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At least 631 records · Page 35

Gradient-based constrained optimization using a database of linear reduced-order models

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential Equation (PDE). A key component of this methodology is the construction, during an offline phase, of a database of pointwise, linear, Projection-based Reduced-Order Models (PROM)s associated with a design parameter space and the linear PDE(s). A parameter sampling procedure based on an appropriate saturation assumption is proposed to maximize the efficiency of such a database of PROMs. A real-time method is also presented for interpolating at any queried but unsampled parameter vector in the design parameter space the relevant sensitivities of a PROM. The practical feasibility, computational advantages, and performance of the proposed methodology are demonstrated for several realistic, nonlinear, aerodynamic shape optimization problems governed by linear aeroelastic constraints.

97 MATHEMATICS AND COMPUTING↗

Identification of subsurface structures using electromagnetic data and shape priors

We consider the inverse problem of identifying large-scale subsurface structures using the controlled source electromagnetic method. To identify structures in the subsurface where the contrast in electric conductivity can be small, regularization is needed to bias the solution towards preserving structural information. We propose to combine two approaches for regularization of the inverse problem. In the first approach we utilize a model-based, reduced, composite representation of the electric conductivity that is highly flexible, even for a moderate number of degrees of freedom. With a low number of parameters, the inverse problem is efficiently solved using a standard, second-order gradient-based optimization algorithm. Further regularization is obtained using structural prior information, available, e.g., from interpreted seismic data. The reduced conductivity representation is suitable for incorporation of structural prior information. Such prior information cannot, however, be accurately modeled with a gaussian distribution. To alleviate this, we incorporate the structural information using shape priors. The shape prior technique requires the choice of kernel function, which is application dependent. We argue for using the conditionally positive definite kernel which is shown to have computational advantages over the commonly applied gaussian kernel for our problem. Numerical experiments on various test cases show that the methodology is able to identify fairly complex subsurface electric conductivity distributions while preserving structural prior information during the inversion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Numerical Method for High Energy X-Ray Source Shape Reconstruction

Quantifying the source shape of a pulsed power X-ray imaging system is essential in determining a lower bound for the overall resolution of the system. A method of reconstructing the source shape involves solving an inverse problem with an operator matrix of size n x n, where n is the number of pixels in the image. Building and inverting such a large matrix quickly becomes intractable as n increases due to both memory and computational constraints, even in well-posed problems. The ill-posed nature of this problem adds further complications, making direct inversion unstable. Taking advantage of the structure of the operator matrix and utilizing the Projected Newton and Conjugate Gradient algorithms, we are able to perform reconstructions of images that are orders of magnitude larger than previously possible.

97 MATHEMATICS AND COMPUTING↗

The AGORA High-resolution Galaxy Simulations Comparison Project. VIII. Disk Formation and Evolution of Simulated Milky Way Mass Galaxy Progenitors at 1 < z < 5

We investigate how differences in the stellar feedback produce disks with different morphologies in Milky Way–like progenitors over 1 ≤ z ≤ 5, using eight state-of-the-art cosmological hydrodynamics simulation codes in the AGORA project. In three of the participating codes, a distinct, rotation-dominated inner core emerges with a formation timescale of ≲300 Myr, largely driven by a major merger event, while two other codes exhibit similar signs of wet compaction—gaseous shrinkage into a compact starburst phase—at earlier epochs. The remaining three codes show only weak evidence of wet compaction. Consequently, we divide the simulated galaxies into two groups: those with strong compaction signatures and those with weaker ones. Galaxies in these two groups differ in size, stellar age gradients, and disk-to-total mass ratios. Specifically, codes with strong wet compaction build their outer disks in an inside-out fashion, leading to negative age gradients, whereas codes with weaker compaction feature flat or positive age gradients caused primarily by outward stellar migration. Although the stellar half-mass radii of these two groups diverge at z ∼ 3, the inclusion of dust extinction brings their sizes and shapes in mock observations closer to each other and to observed galaxies. We attribute the observed morphological differences primarily to variations in the stellar feedback implementations—such as delayed cooling timescales, and feedback strengths—that regulate both the onset and duration of compaction. Overall, our results suggest that disk assembly at high redshifts is highly sensitive to the details of the stellar feedback prescriptions in simulations.

Jung, Minyong [Seoul National Univ. (Korea, Republ↗

Micromechanical predictions of crack propagation and fracture energy in a single fiber boron/aluminum model composite

The axisymmetric finite element model and associated computer program developed for the analysis of crack propagation in a composite consisting of a single broken fiber in an annular sheath of matrix material was extended to include a constant displacement boundary condition during an increment of crack propagation. The constant displacement condition permits the growth of a stable crack, as opposed to the catastropic failure in an earlier version. The finite element model was refined to respond more accurately to the high stresses and steep stress gradients near the broken fiber end. The accuracy and effectiveness of the conventional constant strain axisymmetric element for crack problems was established by solving the classical problem of a penny-shaped crack in a thick cylindrical rod under axial tension. The stress intensity factors predicted by the present finite element model are compared with existing continuum results.

Adams, D. F.↗

Adiabatic theory in regions of strong field gradients

The theory for the generalized first invariant for adiabatic motion of charged particles in regions where there are large gradients in magnetic or electric fields is developed. The general condition for an invariant to exist in such regions is that the potential well in which the particle oscillates change its shape slowly as the particle drifts. It is shown how the Kruskal (1962) procedure can be applied to obtain expressions for the invariant and for drift velocities that are asymptotic in a smallness parameter epsilon. The procedure is illustrated by obtaining the invariant and drift velocities for particles traversing a perpendicular shock, and the generalized invariant is compared with the magnetic moment, and the drift orbits with the actual orbits, for a particular case. In contrast to the magnetic moment, the generalized first invariant is better for large gyroradii (large kinetic energies) than for small gyroradii. Expressions for the invariant when an electrostatic potential jump is imposed across the perpendicular shock, and when the particle traverses a rotational shear layer with a small normal component of the magnetic field are given.

Whipple, E. C.↗

Long-time behavior of material-surface curvature in isotropic turbulence

The behavior at large times of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. The main objectives are: to study the asymptotic behavior of the pdf curvature as a function of initial curvature and shape; and to establish whether the curvature of an initially plane material element goes to a stationary probability distribution. The evidence available in the literature about the asymptotic curvature-pdf of initially flat surfaces is ambiguous, and the conjecture is that it is quasi-stationary. In this work several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times the moments of the logarithm of curvature are independent of the initial pdf of curvature. This, it is argued, supports the view that the curvature attains a stationary distribution at long times. It is also shown that, irrespective of initial shape or curvature, the shape of any material element at long times is cylindrical with a high probability.

Girimaji, S. S.↗

An Analytical Model for Non-Uniform Magnetic Field Effects on Two-Dimensional Laminar Jet Diffusion Flames

In 1846, Michael Faraday found that permanent magnets could cause candle flames to deform into equatorial disks. He believed that the change in flame shape was caused by the presence of charged particles within the flames interacting with the magnetic fields. Later researchers found that the interaction between the flame ions and the magnetic fields were much too small to cause the flame deflection. Through a force analysis, von Engel and Cozens showed that the change in the flame shape could be attributed to the diamagnetic flame gases in the paramagnetic atmosphere. Paramagnetism occurs in materials composed of atoms with permanent magnetic dipole moments. In the presence of magnetic field gradients, the atoms align with the magnetic field and are drawn into the direction of increasing magnetic field. Diamagnetism occurs when atoms have no net magnetic dipole moment. In the presence of magnetic gradient fields, diamagnetic substances are repelled towards areas of decreasing magnetism. Oxygen is an example of a paramagnetic substance. Nitrogen, carbon monoxide and dioxide, and most hydrocarbon fuels are examples of diamagnetic substances. In order to evaluate the usefulness of these magnets in altering flame behavior, a study has been undertaken to develop an analytical model to describe the change in the flame length of a laminar diffusion jet in the presence of a nonuniform magnetic field.

Calvert, M. E.↗

Computer Code for Nanostructure Simulation

Due to their small size, nanostructures can have stress and thermal gradients that are larger than any macroscopic analogue. These gradients can lead to specific regions that are susceptible to failure via processes such as plastic deformation by dislocation emission, chemical debonding, and interfacial alloying. A program has been developed that rigorously simulates and predicts optoelectronic properties of nanostructures of virtually any geometrical complexity and material composition. It can be used in simulations of energy level structure, wave functions, density of states of spatially configured phonon-coupled electrons, excitons in quantum dots, quantum rings, quantum ring complexes, and more. The code can be used to calculate stress distributions and thermal transport properties for a variety of nanostructures and interfaces, transport and scattering at nanoscale interfaces and surfaces under various stress states, and alloy compositional gradients. The code allows users to perform modeling of charge transport processes through quantum-dot (QD) arrays as functions of inter-dot distance, array order versus disorder, QD orientation, shape, size, and chemical composition for applications in photovoltaics and physical properties of QD-based biochemical sensors. The code can be used to study the hot exciton formation/relation dynamics in arrays of QDs of different shapes and sizes at different temperatures. It also can be used to understand the relation among the deposition parameters and inherent stresses, strain deformation, heat flow, and failure of nanostructures.

Filikhin, Igor↗

Transparent Large Strain Thermoplastic Polyurethane Magneto-Active Nanocomposites

Smart adaptive materials are an important class of materials which can be used in space deployable structures, morphing wings, and structural air vehicle components where remote actuation can improve fuel efficiency. Adaptive materials can undergo deformation when exposed to external stimuli such as electric fields, thermal gradients, radiation (IR, UV, etc.), chemical and electrochemical actuation, and magnetic field. Large strain, controlled and repetitive actuation are important characteristics of smart adaptive materials. Polymer nanocomposites can be tailored as shape memory polymers and actuators. Magnetic actuation of polymer nanocomposites using a range of iron, iron cobalt, and iron manganese nanoparticles is presented. The iron-based nanoparticles were synthesized using the soft template (1) and Sun's (2) methods. The nanoparticles shape and size were examined using TEM. The crystalline structure and domain size were evaluated using WAXS. Surface modifications of the nanoparticles were performed to improve dispersion, and were characterized with IR and TGA. TPU nanocomposites exhibited actuation for approximately 2wt% nanoparticle loading in an applied magnetic field. Large deformation and fast recovery were observed. These nanocomposites represent a promising potential for new generation of smart materials.

Yoonessi, Mitra↗

Phobos Mobility Simulation

Phobos, the larger of Mars' moons, provides a potential staging location for human exploration of the Martian surface. Its low gravity (about 1/200th of Earth) and lack of atmosphere makes it an attractive destination before a more complex human landing on Mars is attempted. While easier to approach and depart than Mars itself, Phobos provides unique challenges to visiting crews. It is irregularly shaped, so its local gravitational field does not always point straight down with respect to the visible horizon. It is very close to Mars and tidally locked, so the Martian gravity gradient and applied acceleration greatly affect the perceived surface gravity direction and magnitude. This simulation allows the assessment of unique mobility approaches on the surface of Phobos, including hopping in particular.

Bielski, Paul↗

Microcoleus (Cyanobacteria) form watershed-wide populations without strong gradients in population structure

The relative importance of separation by distance and by environment to population genetic diversity can be conveniently tested in river networks, where these two drivers are often independently distributed over space. To evaluate the importance of dispersal and environmental conditions in shaping microbial population structures, we performed genome-resolved metagenomic analyses of benthic Microcoleus -dominated cyanobacterial mats collected in the Eel and Russian River networks (California, USA). The 64 Microcoleus genomes were clustered into three species that shared >96.5% average nucleotide identity (ANI). Most mats were dominated by one strain, but minor alleles within mats were often shared, even over large spatial distances (>300 km). Within the most common Microcoleus species, the ANI between the dominant strains within mats decreased with increasing spatial separation. However, over shorter spatial distances (tens of kilometres), mats from different subwatersheds had lower ANI than mats from the same subwatershed, suggesting that at shorter spatial distances environmental differences between subwatersheds in factors like canopy cover, conductivity, and mean annual temperature decreases ANI. Since mats in smaller creeks had similar levels of nucleotide diversity (π) as mats in larger downstream subwatersheds, within-mat genetic diversity does not appear to depend on the downstream accumulation of upstream-derived strains. The four-gamete test and sequence length bias suggest recombination occurs between almost all strains within each species, even between populations separated by large distances or living in different habitats. Overall, our results show that, despite some isolation by distance and environmental conditions, sufficient gene-flow occurs among cyanobacterial strains to prevent either driver from producing distinctive population structures across the watershed.

59 BASIC BIOLOGICAL SCIENCES↗

Leaf turgor loss point shapes local and regional distributions of evergreen but not deciduous tropical trees

Summary The effects of climate change on tropical forests will depend on how diverse tropical tree species respond to drought. Current distributions of evergreen and deciduous tree species across local and regional moisture gradients reflect their ability to tolerate drought stress, and might be explained by functional traits. We measured leaf water potential at turgor loss (i.e. ‘wilting point’; π tlp ), wood density (WD) and leaf mass per area (LMA) on 50 of the most abundant tree species in central Panama. We then tested their ability to explain distributions of evergreen and deciduous species within a 50 ha plot on Barro Colorado Island and across a 70 km rainfall gradient spanning the Isthmus of Panama. Among evergreen trees, species with lower π tlp were associated with drier habitats, with π tlp explaining 28% and 32% of habitat association on local and regional scales, respectively, greatly exceeding the predictive power of WD and LMA. In contrast, π tlp did not predict habitat associations among deciduous species. Across spatial scales, π tlp is a useful indicator of habitat preference for tropical tree species that retain their leaves during periods of water stress, and holds the potential to predict vegetation responses to climate change.

59 BASIC BIOLOGICAL SCIENCES↗

Effect of Processing Parameters and Shape of Blade on the Solidification of Single-Crystal CMSX-4 Ni-Based Superalloy

The effect of mold withdrawal velocity, heater and pouring temperatures and the thickness of blade root on the solidification parameters and shape of the liquidus isotherm as well as microstructure of single-crystal CMSX-4 nickel-based superalloy, manufactured by the Bridgman method, has been analyzed in the article. The temperature gradient G, solidification rate v and location of the liquidus isotherm were determined in relation to the radiation baffle on the basis of temperature measurements conducted in nine test points along the height of castings (140 mm) with different thicknesses of root (27, 15 and 7 mm) and withdrawal velocities of 3 and 5 mm/min. The increase of root thickness, relative to the airfoil, resulted in the rise of inhomogeneity of solidification parameters as well as the primary dendrite arm spacing and unsteady state solidification along the whole blade height. However, in the case of blade with constant thickness, the steady-state solidification was created at the distance of 65 to 130 mm from its base. The increase of mold withdrawal velocity caused the decrease of temperature gradient. However, the solidification rate was different from the mold withdrawal velocity, especially in the root and middle part of the airfoil. The increase of heater temperature resulted in a rise of temperature gradient and reduction of the curvature of the liquidus isotherm, whereas the pouring temperature did not affect the solidification parameters in the blade. Particularly unfavorable conditions of the solidification process could occur in the middle part of the airfoil and root because of the lowest value of G/v and the largest primary dendrite arm spacing.

36 MATERIALS SCIENCE↗

Consensus Equilibrium for Subsurface Delineation

Heterogeneity and insufficient site characterization limit our knowledge of the subsurface. Inversion techniques, which minimize the mismatch between observations and model predictions, have become an essential tool of subsurface characterization. Most optimization-based approaches fail to incorporate various implicit priors and capture the geological complexity. We overcome these limitations by deploying the plug-and-play and consensus equilibrium (CE) strategies, which provide a flexible framework for image reconstruction. Our CE methodology for spatial delineation of geologic formations consists of an image denoiser and a variational auto-encoder (deep learning-based emulator). The former ameliorates the reconstruction noise, yielding well-defined geological structures; its mathematical equivalence with the proximal operator allows the deployment of advanced denoisers (e.g., CNN-based denoiser) that do not correspond to a regularization objective. The latter defines a geology prior that imposes a geological constraint, for example, continuity and shape of geological features, onto the reconstructed image. Here, we conduct a series of numerical experiments dealing with transient two-dimensional flow driven by a pumping well and natural hydraulic head gradient. They demonstrate the CE framework's ability to delineate, both probabilistically and deterministically, complex subsurface environments with sufficient quality.

42 ENGINEERING↗

Electron-scale temperature gradients in kinetic equilibrium: MMS observations and Vlasov–Maxwell solutions

For an ideal gas, the notion of thermodynamic equilibrium requires that the system’s temperature be spatially uniform. We demonstrate that for a collisionless plasma, kinetic equilibrium can be achieved even in the presence of a temperature gradient. Motivated by recent MMS magnetopause observations of thin current layers exhibiting electron-scale temperature gradients, here we present an exact solution to the Vlasov-Maxwell system which accounts for the observed electron temperature gradient and reproduces much of the plasma’s spatial variation along one dimension. Furthermore, the current layer in the Vlasov-Maxwell model is self-consistently supported by a prominent crescent shaped electron velocity distribution that naturally arises due to the temperature transition, which agrees with the electron distribution structures measured by MMS during two asymmetric current layers encountered at the magnetopause.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of duration of 120 oC baking on the performance on superconducting radio frequency niobium cavities

Over the last decade much attention was given in increasing the quality factor of superconducting radio frequency (SRF) cavities by impurity doping. Prior to the era of doping, the final cavity processing technique to achieve the high accelerating gradient includes the ?in situ? low temperature baking of SRF cavities at temperature ~ 120 oC for several hours. Here, we present the results of a series of measurements on 1.3 GHz TESLA shape single-cell cavities with successive low temperature baking at 120 oC up to 96 hours. The experimental data were analyzed with available theory of superconductivity to elucidate the effect of the duration of low temperature baking on the superconducting properties of cavity materials as well as the rf performance. In addition, the rf loss related to the trapping of residual magnetic field refereed as flux trapping sensitivity was measured with respect to the duration of 120 oC bake.

Khanal, B. D.↗

On the controllability of a long flexible beam in orbit

The equations of planar motion for a long, flexible free-free beam in orbit are developed and include the effects of gravity-gradient torques and control torques resulting from actuators assumed to be located at specific points along the beam. The control devices are used to control both the orientation as well as the shape of the beam. Application of two classes of theorems to the linearized form of these equations is used to establish necessary and sufficient conditions for controllability for different combinations of number/location of actuators with the number of modes contained in the mathematical model. It is seen that the number of actuators, if properly located, can be less than the number of modes in the system model. A numerical example illustrates the controlled response to an initial perturbation in both pitch angle as well as beam shape.

Bainum, P. M.↗