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DOE OSTI2023

Magnetic field evolution and reconnection in low resistivity plasmas

The mathematics and physics of each of the three aspects of magnetic field evolution—topology, energy, and helicity—are remarkably simple and clear. When the resistivity η is small compared to an imposed evolution, a/v , timescale, which means $R$ m ≡ μ 0 va/η $\gg$ 1, magnetic field-line chaos dominates the evolution of field-line topology in three-dimensional systems. Chaos has no direct role in the dissipation of energy. A large current density, j η ≡ vB/η, is required for energy dissipation to be on a comparable timescale to the topological evolution. Nevertheless, chaos plus Alfvén wave damping explain why both timescales tend to be approximately an order of magnitude longer than the evolution timescale a/v. Magnetic helicity is injected onto tubes of field lines when boundary flows have vorticity. Chaos can spread but not destroy magnetic helicity. Resistivity has a negligible effect on helicity accumulation when $R$ m $\gg$ 1. Helicity accumulates within a tube of field lines until the tube erupts and moves far from its original location.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

Bayesian inference↗

DOE OSTI2022

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2000

On the Origin of Monsoon

It is a long-held fundamental belief that the basic cause of a monsoon is land-sea thermal contrast on the continental scale. Through general circulation model experiments we demonstrate that this belief should be changed. The Asian and Australian summer monsoon circulations are largely intact in an experiment in which Asia, maritime continent, and Australia are replaced by ocean. It is also shown that the change resulting from such replacement is in general due more to the removal of topography than to the removal of land-sea contrast. Therefore, land-sea contrast plays only a minor modifying role in Asian and Australian summer monsoons. This also happens to the Central American summer monsoon. However, the same thing cannot be said of the African and South American summer monsoons. In Asian and Australian winter monsoons land-sea contrast also plays only a minor role. Our interpretation for the origin of monsoon is that the summer monsoon is the result of ITCZ's (intertropical convergence zones) peak being substantially (more than 10 degrees) away from the equator. The origin of the ITCZ has been previously interpreted by Chao. The circulation around thus located ITCZ, previously interpreted by Chao and Chen through the modified Gill solution and briefly described in this paper, explains the monsoon circulation. The longitudinal location of the ITCZs is determined by the distribution of surface conditions. ITCZ's favor locations of higher SST as in western Pacific and Indian Ocean, or tropical landmass, due to land-sea contrast, as in tropical Africa and South America. Thus, the role of landmass in the origin of monsoon can be replaced by ocean of sufficiently high SST. Furthermore, the ITCZ circulation extends into the tropics in the other hemisphere to give rise to the winter monsoon circulation there. Also through the equivalence of land-sea contrast and higher SST, it is argued that the basic monsoon onset mechanism proposed by Chao is valid for all monsoons.

Chao, Winston C.↗

NASA NTRS2002

Single and Double ITCZ in Aqua-Planet Models with Globally and Temporally Uniform Sea Surface Temperature and Solar Insolation: An Interpretation

Previous studies (Chao 2000, Chao and Chen 2001, Kirtman and Schneider 2000, Sumi 1992) have shown that, by means of one of several model design changes, the structure of the ITCZ in an aqua-planet model with globally uniform SST and solar angle (U-SST-SA) can change between a single ITCZ at the equator and a double ITCZ straddling the equator. These model design changes include switching to a different cumulus parameterization scheme (e.g., from relaxed Arakawa Schubert scheme (RAS) to moist convective adjustment scheme (MCA)), changes within the cumulus parameterization scheme, and changes in other aspects of the model, such as horizontal resolution. Sometimes only one component of the double ITCZ shows up; but still this is an ITCZ away from the equator, quite distinct from a single ITCZ over the equator. Since these model results were obtained by different investigators using different models which have yielded reasonable general circulation, they are considered as reliable. Chao and Chen (2001; hereafter CC01) have made an initial attempt to interpret these findings based on the concept of rotational ITCZ attractors that they introduced. The purpose of this paper is to offer a more complete interpretation.

Chao, Winston C.↗

DOE OSTI2024

Approximate entropy analysis for nonlinear beam dynamics

In this paper, we applied an approximate entropy (ApEn) analysis to nonlinear beam dynamics. Due to the presence of strong nonlinear magnets, the degree of chaos in beam motion gradually increases proportionally with its amplitude. Such chaos can be quantitatively characterized with ApEn of beam turn-by-turn readings. ApEn analysis is a technique used to quantify the amount of regularity and the unpredictability of fluctuations with respect to time-series data. The ApEn, when applied as a chaos indicator, can then be used for nonlinear lattice optimization and analysis. The National Synchrotron Light Source II (NSLS-II) electron storage ring lattice was used as an example of a real-world application of our technique. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Approximate Entropy Analysis for Nonlinear Beam Dynamics

43 PARTICLE ACCELERATORS↗

NASA NTRS1985

Fluvial Drainage Basins and Valley Networks: Eastern Margaritifer Sinus, Mars

The fluvial drainage of the eastern Margaritifer Sinus (MC-19NE, SE) and northeastern Argyre (MC-26NE) Quadrangles is dominated by two major longitudinal valley networks, the Parana/Loire system on the east, and the Samara Himera system to the west. It is believed that both of these drainages are through-going to the northwest and debouch into Margaritifer Chaos (general location: 12S, 22.5W). The Parana/Loire drainage is bounded on the east in part by an ancient multi-ringed impact basin. The Parana multi-digitate network drains northwest into a depositional basin, and impact basin floor, characterized by positive relief chaos. It is believed that Loire Vallis heads in the basin; thus Parana and Loire Valles may be treated as one system. Samara Valles heads in the northeastern Argyre Quadrangle and extends as a major truck valley to the northwest. Samara Valles cuts through the hills forming one of the concentric rings of the Ladon impact basin and joins the Himera drainage to trend in a more northerly direction to Margaritifer Chaos. The downstream portion of Himera is considered to be part of the Samara

Boothroyd, J. C.↗

NASA NTRS1988

Recent insights into instability and transition to turbulence in open-flow systems

Roads to turbulence in open-flow shear layers are interpreted as sequences of often competing instabilities. These correspond to primary and higher order restructurings of vorticity distributions which culminate in convected spatial disorder (with some spatial coherence on the scale of the shear layer) traditionally called turbulence. Attempts are made to interpret these phenomena in terms of concepts of convective and global instabilities on one hand, and of chaos and strange attractors on the other. The first is fruitful, and together with a review of mechanisms of receptivity provides a unifying approach to understanding and estimating transition to turbulence. In contrast, current evidence indicates that concepts of chaos are unlikely to help in predicting transition in open-flow systems. Furthermore, a distinction should apparently be made between temporal chaos and the convected spatial disorder of turbulence past Reynolds numbers where boundary layers and separated shear layers are formed.

Morkovin, Mark V.↗

NASA NTRS1987

Nonlinear dynamics, fractals, cardiac physiology and sudden death

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Goldberger, Ary L.↗

NASA NTRS1990

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Scargle, Jeffrey D.↗

NASA NTRS1990

Period and phase of the 88-year solar cycle and the Maunder minimum - Evidence for a chaotic sun

The problem of whether the solar dynamo is quasi-periodic or chaotic is addressed by examining 1500 years of sunspot, geomagnetic, and auroral activity cycles. Sub-harmonics were found of the fundamental solar cycle period during the years preceding the Maunder minimum and loss of phase of the subharmonic on emergence from it. These phenomena are indicative of chaos. They indicate that the solar dynamo is chaotic and is operating in a region close to the transition between period doubling and chaos. Since Maunder-type minima reoccur irregularly for millennia, it appears that the sun remains close to this transition to and from chaos. This is postulated to be a universal characteristic of solar type stars caused by feedback in the dynamo number.

Feynman, J.↗

NASA NTRS1992

Self-organized rock textures and multiring structure in the Duolun crater

The Duolun impact crater is a multiring basin located 200 km north of Beijing. From the center to the edge of the crater there are innermost rim, inner ring, outer rim, and outermost ring. Recently, we have found some self-organized textures or chaos phenomena in shock-metamorphic rocks from the Duolun impact crater, such as turbulence in matrices of impact glass, oscillatory zoning, or chemical chaos of spherulites in spherulitic splashed breccia, fractal wavy textures or self-similar wavy textures with varied scaling in impact glass, and crystallite beams shaped like Lorentz strange attractors. The rare phenomena indicate that the shock-metamorphic rocks from Duolun crater are formed far from equilibrium. If impact cratering generates momentarily under high-pressure and superhigh-temperature, occurrence of those chaos phenomena in shock-metamorphic rock is not surprising.

Wu, Siben↗

NASA NTRS1994

A comparative survey of current and proposed tropospheric refraction-delay models for DSN radio metric data calibration

The standard tropospheric calibration model implemented in the operational Orbit Determination Program is the seasonal model developed by C. C. Chao in the early 1970's. The seasonal model has seen only slight modification since its release, particularly in the format and content of the zenith delay calibrations. Chao's most recent standard mapping tables, which are used to project the zenith delay calibrations along the station-to-spacecraft line of sight, have not been modified since they were first published in late 1972. This report focuses principally on proposed upgrades to the zenith delay mapping process, although modeling improvements to the zenith delay calibration process are also discussed. A number of candidate approximation models for the tropospheric mapping are evaluated, including the semi-analytic mapping function of Lanyi, and the semi-empirical mapping functions of Davis, et. al.('CfA-2.2'), of Ifadis (global solution model), of Herring ('MTT'), and of Niell ('NMF'). All of the candidate mapping functions are superior to the Chao standard mapping tables and approximation formulas when evaluated against the current Deep Space Network Mark 3 intercontinental very long baselines interferometry database.

Estefan, J. A.↗

NASA NTRS1995

The circum-Chryse region as a possible example of a hydrologic cycle on Mars: Geologic observations and theoretical evaluation

Moore, Jeffrey M.↗

NASA NTRS1996

Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field

Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.

Konkov, L. E.↗

NASA NTRS1995

The circum-Chryse region as a possible example of a hydrologic cycle on Mars: Geologic observations and theoretical evaluation

The transection and superposition relationships among channels, chaos, surface materials units, and other features in the circum-Chryse region of Mars were used to evaluate relative age relationships and evolution of flood events. Channels and chaos in contact (with one another) were treated as single discrete flood-carved systems. Some outflow channel systems form networks and are inferred to have been created by multiple flood events. Within some outflow channel networks, several separate individual channel systems can be traced to a specific chaos which acted as flood-source area to that specific flood channel. Individual flood-carved systems were related to widespread materials units or other surface features that served as stratigraphic horizons. Chryse outflow channels are inferred to have formed over most of the perceivable history of Mars. Outflow channels are inferred to become younger with increasing proximity to the Chryse basin. In addition, outflow channels closer to the basin show a greater diversity in age. The relationship of subsequent outflow channel sources to the sources of earlier floods is inferred to disfavor episodic flooding due to the progressive tapping of a juvenile near-surface water supply. Instead, we propose the circum-Chryse region as a candidate site of past hydrological recycling. The discharge rates necessary to carve the circum-Chryse outflow channels would have inevitably formed temporary standing bodies of H2O on the Martian surface where the flood-waters stagnated and pooled (the Chryse basin is topographically enclosed). These observations and inferences have led us to formulate and evaluate two hypotheses: (1) large amounts of the sublimated H2O off the Chryse basin flood lakes precipitated (snowed) onto the flood-source highlands and this H2O was incorporated into the near surface, recharging the H2O sources, making possible subsequent deluges; and (2) ponded flood-water in Chryse basin drained back down an anti basinward dipping subsurface layer accessed along the southern edge of the lake, recharging the flood-source aquifers. H2O not redeposited in the flood-source region was largely lost to the hydrologic cycle. This loss progressively lowered the vitality of the cycle, probably by now killing it. Our numerical evaluations indicate that of the two hypotheses we formulated, the groundwater seep cycle seems by far the more viable. Optimally, approx. 3/4 of the original mass of an ice-covered cylindrical lake (albedo 0.5, 1 km deep, 100-km radius, draining along its rim for one quarter of its circumference into substrata with a permeability of 3000 darcies) can be modeled to have moved underground (on timescales of the order of 10(exp 3) years) before the competing mechanisms of sublimation and freeze down choked off further water removal. Once underground, this water can travel distances equal to the separation between Chryse basin and flood-source sites in geologically short (approx. 10(exp 6) year-scale) times. Conversely, we calculate that optimally only approx. 40% of the H2O carried from Chryse can condense at the highlands, and most of the precipitate would either collect at the base of the highlands/lowlands scarp or sublimate at rates greater than it would accumulate over the flood-source sites. Further observations from forthcoming missions may permit the determination of which mechanisms may have operated to recycle the Chryse flood-waters.

Moore, Jeffrey M.↗

NASA NTRS1995

The Circum-Chryse Region as a Possible Example of a Hydrologic Cycle on Mars: Geologic Observations and Theoretical Evaluation

The transection and superposition relationships among channels, chaos, surface materials units, and other features in the circum-Chryse region of Mars were used to evaluate relative age relationships and evolution of flood events. Channels and chaos in contact (with one another) were treated as single discrete flood-carved systems. Some outflow channel systems form networks and are inferred to have been created by multiple flood events. Within some outflow channel networks, several separate individual channel systems can be traced to a specific chaos which acted as flood-source area to that specific flood channel. Individual flood-carved systems were related to widespread materials units or other surface features that served as stratigraphic horizons. Chryse outflow channels are inferred to have formed over most of the perceivable history of Mars. Outflow channels are inferred to become younger with increasing proximity to the Chryse basin. In addition, outflow channels closer to the basin show a greater diversity in age. The relationship of subsequent outflow channel sources to the sources of earlier floods is inferred to disfavor episodic flooding due to the progressive tapping of a juvenile near-surface water supply. Instead, we propose the circum-Chryse region as a candidate site of past hydrological recycling. The discharge rates necessary to carve the circum-Chryse outflow channels would have inevitably formed temporary standing bodies of H2O on the Martian surface where the flood-waters stagnated and pooled (the Chryse basin is topographically enclosed). These observations and inferences have led us to formulate and evaluate two hypotheses: (1) large amounts of the sublimated H2O off the Chryse basin flood lakes precipitated (snowed) onto the flood-source highlands and this H2O was incorporated into the near surface, recharging the H2O sources, making possible subsequent deluges; and (2) ponded flood-water in Chryse basin drained back down an anti basinward dipping subsurface layer accessed along the southern edge of the lake, recharging the flood-source aquifers. H2O not redeposited in the flood-source region was largely lost to the hydrologic cycle. This loss progressively lowered the vitality of the cycle, probably by now killing it. Our numerical evaluations indicate that of the two hypotheses we formulated, the groundwater seep cycle seems by far the more viable. Optimally, approximately 3/4 of the original mass of an ice-covered cylindrical lake (albedo 0.5, 1 km deep, 100-km radius, draining along its rim for one quarter of its circumference into substrata with a permeability of 3000 darcies) can be modeled to have moved underground (on timescales of the order of 10(exp 3) years) before the competing mechanisms of sublimation and freeze down choked off further water removal. Once underground, this water can travel distances equal to the separation between Chryse basin and flood-source sites in geologically short (approximately 10(exp 6) year-scale) times. Conversely, we calculate that optimally only approximately 40% of the H2O carried from Chryse can condense at the highlands, and most of the precipitate would either collect at the base of the highlands/lowlands scrap or sublimate at rates greater than it would accumulate over the flood-source sites. Further observations from forthcoming missions may permit the determination of which mechanisms may have operated to recycle the Chryse flood-waters.

Moore, Jeffrey M.↗