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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Collisional alpha transport in a weakly non-quasisymmetric stellarator magnetic field

Alpha particle confinement is a serious concern in stellarators and provides strong motivation for optimizing magnetic field configurations. In addition to the collisionless confinement of trapped alphas in stellarators, excessive collisional transport of the trapped alpha particles must be avoided while they tangentially drift due to the magnetic gradient (the ∇B drift). The combination of pitch angle scatter off the background ions and the ∇B drift gives rise to two narrow boundary layers in the trapped region. The first is at the trapped-passing boundary and enables the finite trapped response to be matched to the vanishing passing response of the alphas. The second layer is a region that encompasses the somewhat more deeply trapped alphas with vanishing tangential ∇B drift. Away from (and between) these boundary layers, collisions are ineffective and the alpha ∇B drift simply balances the small radial drift of the trapped alphas. As this balance does not vanish as the trapped-passing boundary is approached, the first collisional boundary layer is necessary and gives rise to √ν transport, with ν the collision frequency. The vanishing of the tangential drift results in a separate, somewhat wider boundary layer, and significantly stronger superbanana plateau transport that is independent of collisionality. The constraint imposed by the need to avoid significant energy depletion loss in the slowing down tail distribution function sets the allowed departure of a stellarator from an optimal quasisymmetric configuration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRSDate not supplied

Decision Aid for Conjunction Risk Mitigation by Differential Drag

In the previous five years, the rate of conjunctions that the NASA Conjunction Assessment Risk Analysis (CARA) team processed and analyzed has more than tripled. (NASA CARA, 2024) New missions in the early development phases are now required to plan for dealing with conjunctions under the present space environment, and also projecting forward into a future likely with even further increased utilization of the space environment. Some missions are investigating the possibility of using differential drag to remediate conjunctions without expending limited fuel or for missions without propulsive capabilities. The NASA CARA team studied the historical record of conjunctions to evaluate the circumstances under which differential drag may be successfully applied and have developed a series of tables to use as a decision aid for missions considering differential drag. Currently, if a CARA-protected mission with maneuvering capabilities is predicted to have a conjunction with probability of collision (Pc) greater than 7E-5 (the default value of the ‘yellow threshold’, which may have some other value agreed by CARA and the mission during the Orbital Collison Avoidance Planning (OCAP) process), CARA will use its Maneuver Trade Space (MTS) tool to evaluate and recommend options for the timing and magnitude of a risk mitigation maneuver (RMM), based on the mission’s capabilities. If the conjunction’s Pc is greater than 1E-4, the ‘red threshold’, then an RMM must be executed per NASA Procedural Requirements (NPR) 8079.1 (NASA, 2023), although missions may execute an RMM even if the Pc is lower. The magnitude of the maneuver is typically a few cm/s, and CARA estimates how many will be required for the mission’s nominal lifetime – typically a few per year – during the OCAP process, to inform the mission’s delta-V requirement. For traditional satellites, this is usually smaller than other requirements for orbit insertion, maintenance, and disposal, but for CubeSats or other small satellite missions, a propulsion system may not provide much more than a few cm/s of delta-V or may not fit at all within the available budget of money, time, size, weight, and/or power (SWaP). Conversely, CubeSats often have deployable solar panels, which offer the capacity to have much higher areas facing some directions than others. Such a mission can instead use ‘differential drag’ to remediate a conjunction -- in other words, change its drag area (usually increasing) to deviate from the predicted collision course. This is how Planet’s Dove spacecraft maintain their formations and remediate conjunction risks without having on-board propulsion (Foster, et al., 2017) (Griffith, et al., 2021). CARA has been developing improvements to MTS to support differential-drag for NASA's missions -- where it is effective. CARA records all conjunctions of their protected payloads, with historical records starting in 2005 (with significant conjunction events starting to occur on or after 2013). From this record, approximately 7,300 had a Pc greater than 1E-4 at 3 days prior to the time of closest approach, the time analyzed for differential drag efficacy. Of those, approximately 4,300 had fully-defined covariance matrices stored for both the primary and secondary objects; this set of conjunctions is the basis for the analysis of this work. CARA’s MTS tool was used to propagate the primary satellite forward from that decision point with varying degrees of increase to ballistic coefficient (BC). Because these conjunctions came from multiple missions, the nondimensional ‘delta-BC’ factor was used to quantify and normalize the increase in ballistic coefficient, defined as follows: Delta-BC = BC_new / BC_old - 1 Positive delta-BC factors represent an increase in drag compared to the nominal attitude, while negative delta-BC factors (to a minimum of -1) represent a decrease in drag. At the conclusion of the differential-drag ‘maneuver’, the Pc was recalculated to evaluate whether or not the conjunction was mitigated (Pc < 3E-6). These results were then binned and sorted along several axes, including altitude, amount of delta-BC, and (pre-maneuver) rate of energy dissipation (EDR), to identify underlying patterns. The altitude plot is shown in Figure 1. To validate this analysis, we consulted the record of a NASA mission which uses differential drag to maintain its orbit and remediate conjunction risk. CARA’s empirical record of the mission’s orbit history suggests it achieves a delta-BC of 2.2. Of the twenty-one RMM plans that were submitted by this mission, eighteen were matched with conjunctions in the historical record; of those, twelve were successfully remediated (final measured Pc < 3E-6), and six were not. This is consistent with the expected efficacy for missions orbiting at that altitude. We are presently simulating this mission’s RMMs with MTS; this work is ongoing, but so far, the MTS results are qualitatively in agreement with the empirical results -- correctly predicting that a maneuver would or would not remediate a conjunction, if not exactly matching the final post-remediation Pc value. We found that differential drag was most successful for satellites with perigees below 560 km, and which could adopt an average delta-BC of 2 or greater (that is, increasing their ballistic coefficient by a factor of 3). However, this is a difficult threshold for a mission to clear; very few spacecraft are capable of adopting a high-drag configuration for 72 hours continuously. Planet’s Dove spacecraft use differential drag to remediate conjunctions (Griffith, et al., 2021), and they have a maximum delta-BC factor of 9, but in practice (with mission and charging constraints) they achieve a time-averaged delta-BC that is closer to 2 (Foster, et al., 2017). A mission’s differential drag utility strongly depends on the operational constraints that has the capacity to limit the time-averaged delta-BC. A mission with a high maximum delta-BC of 5 or more can have an effective delta-BC of less than 1 due to operational constraints such as instrument and solar panel pointing, especially if this constraint results in holding an intermediate drag value for most of its orbit. CARA has developed tables that can be used as decision aids to advise missions-in-development about the best way to utilize their differential drag capabilities. For missions below 560 km with the operational flexibility to devote multiple days to holding a high-drag configuration (or a sufficiently high drag ratio to compensate for limitations on that time), they are -- more likely than not -- able to successfully remediate high-risk conjunctions. Conversely, missions that do not meet these exacting criteria -- most missions -- can instead be advised to use on-board propulsion systems to perform RMMs, or to turn their minimum-area face towards the approach vector, thereby reducing Pc at the moment of conjunction due to the decreased Hard-Body Radius (HBR), that is a strongly correlated variable in the Pc calculations. (NASA, 2023)

conjunction assessment↗
DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗
DOE OSTI2020

Behavioral responses of fish to a current-based hydrokinetic turbine under mutliple operational conditions

There is significant international interest in developing current-based marine and hydrokinetic (MHK) technologies to capture the power of tidal energy. However, concerns have been raised regarding the ecological effects of these projects on fish, including the risk of blade collision and behavioral impacts such as the disruption of migratory behavior and food acquisition and displacement from preferred habitats. In this study, we conducted mobile hydroacoustic surveys to track fish as they approached a tidal turbine deployed in Cobscook Bay, Maine. There was a significant decline in fish numbers with decreasing distance to the turbine, beginning approximately 140 m from the turbine. Similar declines were not observed at control transects or when the turbine was not spinning. The decline in fish numbers appeared to be the result of horizontal displacement, not vertical, movements to avoid the turbine. Noise rather than visual cues or flow field disturbance seemed to be a likely explanation for the reduced number of fish near the turbine. This finding, combined with near-field blade collision studies indicating a low probability of encounter, suggests that a single turbine poses a low collision risk to pelagic fish and that a single turbine is likely to result in minimal behavioral responses by fish. However, the risk may be different with additional devices, which will become more relevant as commercial-scale MHK arrays come under consideration. Therefore, the risks associated with commercial-scale operations will ultimately have to be evaluated to fully understand the ecological impacts of MHK devices.

42 ENGINEERING↗
DOE OSTI2017

Unifying the Micro and Macro Properties of AGN Feeding and Feedback

We unify the feeding and feedback of supermassive black holes with the global properties of galaxies, groups, and clusters by linking for the first time the physical mechanical efficiency at the horizon and megaparsec scale. The macro hot halo is tightly constrained by the absence of overheating and overcooling as probed by X-ray data and hydrodynamic simulations (ε{sub BH}≃10{sup −3} T{sub x,7.4}). The micro flow is shaped by general-relativistic effects tracked by state-of-the-art GR-RMHD simulations (ε{sub ∙}≃0.03). The supermassive black hole properties are tied to the X-ray halo temperature T{sub x}, or related cosmic scaling relation (as L{sub x}). The model is minimally based on first principles, such as conservation of energy and mass recycling. The inflow occurs via chaotic cold accretion (CCA), the rain of cold clouds condensing out of the quenched cooling flow and then recurrently funneled via inelastic collisions. Within 100s gravitational radii, the accretion energy is transformed into ultrafast 10{sup 4} km s{sup −1} outflows (UFOs) ejecting most of the inflowing mass. At larger radii, the energy-driven outflow entrains progressively more mass: at roughly kiloparsec scale, the velocities of the hot/warm/cold outflows are a few 10{sup 3}, 1000, and 500 km s{sup −1}, with median mass rates ∼ 10, 100, and several 100 M{sub ⊙} yr{sup −1}, respectively. The unified CCA model is consistent with the observations of nuclear UFOs and ionized, neutral, and molecular macro outflows. We provide step-by-step implementation for subgrid simulations, (semi)analytic works, or observational interpretations that require self-regulated AGN feedback at coarse scales, avoiding the a-posteriori fine-tuning of efficiencies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Verification of the LOTUS code with C5G7 benchmark

In this study, the verification of the neutron transport code LOTUS through the well-known C5G7 benchmark is performed. LOTUS uses the current coupled collision probability method with the expansion of the flux by orthogonal polynomials (CCCPO) for the solution of the neutron transport equation. The expansion of the flux by orthogonal polynomials allows one to avoid discretization of the calculation regions and significantly decreases the simulation time. The results of the LOTUS calculations are compared with the results of the reference OpenMC Monte Carlo simulations. The results of the comparison demonstrate almost perfect agreement with Monte-Carlo for the second order of the flux expansion. Even though the results obtained in the presented study agree well with the results of reference Monte Carlo calculations, further investigations are necessary for a better understanding of the stability and limitations of the code.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1979

An angular momentum approximation for molecular collisions in the presence of intense laser radiation

An approximation to a previously presented rigorous description of molecular (atom-atom) collisions occurring in the presence of intense radiation is investigated. This rigorous description explicitly considers the angular momentum transferred between the molecule and the radiation field in the absorption or emission of a photon, but involves a complicated system of close-coupled equations which must be solved independently for each projection M of the initial, total molecular angular momentum. (This is a direct consequence of the lack of rotational invariance in the molecule-field problem). These equations are solved for a model system which mimics the collision of a halogen with a rare gas atom. Empirical observations made in the course of performing these calculations lead to the development of an approximation which avoids the repeated calculations for each initial M. This orientational average approximation greatly reduces the effort required to describe the system, and for the model calculation, yields accurate results for field intensities as high as 10 GW/sq cm.

Devries, P. L.↗
NASA NTRS2019

Alternative Surveillance Fast Time Simulation with Sensor Uncertainties and Mitigation

This presentation describes a simulation plan for the fast time simulation 3 for the modeling and simulation team in the UAS (Unmanned Aircraft Systems) in the NAS (National Airspace System)project. Objectives: Investigate the effect of limited surveillance volume and realistic radar noise on DAA (Detect and Avoid) performance; Evaluate the ability of the sensor uncertainty mitigation (SUM) feature of the DAIDALUS [Dectect and Avoid...] algorithm to improve DAA alerting and guidance [Includes content on SWaP-C (size, weight, power, and cost) of unmanned aircraft; and Near-mid-air-collision (NMAC).]

UAS↗
DOE OSTI2016

Apparatus for magnetic and electrostatic confinement of plasma

An apparatus and method for containing plasma and forming a Field Reversed Configuration (FRC) magnetic topology are described in which plasma ions are contained magnetically in stable, non-adiabatic orbits in the FRC. Further, the electrons are contained electrostatically in a deep energy well, created by tuning an externally applied magnetic field. The simultaneous electrostatic confinement of electrons and magnetic confinement of ions avoids anomalous transport and facilitates classical containment of both electrons and ions. In this configuration, ions and electrons may have adequate density and temperature so that upon collisions ions are fused together by nuclear force, thus releasing fusion energy. Moreover, the fusion fuel plasmas that can be used with the present confinement system and method are not limited to neutronic fuels only, but also advantageously include advanced fuels.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRSDate not supplied

A Provably Correct Floating-Point Implementation of Well Clear Avionics Concepts

The NASA DAIDALUS library provides formal definitions for Detect-and-Avoid avionics concepts such as when an aircraft is well-clear with respect to the surrounding air traffic, i.e., it does not operate in such proximity to create a collision hazard. While several properties are proven correct for DAIDALUS assuming ideal real number arithmetic, an actual implementation that uses floating-point numbers may behave unexpectedly because of round-off errors and run-time exceptions. This paper presents an experience report on the application of a formal methods toolchain to extract and verify floating-point C code from a real-valued specification of the well-clear module of DAIDALUS. This toolchain comprises the PVS theorem prover, the PRECiSA floating-point analyzer and code generator, and the Frama-C analysis suite. The generated code is automatically instrumented to detect when the control flow of the floating-point program may diverge from the ideal real number specification, and it is annotated with contracts that state the maximum accumulated round-off error. The absence of overflows is also formally verified for the generated code. In order to apply the toolchain to an industrial case study such as DAIDALUS, a formally verified pre-processing of the input specification is performed, which includes a program slicing and several semantic-preserving simplifications.

Program verification↗
NASA NTRS2010

Guidance and Control System for a Satellite Constellation

A distributed guidance and control algorithm was developed for a constellation of satellites. The system repositions satellites as required, regulates satellites to desired orbits, and prevents collisions. 1. Optimal methods are used to compute nominal transfers from orbit to orbit. 2. Satellites are regulated to maintain the desired orbits once the transfers are complete. 3. A simulator is used to predict potential collisions or near-misses. 4. Each satellite computes perturbations to its controls so as to increase any unacceptable distances of nearest approach to other objects. a. The avoidance problem is recast in a distributed and locally-linear form to arrive at a tractable solution. b. Plant matrix values are approximated via simulation at each time step. c. The Linear Quadratic Gaussian (LQG) method is used to compute perturbations to the controls that will result in increased miss distances. 5. Once all danger is passed, the satellites return to their original orbits, all the while avoiding each other as above. 6. The delta-Vs are reasonable. The controller begins maneuvers as soon as practical to minimize delta-V. 7. Despite the inclusion of trajectory simulations within the control loop, the algorithm is sufficiently fast for available satellite computer hardware. 8. The required measurement accuracies are within the capabilities of modern inertial measurement devices and modern positioning devices.

Bryson, Jonathan Lamar↗
NASA NTRS2017

UAS Well Clear Recovery Against Non-Cooperative Intruders Using Vertical Maneuvers

This paper documents a study that drove the development of a mathematical expression in the minimum operational performance standards (MOPS) of detect-and-avoid (DAA) systems for unmanned aircraft systems (UAS). This equation describes the conditions under which vertical maneuver guidance could be provided during recovery of well clear separation with a non-cooperative VFR aircraft in addition to horizontal maneuver guidance. Although suppressing vertical maneuver guidance in these situations increased the minimum horizontal separation from 500 to 800 feet, the maximum severity of loss of well clear increased in about 35 of the encounters compared to when a vertical maneuver was preferred and allowed. Additionally, analysis of individual cases led to the identification of a class of encounter where vertical rate error had a large effect on horizontal maneuvers due to the difficulty of making the correct left-right turn decision: crossing conflict with intruder changing altitude. These results supported allowing vertical maneuvers when UAS vertical performance exceeds the relative vertical position and velocity accuracy of the DAA tracker given the current velocity of the UAS and the relative vertical position and velocity estimated by the DAA tracker. Looking ahead, these results indicate a need to improve guidance algorithms by utilizing maneuver stability and near mid-air collision risk when determining maneuver guidance to regain well clear separation.

detect and avoid↗
DOE OSTI2020

Dynamical Instabilities in Systems of Multiple Short-period Planets Are Likely Driven by Secular Chaos: A Case Study of Kepler-102

We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in ∼20% of the cases on a wide range of timescales (up to 5 × 10{sup 9} orbits) and over an unexpectedly wide range of initial dynamical spacings. To identify the triggers of long-term instability in multiplanet systems, we investigated in detail the five-planet Kepler-102 system. Despite having several near-resonant period ratios, we find that mean-motion resonances are unlikely to directly cause instability for plausible planet masses in this system. Instead, we find strong evidence that slow inward transfer of angular momentum deficit (AMD) via secular chaos excites the eccentricity of the innermost planet, Kepler-102 b, eventually leading to planet–planet collisions in ∼80% of Kepler-102 simulations. Kepler-102 b likely needs a mass ≳0.1 M {sub ⊕}, hence a bulk density exceeding about half Earth’s, in order to avoid dynamical instability. To investigate the role of secular chaos in our wider set of simulations, we characterize each planetary system’s AMD evolution with a “spectral fraction” calculated from the power spectrum of short integrations (∼5 × 10{sup 6} orbits). We find that small spectral fractions (≲0.01) are strongly associated with dynamical stability on long timescales (5 × 10{sup 9} orbits) and that the median time to instability decreases with increasing spectral fraction. Our results support the hypothesis that secular chaos is the driver of instabilities in many nonresonant multiplanet systems and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long-term (in)stability of multiplanet systems from short simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION

The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (i.e., ∼10{sup −12}). The results of collision integrals and their derivatives for −7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10{sup −10}. For very weakly coupled plasma ( ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10{sup −11}. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’; for an attractive potential, the results in cases of intermediate and strong coupling show significant differences. The resulting resistance coefficients are tested in the solar model. Comparing with the widely used models of Cox et al. and Thoul et al., the resistance coefficients in the screened Coulomb potential lead to a slightly weaker effect in the solar model, which is contrary to the expectation of attempts to solve the solar abundance problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Quasilinear theory: the lost ponderomotive effects and why they matter

Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1977

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum mechanical theories of collision induced electronic transitions. Within the two state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases are considered: the avoided crossing between two potential surfaces; and the spin orbit interaction due to a P-2 halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations.

Jaffe, R. L.↗
NASA NTRS2009

A Single Conjunction Risk Assessment Metric: the F-Value

The Conjunction Assessment Team at NASA Goddard Space Flight Center provides conjunction risk assessment for many NASA robotic missions. These risk assessments are based on several figures of merit, such as miss distance, probability of collision, and orbit determination solution quality. However, these individual metrics do not singly capture the overall risk associated with a conjunction, making it difficult for someone without this complete understanding to take action, such as an avoidance maneuver. The goal of this analysis is to introduce a single risk index metric that can easily convey the level of risk without all of the technical details. The proposed index is called the conjunction "F-value." This paper presents the concept of the F-value and the tuning of the metric for use in routine Conjunction Assessment operations.

Frigm, Ryan Clayton↗
NASA NTRS2010

Algorithm That Synthesizes Other Algorithms for Hashing

An algorithm that includes a collection of several subalgorithms has been devised as a means of synthesizing still other algorithms (which could include computer code) that utilize hashing to determine whether an element (typically, a number or other datum) is a member of a set (typically, a list of numbers). Each subalgorithm synthesizes an algorithm (e.g., a block of code) that maps a static set of key hashes to a somewhat linear monotonically increasing sequence of integers. The goal in formulating this mapping is to cause the length of the sequence thus generated to be as close as practicable to the original length of the set and thus to minimize gaps between the elements. The advantage of the approach embodied in this algorithm is that it completely avoids the traditional approach of hash-key look-ups that involve either secondary hash generation and look-up or further searching of a hash table for a desired key in the event of collisions. This algorithm guarantees that it will never be necessary to perform a search or to generate a secondary key in order to determine whether an element is a member of a set. This algorithm further guarantees that any algorithm that it synthesizes can be executed in constant time. To enforce these guarantees, the subalgorithms are formulated to employ a set of techniques, each of which works very effectively covering a certain class of hash-key values. These subalgorithms are of two types, summarized as follows: Given a list of numbers, try to find one or more solutions in which, if each number is shifted to the right by a constant number of bits and then masked with a rotating mask that isolates a set of bits, a unique number is thereby generated. In a variant of the foregoing procedure, omit the masking. Try various combinations of shifting, masking, and/or offsets until the solutions are found. From the set of solutions, select the one that provides the greatest compression for the representation and is executable in the minimum amount of time. Given a list of numbers, try to find one or more solutions in which, if each number is compressed by use of the modulo function by some value, then a unique value is generated.

James, Mark↗