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Recent advances in reduction methods for nonlinear problems

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

Noor, A. K.↗

Galactic cosmic ray transport methods and radiation quality issues

An overview of galactic cosmic ray (GCR) interaction and transport methods, as implemented in the Langley Research Center GCR transport code, is presented. Representative results for solar minimum, exo-magnetospheric GCR dose equivalents in water are presented on a component by component basis for various thicknesses of aluminum shielding. The impact of proposed changes to the currently used quality factors on exposure estimates and shielding requirements are quantified. Using the cellular track model of Katz, estimates of relative biological effectiveness (RBE) for the mixed GCR radiation fields are also made.

Townsend, L. W.↗

Noise Radiation by Instability Waves in Coaxial Jets

In this paper predictions are made for the noise radiation from supersonic coaxial jets. The noise in the downstream arc of a supersonic jet is dominated by highly directional radiation from the supersonically convecting large scale structures in the jet mixing layer. Since the mean flow is not described easily in terms of simple analytic functions, a numerical prediction is made for its development. The compressible Reynolds-averaged boundary layer equations in cylindrical polar coordinates are solved. A mixing length turbulence model is used. Empirical correlations are developed the effects of velocity and temperature ratio and Mach number. Both normal and inverted velocity profiles are considered. Comparisons with measurements for both single and coaxial jets show good agreement. The large scale structures are modeled as instability waves. The noise radiation generated by the instability waves is determined by a matching between the inner instability wave solution and the outer acoustic solution. Predictions are made for the differences between the noise radiated by coaxial jets with different operating conditions and a single equivalent jet with the same exit area, thrust, and mass-flow.

Dahl, Milo D.↗

Color banding on Georges Bank as viewed by coastal zone color scanner

Observations of Georges Bank by coastal zone color scanner (CZCS) show bandlike patterns that appear to be related to the large sand dunes and ridges which dominate the bottom topography there. Ship measurements of temperature and chlorophyll on Georges Bank in July 1979 also reflect the influence of the underwater dune fields. The cause of the banding in the CZCS data is unknown but is speculated to be the creation of alternating zones of divergence and convergence by tidal currents as the water flows over the underwater dune-trough configuration. The banding observed by CZCS appears to be seasonal, following the sequence of primary production in the Gulf of Maine, and is believed to be important to biological processes as a site of new production and/or as an effective transport mechanism. Any future models that attempt to interrelate tidal mixing and primary production must consider bottom topography and secondary flows.

Yentsch, C. S.↗

Gender Differences in Isokinetic Strength after 60 and 90 d Bed Rest

Recent reports suggest that changes in muscle strength following disuse may differ between males and females. PURPOSE: To examine potential gender differences in strength changes following 60 and 90 d of experimental bed rest. METHODS: Isokinetic extensor and flexor strength of the knee (60deg and 180deg/s, concentric only), ankle (30deg/s, concentric and eccentric), and trunk (60deg/s, concentric only) were measured following 60 d (males: n=4, 34.5+/-9.6 y; females: n=4, 35.5+/-8.2 y) and 90 d (males: n=10, 31.4+/-4.8 y; females: n=5, 37.6+/-9.9 y) of 6-degree head-down-tilt bed rest (BR; N=23). Subjects were fed a controlled diet (55%/15%/ 30%, CHO/PRO/FAT) that maintained body weight within 3% of the weight recorded on Day 3 of bed rest. After a familiarization session, testing was conducted 6 d before BR and 2 d after BR completion. Peak torque and total work were calculated for the tests performed. To allow us to combine data from both 60- and 90-d subjects, we used a mixed-model statistical analysis in which time and gender were fixed effects and bed rest duration was a random effect. Log-transformations of strength measures were utilized when necessary in order to meet statistical assumptions. RESULTS: Main effects were seen for both time and gender (p<0.05), showing decreased strength in response to bed rest for both males and females, and males stronger than females for most strength measures. Only one interaction effect was observed: females exhibited a greater loss of trunk extensor peak torque at 60 d versus pre-BR, relative to males (p=0.004). CONCLUSION: Sixty and 90 d of BR induced significant losses in isokinetic muscle strength of the locomotor and postural muscles of the knee, ankle, and trunk. Although males were stronger than females for most of the strength measures that we examined, only changes in trunk extensor peak torque were greater for females than males at day 60 of bed rest

English, K. L.↗

Tropospheric Bromine Chemistry: Implications for Present and Pre-industrial Ozone and Mercury

We present a new model for the global tropospheric chemistry of inorganic bromine (Bry) coupled to oxidant-aerosol chemistry in the GEOS-Chem chemical transport model (CTM). Sources of tropospheric Bry include debromination of sea-salt aerosol, photolysis and oxidation of short-lived bromocarbons, and transport from the stratosphere. Comparison to a GOME-2 satellite climatology of tropospheric BrO columns shows that the model can reproduce the observed increase of BrO with latitude, the northern mid-latitudes maximum in winter, and the Arctic maximum in spring. This successful simulation is contingent on the HOBr + HBr reaction taking place in aqueous aerosols and ice clouds. Bromine chemistry in the model decreases tropospheric ozone mixing ratios by <1-8 nmol/mol (6.5% globally), with the largest effects in the northern extratropics in spring. The global mean tropospheric OH concentration decreases by 4 %. Inclusion of bromine chemistry improves the ability of global models (GEOS-Chem and p-TOMCAT) to simulate observed 19th-century ozone and its seasonality. Bromine effects on tropospheric ozone are comparable in the present-day and pre-industrial atmospheres so that estimates of anthropogenic radiative forcing are minimally affected. Br atom concentrations are 40% higher in the pre-industrial atmosphere due to lower ozone, which would decrease by a factor of 2 the atmospheric lifetime of elemental mercury against oxidation by Br. This suggests that historical anthropogenic mercury emissions may have mostly deposited to northern mid-latitudes, enriching the corresponding surface reservoirs. The persistent rise in background surface ozone at northern mid-latitudes during the past decades could possibly contribute to the observations of elevated mercury in subsurface waters of the North Atlantic.

bromine↗

Measurement of the weak mixing angle at 13 TeV with the CMS detector

This document summarizes work in experimental high-energy physics completed as part of the author’s doctoral studies. The central piece of this thesis is the precision measurement of the effective weak mixing angle at the CMS detector. The effective weak mixing angle is a key parameter in the standard model of particle physics and is sensitive to radiative corrections from beyond standard model physics. The measurement is made by using the forward backwards asymmetry of Drell-Yan dilepton pairs. The data is from proton proton collisions at √s =13 TeV collected in Run 2 of the LHC from 2016-2018. The measurement uses dimuon and dielectron pairs and includes a special class of forward electrons developed for this measurement that do not rely on the tracking subdetector. Using the CT18Z parton distribution function set the weak mixing angle was determined to be [equation did not render] The largest contribution to the uncertainty comes from the parton distribution functions.

Taus, Rhys [Rochester U.]↗

𝐷-shell mixing in light baryons and its effect on the orbital motion

The standard description of the nucleon in the nonrelativistic quark model is an 1S,L = 0 state without orbital motion. Yet, there are several indications from phenomenology that an admixture of states with nonzero orbital motion maybe substantial. In this paper we focus on the “second shell” of the nucleon excitations (D-shell), for which we give a modern description of the wave functions. We follow it by investigating what we call a “maximal mixing” scenario, assuming a hypothetical long-range tensor force. We give the explicit wave functions for all states, before and after mixing, and reassess many predictions such as the magnetic moments, the standard and transitional form-factors from the nucleon to N*. Unexpectedly, in this scenario we can reproduce the long-puzzling features of the Roper resonance N*(1440). But even in this extreme case, the admixture of the 1D,L = 2 state to a nucleon remains significantly smaller than expected from phenomenology.

Baryons↗

Parametric studies with an atmospheric diffusion model that assesses toxic fuel hazards due to the ground clouds generated by rocket launches

Parametric studies were made with a multilayer atmospheric diffusion model to place quantitative limits on the uncertainty of predicting ground-level toxic rocket-fuel concentrations. Exhaust distributions in the ground cloud, cloud stabilized geometry, atmospheric coefficients, the effects of exhaust plume afterburning of carbon monoxide CO, assumed surface mixing-layer division in the model, and model sensitivity to different meteorological regimes were studied. Large-scale differences in ground-level predictions are quantitatively described. Cloud alongwind growth for several meteorological conditions is shown to be in error because of incorrect application of previous diffusion theory. In addition, rocket-plume calculations indicate that almost all of the rocket-motor carbon monoxide is afterburned to carbon dioxide CO2, thus reducing toxic hazards due to CO. The afterburning is also shown to have a significant effect on cloud stabilization height and on ground-level concentrations of exhaust products.

Stewart, R. B.↗

The impact of long-range dispersal on gene surfing

Range expansions lead to distinctive patterns of genetic variation in populations, even in the absence of selection. These patterns and their genetic consequences have been well studied for populations advancing through successive short-ranged migration events. However, most populations harbor some degree of long-range dispersal, experiencing rare yet consequential migration events over arbitrarily long distances. Although dispersal is known to strongly affect spatial genetic structure during range expansions, the resulting patterns and their impact on neutral diversity remain poorly understood. Here, we systematically study the consequences of long-range dispersal on patterns of neutral variation during range expansion in a class of dispersal models which spans the extremes of local (effectively short-ranged) and global (effectively well-mixed) migration. We find that sufficiently long-ranged dispersal leaves behind a mosaic of monoallelic patches, whose number and size are highly sensitive to the distribution of dispersal distances. We develop a coarse-grained model which connects statistical features of these spatial patterns to the evolution of neutral diversity during the range expansion. We show that growth mechanisms that appear qualitatively similar can engender vastly different outcomes for diversity: Depending on the tail of the dispersal distance distribution, diversity can be either preserved (i.e., many variants survive) or lost (i.e., one variant dominates) at long times. Our results highlight the impact of spatial and migratory structure on genetic variation during processes as varied as range expansions, species invasions, epidemics, and the spread of beneficial mutations in established populations.

59 BASIC BIOLOGICAL SCIENCES↗

Direct numerical simulation of supercritical oxy-methane mixing layers with CO 2 substituted counterparts

Direct numerical simulations (DNS) of temporally developing, three dimensional, CH 4 /CO 2 , CH 4 /O 2 and CO 2 /O 2 mixing layers, are conducted at a supercritical pressure of 300 atm. To effectively model the supercritical regime, the employed formulation includes the compressible form of the governing equations, the cubic Peng-Robinson equation of state and a generalized formulation for heat and mass flux vectors derived from non-equilibrium thermodynamics and fluctuation theory. A linear inviscid stability analysis is also performed for each case, to determine its most unstable wavelength. Flow visualizations reveal the presence of high density gradient magnitude regions for all three mixing layers, with conditional averages indicating increased presence of heavier fluid species within these regions. No significant departures are observed from perfect gas behavior, with compressibility factors very close to unity for all three mixing cases. Applicability of presumed probability density function methods (PDF) is examined for the three supercritical mixing layers. An a priori analysis is also conducted to investigate various simplifying assumptions employed in modeling various subgrid scale (SGS) flux models. Two additional terms are identified in the large eddy simulations (LES) equations, the gradient of SGS contribution of pressure in the momentum equation and the gradient of SGS contribution of heat flux in energy equation, whose magnitudes are similar and comparable with their respective resolved terms. The performance of the scale similarity model to represent these additional terms is investigated. Lastly, the performance of Smagorinsky, gradient and scale similarity models are also investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Numerical Simulation of Rocket Exhaust Interaction with Lunar Soil

This technology development originated from the need to assess the debris threat resulting from soil material erosion induced by landing spacecraft rocket plume impingement on extraterrestrial planetary surfaces. The impact of soil debris was observed to be highly detrimental during NASA s Apollo lunar missions and will pose a threat for any future landings on the Moon, Mars, and other exploration targets. The innovation developed under this program provides a simulation tool that combines modeling of the diverse disciplines of rocket plume impingement gas dynamics, granular soil material liberation, and soil debris particle kinetics into one unified simulation system. The Unified Flow Solver (UFS) developed by CFDRC enabled the efficient, seamless simulation of mixed continuum and rarefied rocket plume flow utilizing a novel direct numerical simulation technique of the Boltzmann gas dynamics equation. The characteristics of the soil granular material response and modeling of the erosion and liberation processes were enabled through novel first principle-based granular mechanics models developed by the University of Florida specifically for the highly irregularly shaped and cohesive lunar regolith material. These tools were integrated into a unique simulation system that accounts for all relevant physics aspects: (1) Modeling of spacecraft rocket plume impingement flow under lunar vacuum environment resulting in a mixed continuum and rarefied flow; (2) Modeling of lunar soil characteristics to capture soil-specific effects of particle size and shape composition, soil layer cohesion and granular flow physics; and (3) Accurate tracking of soil-borne debris particles beginning with aerodynamically driven motion inside the plume to purely ballistic motion in lunar far field conditions. In the earlier project phase of this innovation, the capabilities of the UFS for mixed continuum and rarefied flow situations were validated and demonstrated for lunar lander rocket plume flow impingement under lunar vacuum conditions. Applications and improvements to the granular flow simulation tools contributed by the University of Florida were tested against Earth environment experimental results. Requirements for developing, validating, and demonstrating this solution environment were clearly identified, and an effective second phase execution plan was devised. In this phase, the physics models were refined and fully integrated into a production-oriented simulation tool set. Three-dimensional simulations of Apollo Lunar Excursion Module (LEM) and Altair landers (including full-scale lander geometry) established the practical applicability of the UFS simulation approach and its advanced performance level for large-scale realistic problems.

Liever, Peter↗

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Mixing Effects in the V1 Band of NH3 - II

Line mixing effects have been calculated in the ν1 parallel band of self-broadened NH3. The theoretical approach is an extension of a semi-classical model to symmetric-top molecules with inversion symmetry developed in the companion paper [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. This model takes into account line coupling effects and hence enables the calculation of the entire relaxation matrix. A detailed analysis of the various coupling mechanisms is carried out for Q and R inversion doublets. The model has been applied to the calculation of the shape of the Q branch and of some R manifolds for which an obvious signature of line mixing effects has been experimentally demonstrated. Comparisons with measurements show that the present formalism leads to an accurate prediction of the available experimental line shapes. Discrepancies between the experimental and theoretical sets of first order mixing parameters are discussed as well as some extensions of both theory and experiment.

Boulet, C.↗

Simulation of Oxygen Disintegration and Mixing With Hydrogen or Helium at Supercritical Pressure

The simulation of high-pressure turbulent flows, where the pressure, p, is larger than the critical value, p(sub c), for the species under consideration, is relevant to a wide array of propulsion systems, e.g. gas turbine, diesel, and liquid rocket engines. Most turbulence models, however, have been developed for atmospheric-p turbulent flows. The difference between atmospheric-p and supercritical-p turbulence is that, in the former situation, the coupling between dynamics and thermodynamics is moderate to negligible, but for the latter it is very significant, and can dominate the flow characteristics. The reason for this stems from the mathematical form of the equation of state (EOS), which is the perfect-gas EOS in the former case, and the real-gas EOS in the latter case. For flows at supercritical pressure, p, the large eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas EOS. The equations use transport properties that depend on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid scale (SGS) fluxes, but also new SGS terms, each denoted as a correction. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations, and represent differences between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) that is the difference between the filtered divergence of the heat flux and the divergence of the heat flux computed as a function of the filtered flow field. In a previous study, there was only partial success in modeling the q-correction term, but in this innovation, success has been achieved by using a different modeling approach. This analysis, based on a temporal mixing layer Direct Numerical Simulation database, shows that the focus in modeling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES heat flux calculation. Further, results for a study conducted for temporal mixing layers initially containing oxygen in the lower stream, and hydrogen or helium in the upper stream, show that, for any LES, including SGS-flux models (constant-coefficient Gradient or Scale-Similarity models, dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/Gradient models), the inclusion of the q-correction in the LES leads to the theoretical maximum reduction of the SGS heat-flux difference. The remaining error in modeling this new subgrid term is thus irreducible.

Bellan, Josette↗

Axion periodicity and coupling quantization in the presence of mixing

Mixing of axion fields is widely used to generate EFTs with phenomenologically advantageous features, such as hierarchies between axion couplings to different gauge fields and/or large effective field ranges. While these features are strongly constrained by periodicity for models with only a single axion, mixing has been used in the literature (sometimes incorrectly) to try to evade some of these constraints. In this paper, we ask whether it is possible to use axion mixing to generate an EFT of axions that evades these constraints by flowing to a theory of a non-compact scalar in the IR. We conclude that as long as the light axion is exactly massless, it will inherit the periodicity and associated constraints of the UV theory. However, by giving the light axion a mass, we can relax these constraints with effects proportional to the axion mass squared, including non-quantized couplings and the realignment of monodromy to a light axion with a larger field range. To show this, we consider various examples of axions mixing with other axions or with non-compact scalar fields, and work in a basis where coupling quantization is manifest. This basis makes it clear that in the case where an axion is eaten through the Higgs or Stückelberg mechanism, the light axion does not have a large effective field range, in contrast to some recent claims in the literature. Additionally, we relate our results about axion EFTs to a well-known fact about gauge theory: that QFTs with compact gauge groups in the UV flow to QFTs with compact gauge groups in the IR, and make this correspondence precise in the 2+1 dimensional case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A grid of model atmospheres for metal-deficient giant stars. I

A grid of flux-constant model atmospheres for stars with effective temperatures between 3750 and 6000 K, log g between 0.75 and 3.0, and (A/H) between -3.0 and 0.0 has been constructed. The line absorption is approximated by opacity distribution functions. Metal lines and molecular lines, including those from the infrared bands of CO and CN, are taken into account. The variation of the structure of the models with metal abundance and microturbulence parameter is found to be quite regular and not very drastic. The surface cooling produced by CO is important for all the models with a maximum temperature of 5000 K, while CN mainly causes a backwarming effect but is not very important for solar CNO abundances. The effects of convection, estimated by using the mixing-length approximation, are important only for the coldest models. The models compare very well with models from overlapping regions of other grids. A solar model consistent with the grid models is found to agree satisfactorily with empirical solar model atmospheres. The careful use of scaled solar models for stars with (A/H) approximately equal to zero is justified.

Gustafsson, B.↗

Subsurface Cooling and Sea Surface Temperature Pattern Formation Over the Equatorial Pacific

Abstract The equatorial cold tongue region has not warmed up in response to historical radiative forcing in the real world, contrary to the strong warming often simulated by climate models. Here we demonstrate that climate models fail to represent one or both of the key processes driving observed sea surface temperature (SST) pattern formation: a realistic surface wind stress pattern shaping subsurface cooling through wind‐driven circulation changes, and effective connectivity between subsurface and surface temperatures via upwelling and mixing. Consequently, none of the models approximate the observed lack of cold tongue SST warming and strengthening of zonal SST gradient across the equatorial Pacific. Furthermore, those that come closest achieve this due to interhemispheric warming differences rather than equatorial dynamics as observed. Addressing different origins of subsurface cooling in observations and simulations, and how they connect to SST, will lead to improved understanding of tropical Pacific SST changes to date and how they will evolve in the future.

Jiang, Feng [Lamont‐Doherty Earth Observatory Colu↗

Thermofluid analysis of the SSME preburner using a gas-gas diffusion model for oxygen and hydrogen combustion at supercritical pressures

The paper discusses the thermofluid analysis of the Space Shuttle Main Engine (SSME) fuelside preburner. The governing equations have been solved numerically to predict flow, heat transfer, mixing, and combustion. A two-fluid approach is adopted in which oxygen is regarded as one fluid and hydrogen is regarded as the other fluid. The chemical kinetics is assumed to be very fast so that combustion is primarily controlled by the rate of mixing between oxygen and hydrogen. The preburner pressure is much greater than the critical pressures of oxygen and hydrogen; hence, a gas-gas diffusion model (rather than an evaporation model) has been developed to compute the rate of interphase mixing. Empirical correlations have been incorporated to account for the effect of slip on the interphase exchange. A sensitivity study has been performed with various model parameters. It is observed that the model can predict possibility of incomplete combustion and local regions of high temperatures under steady operating conditions. Some of these anomalies have been observed in actual tests, and the numerical model is useful for understanding possible causes and remedies. At least some measurements are needed for quantitative verification of the model.

Prakash, C.↗