity and, secondarily, in translation speed; intensification exhibits similar central behavior across frameworks with variability in extremes. Translation speed shows the most uniform coastal agreement. These findings provide a decision envelope for wind-focused risk screening and clarify where uncertainty should be carried forward; wind-only results represent a lower bound on total hazard, motivating integration of surge and rainfall modules and a companion, asset-level damage analysis.
A Candidate Wake Vortex Strength Definition for Application to the NASA Aircraft Vortex Spacing System (AVOSS)
A significant effort is underway at NASA Langley to develop a system to provide dynamical aircraft wake vortex spacing criteria to Air Traffic Control (ATC). The system under development, the Aircraft Vortex Spacing System (AVOSS), combines the inputs of multiple subsystems to provide separation matrices with sufficient stability for use by ATC and sufficient monitoring to ensure safety. The subsystems include a meteorological subsystem, a wake behavior prediction subsystem, a wake sensor subsystem, and system integration and ATC interfaces. The proposed AVOSS is capable of using two factors, singly or in combination, for reducing in-trail spacing. These factors are wake vortex motion out of a predefined approach corridor and wake decay below a strength that is acceptable for encounter. Although basic research into the wake phenomena has historically used wake total circulation as a strength parameter, there is a requirement for a more specific strength definition that may be applied across multiple disciplines and teams to produce a real-time, automated system. This paper presents some of the limitations of previous applications of circulation to aircraft wake observations and describes the results of a preliminary effort to bound a spacing system strength definition.
The Effect of a Rotating Magnetic Field on Rayleigh-Benard Convection
A destabilizing vertical temperature gradient and a rotating magnetic field have been applied to a cylindrical column of liquid gallium. The convective flows which arise as a function of these driving parameters are identified. For small magnetic field strengths, a region of stationary flow is observed. This region is bounded by critical values of the Rayleigh and Hartmann numbers. As the rotating magnetic field is increased, the critical Rayleigh number can increase by more than a factor of 10. The rotating magnetic field itself induces an instability at a critical value of the Hartmann number independent of the Rayleigh number. The nature of the bifurcations (whether subcritical or supercritical) and the convective flows occurring at the critical Rayleigh numbers are dependent upon the Hartmann number. In the stationary flow region, the rotating magnetic field can induce fluid motion with velocities on the order of cm/s. Thus, a rotating magnetic field can be used to achieve the benefits of forced convection during crystal growth processes without triggering deleterious instabilities.
On Target to Mars
This viewgraph presentation reviews the use of Descent Image Motion Estimation System (DIMES) for the descent of a spacecraft onto the surface of Mars. In the past this system was used to assist in the landing of the MER spacecraft. The overall algorithm is reviewed, and views of the hardware, and views from Spirit's descent are shown. On Spirit, had DIMES not been used, the impact velocity would have been at the limit of the airbag capability and Spirit may have bounced into Endurance Crater. By using DIMES, the velocity was reduced to well within the bounds of the airbag performance and Spirit arrived safely at Mars. Views from Oppurtunity's descent are also shown. The system to avoid and detect hazards is reviewed next. Landmark Based Spacecraft Pinpoint Landing is also reviewed. A cartoon version of a pinpoint landing and the various points is shown. Mars s surface has a large amount of craters, which are ideal landmarks . According to literatures on Martian cratering, 60 % of Martian surface is heavily cratered. The ideal (craters) landmarks for pinpoint landing will be between 1000 to 50 meters in diagonal The ideal altitude for position estimation should greater than 2 km above the ground. The algorithms used to detect and match craters are reviewed.