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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Chaotic roots of the modular multiplication dynamical system in Shor's algorithm

Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an integrable system, which is paradoxical from the viewpoint of quantum chaos, given that the classical limit of the modular multiplication operator is a highly chaotic system that occupies the “maximally random” Bernoulli level of the classical ergodic hierarchy. In this work, we approach this apparent paradox from a quantum dynamical systems viewpoint, and consider whether signatures of ergodicity and chaos may indeed be encoded in such an “integrable” quantization of a chaotic system. We show that Shor's modular multiplication operator, in specific cases, can be written as a superposition of quantized 𝐴-baker's maps exhibiting more typical signatures of quantum chaos and ergodicity. This work suggests that the integrability of Shor's modular multiplication operator may stem from the interference of other “chaotic” quantizations of the same family of maps, and paves the way for deeper studies on the interplay of integrability, ergodicity, and chaos in and via quantum algorithms.

Dynamical systems↗
DOE OSTI2021

The Indian Ocean, its supra-subduction history, and implications for ophiolites

We report Ophiolite complexes represent fragments of ocean crust and mantle formed at spreading centers and emplaced on land. The setting of their origin, whether at mid-ocean ridges, back-arc basins, or forearc basins has been debated. Geochemical classification of many ophiolite extrusive rocks reflect an approach interpreting their tectonic environment as the same as rocks with similar compositions formed in various modern oceanic settings. This approach has pointed to the formation of many ophiolitic extrusive rocks in a supra-subduction zone (SSZ) environment. Paradoxically, structural and stratigraphic evidence suggests that many apparent SSZ-produced ophiolite complexes are more consistent with mid-ocean ridge settings. Compositions of lavas in the southeastern Indian Ocean resemble those of modern SSZ environments and SSZ ophiolites, although Indian Ocean lavas clearly formed in a mid-ocean ridge setting. These facts suggest that an interpretation of the tectonic environment of ophiolite formation based solely on their geochemistry may be unwarranted. New seismic images revealing extensive Mesozoic subduction zones beneath the southern Indian Ocean provide one mechanism to explain this apparent paradox. Cenozoic mid-ocean-ridge–derived ocean floor throughout the southern Indian Ocean apparently formed above former sites of subduction. Compositional remnants of previously subducted mantle in the upper mantle were involved in generation of mid-ocean ridge lavas. The concept of historical contingency may help resolve the ambiguity on understanding the environment of origin of ophiolites. Many ophiolites with “SSZ” compositions may have formed in a mid-ocean ridge setting such as the southeastern Indian Ocean.

58 GEOSCIENCES↗
DOE OSTI2023

Red-green-bleached redox interfaces in the proximal Permian Cutler red beds: implications for regional fluid alteration

Siliciclastic strata of the Colorado Plateau attract attention for their striking red, green, bleached, and variegated colors that potentially record both early depositional and later diagenetic events. We investigated the proximal-most strata of the Paradox Basin, from their onlap contact with the Precambrian basement of the Uncompahgre Plateau to the younger Cutler strata exposed within 10 km of the Uncompahgre Plateau to attempt to understand the significance of the striking colors that occur here. These strata preserve a complex geology associated with buried paleorelief and sediment-related permeability variations at a major basin-uplift interface. Strata exposed within ~1.5 km of the onlap contact exhibit a pervasive drab color in contrast to the generally red colors that predominate farther from this front. In-between, strata commonly host variegated red/green/bleached intercalations. Thin-section petrography, SEM, XRD, Raman spectroscopy, Mössbauer spectroscopy, and whole-rock geochemistry of samples representing different color variations from demonstrate that water–rock interactions charged the rocks with Fe(II) that persists primarily in the phyllosilicate fraction. Color variations reflect grain-size differences that allowed the reduction of fluids from regional fault and basement/fill contacts to permeate coarser-grained Cutler sediments. Hematite and chlorite occur in both red and green sediments but are absent in the bleached sediments. Pervasive hematite in both red and green layers suggests that sediments were hematite-rich before later alteration. Chlorite and smectite are elevated in green samples and inversely correlated with biotite content. Green coloration is generally associated with 1) coarser grain sizes, 2) spatial association with basement contacts, 3) elevated smectite and/or chlorite, 4) less total Fe but greater Fe(II)/Fe(III) primarily in the phyllosilicate fraction, and 5) uranium enrichment. The bleached coloration reflects the removal of pigmentary Fe(III) oxide, while the green coloration is due to the removal of pigmentary hematite and the abundance of Fe(II)-bearing phyllosilicates. Abundant mixed-layer and swelling clays such as smectite, illite/smectite, and chlorite/smectite (including tosudite) dominate the mineralogy of the clay fraction. These results are consistent with other studies demonstrating fault-associated fluid alteration in the Paradox Basin region. However, the pervasive greening was not observed in many of these studies and appears to reflect the unique aspects of the paleovalley system and the importance of biotite alteration to Fe(II)-bearing phyllosilicates.

58 GEOSCIENCES↗
NASA NTRS1974

Impact-induced fractionation in the lunar highlands

A synthesis of the relevant data concerning lunar highland polymict breccias from the fields of petrography, chemistry, photogeology, and impact studies compels the prediction that the breccias should have homogeneous matrices from rock to rock within regions of the highlands of limited size where impact mixing has been efficient and extensive. But the matrices of returned breccias, even from one landing site, display a wide range in composition. This incompatibility between prediction and observation is a paradox that may be resolved by a process that acts after impact mixing to cause a differentiation of the breccia compositions. Partial melting of the local surficial material, and separation of melt and residue in ejecta and/or fall-back blankets, is compatible with the reviewed data and may resolve the paradox.

Warner, J. L.↗
NASA NTRS1977

Lunar highland rock types: Their implications for impact-induced fractionation

Lunar rocks may be classified into three major groups: (1) coarse-grained igneous rocks, (2) fine-grained igneous rocks, and (3) breccias. Group 1 is interpreted as primitive lunar crustal rocks that display various degrees of crushing and/or annealing. Group 2 is interpreted as volcanic rocks. Group 3 is interpreted as resulting from impacts on the lunar surface and is subdivided on the basis of matrix textures into fragmental breccias, crystalline breccias that have been annealed, and crystalline breccias with igneous matrices. A synthesis of the data concerning lunar highlands polymict breccias compels the prediction that the breccias should have homogeneous matrices from rock to rock within regions of the highlands of limited size where impact mixing has been efficient and extensive. But the returned breccias, even from one landing site, display a wide range in composition. This incompatibility between prediction and observation is a paradox that may be resolved by a process that acts after impact mixing to cause a differentiation of the breccia compositions. Partial melting of the local average crustal composition (as modeled by the average soil composition for each site) and separation of melt and residue in ejecta and/or fall-back blankets are compatible with the reviewed data and may resolve the paradox.

Phinney, W. C.↗
NASA NTRS1981

Alternative formulations of magnetospheric plasma electrodynamics

The fundamental equations of magnetospheric plasma electrodynamics are considered from a theoretical standpoint that stresses the basic equivalence of various seemingly different formal representations. The mathematical properties of vector fields are reviewed, and their implications in electrodynamics are studied. The irrotational and solenoidal parts of the electric field are associated with two physically distinct types of sources. Relativistic covariance and gauge invariance in electromagnetic theory are reviewed and discussed in the context of an approach in which the mathematical properties of vector fields are taken as primary concepts. Special attention is given to the use and interpretation of the Coulomb gauge potential functions. This choice of gauge is sometimes regarded with undue suspicion, possibly because of a certain paradox concerning causality. The paradox is discussed and resolved. Useful properties of the Coulomb gauge are identified. These need not be limited to the case of slow time variations and can extend beyond the limits of validity of ideal MHD theory.

Cragin, B. L.↗
NASA NTRS1985

The origin of pristine KREEP: Effects of mixing between ur KREEP and the magmas parental to the MG-rich cumulates

The magnesium/incompatible elements paradox is explained by a model that considers not only the magmasphere, but also its aftermath. A systematic mixing of primitive magnesium rich material with residual liquid is discussed as a method to account for the paradox that KREEP basalts, despite their high incompatible element contents, have moderate magnesium ratios. The KREEP basalts are compared with mare basalts.

Warren, P. H.↗
NASA NTRS1990

Origin and dynamics of emission line clouds in cooling flow environments

The author suggests that since clouds are born co-moving in a turbulent intra-cluster medium (ICM), the allowed parameter space can now be opened up to a more acceptable range. Large-scale motions can be driven in the central parts of cooling flows by a number of mechanisms including the motion of the central and other galaxies, and the dissipation of advected, focussed rotational and magnetic energy. In addition to the velocity width paradox, two other paradoxes (Heckman et al. 1989) can be solved if the ICM is turbulent. Firstly, the heating source for the emission line regions has always been puzzling - line luminosities are extremely high for a given (optical or radio) galaxy luminosity compared to those in non-cooling flow galaxies, therefore a mechanism peculiar to cooling flows must be at work. However most, if not all, previously suggested heating mechanisms either fail to provide enough ionization or give the wrong line ratios, or both. The kinetic energy in the turbulence provides a natural energy source if it can be efficiently converted to cloud heat. Researchers suggest that this can be done via magneto-hydrodynamic waves through plasma slip. Secondly, while the x ray observations indicate extended mass deposition, the optical line emission is more centrally concentrated. Since many of the turbulence-inducing mechanisms are strongest in the central regions of the ICM, so is the method of heating. In other words material is dropping out everywhere but only being lit up in the center.

Loewenstein, Michael↗
NASA NTRS2000

Role of Collective Effects in Dominance of Scattering Off Thermal Ions Over Langmuir Wave Decay: Analysis, Simulations, and Space Applications

Langmuir waves driven to high levels by beam instabilities are subject to nonlinear processes, including the closely related processes of scattering off thermal ions (STI) and a decay process in which the ion response is organized into a product ion acoustic wave. Calculations of the nonlinear growth rates predict that the decay process should always dominate STI, creating two paradoxes. The first is that three independent computer simulation studies show STI proceeding, with no evidence for the decay at all. The second is that observations in space of type 3 solar radio bursts and Earth's foreshock, which the simulations were intended to model, show evidence for the decay proceeding but no evidence for STI. Resolutions to these paradoxes follow from the realization that a nonlinear process cannot proceed when its growth rate exceeds the minimum frequency of the participating waves, since the required collective response cannot be maintained and the waves cannot respond appropriately, and that a significant number of e-foldings and wave periods must be contained in the time available. It is shown that application of these 'collective' and 'time scale' constraints to the simulations explains why the decay does not proceed in them, as well as why STI proceeds in specific simulations. This appears to be the first demonstration that collective constraints are important in understanding nonlinear phenomena. Furthermore, applying these constraints to space observations, it is predicted that the decay should proceed (and dominate STI) in type 3 sources and the high beam speed regions of Earth's foreshock for a specific range of wave levels, with a possible role for STI alone at slightly higher wave levels. Deeper in the foreshock, for slower beams and weaker wave levels, the decay and STI are predicted to become ineffective. Suggestions are given for future testing of the collective constraint and an explanation for why waves in space are usually much weaker than in the simulations.

Cairns, Iver H.↗
NASA NTRS2002

Orbital Noise in the Earth System is a Common Cause of Climate and Greenhouse-Gas Fluctuation

The mismatch between fossil isotopic data and climate models known as the cool-tropic paradox implies that either the data are flawed or we understand very little about the climate models of greenhouse warming. Here we question the validity of the climate models on the scientific background of orbital noise in the Earth system. Our study shows that the insolation pulsation induced by orbital noise is the common cause of climate change and atmospheric concentrations of carbon dioxide and methane. In addition, we find that the intensity of the insolation pulses is dependent on the latitude of the Earth. Thus, orbital noise is the key to understanding the troubling paradox in climate models.

Liu, H. S.↗
NASA NTRS2004

Interpretation of TOMS Observations of Tropical Tropospheric Ozone with a Global Model and In Situ Observations

We interpret the distribution of tropical tropospheric ozone columns (TTOCs) from the Total Ozone Mapping Spectrometer (TOMS) by using a global three-dimensional model of tropospheric chemistry (GEOS-CHEM) and additional information from in situ observations. The GEOS-CHEM TTOCs capture 44% of the variance of monthly mean TOMS TTOCs from the convective cloud differential method (CCD) with no global bias. Major discrepancies are found over northern Africa and south Asia where the TOMS TTOCs do not capture the seasonal enhancements from biomass burning found in the model and in aircraft observations. A characteristic feature of these northern topical enhancements, in contrast to southern tropical enhancements, is that they are driven by the lower troposphere where the sensitivity of TOMS is poor due to Rayleigh scattering. We develop an efficiency correction to the TOMS retrieval algorithm that accounts for the variability of ozone in the lower troposphere. This efficiency correction increases TTOC's over biomass burning regions by 3-5 Dobson units (DU) and decreases them by 2-5 DU over oceanic regions, improving the agreement between CCD TTOCs and in situ observations. Applying the correction to CCD TTOCs reduces by approximately DU the magnitude of the "tropical Atlantic paradox" [Thompson et al, 2000], i.e. the presence of a TTOC enhancement over the southern tropical Atlantic during the northern African biomass burning season in December-February. We reproduce the remainder of the paradox in the model and explain it by the combination of upper tropospheric ozone production from lightning NOx, peristent subsidence over the southern tropical Atlantic as part of the Walker circulation, and cross-equatorial transport of upper tropospheric ozone from northern midlatitudes in the African "westerly duct." These processes in the model can also account for the observed 13-17 DU persistent wave-1 pattern in TTOCs with a maximum above the tropical Atlantic and a minimum over the tropical Pacific during all seasons. The photochemical effects of mineral dust have only a minor role on the modeled distribution of TTOCs, including over northern Africa, due to multiple competing effects. The photochemical effects of mineral dust globally decease annual mean OH concentrations by 9%. A global lightning NOx source of 6 Tg N yr(sup -1) in the model produces a simulation that is most consistent with TOMS and in situ observations.

Martin, Randall V.↗
NASA NTRS2001

Evolution, language and analogy in functional genomics

Almost a century ago, Wittgenstein pointed out that theory in science is intricately connected to language. This connection is not a frequent topic in the genomics literature. But a case can be made that functional genomics is today hindered by the paradoxes that Wittgenstein identified. If this is true, until these paradoxes are recognized and addressed, functional genomics will continue to be limited in its ability to extrapolate information from genomic sequences.

Evolution, Molecular↗
NASA NTRS2005

Should We Believe Atmospheric Temperatures Measured by Entry Accelerometers Traveling at "Slow" Near-Sonic Speeds?

Mars Pathfinder's Accelerometer instrument measured an unexpected and large temperature inversion between 10 and 20 kilometer altitude. Other instruments have failed to detect similar temperature inversions. I test whether this inversion is real or not by examining what changes have to be made to the assumptions in the accelerometer data processing to obtain a more "expected" temperature profile. Changes in derived temperature of up to 30K, or 15%, are necessary, which correspond to changes in derived density of up to 25% and changes in derived pressure of up to 10%. If the drag coefficient is changed to satisfy this, then instead of decreasing from 1.6 to 1.4 from 20 kilometers to 10 kilometers, the drag coefficient must increase from 1.6 to 1.8 instead. If winds are invoked, then speeds of 60 meters per second are necessary, four times greater than those predicted. Refinements to the equation of hydrostatic equilibrium modify the temperature profile by an order of magnitude less than the desired amount. Unrealistically large instrument drifts of 0.5-1.0 meters per square second are needed to adjust the temperature profile as desired. However, rotational contributions to the accelerations may have the necessary magnitude and direction to make this correction. Determining whether this hypothesis is true will require further study of the rigid body equations of motion, with detailed knowledge of the positions of all six accelerometers. The paradox concerning this inversion is not yet resolved. It is important to resolve it because the paradox has some startling implications. At one extreme, are temperature profiles derived from accelerometers inherently inaccurate by 20K or more? At the other extreme, are RS temperature profiles inaccurate by this same amount?

Withers, Paul↗
NASA NTRS1994

Characteristics of Patent Foramen Ovale Associated with Cryptogenic Stroke: A Biplane Transesophageal Echocardiography Study

Patent foramen ovale is associated with ischemic stroke in patients without a clearly identifiable etiology for stroke (cryptogenic stroke). Paradoxical embolization is thought to be a potential mechanism. However, patent foramen ovale is also found in patients with known cause of stroke. Therefore, using contrast transesophageal echocardiography, we characterized the patent foramen ovale in cryptogenic stroke patients to assess morphological factors that may contribute to paradoxical embolization. Methods: Contrast transesophageal echocardiographic studies of 74 consecutive patients referred for ischemic stroke were reviewed. Twenty-three patients with patent foramen ovale were identified. These patients were classified as having strokes of determined origin or cryptogenic strokes according to criteria developed for the Stroke Data Bank of the National Institute of Neurological Disorders and Stroke. Separation of septum primum from secundum and the number of microbubbles appearing in left atrium were then quantitated. These parameters were compared between patients with cryptogenic stroke and those with known cause of stroke. Results: The patent foramen ovale dimension was significantly larger in patients with cryptogenic stroke compared with patients with an identifiable cause of stroke (2.1+/-1.7 mm versus 057+/-0.78 mm [mean+/-SD]; P<.01). The number of microbubbles was also greater in patients with cryptogenic stroke compared with patients with an identifiable cause of stroke (13.9+/-10.7 versus 1.62+/-0.8 [mean+/-SD]; P<.0005). Conclusions: Patients with cryptogenic stroke have larger patent foramen ovale with more extensive right-to-left inter-atrial shunting than patients with stroke of determined cause. Transesophageal echocardiographically identifiable characteristics of patent foramen ovale may be important in defining the clinical significance of individual patent foramina.

Homma, S.↗
NASA NTRS2011

Warp Field Mechanics 101

This paper will begin with a short review of the Alcubierre warp drive metric and describes how the phenomenon might work based on the original paper. The canonical form of the metric was developed and published in [6] which provided key insight into the field potential and boost for the field which remedied a critical paradox in the original Alcubierre concept of operations. A modified concept of operations based on the canonical form of the metric that remedies the paradox is presented and discussed. The idea of a warp drive in higher dimensional space-time (manifold) will then be briefly considered by comparing the null-like geodesics of the Alcubierre metric to the Chung-Freese metric to illustrate the mathematical role of hyperspace coordinates. The net effect of using a warp drive technology coupled with conventional propulsion systems on an exploration mission will be discussed using the nomenclature of early mission planning. Finally, an overview of the warp field interferometer test bed being implemented in the Advanced Propulsion Physics Laboratory: Eagleworks (APPL:E) at the Johnson Space Center will be detailed. While warp field mechanics has not had a Chicago Pile moment, the tools necessary to detect a modest instance of the phenomenon are near at hand.

White, Harold↗
NASA NTRS2013

Perspectives on Intracluster Enrichment and the Stellar Initial Mass Function in Elliptical Galaxies

The amount of metals in the Intracluster Medium (ICM) in rich galaxy clusters exceeds that expected based on the observed stellar population by a large factor. We quantify this discrepancy--which we term the "cluster elemental abundance paradox"--and investigate the required properties of the ICM-enriching population. The necessary enhancement in metal enrichment may, in principle, originate in the observed stellar population if a larger fraction of stars in the supernova-progenitor mass range form from an initial mass function (IMF) that is either bottom-light or top-heavy, with the latter in some conflict with observed ICM abundance ratios. Other alternatives that imply more modest revisions to the IMF, mass return and remnant fractions, and primordial fraction, posit an increase in the fraction of 3-8 solar mass stars that explode as SNIa or assume that there are more stars than conventionally thought--although the latter implies a high star formation efficiency. We discuss the feasibility of these various solutions and the implications for the diversity of star formation, the process of elliptical galaxy formation, and the nature of this hidden source of ICM metal enrichment in light of recent evidence of an elliptical galaxy IMF that, because it is skewed to low masses, deepens the paradox.

Lowenstein, Michael↗
NASA NTRS2013

Saturn's F Ring Core: Calm in the Midst of Chaos

The long-term stability of the narrow F Ring core has been hard to understand. Instead of acting as "shepherds", Prometheus and Pandora together stir the vast preponderance of the region into a chaotic state, consistent with the orbits of newly discovered objects like S/2004S6. We show how a comb of very narrow radial locations of high stability in semimajor axis is embedded within this otherwise chaotic region. The stability of these semimajor axes relies fundamentally on the unusual combination of rapid apse precession and long synodic period which characterizes the region. This situation allows stable "antiresonances" to fall on or very close to traditional Lindblad resonances which, under more common circumstances, are destabilizing. We present numerical integrations of tens of thousands of test particles over tens of thousands of Prometheus orbits that map out the effect. The stable antiresonance zones are most stable in a subset of the region where Prometheus first-order resonances are least cluttered by Pandora resonances. This region of optimum stability is paradoxically closer to Prometheus than a location more representative of "torque balance", helping explain a longstanding paradox. One stable zone corresponds closely to the currently observed semimajor axis of the F Ring core. While the model helps explain the stability of the narrow F Ring core, it does not explain why the F Ring material all shares a common apse longitude; we speculate that collisional damping at the preferred semimajor axis (not included in the current simulations) may provide that final step. Essentially, we find that the F Ring core is not confined by a combination of Prometheus and Pandora, but a combination of Prometheus and precession.

Planetary Rings↗
NASA NTRS2018

Is Water Necessary for Life?

The universality of water as the solvent for life is usually justified by its role in supporting the rich organic chemistry. It has been pointed out, however, that even richer synthetic chemistry is possible in other organic solvents. Does it mean that water is not necessary for life? Here, other, essential criteria for solvent for life that have not been sufficiently considered are discussed. In biological systems, complex molecules are not only constantly synthesized but also degraded. Solvent-mediated degradation is essential for regulating cell content, preventing overcrowding and allowing for recycling organic material. Achieving a balance between synthetic and degradative processes is facile in water, but not in many other organic liquids. Thus, the so-called “water paradox” according to which water is both necessary to life and toxic to biopolymer synthesis might not be paradoxical at all. The machinery of life is based on non-covalent interactions that do not involve making or breaking chemical bonds. Their strength needs to be properly tuned. If they are too weak, there might be undesired response to natural fluctuations of physical or chemical parameters. If they are too strong, the kinetics and energetics of cellular processes could adversely influenced. The solvent must allow for balancing these interactions, which provides strong, universal constraints on the medium for life. Water influences non-covalent interactions mainly by two mechanisms. First, it reduces strong, electrostatic interactions between molecules, chemical groups or atoms carrying electric charge or dipole. Second, it induces the hydrophobic effect, the tendency to remove non-polar (hydrophobic) molecules and groups from direct contact with aqueous solution and, instead, interact with each other. In living systems, the hydrophobic effect is largely responsible for self-organization of molecules to more complex structures, such as aggregation of lipid molecules to form biological membranes and protein folding. Water exists as stable liquid in a large temperature range, and the hydrophobic effects are a consequence of the temperature insensitivity of essential properties of its liquid state. In summary, water accomplishes an amazing feat – it reduces strong interactions between dissolved species and simultaneously increases the strength of weak interactions, bringing all of them to the right range. Once we consider not only synthetic capabilities but also other required traits of the solvent for life, no viable alternative to water is currently known.

Life↗