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At least 19 records

Sufficient conditions for a local minimum of the Bolza problem with a scalar terminal point constraint

Sufficient conditions for a weak relative minimum for a form of the Bolza problem of variational calculus are derived. Testing of the second-order conditions requires the backward integration of fewer matrix elements than in the case of most previously published sets of conditions. The derivation is felt to be more complete and straightforward than previous derivations. The variational problem considered is relatively simple, with just a scalar constraint to implicitly or explicitly determine the final time, in order to avoid the complexities associated with controllability considerations. Sufficient conditions for a local minimum for more general optimal control problems can be approached by building upon the derivation and results presented here.

Wood, Lincoln J.↗

Effect of a localized minimum in equatorial field strength on resistive tearing instability in the geomagnetotail

A two-dimensional, resistive-MHD computer code is used to investigate the spontaneous reconnection of magnetotaillike configurations. The initial conditions adopted in the simulations are of two types: (1) in which the equatorial normal magnetic field component B(ze) declines monotonically down the tail, and (2) in which B(ze) exhibits a deep minimum in the near-earth plasma sheet. To represent the case where the earthward convection stops before the X line forms, zero-flow boundary conditions are imposed at the edges of the computational box. The initial configurations are in equilibrium and table within ideal MHD. The dynamic evolution of the system starts after the resistivity is turned on. The main results of these simulations basically support the neutral-line model of substorms and confirm Birn's (1980) computer studies. Spontaneous formation of an X-type neutral point and a single O-type plasmoid with strong tailward flow on the tailward side of the X point is found. The time interval from the turning on of the resistivity to the formation of a plasmoid is much shorter in the case where there is an initial deep minimum. A simple analytic calculation is also carried out to demonstrate why the configuration with a deep minimum is more susceptible to the development of the neutral point.

Hau, L.-N.↗

Sufficient conditions for a local minimum of the Bolza problem with multiple terminal point constraints

Sufficient conditions for a weak relative minimum are derived for a form of the Bolza problem of variational calculus. The derivation ties together first-order and second-order conditions in a unified consistent manner, addresses controllability considerations in some detail, and clarifies some small inconsistencies in earlier work. The resulting second-order conditions of optimality involve the integration of fewer backward-sweep matrix elements than the standard conditions in the literature for problems with an unspecified final time. As a result, the backward-sweep matrices have the same general structure and dimensionality whether the final time is specified or free, with the terminal values of two of three sweep matrices being more complicated in the latter case.

Wood, Lincoln J.↗

Sufficient conditions for a local minimum of the Bolza problem with a variable initial point

Sufficient conditions for a weak relative minimum of a form of the Bolza problem of variational calculus are derived. The variational problem considered includes arbitrary numbers of constraints on the initial and terminal points, but assumes no control constraints or interior point constraints. Testing of the second-order conditions requires the backward integration of fewer matrix elements than in the case of previously published sets of conditions. The derivation, though lengthy, is felt to be simpler in concept than previous derivations. The application of these conditions is demonstrated in the context of a simple geometric problem.

Wood, Lincoln J.↗

Robustness of quasi-symmetry along parametric boundary variation

Quasi-symmetry is a guiding principle to modern stellarator optimization for improved plasma confinement. However, the robustness of optimized configurations, which can be crucial for maintaining performance under diverse engineering constraints and practical limitations, has received relatively little attention. Here, in this work, we present various case studies on this robustness, by investigating variations in 1/ v neoclassical transport when plasma configurations are smoothly altered across distinct optimized targets. These targets, optimized from different families—quasi-axisymmetric, quasi-helical, and quasi-isodynamic—are approximately matched in major radius as part of a flexible stellarator design. Our study shows that an optimized target does not always represent a local minimum in transport and that the robustness of a local minimum when present can vary significantly. Furthermore, there are configurations which belong to no established families but have transport levels as low as those of optimized targets. These results highlight the importance of conducting extended searches with key parametric variations around optimized configurations, to ensure its robustness as well as flexibility if desired.

neoclassical transport↗

Thermal Radiator Pointing for International Space Station

In order to provide thermal radiation environments that result in adequate beat rejection, the single-phase, liquid ammonia (NH3) heat rejection system on the International Space Station (ISS) requires that its two thermal radiator wings be dynamically rotated as the ISS travels through its orbit. This paper discusses the closed-loop, thermal radiator pointing system that is used on ISS to ensure adequate heat rejection by the radiators, while preventing freezing of the ammonia under low heat loads and cold-environmental conditions. Although initial designs used an open-loop approach for radiator pointing, concerns about performance robustness, algorithm complexity, memory requirements, and sustaining support drove the development of a more robust, simpler, closed-loop system. Hence, the challenge of the closed-loop system was to utilize existing sensors, actuators and computers to fit into the existing hardware and software architecture of the ISS. Using a proportional-integral (PI) control architecture with limited output and an anti-windup integrator, the temperature of the ammonia coming out of the radiator is measured and controlled by adjusting the radiator wing orientation. The radiator wing orientation for the local minimum environment is fed forward to the control system, and the closed-loop controller is used to generate a bias off of that local minimum environment in order to heat up the ammonia when necessary to avoid freezing. In the earth's shadow, the controller is suspended and the radiator wing is oriented to face the earth, the local maximum thermal environment which further prevents freezing of the ammonia. This control architecture is shown to provide adequate heat rejection and avoid freezing of the ammonia, even though the physical system consists of large transport delays and time-varying dynamics which change dramatically due to orbit motion and variable heat loads.

Green, Scott↗

Asymmetric equilibrium core structures of pyramidal-II < c + a > dislocations in ten hexagonal-close-packed metals

The structures of pyramidal-II < c + a > dislocations, one of the most important defects in structural hexagonal-close-packed (HCP) metals, have not been fully characterized for many of the HCP metals in use today. Here, we employ ab initio informed phase-field dislocation dynamics to determine the minimum energy structure of pyramidal {1¯1¯22} < 11¯23 > dislocations in ten HCP metals, including Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. As input for the simulations, we calculate, using first-principles density functional theory, the {1¯1¯22} generalized stacking fault energy (GSFE) curves for all ten metals. From these calculations, it is found that magnetism in Co is necessary for achieving a local minimum in the GSFE curve. We observe in simulations that edge and screw character dislocations split into two partials separated by a low-energy intrinsic stacking fault. The splitting distance is shown to scale inversely with the local minimum energy normalized by the product of its shear modulus and Burgers vector. Interestingly, some HCP metals exhibit an asymmetric structure, with either unequal partial Burgers vectors or widths, in contrast to the symmetric configuration expected from linear elastic dislocation theory. We explain these structures by properties of the local maxima in their GSFE curves. Metals with larger degrees of elastic anisotropy result in dislocations with larger splitting distances than would be expected under the commonly used assumption of elastic isotropy. Furthermore, these findings on the sizes and asymmetry in the structures of pyramidal-II < c + a > dislocations are fundamental to understanding how these dislocations glide and interact or react with other defects when these metals are mechanically strained.

36 MATERIALS SCIENCE↗

Heliospheric shocks and catastrophe theory

Various configurations of forward and reverse shocks that occur in the outer heliosphere can be classified using catastrophe theory. The existence of a forward shock is associated with a local maximum of a polynomial, and the existence of a reverse shock is associated with a local minimum of a polynomial. A configuration with N forward shocks and N reverse shocks corresponds to a polynomial with N maxima and N minima. The formation of forward and reverse shocks corresponds to the creation of maxima and minima of a polynomial, which is described by the separatrices of the catastrophes. The coalescence of two forward (reverse) shocks corresponds to the situation when two maxima (minima) of a polynomial have equal values, and the interaction of a forward shock with a reverse shock corresponds to a polynomial with a local maximum equal to a local minimum; these situations are described by the Maxwell sets of the appropriate catastrophes.

Burlaga, L. F.↗

Cloud Morphology Evolution in Arctic Cold‐Air Outbreak: Two Cases During COMBLE Period

Abstract Cloud feedbacks play an important role in Arctic warming. Cloud morphology, for example, cloud size and spatial distributions, is among key factors that directly impact their radiative effects. In this work, we use two cases observed during the Cold‐air Outbreak (CAO) in the Marine Boundary Layer Experiment (COMBLE) to study the evolution of cloud size distributions as an air mass is advected from the Arctic over a comparatively warm ocean and cloud mesoscale organization changes from rolls to cells. Cloud objects are identified from Moderate Resolution Imaging Spectroradiometer (MODIS) reflectance images through an object segmentation procedure and roll breakup is identified by homogeneities in cloud water path (CWP). Roll breakup is found to be accompanied by a local minimum in wind shear and local maxima in cloud size and marine cold air outbreak index. The mean cloud horizontal aspect ratio has weak fetch dependency and is around 2 in roll, transition, and cell regimes. Regardless of distance from the ice edge, smaller clouds (<10 km 2 ) dominate the population number but not cloud cover. Cloud size distributions show bimodality in transition and cell regimes. For clouds with comparable sizes, mean nearest neighbor distances normalized by equivalent cloud radius converge to a single value for all regimes and for all but the smallest clouds, suggesting that clouds of comparable sizes in CAOs are separated by distance proportional to their sizes. The presented statistical results pave the way to evaluating model simulated cloud organizations during CAO events.

54 ENVIRONMENTAL SCIENCES↗

Algorithms For Segmentation Of Complex-Amplitude SAR Data

Several algorithms implement improved method of segmenting highly speckled, high-resolution, complex-amplitude synthetic-aperture-radar (SAR) digitized images into regions, within each backscattering characteristics similar or homogeneous from place to place. Method provides for approximate, deterministic solution by two alternative algorithms almost always converging to local minimums: one, Iterative Conditional Modes (ICM) algorithm, which locally maximizes posterior probability density of region labels; other, Maximum Posterior Marginal (MPM) algorithm, which maximizes posterior marginal density of region labels at each pixel location. ICM algorithm optimizes reconstruction of underlying scene. MPM algorithm minimizes expected number of misclassified pixels, possibly better in remote sensing of natural scenes.

Rignot, Eric J. M.↗

Iterated projected position algorithm for constructing exponentially localized generalized Wannier functions for periodic and nonperiodic insulators in two dimensions and higher

Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend on a choice of unitary transform known as a gauge transformation. Over the past few decades, there have been many works that have focused on optimizing the choice of the gauge so that the corresponding Wannier functions are maximally localized or reflect some symmetry of the underlying system. In this work, we consider fully nonperiodic materials where the usual Wannier functions are not well defined and gauge optimization is impractical. To tackle the problem of calculating exponentially localized generalized Wannier functions in both periodic and nonperiodic systems, we discuss the ‘iterated projected position (IPP)” algorithm. Here, the IPP algorithm is based on matrix diagonalization and therefore unlike optimization-based approaches, it does not require initialization and cannot get stuck at a local minimum. Furthermore, the IPP algorithm is guaranteed by a rigorous analysis to produce exponentially localized functions under certain mild assumptions. We numerically demonstrate that the IPP algorithm can be used to calculate exponentially localized bases for the Haldane model, the Kane-Mele model (in both Z 2 invariant even and Z 2 invariant odd phases), and the p x + ip y model on a quasicrystal lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Goodrich, Michael S.↗

A Change in the Solar He II EUV Global Network Structure as an Indicator of the Geo-Effectiveness of Solar Minima

Solar activity during 2007 - 2009 was very low, causing anomalously low thermospheric density. A comparison of solar extreme ultraviolet (EUV) irradiance in the He II spectral band (26 to 34 nm) from the Solar Extreme ultraviolet Monitor (SEM), one of instruments on the Charge Element and Isotope Analysis System (CELIAS) on board the Solar and Heliospheric Observatory (SOHO) for the two latest solar minima showed a decrease of the absolute irradiance of about 15 +/- 6 % during the solar minimum between Cycles 23 and 24 compared with the Cycle 22/23 minimum when a yearly running-mean filter was used. We found that some local, shorter-term minima including those with the same absolute EUV flux in the SEM spectral band show a higher concentration of spatial power in the global network structure from the 30.4 nm SOHO/Extreme ultraviolet Imaging Telescope (EIT) images for the local minimum of 1996 compared with the minima of 2008 - 2011.We interpret this higher concentration of spatial power in the transition region's global network structure as a larger number of larger-area features on the solar disk. These changes in the global network structure during solar minima may characterize, in part, the geo-effectiveness of the solar He II EUV irradiance in addition to the estimations based on its absolute levels.

Solar extreme ultraviolet irradiance↗

Enabling Long-range Exploration in Minimization of Multimodal Functions

We consider the problem of minimizing multi-modal loss functions with a large number of local optima. Since the local gradient points to the direction of the steepest slope in an infinitesimal neighborhood, an optimizer guided by the local gradient is often trapped in a local minimum. To address this issue, we develop a novel nonlocal gradient to skip small local minima by capturing major structures of the loss’s landscape in black-box optimization. The nonlocal gradient is defined by a directional Gaussian smoothing (DGS) approach. The key idea of DGS is to conducts 1D long-range exploration with a large smoothing radius along d orthogonal directions in Rd, each of which defines a nonlocal directional derivative as a 1D integral. Such long-range exploration enables the nonlocal gradient to skip small local minima. The d directional derivatives are then assembled to form the nonlocal gradient. We use the Gauss-Hermite quadrature rule to approximate the d 1D integrals to obtain an accurate estimator. The superior performance of our method is demonstrated in three sets of examples, including benchmark functions for global optimization, and two real-world scientific problems.

Zhang, Jiaxin↗

The density minimum at the earth's magnetic equator

Observations of the density structure in the plasmapause region reveal the existence of a local minimum in the total electron density at the magnetic equator. Data from the plasma wave instrument and ion mass spectrometer on the DE-1 satellite are used to study this phenomenon. The density depletion typically extends from +/- 5 to +/- 20 deg in latitude and is found at altitudes from 2 to 5 RE. Density depletions of 10-70 percent are found in regions where the off-equator density ranges from 10 to 1000/cu cm. This density structure is associated with equator crossings where the thermal plasma has been heated over normal plasmasphere values. The heated plasma is the equatorially trapped plasma previously reported from DE 1 and the SCATHA satellite. Within the plasmasphere, the drop in total (electron) density corresponds to a decrease in the cold-ion density, in both H(+) and He(+). There is a rough pressure balance provided by the warm tail of the distribution, which is a few percent by density but 1-2 orders of magnitude higher in temperature.

Olsen, R. C.↗

New Evidence for Equatorially Trapped Thermal Plasma During Early Post-Storm Recovery

Almost 20 years ago Olsen et al. [1987] reported Dynamics Explorer 1 Retarding Ion Mass Spectrometer observations of equatorially trapped, cold ions in the vicinity of the plasmapause. In that study the trapped population corresponded to a local minimum in density at the magnetic equator. During that time period observations were uncovered of a local maximum in plasma density at the equator. Until IMAGE there has been no good opportunity to experimentally revisit this topic, however until now no direct evidence of a relevant equatorial process has been recognized near the plasmapause during early recovery conditions. It appears that evidence has now been found in both the Extreme Ultraviolet Imager and Radio Plasma Imager observations. The observations, conditions, and properties of what appears to be an equatorially trapped and enhanced density near the magnetic equator will be presented and discussed.

Gallagher, D. L.↗

Geometric decoherence time in Lindbladian dynamics

The onset of decoherence in open many-body systems lacks a dynamical timescale grounded in the loss of bipartite entanglement. Here, we introduce the geometric decoherence time, defined as the earliest moment the monotone relation between logarithmic negativity and Rényi-$\frac{1}{2}$ entropy—exactly equal across any bipartition for pure states—breaks down under open-system evolution, signaling entropy growth without accompanying entanglement growth. We establish this criterion in both single-particle Gaussian dynamics and many-body Lindbladian evolution. We show that quantum mutual information provides a complementary long-time diagnostic: Its asymptotic vanishing is equivalent to factorization of the steady state across the bipartition, a condition strictly stronger than separability, and whenever a product steady state is approached exponentially in trace norm, negativity and mutual information share the same decay rate. In the presence of a strong symmetry, this tracking can fail—residual classical correlations can survive after entanglement has vanished. In the Kitaev chain with balanced gain and loss, we derive a closed-form solution and show that the topological phase sustains longer coherence times than the trivial phase at identical dissipation, with a local minimum at the chiral-symmetric point. In the interacting XXZ chain, exact many-body evolution shows that local 𝑍 dephasing preserves residual classical correlations, whereas gain and loss restore the mutual-information tracking of negativity. Furthermore, our results establish the geometric decoherence time as a dynamical scale tracking the onset of decoherence.

74 ATOMIC AND MOLECULAR PHYSICS↗

The faintest stars - The luminosity and mass functions at the bottom of the main sequence

We present IR K-band photometry of complete samples of VLM candidates constructed from IIIaF and IVN plates in 10 fields taken as part of the POSSII and UKSRC surveys. Using the I-K colors constructed for these stars we estimate a bolometric luminosity function which extends to M(Bol) = 13.75. We find significant evidence for a luminosity function decreasing toward these luminosities. We also find that our results are consistent with those of studies based on the Nearby Star sample, when those data are presented as a bolometric luminosity function. We convert our observed luminosity function into a mass function, which extends with reasonable statistics to 0.08 solar masses - the H-burning minimum mass. We find significant evidence for features in the mass function at these masses. Specifically, the mass function 'turns over' at 0.25 solar mass, goes through a local minimum at about 0.15 solar mass, and may increase again below 0.1 solar mass - none of these features are predicted by any of the current theories of star formation. Lastly, the mass density we observe just above the H-burning minimum mass makes it difficult to envisage brown dwarfs contributing significant quantities of missing mass without invoking either a mass function in this region significantly steeper than that seen for main-sequence stars, or an extremely low cutoff mass to the mass function.

Tinney, Christopher G.↗