A new proof of superposition of dressed particles in plasma kinetic theory
Superposition of dressed particles in plasma kinetic theory proved by using generalized stochastic equation for conditional probability density for one particle
Liu, C. H.↗
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Boulder tracks and nature of lunar soil.
Boulder tracks from 19 different locations on the Moon, observable in Lunar Orbiter photographs, have been examined. Measurements of the track width indicate that some of the boulders sank considerably deeper than others. It is suggested that lunar surface materials vary from place to place; the state of compaction (density of lunar soil) is probably one of the significant variables. Using bearing capacity theory, modified to be applicable to the rolling boulder problem by theoretical studies and extensive testing, the friction angle of the lunar soil was estimated. Most of the results were between 24 and 47 degrees with an arithmetic average of 37 degrees.
Hovland, H. J.↗
Tracking performance of symbol synchronizers for Manchester coded data
The implementation and tracking performance of symbol synchronizers for Manchester coded data is presented with motivation provided by maximum a posteriori (MAP) estimation theory. Certain physically relizable closed-loop structures, readily implemented in practice, are suggested by the theory for uncoded data symbols with arbitrary data transition probabilities. The tracking performance of these loops is optimized and comparisons are made among the various configurations over a wide range of system parameters. Although not the major intent of the paper, the acquisition problem is briefly addressed.
Simon, M. K.↗
An application of synthetic seismicity in earthquake statistics - The Middle America Trench
The way in which seismicity calculations which are based on the concept of fault segmentation incorporate the physics of faulting through static dislocation theory can improve earthquake recurrence statistics and hone the probabilities of hazard is shown. For the Middle America Trench, the spread parameters of the best-fitting lognormal or Weibull distributions (about 0.75) are much larger than the 0.21 intrinsic spread proposed in the Nishenko Buland (1987) hypothesis. Stress interaction between fault segments disrupts time or slip predictability and causes earthquake recurrence to be far more aperiodic than has been suggested.
Ward, Steven N.↗
Asteroid orbital error analysis: Theory and application
We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).
Muinonen, K.↗
Predicting Satellite Close Approaches Using Statistical Parameters in the Context of Artificial Intelligence
In order to ensure a sustainable use of low earth orbit in particular and near Earth space in general, reliable and effective close approach prediction be-tween space objects is key. Only this allows for efficient and timely colli-sion avoidance. Space Situational Awareness (SSA) for commercial and government missions will be facing the rapidly growing amount of small and potentially less agile satellites as well as debris in the near earth realm, such as the increase in CubeSat launches and upcoming large constellations. At the same time, space object detection capabilities are expected to increase significantly, allowing for the reliable detection of smaller objects, e.g. when the Air Force Space Fence radar becomes operational. In combination, the space object catalog is expected to increase tremendously in size. In this paper, we introduce an investigative approach based on the latest capabili-ties in artificial intelligence in fostering the potential for fast and accurate close approach predictions. We consider the study of statistical and infor-mation theory parameters in contrast and complementary to the classical probability of collision computation alone, in order to determine the feasi-bility of reliably predicting close approaches.
Mashiku, A.↗
Predicting Satellite Close Approaches Using Statistical Parameters in the Context of Artificial Intelligence
In order to ensure a sustainable use of low earth orbit in particular and near Earth space in general, reliable and effective close approach prediction be-tween space objects is key. Only this allows for efficient and timely colli-sion avoidance. Space Situational Awareness (SSA) for commercial and government missions will be facing the rapidly growing amount of small and potentially less agile satellites as well as debris in the near earth realm, such as the increase in CubeSat launches and upcoming large constellations. At the same time, space object detection capabilities are expected to increase significantly, allowing for the reliable detection of smaller objects, e.g. when the Air Force Space Fence radar becomes operational. In combination, the space object catalog is expected to increase tremendously in size. In this paper, we introduce an investigative approach based on the latest capabili-ties in artificial intelligence in fostering the potential for fast and accurate close approach predictions. We consider the study of statistical and infor-mation theory parameters in contrast and complementary to the classical probability of collision computation alone, in order to determine the feasi-bility of reliably predicting close approaches.
Mashiku, Alinda↗
Properties and Astrophysical Implications of the 150 M Binary Black Hole Merger GW190521
The gravitational-wave signal GW190521 is consistent with a binary black hole (BBH) merger source at redshift 0.8 with unusually high component masses, 85 (+21,-14) Mꙩ and 66 (+17,-18) Mꙩ, compared to previously reported events, and shows mild evidence for spin-induced orbital precession. The primary falls in the mass gap predicted by (pulsational) pair-instability supernova theory, in the approximate range 65–120 Mꙩ. The probability that at least one of the black holes in GW190521 is in that range is 99.0%. The final mass of the merger (142 (+28,-16) Mꙩ) classifies it as an intermediate-mass black hole. Under the assumption of a quasi-circular BBH coalescence, we detail the physical properties of GW190521’s source binary and its post-merger remnant, including component masses and spin vectors. Three different waveform models, as well as direct comparison to numerical solutions of general relativity, yield consistent estimates of these properties. Tests of strong-field general relativity targeting the merger-ringdown stages of the coalescence indicate consistency of the observed signal with theoretical predictions. We estimate the merger rate of similar systems to be 0.13 (+0.30,-0.11)Gp/cu.c yr. We discuss the astrophysical implications of GW190521 for stellar collapse and for the possible formation of black holes in the pair-instability mass gap through various channels: via (multiple) stellar coalescences, or via hierarchical mergers of lower-mass black holes in star clusters or in active galactic nuclei. We find it to be unlikely that GW190521 is a strongly lensed signal of a lower-mass black hole binary merger. We also discuss more exotic possible sources for GW190521, including a highly eccentric black hole binary, or a primordial black hole binary.
R. Abbott↗
Finding Bounded Rational Equilibria: Iterative Focusing - Part 1
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights from the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.
Wolpert, David H.↗
Finding Bounded Rational Equilibria: Alternative Lagrangians and Uncountable Move Spaces - Part 2
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights &om the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.
Wolpert, David H.↗
Processing of telemetry data generated by sensors moving in a varying field.
Telemetry data processing problems noting error sources, probability distribution of counts in counting processes, sensor relay during motion in varying field, etc
STATISTICAL COMMUNICATION THEORY↗
Atmospheric drag as the cause of the secular decrease in the semimajor axis of LAGEOS's orbit
An unmodeled acceleration is causing the semimajor axis of LAGEOS to decrease at the rate of about 1.1 mm/day. Drag from charged particles or neutral helium or both is the most probable cause. The rate of orbital decay is conceivably explained by the theories of charged particle drag. Unfortunately, these theories are not yet developed to the point where a definitive statement as to the importance of charged particle drag can be made. Neutral helium may also be the cause of the orbital decay. While the abundance required to account for the secular decrease is high, it also helps solve the 'helium problem'. Neutral hydrogen probably accounts for no more than 12 percent of the observed decay.
Rubincam, D. P.↗
Electronic excitation of ground state atoms by collision with heavy gas particles
Most of the important chemical reactions which occur in the very high temperature air produced around space vehicles as they enter the atmosphere were investigated both experimentally and theoretically, to some extent at least. One remaining reaction about which little is known, and which could be quite important at the extremely high temperatures that will be produced by the class of space vehicles now contemplated - such as the AOTV - is the excitation of bound electron states due to collisions between heavy gas particles. Rates of electronic excitation due to free electron collisions are known to be very rapid, but because these collisions quickly equilibrate the free and bound electron energy, the approach to full equilibrium with the heavy particle kinetic energy will depend primarily on the much slower process of bound electron excitation in heavy particle collisions and the subsequent rapid transfer to free electron energy. This may be the dominant mechanism leading to full equilibrium in the gas once the dissociation process has depleted the molecular states so the transfer between molecular vibrational energy and free electron energy is no longer available as a channel for equilibration of free electron and heavy particle kinetic energies. Two mechanisms seem probable in electronic excitation by heavy particle impact. One of these is the collision excitation and deexcitation of higher electronic states which are Rydberg like. A report, entitled 'Semi-Classical Theory of Electronic Excitation Rates', was submitted previously. This presented analytic expressions for the transition probabilities, assuming that the interaction potential is an exponential repulsion with a perturbation ripple due to the dipole-induced dipole effect in the case of neutral-neutral collisions, and to the ion-dipole interaction in the case of ion-neutral collisions. However the above may be, there is little doubt that excitation of ground state species by collision occurs at the point where the initial and final potentials cross, or at least come very close. Therefore, this mechanism would be applicable to the case where a gas is initially at very low temperature suddenly subjected to high energy heavy particle bombardment. This situation would model the measurement of excitation cross section by molecular beam techniques, for example. The purpose is to report values of cross sections and rate coefficients for collision excitation of ground state atoms estimated with the Landau-Zener transition theory and to compare results with measurement of excitation cross sections for a beam of Hydrogen atoms impacting Argon atom targets. Some very dubious approximations are used, and the comparison with measurement is found less than ideal, but results are at least consistent within order of magnitude. The same model is then applied to the case of N-N atom collisions, even though the approximations then become even more doubtful. Still the rate coefficients obtained are at least plausible in both magnitude and functional form, and as far as I am aware these are the only estimates available for such rate coefficients.
Hansen, C. Frederick↗
Anomalous growth of single ice crystals in solution
It is shown that major discrepancies exist between experiments and theory for ice crystal growth from solution. Accurate data, taken in a microgravity environment, approximate analytical models, and exact (probably numerical) models all are needed to advance our understanding of ice crystal growth phenomena. A new approximate semi-empirical theory is presented which predicts that a relatively sharp transition from natural convection control to diffusion control for ice growth in pure water occurs at a subcooling of about 10 C (a reduced temperature difference of about 0.125). No reliable data exist to test this prediction. The theory also predicts qualitatively the growth of ice in NaCl solution in which maxima in the growth rates are observed at various levels of subcooling.
Gill, W. N.↗
The random coding bound is tight for the average code.
The random coding bound of information theory provides a well-known upper bound to the probability of decoding error for the best code of a given rate and block length. The bound is constructed by upperbounding the average error probability over an ensemble of codes. The bound is known to give the correct exponential dependence of error probability on block length for transmission rates above the critical rate, but it gives an incorrect exponential dependence at rates below a second lower critical rate. Here we derive an asymptotic expression for the average error probability over the ensemble of codes used in the random coding bound. The result shows that the weakness of the random coding bound at rates below the second critical rate is due not to upperbounding the ensemble average, but rather to the fact that the best codes are much better than the average at low rates.
Gallager, R. G.↗
On the theory of tunnelling in electron and proton transfer reactions.
The concept of tunnelling in the theory of electron and proton transfer reactions has recently been questioned on the ground that the situation is a nonstationary one. It has been suggested that time-dependent perturbation theory should be applied to obtain the quantum mechanical transition probability. We have done this for a square barrier. The result for most reactions is the same as obtained by the WKB approximation.
Sen, R. K.↗
The orbit properties of colliding co-orbiting bodies
It is generally assumed that an ensemble of small bodies located in similar Keplarian orbits will, because of collisions, tend to disperse into more and more dissimilar orbits. For example, it is thought that the asteroids may represent the remnants of a few larger bodies that broke up or failed to fully accrete. A proposed experiment using the space station consists of an ensemble of small bodies or particles released gently from a central location in a large chamber, much like the breaking of billiard balls. The particles would them co-orbit and occasionally collide. Their subsequent behavior could be monitored by several video recorders, their linear and angular velocities before and after collision calculated, and their general behavior studied. This experiment could yield results of fundamental importance for theories of the origin of the planets, asteroids, comets, and probably ring systems.
Freeman, J. W.↗
Limit on overshooting from the convective core in upper main-sequence stars
Overshooting of convective elements far beyond the classical Schwarzschild convective core boundary in theoretical models of massive ZAMS stars is found to lead to significant reductions of stellar luminosity and radius, provided that the temperature gradient in the overshoot region can be approximated by the adiabatic gradient. Comparison of these theoretical models with binary star data for the range of 5-15 solar masses indicates that the ratio of overshoot distance to pressure scale height is probably less than 1.5. This result apparently excludes any overshooting theories that predict very extended adiabatic convective cores.
Stothers, Richard B.↗