On energy bounds derived from the conjugate eigenvalue problem
Atomic system ground state energy upper bound, considering internuclear distances and removal of restriction for negative definite potential energy operator
Epstein, S. T.↗
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A bound on the rate-distortion function and application to images.
An upper bound on the rate-distortion function for discrete ergodic sources with memory is developed by partitioning the source sample space into a finite number of disjoint subsets and bounding the rates for each subset. The bound depends only on the mean vectors and covariance matrices for the subsets and is easy to compute. It is tighter than the Gaussian bound for sources that exhibit clustering of either the values or covariances of successive source outputs. The bound is evaluated for a certain class of pictorial data using both one-dimensional and two-dimensional blocks of picture elements. Two-dimensional blocks yield a tighter bound than one-dimensional blocks; both result in a significantly tighter bound than the Gaussian bound.
Tasto, M.↗
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.↗
Beryllium and boron constraints on an early Galactic bright phase
The recent observations of Be and B in metal-deficient halo dwarfs are used to constrain a 'bright phase' of enhanced cosmic-ray flux in the early Galaxy. Assuming that this Be and B arises from cosmic-ray spallation in the early Galaxy, limits are placed on the intensity of the early (Population II) cosmic-ray flux relative to the present (Population I) flux. A simple estimate of bounds on the flux ratio is 1 - 40. This upper bound would restrict galaxies like our own from producing neutrino fluxes that would be detectable in any currently proposed detectors. It is found that the relative enhancement of the early flux varies inversely with the relative time of enhancement. It is noted that associated gamma-ray production via pp - pi sup 0 pp may be a significant contribution to the gamma-ray background above 100 MeV.
Fields, Brian D.↗
Molecular Dynamics Modeling of Carbon Nanotube Composite Fracture Using ReaxFF
Carbon nanotube (CNT) fiber reinforced composites with specific tensile strengths and moduli approaching those of aerospace grade carbon fiber composites have recently been reported. This achievement was enabled by the emerging availability of high N/tex yarns in kilometer-scale quantities. While the production of this yarn is an impressive advance, its strength is still much lower than that of the individual CNTs comprising the yarn. Closing this gap requires understanding load transfer between CNTs at the nanometer dimensional scale. This work uses reactive molecular dynamics simulations to gain an understanding at the nanometer scale of the key factors that determine CNT nanocomposite mechanical performance, and to place more realistic upper bounds on the target properties. While molecular dynamics simulations using conventional force fields can predict elastic properties, the ReaxFF reactive forcefield can also model fracture behavior because of its ability to accurately describe bond breaking and formation during a simulation. The upper and lower bounds of CNT composite properties are investigated by comparing systems composed of CNTs continuously connected across the periodic boundary with systems composed of finite length CNTs. These lengths, effectively infinite for the continuous tubes and an aspect ratio of 13 for the finite length case, result from practical limitations on the number of atoms that can be included in a simulation. Experimentally measured aspect ratios are typically on the order of 100,000, so the calculated results should represent upper and lower limits on experimental mechanical properties. Finally, the effect of various degrees of covalent crosslinking between the CNTs and amorphous carbon matrix is considered to identify the amount of CNT-matrix covalent bonding that maximizes overall composite properties.
Jensen, Benjamin D.↗
Bounds on the probability of error due to intersymbol interference for correlated digital signals
Upper bound on error probability due to intersymbol interference for correlated and uncorrelated digital signals, presenting examples for data communication systems
Glave, F. E.↗
The Mystery of Io's Warm Polar Regions: Implications for Heat Flow
Unexpectedly warm polar temperatures further support the idea that Io is covered virtually everywhere by cooling lava flows. This implies a new heat flow component. Io's heat flow remains constrained between a lower bound of (approximately) 2.5 W m(exp -2) and an upper bound of (approximately) 13 W m(exp -2). Additional information is contained in the original extended abstract.
Matson, D. L.↗
A lower bound for the decoder error probability of the linear MDS code
A lower bound for the decoder error probability (P sub E (u)) of a linear maximum distance separable (MDS) code is derived by counting the dominant types of decoding words around code words. It is shown that the lower bound derived is similar in form, and close numerically, to the upper bound derived.
Cheung, K.-M.↗
Thermodynamic models for bounding pressurant mass requirements of cryogenic tanks
Thermodynamic models have been formulated to predict lower and upper bounds for the mass of pressurant gas required to pressurize a cryogenic tank and then expel liquid from the tank. Limiting conditions are based on either thermal equilibrium or zero energy exchange between the pressurant gas and initial tank contents. The models are independent of gravity level and allow specification of autogenous or non-condensible pressurants. Partial liquid fill levels may be specified for initial and final conditions. Model predictions are shown to successfully bound results from limited normal-gravity tests with condensable and non-condensable pressurant gases. Representative maximum collapse factor maps are presented for liquid hydrogen to show the effects of initial and final fill level on the range of pressurant gas requirements. Maximum collapse factors occur for partial expulsions with large final liquid fill fractions.
Vandresar, Neil T.↗
A lower bound on the minimum Euclidean distance of trellis-coded modulation schemes
A lower bound on the minimum free Euclidean distance of trellis-coded modulation (TCM) is derived that guarantees the existence of good TCM codes of any complexity. The bound is used to compare trellis codes combined with phase-shift keying, pulse amplitude modulation, and quadrature amplitude-shift keying modulation. This random coding bound is the first lower bound on the free distance of trellis codes, is tighter than any upper bound for large constraint lengths, and predicts the asymptotic performance of TCM when the complexity of the code becomes large. The bound can be used with any code rate and any modulation scheme and shows that the free distance increases linearly with the constraint length for large values of the constraint length.
Rouanne, Marc↗
Efficient Cache use for Stencil Operations on Structured Discretization Grids
We derive tight bounds on the cache misses for evaluation of explicit stencil operators on structured grids. Our lower bound is based on the isoperimetrical property of the discrete octahedron. Our upper bound is based on a good surface to volume ratio of a parallelepiped spanned by a reduced basis of the interference lattice of a grid. Measurements show that our algorithm typically reduces the number of cache misses by a factor of three, relative to a compiler optimized code. We show that stencil calculations on grids whose interference lattice have a short vector feature abnormally high numbers of cache misses. We call such grids unfavorable and suggest to avoid these in computations by appropriate padding. By direct measurements on a MIPS R10000 processor we show a good correlation between abnormally high numbers of cache misses and unfavorable three-dimensional grids.
Frumkin, Michael↗
Jet-Front Speed and the Origin of Jets in Polar Coronal Holes
The area-average strength of the open magnetic field in the polar coronal holes can be estimated from the radial component of the magnetic field measured by Ulysses in the solar wind, the fraction of the solar sphere covered by the polar coronal holes, and the fraction of the heliosphere filled by the fast solar wind from the polar coronal holes. For the present minimum phase of the solar cycle, the estimated strength is approximately 10 G. Using this strength for the ambient open field in the standard reconnection model for jets in coronal holes, we obtain for any given jet-front speed a lower bound on the initial temperature of the expanding jet-front plasma, and an upper bound on the ambient plasma density at the reconnection site. These two bounds indicate the following. For jet-front speeds of approximately 1000 km/s, (1) the reconnection site has to be in the low corona or upper transition region (n(e) is less than 10(exp 9) cm(exp -3)), not in the lower transition region or chromosphere, (2) the jet-front plasma is initially heated to T greater than approximately 10(exp 7) K, and (3) hence a compact X-ray flare is produced at the base of the jet. For jet-front speeds less than approximately 100 km/s, (1) the jet can be produced by reconnection in the lower transition region (approximately 10(exp 9) less than n(e) less than approximately 10(exp 10) cm(exp-3)) or upper chromosphere (approximately 10(exp 10) less than n(e) less than approximately 10(exp 12) cm-3), (2) the initial temperature of the jet-front plasma can be less than 10(exp 6) K, and (3) hence some EUV and H(alpha) jet-type macrospicules may be produced with no detectable X-ray emission.
Moore, Ron↗
Optimal filtering in the presence of unmodeled time correlated driving disturbances.
In many realistic data filtering problems, the cross correlation of the state estimation error and the state forcing function is unknown due to the poor knowledge of the time history of the forcing function. In this paper, the conservative and minimal approximation to the cross correlation terms is presented. It requires only the knowledge of the estimation error covariance and the forcing function covariance, with the choice of an associated free parameter left to the user. If the estimation error covariance and/or the forcing function covariance are bounded from above but not known exactly, the cross correlation approximation using those upper bounds remains conservative. This cross correlation approximation leads to a conservative approximation to the estimation error covariance matrix differential equation between measurement times. The free parameter is determined as the analytic solution to an associated optimal control problem. The procedure is expanded to include discrete linear measurement incorporation.
Fraser, D. C.↗
Formation of Jupiter and Saturn
An overview of current theories of the formation of our Solar System, with emphasis on giant planets, is presented. The most detailed models are based upon observations of planets and smaller bodies within our own Solar System and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Larger disk mass allows for faster growth of solid planetary bodies. The ability of a solid planet to trap gas from the protoplanetary disk increases rapidly as its mass increases (because the depth of its gravitational potential well increases), but decreases as the planetesimal accretion rate is increased (as it becomes hotter). The net effect of increasing disk mass is that gas giant planets form more rapidly, but with larger core masses. Observations of circumstellar disks suggest an upper bound on the time available prior to dissipation of the gas, and planetary models place upper limits on core sizes. Together, these constraints suggest that Jupiter and Saturn formed in 1-10 million years, and the density of solids in the region of their formation was a few times as large as the lower bound provided by the traditional minimum mass nebula.
Lissauer, Jack J.↗
Formation of Jupiter and Saturn
An overview of current theories of the formation of our Solar System, with emphasis on giant planets, is presented. The most detailed models are based upon observations of planets and smaller bodies within our own Solar System and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Larger disk mass allows for faster growth of solid planetary bodies. The ability of a solid planet to trap gas from the protoplanetary disk increases rapidly as its mass increases (because the depth of its gravitational potential well increases), but decreases as the planetesimal accretion rate is increased (as it becomes hotter). The net effect of increasing disk mass is that gas giant planets form more rapidly, but with larger core masses. Observations of circumstellar disks suggest an upper bound on the time available prior to dissipation of the gas, and planetary models place upper limits on core sizes. Together, these constraints suggest that Jupiter and Saturn formed in 1 - 10 million years, and the density of solids in the region of their formation was a few times as large as the lower bound provided by the traditional minimum mass nebula.
Lissauer, Jack J.↗
Control design for robust stability in linear regulators: Application to aerospace flight control
Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.
Yedavalli, R. K.↗
Existence of the time optimal control for robotic manipulators
Using Filipov's Theorem, it is shown that the conditions oif nonfinite escape of trajectories, reachability, and convexity of the dynamics over all admissible controls are needed for the existence of a time optimal solution for the robotic equation. With a lower bound for the finite-escape time established using a Liapunov approach, and an upper bound for the time to reach the target established using the exact linearization idea, a single inequality is found which is closely related to the coriolis and the centrifugal terms, the absence of which implies that the domain of existence of the optimal solution can be made arbitrarily large with a large torque constraint. As the work space is finite, this is essentially a global result in practical situations.
Wen, J.↗
Reduced conservatism in stability robustness bounds by state transformation
This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.
Yedavalli, R. K.↗