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NASA NTRS1991

Computational micromechanics of woven composites

The bounds on the equivalent elastic material properties of a composite are presently addressed by a unified energy approach which is valid for both unidirectional and 2D and 3D woven composites. The unit cell considered is assumed to consist, first, of the actual composite arrangement of the fibers and matrix material, and then, of an equivalent pseudohomogeneous material. Equating the strain energies due to the two arrangements yields an estimate of the upper bound for the material equivalent properties; successive increases in the order of displacement field that is assumed in the composite arrangement will successively produce improved upper bound estimates.

Hopkins, Dale A.↗
NASA NTRS1993

Theoretical study of the lowest 5Pi and 5Sigma(+) states of CO

Large one-particle basis sets and the internally contracted multireference configuration-interaction treatment of electron correlation were used to characterize the lowest 5Pi and 5Sigma(+) states of CO. It was found that the (1)5Sigma(+) state is weakly bound with an r(e) of 4.76 a(0), supporting results of calculations by Rosenkrantz et al. (1992). The (1)5Pi state has a weakly bound outer well and a significantly bound inner well.

Bauschlicher, Charles W., Jr.↗
NASA NTRS1993

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↗
NASA NTRS1993

A Performance Prediction Model for a Fault-Tolerant Computer During Recovery and Restoration

The modeling and design of a fault-tolerant multiprocessor system is addressed. In particular, the behavior of the system during recovery and restoration after a fault has occurred is investigated. Given that a multicomputer system is designed using the Algorithm to Architecture to Mapping Model (ATAMM), and that a fault (death of a computing resource) occurs during its normal steady-state operation, a model is presented as a viable research tool for predicting the performance bounds of the system during its recovery and restoration phases. Furthermore, the bounds of the performance behavior of the system during this transient mode can be assessed. These bounds include: time to recover from the fault (t(sub rec)), time to restore the system (t(sub rec)) and whether there is a permanent delay in the system's Time Between Input and Output (TBIO) after the system has reached a steady state. An implementation of an ATAMM based computer was developed with the Generic VHSIC Spaceborne Computer (GVSC) as the target system. A simulation of the GVSC was also written based on the code used in ATAMM Multicomputer Operating System (AMOS). The simulation is in turn used to validate the new model in the usefulness and accuracy in tracking the propagation of the delay through the system and predicting the behavior in the transient state of recovery and restoration. The model is validated as an accurate method to predict the transient behavior of an ATAMM based multicomputer during recovery and restoration.

Stoughton, John W.↗
NASA NTRS1993

Thermal studies of Martian channels and valleys using Termoskan data: New results

The Termoskan instrument onboard the Phobos '88 spacecraft acquired the highest-spatial-resolution thermal data ever obtained for Mars. Included in the thermal images are 2 km/pixel midday observations of several major channel and valley systems, including significant portions of Shalbatana Vallis, Ravi Vallis, Al-Qahira Vallis, Ma'adim Vallis, the channel connecting Valles Marineris with Hydraotes Chaos, and channel material in Eos Chasma. Termoskan also observed small portions of the southern beginnings of Simud, Tiu, and Ares Valles and some channel material in Gangis Chasma. Simultaneous broad band visible data were obtained for all but Ma'adim Vallis. We find that most of the channels and valleys have higher inertias than their surroundings, consistent with Viking IRTM-based thermal studies of Martian channels. We see for the first time that thermal inertia boundaries closely match all flat channel floor boundaries. Combining Termoskan thermal data, relative observations from Termoskan visible channel data, Viking absolute bolometric albedos, and a thermal model of the Mars surface, we have derived lower bounds on channel thermal inertias. Lower bounds on typical channel thermal inertias range from 8.4 to 12.5 (10(exp -3) cal cm(exp -2) s(exp -1/2)K(exp -1)) (352 to 523 in SI units). Lower bounds on inertia differences with the surrounding heavily cratered plains range from 1.1 to 3.5 (46 to 147 in SI units). Atmospheric and geometric effects are not sufficient to cause the inertia enhancements. We agree with previous researchers that localized, dark, high inertia areas within channels are likely eolian in nature. However, the Temloskan data show that eolian deposits do not fill the channels, nor are they responsible for the overall thermal inertia enhancement. Thermal homogeneity and strong correlation of thermal boundaries with the channel floor boundaries lead us to favor noneolian overall explanations.

Betts, B. H.↗
NASA NTRS1993

Robust control design with real parameter uncertainty using absolute stability theory

The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.

How, Jonathan P.↗
NASA NTRS1994

Rotational relaxation of molecular hydrogen at moderate temperatures

Using a coupled rotation-vibration-dissociation model the rotational relaxation times for molecular hydrogen as a function of final temperature (500-5000 K), in a hypothetical scenario of sudden compression, are computed. The theoretical model is based on a master equation solver. The bound-bound and bound-free transition rates have been computed using a quasiclassical trajectory method. A review of the available experimental data on the rotational relaxation of hydrogen is presented, with a critical overview of the method of measurements and data reduction, including the sources of errors. These experimental data are then compared with the computed results.

COUPLED ROTATION VIBRATION DIS↗
NASA NTRS1994

Performance of mean-frequency estimators for Doppler radar and lidar

The performance of mean-frequency estimators for Doppler radar and lidar measurements of winds is presented in terms of two basic parameters: Phi, the ratio of the average signal energy per estimate to the spectral noise level; and Omega, which is proportional to the number of independent samples per estimate. For fixed Phi and Omega, the Cramer-Rao bound (CRB) (theoretical best performance) for unbiased estimators of mean frequency (normalized by the spectral width of the signal), signal power, and spectral width are essentially independent of the number of data samples M. For large Phi, the estimators of mean frequency are unbiased and the performance is independent of M. The spectral domain estimators and covariance based estimators are bounded by the approximate period of M. The spectral domain estimators and covariance based estimators are bounded by the approximate periodogram CRB. The standard deviation of the maximum-likelihood estimator approaches the exact CRB, which can be more than a factor of 2 better than the performance of the spectral domain estimators or covariance-based estimators for typical Omega. For small Phi, the estimators are biased due to the effects of the uncorrelated noise (white noise), which results in uniformly distributed 'bad' estimates. The fraction of bad estimates is a function of Phi and M with weak dependence on the parameter Omega. Simple empirical models describe the standard deviation of the good estimates and the fraction of bad estimates. For Doppler lidar and for large Phi, better performance is obtained by using many low-energy pulses instead of one pulse with the same total energy. For small Phi, the converse is true.

Frehlich, R. G.↗
NASA NTRS1994

Hot proton anisotropies and cool proton temperatures in the outer magnetosphere

The hot protons of the outer magnetosphere typically exhibit a temperature anistropy such that T(sub perp)/T(sub parallel) greater than 1, where perpendicular and parallel symbols denote directions relative to the background magnetic field. If this anisotrpy is sufficiently large, the electomagneitc proton cyclotron anistropy instability may be excited. This instability is studied using linear Vlasov theory and one-dimensional hybrid simulations for a homogeneous plasma model representative of conditions in the outer magnetosphere with a hot anisotropic proton component (denoted by subscript h) and a cool, initially isotropic proton component (subscript c). Linear theory yields an instability threshold condition on the hot proton temperature anistropy where as the simulations imply an upper bound on T(sub perp h)/T(sub parallel h); both the threshold and the upper bound have similar scaling with the maximum growth rate gamma (sub m), the parallel beta of the hot component, beta(sub parallel h), and the relative density of the hot component n(sub h)/n(sub e). An anlysis of plasma observations from the Los Alamos magnetospheric plasma analyzer (MPA) in geosynchronous orbits finds that the maximum value of the hot proton temperature anisotropy approximately satisfies the predicted scaling with beta(sub parallel h) and nu(sub h)/n(sub e) and yields the proportionality factor that quantifies this upper bound. The simulations are also used to examine the heating of the cool proton cyclotron instability. The simulations yield a scaling for the dimensionless late-time cool proton average temperature T(sub c)/T(sub parallel h) as (n(sub h)/n(sub e))/beta(sub parallel h exp 0.5). Analysis of MPA data shows that the observed values of T(sub c)/T(sub parallel h) have similar scaling and again yield the proportionality factor which quantifies this relationship.

Gary, S. Peter↗
NASA NTRS1994

Theoretical light curve of a Type 2p supernova

The light curve and other observable diagnostics are presented for what should be a typical Type II 'plateau' supernova, the explosion of a 15 solar mass red supergiant. The calculations are carried out using a multi-frequency radiation transport code that includes opacity from all important mechanisms-bound-bound, bound-free, free-free, and electron scattering. It is found that the inclusion of opacity sources besides electron scattering increases the computed lenght of the plateau in the 15 solar mass model by approximately 30 days. Especially important is the ultraviolet cutoff caused by a thick forest of lines. Deposition and escape of gamma-rays from radioactive decay are also accurately simulated. We find that the presence of 0.06 solar mass of ejected Ni-56 extends the length of the plateau from approximately 100 days to approximately 140 dys. Because of the large hydrogen envleope and radius in this model, mixing does not appreciably alter the bolometric light curve, although it does change the gamma-ray light curve significantly. With 0.06 solar mass of ejected Ni-56, the unmixed (mixed) model peaks in escaping gamma-rays at 576 (466) days with gamma-ray luminosity of 3 x 10(exp 38) ergs/s. Except for the local group, the gamma-rays from an extragalactic 15 solar mass SNe IIp will be too faint to detect with any exsiting detectors. However, a Galactic SNe IIp would be quite bright and easily detectable.

Eastman, Ronald G.↗
NASA NTRS1995

Kinematics and dynamics of the MKW/AWM poor clusters

We report 472 new redshifts for 416 galaxies in the regions of the 23 poor clusters of galaxies originally identified by Morgan, Kayser, and White (MKW), and Albert, White, and Morgan (AWM). Eighteen of the poor clusters now have 10 or more available redshifts within 1.5/h Mpc of the central galaxy; 11 clusters have at least 20 available redshifts. Based on the 21 clusters for which we have sufficient velocity information, the median velocity scale is 336 km/s, a factor of 2 smaller than found for rich clusters. Several of the poor clusters exhibit complex velocity distributions due to the presence of nearby clumps of galaxies. We check on the velocity of the dominant galaxy in each poor cluster relative to the remaining cluster members. Significantly high relative velocities of the dominant galaxy are found in only 4 of 21 poor clusters, 3 of which we suspect are due to contamination of the parent velocity distribution. Several statistical tests indicate that the D/cD galaxies are at the kinematic centers of the parent poor cluster velocity distributions. Mass-to-light ratios for 13 of the 15 poor clusters for which we have the required data are in the range 50 less than or = M/L(sub B(0)) less than or = 200 solar mass/solar luminosity. The complex nature of the regions surrounding many of the poor clusters suggests that these groupings may represent an early epoch of cluster formation. For example, the poor clusters MKW7 and MKWS are shown to be gravitationally bound and likely to merge to form a richer cluster within the next several Gyrs. Eight of the nine other poor clusters for which simple two-body dynamical models can be carried out are consistent with being bound to other clumps in their vicinity. Additional complex systems with more than two gravitationally bound clumps are observed among the poor clusters.

Beers, Timothy C.↗
NASA NTRS1995

Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

To improve radiative transfer calculations for inhomogeneous clouds, a consistent means of modeling inhomogeneity is needed. One current method of modeling cloud inhomogeneity is through the use of fractal parameters. This method is based on the supposition that cloud inhomogeneity over a large range of scales is related. An analysis technique named wavelet analysis provides a means of studying the multiscale nature of cloud inhomogeneity. In this paper, the authors discuss the analysis and modeling of cloud inhomogeneity through the use of wavelet analysis. Wavelet analysis as well as other windowed analysis techniques are used to study liquid water path (LWP) measurements obtained during the marine stratocumulus phase of the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment. Statistics obtained using analysis windows, which are translated to span the LWP dataset, are used to study the local (small scale) properties of the cloud field as well as their time dependence. The LWP data are transformed onto an orthogonal wavelet basis that represents the data as a number of times series. Each of these time series lies within a frequency band and has a mean frequency that is half the frequency of the previous band. Wavelet analysis combined with translated analysis windows reveals that the local standard deviation of each frequency band is correlated with the local standard deviation of the other frequency bands. The ratio between the standard deviation of adjacent frequency bands is 0.9 and remains constant with respect to time. This ratio defined as the variance coupling parameter is applicable to all of the frequency bands studied and appears to be related to the slope of the data's power spectrum. Similar analyses are performed on two cloud inhomogeneity models, which use fractal-based concepts to introduce inhomogeneity into a uniform cloud field. The bounded cascade model does this by iteratively redistributing LWP at each scale using the value of the local mean. This model is reformulated into a wavelet multiresolution framework, thereby presenting a number of variants of the bounded cascade model. One variant introduced in this paper is the 'variance coupled model,' which redistributes LWP using the local standard deviation and the variance coupling parameter. While the bounded cascade model provides an elegant two- parameter model for generating cloud inhomogeneity, the multiresolution framework provides more flexibility at the expense of model complexity. Comparisons are made with the results from the LWP data analysis to demonstrate both the strengths and weaknesses of these models.

Gollmer, Steven M.↗
NASA NTRS1997

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.

Noyes, Robert W.↗
NASA NTRS1999

The Reconstruction Problem Revisited

The role of reconstruction in avoiding oscillations in upwind schemes is reexamined, with the aim of providing simple, concise proofs. In one dimension, it is shown that if the reconstruction is any arbitrary function bounded by neighboring cell averages and increasing within a cell for increasing data, the resulting scheme is monotonicity preserving, even though the reconstructed function may have overshoots and undershoots at the cell edges and is in general not a monotone function. In the special case of linear reconstruction, it is shown that merely bounding the reconstruction between neighboring cell averages is sufficient to obtain a monotonicity preservinc,y scheme. In two dimensions, it is shown that some ID TVD limiters applied in each direction result in schemes that are not positivity preserving, i.e. do not give positive updates when the data are positive. A simple proof is given to show that if the reconstruction inside the cell is bounded by the neighboring cell averages (including corner neighbors), then the scheme is positivity preserving. A new limiter that enforces this condition but is not as dissipative as the Minmod limiter is also presented.

Suresh, Ambaby↗
NASA NTRS1999

Recent Development on O(+) - O Collision Frequency and Ionosphere-Thermosphere Coupling

The collision frequency between an oxygen atom and its singly charged ion controls the momentum transfer between the ionosphere and the thermosphere. There has been a long standing discrepancy, extending over a decade, between the theoretical and empirical determination of this frequency: the empirical value of this frequency exceeded the theoretical value by a factor of 1.7. Recent improvements in theory were obtained by using accurate oxygen ion-oxygen atom potential energy curves, and partial wave quantum mechanical calculations. We now have applied three independent statistical methods to the observational data, obtained at the MIT/Millstone Hill Observatory, consisting of two sets A and B. These methods give results consistent with each other, and together with the recent theoretical improvements, bring the ratio close to unity, as it should be. The three statistical methods lead to an average for the ratio of the empirical to the theoretical values equal to 0.98, with an uncertainty of +/-8%, resolving the old discrepancy between theory and observation. The Hines statistics, and the lognormal distribution statistics, both give lower and upper bounds for the Set A equal to 0.89 and 1.02, respectively. The related bounds for the Set B are 1.06 and 1.17. The average values of these bounds thus bracket the ideal value of the ratio which should be equal to unity. The main source of uncertainties are errors in the profile of the oxygen atom density, which is of the order of 11%. An alternative method to find the oxygen atom density is being suggested.

Omidvar, K.↗
NASA NTRS1998

Plate Motions, Regional Deformation, and Time-Variation of Plate Motions

The significant results obtained with support of this grant include the following: (1) Using VLBI data in combination with other geodetical, geophysical, and geological data to bound the present rotation of the Colorado Plateau, and to evaluate to its implications for the kinematics and seismogenic potential of the western half of the conterminous U.S. (2) Determining realistic estimates of uncertainties for VLBI data and then applying the data and uncertainties to obtain an upper bound on the integral of deformation within the "stable interior" of the North American and other plates and thus to place an upper bound on the seismogenic potential within these regions. (3) Combining VLBI data with other geodetic, geophysical, and geologic data to estimate the motion of coastal California in a frame of reference attached to the Sierra Nevada-Great Valley microplate. This analysis has provided new insights into the kinematic boundary conditions that may control or at least strongly influence the locations of asperities that rupture in great earthquakes along the San Andreas transform system. (4) Determining a global tectonic model from VLBI geodetic data that combines the estimation of plate angular velocities with individual site linear velocities where tectonically appropriate. and (5) Investigation of the some of the outstanding problems defined by the work leading to global plate motion model NUVEL-1. These problems, such as the motion between the Pacific and North American plates and between west Africa and east Africa, are focused on regions where the seismogenic potential may be greater than implied by published plate tectonic models.

Gordon, R. G.↗
NASA NTRS1981

Theoretical Treatment of the X(sup 1)Sigma(sup +), A(sup 1)Sigma(sup +), and B(sup 1)Pi states of LiH

Ab initio self-consistent-field plus configuration-interaction calculations are reported for the X(sup 1)Sigma(sup +), A(sup 1)Sigma(sup +), and B(sup 1)Pi states of LiH using a 22(sugma)12(pi)7(delta) function Slater basis set. The resulting dissociation energies, with the experimental values in parentheses, are D(sub e)(X(sup 1)Sigma(sup +)) = 19 972 (20288)/ cm, and D(sub e)(A(sup 1)Sigma(sup +)) = 9042 (8682)/ cm, and D(sup e)(B(sup 1)Pi) = 284 (288) /cm. This is the first ab initio treatment to quantitatively account for the binding in the B(sup 1)Pi state. Calculated dipole moments and electronic transition moments for the X(sup 1)Sigma(sup+)-A(sup 1)Sigma(sup +), X(sup 1)Sigma(sup +)-B((sup 1)Pi, and A(sup 1)Sigma(sup +)- B(sup 1)PI band systems are in excellent agreement with existing theoretical and experimental data. Radiative transition probabilities and lifetimes, including both the bound-bound and bound-free contributions, are computed for all vibrational levels of the A(sup 1)Sigma(sup+) and B(sup 1)Pi states. Comparison with previous results using experimentally based potentials provides insight into the sensitivity of the radiative lifetimes to the detailed nature of the uppermost region of the potentials. Our calculated lifetimes for the lower vibrational levels of the A(sup 1)Sigma(sup +) state are within the experimental uncertainty. Our calculated lifetimes for the three vibrational levels of the B(sup 1)Pi state are in excellent agreement with those of Zemke and Stwalley (values in parentheses), increasing with (upsilon)' from 11.3 (11.3) nsec at (upsilon)' = 0, to 17.0 (17.0) nsec at (upsilon)' = 1, and then to 23.5 (24.0) nsec at (upsilon)' = 2.

Partridge, Harry↗
NASA NTRS2000

On The Computational Capabilities of Physical Systems: Relationship With Conventional Computer Science - Part 2

In the first of this pair of papers, it was proven that there cannot be a physical computer to which one can properly pose any and all computational tasks concerning the physical universe. It was then further proven that no physical computer C can correctly carry out all computational tasks that can be posed to C. As a particular example, this result means that no physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly "processing information faster than the universe does". These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - "physical computation" - is needed to address the issues considered in these papers, which concern real physical computers. While this novel definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. This second paper of the pair presents a preliminary exploration of some of this mathematical structure. Analogues of Chomskian results concerning universal Turing Machines and the Halting theorem are derived, as are results concerning the (im)possibility of certain kinds of error-correcting codes. In addition, an analogue of algorithmic information complexity, "prediction complexity", is elaborated. A task-independent bound is derived on how much the prediction complexity of a computational task can differ for two different reference universal physical computers used to solve that task, a bound similar to the "encoding" bound governing how much the algorithm information complexity of a Turing machine calculation can differ for two reference universal Turing machines. Finally, it is proven that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity), in that there is one and only version of it that can be applicable throughout our universe.

Wolpert, David H.↗