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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Design and Calibration of Autonomous Coherent Doppler Lidar for Space Missions

Developed a new algorithm for the simulation of three dimensional homogeneous turbulent velocity fields. For typical atmospheric conditions it is impossible to produce a simulated velocity field that simultaneously satisfy a given spatial correlation and the corresponding spatial spectrum because of spectral aliasing. The new algorithms produce a turbulent velocity field which has accurate spatial correlations which is required for performance predictions from space-based systems. Developed a new algorithm for extracting the spatial statistics of the atmospheric velocity field using coherent Doppler lidar. The performance of the algorithm was compared with past methods and the new algorithm produces useful results for space-based data, which was not possible before. Developed new methods for verification of the errors in ground-based and space-based Doppler lidar wind measurements. These new methods do not require independent in situ data. This is an important issue for the verification of space-based Doppler lidar measurements of the global wind field. The performance of the new algorithm was compared with past results for both space-based and ground-based operation. The new algorithm has the best performance and is the only algorithm that performed satisfactory for spacebased operation. The performance of coherent Doppler lidar for a space missions with various scanning geometries was determined using computer simulation which contained the effects of random instrumental velocity errors, wind shear, wind variability along the range-gate and from shot-to-shot, and random variations in atmospheric aerosol backscatter over the measurement volume. The bias in the velocity estimates was small and the accuracy in the is typically less than 0.5 m/s for high signal conditions. For a large number of shot per velocity estimate, the threshold signal level for acceptable estimates is proportional to the number of shots to the minus one half power. This agrees with previous results determined for ground-based measurements. The use of multi-element optical detectors for autonomous operation of coherent Doppler lidar was shown to be a very promising technique. Optimal detector geometries were determined by computer simulation of performance: for ground-based testing with a fixed calibration target and for space-based operation using the random surface returns. The effects of refractive turbulence on ground-based calibration of coherent Doppler lidar was determined by computer simulations and compared with theoretical predictions. New techniques were required to correctly predict performance for the focused beam geometry commonly used for verification of space-based operation. An improved velocity estimator was evaluated for space-based applications were signal shot measurements are used to produce vector wind measurements. This permits more accurate measurements when the signal level is not known a priori or not available from multiple shot measurements. The average Doppler lidar signal spectrum including the effects of velocity turbulence was derived and calculated. This permits new estimation algorithms for turbulence based on spectral estimates. In situ atmospheric measurements were conducted and analyzed using an instrumented kite-platform. This work helps provide the required in situ data for verification of Doppler lidar velocity statistics.

Frehlich, Rod G.↗
NASA NTRS1995

Modeling and simulation of a turbulent far wake

Work continued on two projects which had been started during previous years. Both projects involve calculations of the subsonic, turbulent far wake of a two-dimensional object at a Reynolds number of 1000 (based on wake momentum thickness). This flow was used as a test case for direct comparison of various turbulence models and a direct numerical simulations (DNS) of this flow were undertaken. In the turbulence model comparison studies, for any particular model tested, a unique self-similar solution was obtained far enough downstream, regardless of inlet conditions. Furthermore, different turbulence models led to different far-wake equilibrium solutions. No turbulence model could correctly predict all features of the turbulent far wake. For example, the spreading rate and turbulent shear stresses were underpredicted by all the standard models (both two-equation and full Reynolds stress models). In cases where a more correct spreading rate was achieved, it was at the expense of the turbulent kinetic energy, which was overpredicted. In general, the Algebraic Dissipation Rate Model of Gatski and Speziale, 1992, when added to any of the standard models, improved the results dramatically. Also, full Reynolds stress closure models did a much better job at predicting the shapes of both the mean and turbulence profiles, but the spreading rate was not significantly improved over that predicted by the simpler two-equation models. There are two main conclusions from these studies: First, in a comparison such as this, it is not enough to compare just one parameter, like the spreading rate. A good prediction for one parameter does not necessarily imply good predictions for all parameters in a flow. Second, since no turbulence model could correctly predict the turbulent far wake, much of the important physics of turbulent free shear flows is apparently lost by the assumptions inherent in today's methods of turbulence modeling; turbulence models must be improved. Direct simulations of this flow were begun last year in order to provide a data base through which some of the deficiencies of the existing turbulence models could be identified. Quantities such as the pressure-strain correlation, turbulent diffusion, and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. During this summer, diagnostics codes were written which will calculate the parameters mentioned above, along with other single-point and multi-point statistics. The DNS calculations are still in progress at the time of this writing. When these calculations are complete, the diagnostics codes will be applied so that the results can aid turbulence modelers. In addition, the results will show whether or not there exists a universal equilibrium turbulent far wake, independent of initial conditions.

Cimbala, John M.↗
NASA NTRS1971

Determination of the charge of relativistic heavy nuclei from emulsion tracks

The number of delta rays with energies between 50 and 150 keV that are produced by heavy nuclei in emulsions is calculated. The Z(2) dependence predicted by the first Born approximation is corrected by a direct calculation of the Mott exact phase-shift scattering cross section. Comparisons are made with corrections predicted by the second Born approximation. When the phase-shift results are applied to the problem of charge identification, corrections of up to 4 units of charge for 1.457-GeV/nucleon nuclei with charge Z = 75 are found.

Morgan, S. H., Jr.↗
DOE OSTI2019

The evolution of contact prediction: Evidence that contact selection in statistical contact prediction is changing

Over the last few years, the field of protein structure prediction has been transformed by increasingly-accurate contact prediction software. These methods are based on the detection of coevolutionary relationships between residues from multiple sequence alignments. However, despite speculation, there is little evidence of a link between contact prediction and the physico-chemical interactions which drive amino-acid coevolution. Furthermore, existing protocols predict only a fraction of all protein contacts and it is not clear why some contacts are favoured over others. Using a dataset of 863 protein domains, we assessed the physico-chemical interactions of contacts predicted by CCMpred, MetaPSICOV, and DNCON2, as examples of direct coupling analysis, meta-prediction, and deep learning. We considered correctly-predicted contacts and compared their properties against the protein contacts that were not predicted. Predicted contacts tend to form more bonds than non-predicted contacts, which suggests these contacts may be more important than contacts that were not predicted. Comparing the contacts predicted by each method, we found that metaPSICOV and DNCON2 favour accuracy whereas CCMPred detects contacts with more bonds. This suggests that the push for higher accuracy may lead to a loss of physico-chemically important contacts. These results underscore the connection between protein physico-chemistry and the coevolutionary couplings that can be derived from multiple sequence alignments. This relationship is likely to be relevant to protein structure prediction and functional analysis of protein structure and may be key to understanding their utility for different problems in structural biology. We use publicly-available databases. Our code is available for download at http://opig.stats.ox.ac.uk/.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1994

Theoretical versus experimental results for the rotordynamic coefficients of eccentric, smooth, gas annular seal annular gas seals

This viewgraph presentation presents the following results: (1) The analytical results overpredict the experimental results for the direct stiffness values and incorrectly predict increasing stiffness with decreasing pressure ratios. (2) Theory correctly predicts increasing cross-coupled stiffness, K(sub YX), with increasing eccentricity and inlet preswirl. (3) Direct damping, C(sub XX), underpredicts the experimental results, but the analytical results do correctly show that damping increases with increasing eccentricity. (4) The whirl frequency values predicted by theory are insensitive to changes in the static eccentricity ratio. Although these values match perfectly with the experimental results at 16,000 rpm, the results at the lower speed do not correspond. (5) Theoretical and experimental mass flow rates match at 5000 rpm, but at 16,000 rpm the theoretical results overpredict the experimental mass flow rates. (6) Theory correctly shows the linear pressure profiles and the associated entrance losses with the specified rotor positions.

Childs, Dara W.↗
DOE OSTI2024

Acoustic-based monitoring and machine learning of component status for microreactor applications

This report provides a description and assessment of recent efforts to couple acoustic-based experimental measurements and characterization with machine learning models in order to enhance structural health monitoring capabilities for nuclear microreactors. With resilient embedded sensors in development by others supported by programs funded by the US Department of Energy’s Office of Nuclear Energy, the work described herein builds upon ongoing efforts to improve non-destructive testing technology that relates measured acoustic signatures to component stresses and/or structural defects, using a combination of new experimental measurements and machine learning architectures. The experimental procedure remained similar to that developed for the previous year’s demonstration of damage detection by the authors, with the same damaged sample tested under similar applied stress conditions. Notably, a new mounting fixture was designed and implemented to improve measurement consistency and a more sophisticated laser Doppler vibrometer was employed to make high-fidelity vibration measurements. Two nominally identical sets of training data were collected for each experimental setup to better understand the repeatability of the experiment and to better test the generality of trained neural network models. Additionally, we obtained new high-quality 3D mode shapes of the damaged test article at various stress and excitation levels, providing greater insights into the physical response of the sample during testing. Previously, we demonstrated that a machine learning model based on a convolutional neural network can predict structural details of an artificially introduced interface (intact, rough cut, smooth cut), and the applied torque level. In this study, we have transitioned to graph-based neural network architectures to better develop and test a flexible framework that is more suitable to being transferred away from controlled benchtop experiments and into more applied settings where less-structured data inputs may be expected. In general, performance testing of a graph neural network on frequency-domain representations of the data indicates strong and consistent identification of test conditions for datasets recorded on damaged components. With goals of predicting damage location and other changing experimental conditions using limited datasets, predictive models using a graph neural network architecture correctly predicted the applied torque level with an accuracy of 85% using only a single measurement point and predicted within one torque level in 95% of test windows. Predictions of damage location had limited success due to the symmetry and minimal number of the damage scenarios presented during model training. Results were ambiguous as to whether the model could detect the location of the artificial damage, or if it was instead learning the location of a given measurement point on the part and subsequently detecting which points were closest to the location of the damage. This finding will be factored into upcoming planned work on damaged graphite components, where new experimental tests with a larger number and variety of damage scenarios are expected to provide improved validation of recent developments in monitoring methodology.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Understanding the Physics Representation of Deep Learning Models in Environmental Applications

Deep learning (DL) models have been popular in earth and environmental modeling and analysis, which exhibit huge potential in capturing and reconstructing the non-linearity of relevant environmental processes. They are extensively used as analytical tools or emulators for multiple domains (atmosphere, land surface, ocean, and biogeochemistry). Despite their success, their internal working mechanism remains largely unknown. Such a lack of knowledge hinders the identification of physically consistent models that are fully adaptive to non-stationary climate, as well as the development of physics-informed machine learning such as physics-informed neural network (PINN). To establish preliminary knowledge and framework of such physics representation evaluation, this project focuses on an improved understanding of DL models in the environmental applications. DL models are increasingly applied to environmental modeling and prediction. However, they have been evaluated mostly from a performance perspective, and there is a gap in understanding how they represent the known physics internally. Such knowledge is especially critical when applying DL models under climate change conditions, where new inputs are likely outside the ranges of the training datasets. In this project, we reveal how the known physical processes are represented within DL models from both statistical and mechanistic perspectives. Leveraging the traditional model evaluations that focus more on the accuracies of predictions, we establish a framework that examines both the accuracy and physics representation of DL models. This analysis framework can identify DL models that make the correct predictions based on correct physics, thus enhancing the existing explainable artificial intelligence (explainable-AI) portfolio. It lays a foundation for developing novel metrics to evaluate the emerging DL models in environmental applications. This knowledge also informs the development of physics-informed DL models by revealing the direct connections between the known physical processes and specific model components or structures.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1991

Transonic cascade flow prediction using the Navier-Stokes equations

This paper presents results which summarize the work carried out during the last three years to improve the efficiency and accuracy of numerical predictions in turbomachinery flow calculations. A new kind of nonperiodic c-type grid is presented and a Runge-Kutta scheme with accelerating strategies is used as a flow solver. The code capability is presented by testing four different blades at different exit Mach numbers in transonic regimes. Comparison with experiments shows the very good reliability of the numerical prediction. In particular, the loss coefficient seems to be correctly predicted by using the well-known Baldwin-Lomax turbulence model.

Arnone, A.↗
DOE OSTI2024

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (S- o -xyl) 4 ] 2– Complexes

Iron–sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (SMe) 4 ] 2–,3–,4– , we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree–Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (S-o-xyl) 4 ] 2– , via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

Numerical simulation of turbulent trailing edge flows

Numerical simulations of the time-dependent, Reynolds-averaged, Navier-Stokes equations, employing a two-equation turbulence model, are presented and compared with measurements from a series of trailing edge experiments at transonic Mach numbers. The test flows include an asymmetric flow with no separation, an asymmetric flow with a small region of separation and a symmetric flow with a large shock-wave induced separated zone. Comparisons are made for mean surface quantities as well as for mean and fluctuating flow-field quantities. For the trailing-edge flows with little or no separation, the solutions correctly predict all the major features of the flow field. Treatment of the viscous-inviscid interaction was found to be important for predicting these test cases. Two-equation eddy-viscosity turbulence models were found to be adequate for these flows. However, for the shock-wave induced separation case, these turbulence models were inadequate to predict this flow field. Modifications of the turbulence model to correct these deficiencies are discussed.

Horstman, C. C.↗
NASA NTRS1996

Quantifying the Correlation Between Eye-Movement and Perceptual Responses to Moving Plaids

To determine the extent to which the pursuit eye-movement and perceptual systems share a common neural motion-processing pathway, we simultaneously measure the psychophysical and eye-movement responses to drifting plaids in a direction-discrimination task. Correlation between the noise in the eye movements and percepts would suggest a shared neural substrate. Three observers were asked to track a plaid (Type I 90 deg; TF = 4 Hz, SF = 0.6 c/d; direction = -2, 0, or 2 deg), and to respond whether the motion was to the right or left of vertical. The eye-movement direction is computed from the initial 300 ms of saccade-free tracking (near open-loop). On each trial, we use the eye-movement direction to predict the perceptual response. We then compute the probability of successfully predicting the observer's response. We also use SOC analysis as an alternate measure of the correlation. We compare the data from both these analyses to the predictions of two models in which the eye movements and the percept are driven by either a common noisy signal (correlated model) or by two separate noisy signals (uncorrelated model). We also allow for the fact that our measured eye movements are degraded by eye-tracker noise. This noise causes our measured correlation to be lower than the actual biological correlation. The correlations in our data are higher than those predicted by the uncorrelated model, and are similar to the predictions of the correlated model. The proportion of perceptual responses correctly predicted by the eye movements were 0.66, 0.60, 0.73 for the -2, 0, 2 deg stimuli respectively (correlated model 0.65, 0.60, 0.70; uncorrelated model 0.58, 0.51, 0.60).The SOC proportions were 0.71, 0.64, 0.72 (correlated model 0.66, 0.64, 0.69; uncorrelated model 0.5, 0.5, 0.5). These results show that the oculomotor and perceptual system share a performance-limiting noise source and provide strong evidence that a common neural mechanism (perhaps MT or MST) drives both perception and smooth eye movements.

Beutter, Brent R.↗
NASA NTRS1972

Assessment of a transitional boundary layer theory at low hypersonic Mach numbers

An investigation was carried out to assess the accuracy of a transitional boundary layer theory in the low hypersonic Mach number regime. The theory is based upon the simultaneous numerical solution of the boundary layer partial differential equations for the mean motion and an integral form of the turbulence kinetic energy equation which controls the magnitude and development of the Reynolds stress. Comparisions with experimental data show the theory is capable of accurately predicting heat transfer and velocity profiles through the transitional regime and correctly predicts the effects of Mach number and wall cooling on transition Reynolds number. The procedure shows promise of predicting the initiation of transition for given free stream disturbance levels. The effects on transition predictions of the pressure dilitation term and of direct absorption of acoustic energy by the boundary layer were evaluated.

Shamroth, S. J.↗
NASA NTRS1995

Non-LTE line-blanketed model atmospheres of hot stars. 2: Hot, metal-rich white dwarfs

We present several model atmospheres for a typical hot metal-rich DA white dwarf, T(sub eff) = 60,000 K, log g = 7.5. We consider pure hydrogen models, as well as models with various abundances of two typical 'trace' elements-carbon and iron. We calculte a number of Local Thermodynamic Equilibrium (LTE) and non-LTE models, taking into account the effect of numerous lines of these elements on the atmospheric structure. We demostrate that while the non-LTE effects are notvery significant for pure hydrogen models, except for describing correctly the central emission in H-alpha they are essential for predicting correctly the ionization balance of metals, such as carbon and iron. Previously reported discrepancies in LTE abundances determinations using C III and C IV lines are easily explained by non-LTE effects. We show that if the iron abundance is larger than 10(exp -5), the iron line opacity has to be considered not only for the spectrum synthesis, but also in the model construction itself. For such metal abundances, non-LTE metal line-blanketed models are needed for detailed abundance studies of hot, metal-rich white dwarfs. We also discuss the predicted Extreme Ultraviolet (EUV) spectrum and show that it is very sensitive to metal abundances, as well as to non-LTE effects.

Lanz, T.↗
DOE OSTI2022

Accurate Fe–He machine learning potential for studying He effects in BCC-Fe

Nanostructured Ferritic Alloys (NFAs) containing oxide nanoparticles are prospective advanced structural materials in future fusion reactors. Lacking fusion neutron sources with an adequate flux, modeling is critical to understand radiation damage in the NFAs, including helium effects. Machine learning interatomic potentials (MLPs) have been demonstrated to be capable of describing atomic interactions in chemically complex systems with comparable accuracy to density functional theory (DFT) but with much less computational costs. Hence, MLPs are chosen to study He bubble accumulation in chemically complex NFAs. As a preliminary step, we develop a Fe–He potential, based on ~10,000 atomic configurations. The developed MLP accurately predicts the bulk properties of BCC-Fe compared to DFT, including the lattice constant (2.832 Å), elastic constants (c 11 = 271 GPa, c 12 = 141, c 44 = 93), and phonon frequencies (maximum error < 3.5%). The MLP predicts He binding energies in He n V bubbles and He n clusters with a mean absolute error (MAE) of only ~70 meV, which is ~3 to ~5 times smaller than the MAE of binding energies estimated using empirical potentials. The MLP also accurately predicts the migration barrier of interstitial He (64 meV). Furthermore, the MLP correctly predicts the maximum number of He atoms (critical size) at which a He n V bubble (He n cluster) can kick-out a self-interstitial atom (SIA), forming a bigger He n V 2 bubble (He n V bubble). Subsequently, we use the MLP to perform molecular dynamics simulations to investigate the effect of temperature on the critical size of He n V bubbles and He n clusters. We find that the critical size decreases with increasing temperature — indicating that smaller bubbles and clusters can kick-out an SIA at higher temperatures, thereby escalating the He bubble growth. We report the current Fe–He MLP can be further developed to include all chemical interactions in NFAs.

36 MATERIALS SCIENCE↗
NASA NTRS1977

Combustion of liquid sprays at high pressures

The combustion of pressure atomized fuel sprays in high pressure stagnant air was studied. Measurements were made of flame and spray boundaries at pressures in the range 0.1-9 MPa for methanol and n-pentane. At the higher test pressure levels, critical phenomena are important. The experiments are compared with theoretical predictions based on a locally homogeneous two-phase flow model. The theory correctly predicted the trends of the data, but underestimates flame and spray boundaries by 30-50 percent, indicating that slip is still important for the present experiments (Sauter mean diameters of 30 microns at atmospheric pressure under cold flow conditions). Since the sprays are shorter at high pressures, slip effects are still important even though the density ratio of the phases approach one another as the droplets heat up. The model indicates the presence of a region where condensed water is present within the spray and provides a convenient means of treating supercritical phenomena.

Shearer, A. J.↗
NASA NTRS1988

Thermal barrier coating life prediction model development

This report describes work performed to determine the predominat modes of degradation of a plasma sprayed thermal barrier coating system and to develop and verify life prediction models accounting for these degradation modes. The primary TBC system consisted of a low pressure plasma sprayed NiCrAlY bond coat, an air plasma sprayed ZrO2-Y2O3 top coat, and a Rene' 80 substrate. The work was divided into 3 technical tasks. The primary failure mode to be addressed was loss of the zirconia layer through spalling. Experiments showed that oxidation of the bond coat is a significant contributor to coating failure. It was evident from the test results that the species of oxide scale initially formed on the bond coat plays a role in coating degradation and failure. It was also shown that elevated temperature creep of the bond coat plays a role in coating failure. An empirical model was developed for predicting the test life of specimens with selected coating, specimen, and test condition variations. In the second task, a coating life prediction model was developed based on the data from Task 1 experiments, results from thermomechanical experiments performed as part of Task 2, and finite element analyses of the TBC system during thermal cycles. The third and final task attempted to verify the validity of the model developed in Task 2. This was done by using the model to predict the test lives of several coating variations and specimen geometries, then comparing these predicted lives to experimentally determined test lives. It was found that the model correctly predicts trends, but that additional refinement is needed to accurately predict coating life.

Hillery, R. V.↗
NASA NTRS1991

Development of theoretical models of integrated millimeter wave antennas

Extensive radiation patterns for Linear Tapered Slot Antenna (LTSA) Single Elements are presented. The directivity of LTSA elements is predicted correctly by taking the cross polarized pattern into account. A moment method program predicts radiation patterns for air LTSAs with excellent agreement with experimental data. A moment method program was also developed for the task LTSA Array Modeling. Computations performed with this program are in excellent agreement with published results for dipole and monopole arrays, and with waveguide simulator experiments, for more complicated structures. Empirical modeling of LTSA arrays demonstrated that the maximum theoretical element gain can be obtained. Formulations were also developed for calculating the aperture efficiency of LTSA arrays used in reflector systems. It was shown that LTSA arrays used in multibeam systems have a considerable advantage in terms of higher packing density, compared with waveguide feeds. Conversion loss of 10 dB was demonstrated at 35 GHz.

Yngvesson, K. Sigfrid↗
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.↗