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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
NASA NTRS1997

The Nature and Evolutionary History of GRO J1744-28

GRO J1744-28 is the first known X-ray source to display bursts, periodic pulsations, and quasi-periodic oscillations. This source may thus provide crucial clues that will lead to an understanding of the differences in the nature of the X-ray variability from various accreting neutron stars. The orbital period is 11.8 days, and the measured mass function of 1.31 x 10(exp -4) solar mass is one of the smallest among all known binaries. If we assume that the donor star is a low-mass giant transferring matter through the inner Lagrange point, then we can show that its mass is lower than approximately 0.7 solar mass and probably closer to 0.25 solar mass. Higher mass, but unevolved, donor stars are shown to be implausible. We also demonstrate that the current He core mass of the donor star lies in the range of 0.20-0.25 solar mass. Thus, this system is most likely in the final stages of losing its hydrogen-rich envelope, with only a small amount of mass remaining in the envelope. If this picture is correct, then GRO J1744-28 may well represent the closest observational link that we have between the low-mass X-ray binaries and recycled binary pulsars in wide orbits. We have carried out a series of binary evolution calculations and explored, both systematically and via a novel Monte Carlo approach, the range of initial system parameters and input physics that can lead to the binary parameters of the present-day GRO J1744-28 system. The input parameters include both the initial total mass and the core mass of the donor star, the neutron-star mass, the strength of the magnetic braking, the mass-capture fraction, and the specifics of the core mass/radius relation for giants. Through these evolution calculations, we compute probability distributions for the current binary system parameters (i.e., the total mass, core mass, radius, luminosity, and K-band magnitude of the donor star, the neutron star mass, the orbital inclination angle, and the semimajor axis of the binary). Our calculations yield the following values for the GRO J1744-28 system parameters (with 95% confidence limits in parentheses): donor star mass: 0.24 solar mass (0.2-0.7 solar mass); He core mass of the donor star: 0.22 solar mass (0.20-0.25 solar mass); neutron-star mass: 1.7 solar mass (1.39-1.96 solar mass); orbital inclination angle: 18deg (7deg-22deg); semi- major axis: 64 lt-s (60-67 lt-s); radius of the donor star: 6.2 solar radius(6-9 solar radius); luminosity of donor star: 23 solar luminosity (15-49 solar luminosity), and long-term mass transfer rate at the current epoch: 5 x 10(exp -10)solar mass/yr (2 x 10(exp -10) to 5 x 10(exp -9)solar mass/yr). We deduce that the magnetic field of the underlying neutron star lies in the range of approximately 1.8 x 10(exp 11)G to approximately 7 x 10(exp 11)G, with a most probable value of 2.7 x 10(exp 11)G. This is evidently sufficiently strong to funnel the accretion flow onto the magnetic polar caps and suppress the thermonuclear flashes that would otherwise give rise to the type 1 X-ray bursts observed in most X-ray bursters. We present a simple paradigm for magnetic accreting neutron stars where X-ray pulsars, GRO J1744-28, the Rapid Burster, and the type 1 X-ray bursters may form a continuum of possible behaviors among accreting neutron stars, with the strength of the neutron-star magnetic field serving as a crucial parameter that determines the mode of X-ray variability from a given object.

Rappaport, S.↗
NASA NTRS1966

On the statistics of correlator outputs

Characteristic function, probability density function, and probability distribution function computations for correlation detector output, and correlator output statistics

Wintz, P. A.↗
NASA NTRS1969

Fluctuations in monatomic gases.

Fluctuation spectra of monatomic gases, using two time probability distributions for distribution function autocorrelations

Montgomery, D.↗
NASA NTRS1972

Statistical analysis of landing contact conditions for three lifting body research vehicles

The landing contact conditions for the HL-10, M2-F2/F3, and the X-24A lifting body vehicles are analyzed statistically for 81 landings. The landing contact parameters analyzed are true airspeed, peak normal acceleration at the center of gravity, roll angle, and roll velocity. Ground measurement parameters analyzed are lateral and longitudinal distance from intended touchdown, lateral distance from touchdown to full stop, and rollout distance. The results are presented in the form of histograms for frequency distributions and cumulative frequency distribution probability curves with a Pearson Type 3 curve fit for extrapolation purposes.

Larson, R. R.↗
NASA NTRS1972

Evaluation of Skylab IB sensitivity to on-pad winds with turbulence

Computer simulation was performed to estimate displacements and bending moments experienced by the SKYLAB 1B vehicle on the launch pad due to atmospheric winds. The vehicle was assumed to be a beam-like structure represented by a finite number of generalized coordinates. Wind flow across the vehicle was treated as a nonhomogeneous, stationary random process. Response computations were performed by the assumption of simple strip theory and application of generalized harmonic analysis. Displacement and bending moment statistics were obtained for six vehicle propellant loading conditions and four representative reference wind profile and turbulence levels. Means, variances and probability distributions are presented graphically for each case. A separate analysis was performed to indicate the influence of wind gradient variations on vehicle response statistics.

Coffin, T.↗
NASA NTRS1972

A stochastic bioburden model for spacecraft sterilization.

Development of a stochastic model of the probability distribution for the random variable representing the number of microorganisms on a surface as a function of time. The first basic principle associated with bioburden estimation is that viable particles are removed from surfaces. The second notion important to the analysis is that microorganisms in environments and on surfaces occur in clumps. The last basic principle relating to bioburden modeling is that viable particles are deposited on a surface. The bioburden on a spacecraft is determined by the amount and kind of control exercised on the spacecraft assembly location, the shedding characteristics of the individuals in the vicinity of the spacecraft, its orientation, the geographical location in which the assembly takes place, and the steps in the assembly procedure. The model presented has many of the features which are desirable for its use in the spacecraft sterilization programs currently being planned by NASA.

Roark, A. L.↗