INTEGRAL CLOSURE OF RINGS OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS
Proofs of integral closure of differential rings in the solution of linear differential equations
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Proofs of integral closure of differential rings in the solution of linear differential equations
Pressurized suit sealing closure for use in space suits
Mechanically operated pressure sealing closure for space suits
Resistance curve (R-curve) effects due to fiber bridging, crack migration, and other blunting mechanisms are common in composite laminates. These mechanisms can dramatically increase the resistance to crack propagation but can be challenging to simulate. Delamination with R-curves can be analyzed using cohesive zone modeling (CZM) or the virtual crack closure technique (VCCT). Large fracture process zones can be simulated with CZM, but they require highly refined meshes. Coarser meshes can be used with VCCT, but this method is only applicable to small fracture process zones with R-curves defined as functions of position. Therefore, a technique with the computational efficiency of VCCT and the natural ability of cohesive elements to represent large fracture process zones is desirable. An approach is proposed that starts as a CZM in which the cohesive traction separation law (TSL) is separated into high-strength (HS) and low-strength (LS) components. The HS part, which is responsible for the mesh requirements of the CZM analysis, is replaced by VCCT. The combined method is evaluated by analyzing the response of double cantilevered beam specimens. Two specimen layup configurations, [0/90/90/0] 3s and [0/90/90/0] 9s , are evaluated. The R-curve response from each configuration is determined and applied to the constitutive properties of models built with CZM and with VCCT. The results and computational efficiency of the CZM, VCCT, and combined approaches are compared. The results are indicative that a combined cohesive/VCCT approach can enable progressive failure analyses to retain the computational efficiency of VCCT with the ability of the cohesive elements to capture R-curve effects.
The deep borehole disposal (DBD) concept for high-activity waste consists of drilling a large-diameter borehole into crystalline basement rock to a depth of about 5,000 m, placing waste packages in the lower portion of the borehole - the waste emplacement zone - and sealing and plugging the upper portion of the borehole with a combination of bentonite, cement plugs, and sand or crushed rock ballast. The waste emplacement zone is several times deeper than typical mined repositories and is well below the typical maximum depth of fresh groundwater resources. Recent work describes a generic reference case for deep borehole disposal of Cs and Sr capsules stored at the Hanford Site. Two scenarios are described: an undisturbed (nominal) scenario, and disturbed scenario, in which a waste package is stuck adjacent to a transmissive fracture zone in crystalline basement. Simulations of the processes affecting radionuclide release and transport in the two scenarios provide the basis for quantitative post-closure performance assessment (PA) of the reference case. This paper presents a probabilistic PA of the stuck waste package scenario, i.e. uncertainties affecting radionuclide mobilization and transport are propagated through 200 realizations of a predictive model to quantify uncertainties in predicted radionuclide concentrations within the borehole and the fracture zone. Simulations predict no radionuclide transport in the borehole to distances greater than 100 m above the stuck waste package. An assumed lateral pressure gradient results in predictions of limited radionuclide transport in the fracture zone at a lateral distance of 200 m from the stuck waste package. These results complement previous results for the nominal scenario and contribute to the development of a generic safety case for DBD. (authors)
The DOE Standard Canister (DOESC) Remote Canister Closure System is a remotely operated welding and inspection mechanism designed for the packaging of DOE-managed spent nuclear fuel into canisters. The ultrasonic testing (UT) inspection, included in the system, requires the use of water tanks that are opened to act as a couplant between the canister and the sensors. With the couplant, the UT inspection can guarantee accurate results determining imperfections in the weld.
Retrievals of cloud microphysical properties based on passive satellite imagery are especially difficult over snow-covered surfaces because of the bright and cold surface. To help quantify their uncertainties, single-layered overcast liquid-phase Arctic stratus cloud microphysical properties retrieved by using the Clouds and the Earth's Radiant Energy System Edition 2 and Edition 4 (CERES Ed2 and Ed4) algorithms are compared with ground-based retrievals at the Atmospheric Radiation Measurement North Slope of Alaska (ARM NSA) site at Barrow, AK, during the period from March 2000 to December 2006. A total of 206 and 140 snow-free cases (Rsfc ≤ 0.3), and 108 and 106 snow cases (R sfc > 0.3), respectively, were selected from Terra and Aqua satellite passes over the ARM NSA site. The CERES Ed4 and Ed2 optical depth (τ) and liquid water path (LWP) retrievals from both Terra and Aqua are almost identical and have excellent agreement with ARM retrievals under snow-free and snow conditions. In order to reach a radiation closure study for both the surface and top of atmosphere (TOA) radiation budgets, the ARM precision spectral pyranometer-measured surface albedos were adjusted (63.6% and 80% of the ARM surface albedos for snow-free and snow cases, respectively) to account for the water and land components of the domain of 30 km × 30 km. Most of the radiative transfer model calculated SW↓ sfc and SW↑ TOA fluxes by using ARM and CERES cloud retrievals and the domain mean albedos as input agree with the ARM and CERES flux observations within 10 W m -2 for both snow-free and snow conditions. Sensitivity studies show that the ARM LWP and r e retrievals are less dependent on solar zenith angle (SZA), but all retrieved optical depths increase with SZA.
In this work, we evaluate the Community Atmosphere Model Version 5 (CAM5) with a higher-order turbulence closure scheme, named Cloud Layers Unified By Binomials (CLUBB), and a Multiscale Modeling Framework (MMF) with two different microphysics configurations to investigate their influences on rainfall simulations over Southern Amazonia. The two different microphysics configurations in MMF are the one-moment cloud microphysics without aerosol treatment (SAM1MOM) and two-moment cloud microphysics coupled with aerosol treatment (SAM2MOM). Results show that both MMF-SAM2MOM and CLUBB effectively reduce the low biases of rainfall, mainly during the wet season. The CLUBB reduces low biases of humidity in the lower troposphere with further reduced shallow clouds. The latter enables more surface solar flux, leading to stronger convection and more rainfall. MMF, especially MMF-SAM2MOM, unstablizes the atmosphere with more moisture and higher atmospheric temperatures in the atmospheric boundary layer, allowing the growth of more extreme convection and further generating more deep convection. MMF-SAM2MOM significantly increases rainfall in the afternoon, but it does not reduce the early bias of the diurnal rainfall peak; LUBB, on the other hand, delays the afternoon peak time and produces more precipitation in the early morning, due to more realistic gradual transition between shallow and deep convection. MMF appears to be able to realistically capture the observed increase of relative humidity prior to deep convection, especially with its two-moment configuration. In contrast, in CAM5 and CAM5 with CLUBB, occurrence of deep convection in these models appears to be a result of stronger heating rather than higher relative humidity.
Here, we report non-closure of the surface energy balance is a frequently observed phenomenon of hydrometeorological field measurements, when using the eddy-covariance method, which can be ascribed to an underestimation of the turbulent fluxes. Several approaches have been proposed in order to adjust the measured fluxes for this apparent systematic error. However, there are uncertainties about partitioning of the energy balance residual between the sensible and latent heat flux and whether such a correction should be applied on 30-minute data or longer time scales. The data for this study originate from two grassland sites in southern Germany, where measurements from weighable lysimeters are available as reference. The adjusted evapotranspiration rates are also compared with joint energy and water balance simulations using a physically-based distributed hydrological model. We evaluate two adjustment methods: the first one preserves the Bowen ratio and the correction factor is determined on a daily basis. The second one attributes a smaller portion of the residual energy to the latent heat flux than to the sensible heat flux for closing the energy balance for every 30-minute flux integration interval. Both methods lead to an improved agreement of the eddy-covariance based fluxes with the independent lysimeter estimates and the physically-based model simulations. The first method results in a better comparability of evapotranspiration rates, and the second method leads to a smaller overall bias. These results are similar between both sites despite considerable differences in terrain complexity and grassland management. Moreover, we found that a daily adjustment factor leads to less scatter than a complete partitioning of the residual for every half-hour time interval. Lastly, the vertical temperature gradient in the surface layer and friction velocity were identified as important predictors for a potential future parameterization of the energy balance residual.
Three formulations of the turbulence-length scales used in numerical modelling of atmospheric flows are compared. The comparison is made using the Mellor–Yamada–Nakanishi–Niino turbulence closure model within the stable boundary layer local similarity framework. With an appropriate choice of model constants, the model predictions are barely discernible and compare well with the empirical data obtained from the SHEBA campaign.
Abstract The global seasonal cycle of energy in Earth’s climate system is quantified using observations and reanalyses. After removing long-term trends, net energy entering and exiting the climate system at the top of the atmosphere (TOA) should agree with the sum of energy entering and exiting the ocean, atmosphere, land, and ice over the course of an average year. Achieving such a balanced budget with observations has been challenging. Disagreements have been attributed previously to sparse observations in the high-latitude oceans. However, limiting the local vertical integration of new global ocean heat content estimates to the depth to which seasonal heat energy is stored, rather than integrating to 2000 m everywhere as done previously, allows closure of the global seasonal energy budget within statistical uncertainties. The seasonal cycle of energy storage is largest in the ocean, peaking in April because ocean area is largest in the Southern Hemisphere and the ocean’s thermal inertia causes a lag with respect to the austral summer solstice. Seasonal cycles in energy storage in the atmosphere and land are smaller, but peak in July and September, respectively, because there is more land in the Northern Hemisphere, and the land has more thermal inertia than the atmosphere. Global seasonal energy storage by ice is small, so the atmosphere and land partially offset ocean energy storage in the global integral, with their sum matching time-integrated net global TOA energy fluxes over the seasonal cycle within uncertainties, and both peaking in April.
We introduce the notions of n-algebraic complete algebras and n-algebraic completeness, which makes it possible to find algebraic closures of subsets of universal algebras. We clarify how the n-algebraic completeness of an algebra is connected with the pseudodirect product of algebras.
Highlights: • The function of 2-Cys Prxs in rice associated with potassium deficiency tolerance is presented. • OsPRX2 contributes to stomatal closure and improves potassium deficiency tolerance is proposed. • OsPRX2 may be a good candidate to improve K{sup +} efficient tolerance in rice. Peroxiredoxins (Prxs) which are thiol-based peroxidases have been implicated in the toxic reduction and intracellular concentration regulation of hydrogen peroxide. In Arabidopsis thaliana At2-CysPrxB (At5g06290) has been demonstrated to be essential in maintaining the water-water cycle for proper H{sub 2}O{sub 2} scavenging. Although the mechanisms of 2-Cys Prxs have been extensively studied in Arabidopsis thaliana, the function of 2-Cys Prxs in rice is unclear. In this study, a rice homologue gene of At2-CysPrxB, OsPRX2 was investigated aiming to characterize the effect of 2-Cys Prxs on the K{sup +}-deficiency tolerance in rice. We found that OsPRX2 was localized in the chloroplast. Overexpressed OsPRX2 causes the stomatal closing and K{sup +}-deficiency tolerance increasing, while knockout of OsPRX2 lead to serious defects in leaves phenotype and the stomatal opening under the K{sup +}-deficiency tolerance. Detection of K{sup +} accumulation, antioxidant activity of transgenic plants under the starvation of potassium, further confirmed that OsPRX2 is a potential target for engineering plants with improved potassium deficiency tolerance.
Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure. To address these challenges, here we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin’s crack closure integral, which allows for direct control of the applied loads necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin’s integral, since SIFs can be written in closed-form. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle. Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.
To analyze effects of closure of an academic proton treatment center (PTC) on pediatric case volume, distribution, and resident education.
To ensure numerical stability in the vicinity of shocks, a variety of methods have been used, including shock-capturing schemes such as weighted essentially non-oscillatory schemes, as well as the addition of artificial diffusivities to the governing equations. Centered finite difference schemes are often avoided near discontinuities due to the tendency for significant oscillations. However, such schemes have desirable conservation properties compared to many shock-capturing schemes. The objective of this work is to derive all necessary viscous/diffusion terms from first principles and then demonstrate the performance of these analytical terms within a centered differencing framework. The physical Euler equations are spatially-filtered with a Gaussian-like filter. Sub-filter scale (SFS) terms arise in the momentum and energy equations. Analytical closure is provided for each of them by leveraging the jump conditions for a shock. No SFS terms are present in the continuity or species equations. Here, this approach is tested for several problems involving shocks in one and two dimensions. Implemented within a centered difference code, the SFS terms perform well for a range of flow conditions without introducing excessive diffusion.
Photoabsorption reactions have a long and productive history as probes of the response of nuclei to electromagnetic fields. In recent years, there has been a suggestion that the dipole polarisability may be reduced at shell closures, potentially due to the reduced level density. In the current paper, more recent photoabsorption strengths are reanalysed including nuclei on closed proton shells to search for a similar reduction. The previously reported reduction is not reproduced. We conclude that the previously observed reduction may be due to incomplete evaluations of the photoabsorption due to missing cross section contributions and experimental artefacts. More experimental data are necessary to draw a firm conclusion about whether shell effects persist into high excitation energies, especially data which can obviate any systematic effects and look at relative photoabsorption strengths between nuclei.
Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.