Calculation of respiratory indexes and construction of overall oxygen gradients
Physicochemical and biochemical indexes for calculating human oxygen gradients
Lauer, N. V.↗
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A method for calculating laminar viscous, compressible flows with small pressure gradients
A method is presented for calculating laminar viscous, compressible flows in which pressure gradients are assumed to be neglibible in energy conservation and in developing property relations, but not in momentum conservation. The equations are developed from Navier-Stokes equations in a noninertial reference frame. The method is an extension of an approximate method developed for calculating combined forced and contained natural convection in a rotating tank. The restriction to small density and temperature variations in the previous method is removed. For illustration, a two-dimensional simulation of the rotating tank problem is formulated, and the numerical computation procedure to be used is indicated.
Martin, E. D.↗
A limb radiance calculation approach for model atmospheres containing horizontal gradients of temperature and pressure
Limb radiance calculation model for atmospheric carbon dioxide bands with pressure and temperature gradients
Davis, R. E.↗
Efficient approach to obtain free energy gradient using QM/MM MD simulation
The efficient computational approach denoted as charge and atom dipole response kernel (CDRK) model to consider polarization effects of the quantum mechanical (QM) region is described using the charge response and the atom dipole response kernels for free energy gradient (FEG) calculations in the quantum mechanical/molecular mechanical (QM/MM) method. CDRK model can reasonably reproduce energies and also energy gradients of QM and MM atoms obtained by expensive QM/MM calculations in a drastically reduced computational time. This model is applied on the acylation reaction in hydrated trypsin-BPTI complex to optimize the reaction path on the free energy surface by means of FEG and the nudged elastic band (NEB) method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Deep vadose zone respiration contributions to CO2 fluxes from a semi-arid floodplain, Vadose Zone Journal: Dataset
This data package provides lists of parameter values presented in the paper “Deep vadose zone respiration contributions to CO2 fluxes from a semi-arid floodplain” by Tokunaga et al., Vadose Zone J. 2016. Each table or figure from that paper that contains numerical information is represented as a sheet within the Excel file. Table 1 lists depth profile values for particle-size, bulk density, and parameters for correlating moisture contents with matric potentials. Table 2 lists soil respiration fluxes reported in other studies of semi-arid environments. Figure 3. Presents representative relations between moisture contents with matric potentials. Figure 4 presents depth profiles on different dates at site TT03 for hydraulic head, matric head, pore space volumetric air fraction, temperature, and the effective CO2 diffusion coefficient. Figure 5a presents the time-dependence of relative water table elevation (relative to the deepest measured depth during the study), daily CO2 flux rates at the soil surface, and soil temperature at a depth of 0.20 m. Figure 5b presents continuous measurements of CO2 flux and soil temperature. Figure 6 presents depth profiles on different dates of CO2 concentrations in the gas phase at the 5 monitoring stations. Figure 7 presents CO2 surface fluxes calculated by the gradient method, comparisons between calculated and measured rates at the soil surface, CO2 fluxes at 2m depth, and the ratio of deep (2 m) to surface CO2 fluxes.
54 ENVIRONMENTAL SCIENCES↗
Sparsity Applications for Gradient‐Based Optimization of Wind Farms
Optimizing wind farms is essential for designing efficient energy systems, especially as farms grow larger and span multiple sites. However, this optimization becomes increasingly challenging due to the rising computational cost associated with more turbines. Gradient‐based optimization methods scale better than gradient‐free approaches for large problems, but the most computationally expensive component remains the calculation of gradients for the objective function and constraint Jacobians. To address this, we propose leveraging sparsity to accelerate gradient evaluations and reduce the size of the constraint Jacobian. Wind farms naturally exhibit sparsity—many turbines do not influence each other under certain wind directions. However, unlike traditional sparse problems with fixed patterns, wind farm sparsity is dynamic, requiring new strategies to handle changing interactions efficiently. This paper presents a study of sparsity in wind farm optimization and introduces several methods to exploit it. These strategies are tested on multiple farms using the analytic Cumulative Curl model, with gradients computed via automatic differentiation (AD). The same sparsity‐aware techniques are also applicable to finite difference (FD) methods, where they can yield even greater speedups due to the high cost of directional evaluations. Results show that sparse methods achieve up to a 10x speedup with less than ± 5% variance in optimized wake losses compared to traditional methods. These findings suggest that sparsity‐aware optimization not only maintains solution quality but also scales efficiently with farm size, enabling more comprehensive design exploration at reduced computational cost.
17 WIND ENERGY↗
On the use of adjoints in the inversion of observed quasi-static deformation
An adjoint-based conjugate gradient algorithm provides an efficient means for imaging sources of deformation within the Earth, such as volume stresses associated with fluid flow in aquifers and reservoirs. For time intervals over which the overburden deforms elastically, one can calculate the gradient elements for a single model update using just two numerical simulations. The first is a forward run that is used to compute the residuals associated with the given iteration. The second simulation is to evaluate the application of the adjoint operator to the residuals. In this adjoint calculation, the residual displacements are applied as sources at the measurement locations, driving the deformation in the simulation. The volume stress on the source grid blocks, in response to the residual displacements, provide the gradient components. We apply this technique to satellite-based interferometric synthetic aperture radar (InSAR) line-of-sight displacements that were observed over an oil reservoir in California’s Central Valley. Furthermore, we find that the adjoint-based gradient estimates, requiring 18 CPU seconds, agree with conventional numerical calculations that take over 3700 CPU seconds to compute. Conjugate gradient algorithms utilizing the conventional approach and adjoint-based gradient computations give roughly the same reductions in misfit and similar final estimates of reservoir volume change.
58 GEOSCIENCES↗
Quantum-mechanical calculations for the electric field gradients and other electronic properties of lithium hydride - the use of mixed orbital sets.
Electronic wave functions for diatomic lithium hydride molecules, using quantum mechanical calculations
WAVE FUNCTION↗
Design optimization of natural laminar flow bodies in compressible flow
An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions and linear stability analysis of the compressible boundary-layer. In order to reduce the computer time, Granville's transition criterion is used to predict boundary-layer transition and to calculate the gradients of the objective function, and linear stability theory coupled with the e(exp n)-method is used to calculate the objective function at the end of each design iteration. Use of a method to design an axisymmetric body with extensive natural laminar flow is illustrated through the design of a tiptank of a business jet. For the original tiptank, boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10(exp 6). For the designed body shape, a transition Reynolds number of 7.22 x 10(exp 6) is predicted using compressible linear stability theory coupled with the e(exp n)-method.
Dodbele, Simha S.↗
Morning Martian Atmospheric Temperature Gradients and Fluctuations Observed by Mars Pathfinder
We have studied the most prominent atmospheric temperature fluctuations observed during Martian mornings by Mars Pathfinder and have concluded, based on comparisons with wind directions, that they appear to be a result of atmospheric heating associated with the Lander spacecraft. Also, we have examined the morning surface layer temperature lapse rates, which are found to decrease as autumn approaches at the Pathfinder location, and which have mean (and median) values as large as 7.3 K/m in the earlier portions of the Pathfinder landed mission. It is plausible that brief isolated periods with gradients twice as steep are associated with atmospheric heating adjacent to Lander air bag material. In addition, we have calculated the gradient with height of the structure function obtained with Mars Pathfinder, for Mars' atmospheric temperatures measured within about 1.3 m from the surface, assuming a power law dependence, and have found that these gradients superficially resemble those reported for the upper region of the terrestrial stable boundary layer.
Mihalov, John D.↗
A Priori Subgrid Analysis of Temporal Mixing Layers with Evaporating Droplets
Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using three sets of results from a Direct Numerical Simulation (DNS) database, with Reynolds numbers (based on initial vorticity thickness) as large as 600 and with droplet mass loadings as large as 0.5. In the DNS, the gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. The Large Eddy Simulation (LES) equations corresponding to the DNS are first derived, and key assumptions in deriving them are first confirmed by computing the terms using the DNS database. Since LES of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be the sum of the filtered variables and a correction based on the filtered standard deviation; this correction is then computed from the Subgrid Scale (SGS) standard deviation. This model predicts the unfiltered variables at droplet locations considerably better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: the Smagorinsky approach, the Gradient model and the Scale-Similarity formulation. When the proportionality constant inherent in the SGS models is properly calculated, the Gradient and Scale-Similarity methods give results in excellent agreement with the DNS.
Okongo, Nora↗
Thermodynamic evaluation of transonic compressor rotors using the finite volume approach
A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.
Nicholson, S.↗
First principles study of thermal conductivity cross-over in nanostructured zinc-chalcogenides
Systematic first principles studies of zinc-chalcogenides have been performed to understand their thermal transport behaviour. We have applied the Boltzmann transport equation in the relaxation time approximation to calculate the thermal conductivity of ZnS, ZnSe, and ZnTe. We find a thermal conductivity cross-over between ZnS and ZnSe at nanostructure sizes around 0.1–0.2 μm and explain this in terms of the different contributions of phonon modes in these materials. We study the effect of nanostructuring using both the diffusive boundary scattering and confined mean free path limit and discuss the variations in the results. Furthermore, we show the strong influence of isotope scattering on the thermal conductivity. The calculated thermal conductivity is found to be strongly dependent on the volume and we explain the observed differences between local density and generalized gradient approximation calculations. We compare further calculated thermal properties, such as the thermal expansion coefficient, to experiment to validate our approach.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
More realistic band gaps from meta-generalized gradient approximations: Only in a generalized Kohn-Sham scheme
Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is nonmultiplicative, which prevents systematic comparison of meta-GGA band structures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)]. Here, we find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic gaps in the band structure of the exact KS potential, as can be seen by comparing with the gaps of the EXX+RPA OEP potential. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Programming new geometry restraints: Parallelity of atomic groups
Improvements in structural biology methods, in particular crystallography and cryo-electron microscopy, have created an increased demand for the refinement of atomic models against low-resolution experimental data. One way to compensate for the lack of high-resolution experimental data is to use a priori information about model geometry that can be utilized in refinement in the form of stereochemical restraints or constraints. Here, the definition and calculation of the restraints that can be imposed on planar atomic groups, in particular the angle between such groups, are described. Detailed derivations of the restraint targets and their gradients are provided so that they can be readily implemented in other contexts. Practical implementations of the restraints, and of associated data structures, in the Computational Crystallography Toolbox ( cctbx ) are presented.
59 BASIC BIOLOGICAL SCIENCES↗
An explicit finite-volume time-marching procedure for turbulent flow calculations
A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite-volume, time-marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier-Stokes equations. The entire calculation is performed in the physical domain. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is not required. Different time steps are used in the different governing equations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes (length/height - 1000). The method is compared with two test cases. Essentially incompressible turbulent boundary layer flow in an adverse pressure gradient is calculated and the computed distributions of mean velocity and shear are in good agreement with the measurements. Transonic viscous flow in a converging diverging nozzle is calculated; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good.
Nicholson, Stephen↗
An explicit finite-volume time-marching procedure for turbulent flow calculations
A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite-volume, time-marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier-Stokes equations. The entire calculation is performed in the physical domain. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is not required. Different time steps are used in the different governing equations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes (length/height - 1000). The method is compared with two test cases. Essentially incompressible turbulent boundary layer flow in an adverse pressure gradient is calculated and the computed distributions of mean velocity and shear are in good agreement with the measurements. Transonic viscous flow in a converging diverging nozzle is calculated; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good.
Nicholson, Stephen↗
A Galilean and tensorial invariant k-epsilon model for near wall turbulence
A k-epsilon model is proposed for wall bounded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation rate equation is reformulated using this time scale and no singularity exists at the wall. A new parameter R = k/S(nu) is introduced to characterize the damping function in the eddy viscosity. This parameter is determined by local properties of both the mean and the turbulent flow fields and is free from any geometry parameter. The proposed model is then Galilean and tensorial invariant. The model constants used are the same as in the high Reynolds number Standard k-epsilon Model. Thus, the proposed model will also be suitable for flows far from the wall. Turbulent channel flows and turbulent boundary layer flows with and without pressure gradients are calculated. Comparisons with the data from direct numerical simulations and experiments show that the model predictions are excellent for turbulent channel flows and turbulent boundary layers with favorable pressure gradients, good for turbulent boundary layers with zero pressure gradients, and fair for turbulent boundary layer with adverse pressure gradients.
Yang, Z.↗