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Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.
An interactive computer code, written with a readily available software program, Microsoft Excel (Microsoft Corporation, Redmond, WA) is presented which displays 3 D oblique plots of a conserved scalar distribution downstream of jets mixing with a confined crossflow, for a single row, double rows, or opposed rows of jets with or without flow area convergence and/or a non-uniform crossflow scalar distribution. This project used a previously developed empirical model of jets mixing in a confined crossflow to create an Microsoft Excel spreadsheet that can output the profiles of a conserved scalar for jets injected into a confined crossflow given several input variables. The program uses multiple spreadsheets in a single Microsoft Excel notebook to carry out the modeling. The first sheet contains the main program, controls for the type of problem to be solved, and convergence criteria. The first sheet also provides for input of the specific geometry and flow conditions. The second sheet presents the results calculated with this routine to show the effects on the mixing of varying flow and geometric parameters. Comparisons are also made between results from the version of the empirical correlations implemented in the spreadsheet and the versions originally written in Applesoft BASIC (Apple Computer, Cupertino, CA) in the 1980's.
A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.
An interactive computer code, written with a readily available software program, Microsoft Excel (Microsoft Corporation, Redmond, WA) is presented which displays 3 D oblique plots of a conserved scalar distribution downstream of jets mixing with a confined crossflow, for a single row, double rows, or opposed rows of jets with or without flow area convergence and/or a non-uniform crossflow scalar distribution. This project used a previously developed empirical model of jets mixing in a confined crossflow to create an Microsoft Excel spreadsheet that can output the profiles of a conserved scalar for jets injected into a confined crossflow given several input variables. The program uses multiple spreadsheets in a single Microsoft Excel notebook to carry out the modeling. The first sheet contains the main program, controls for the type of problem to be solved, and convergence criteria. The first sheet also provides for input of the specific geometry and flow conditions. The second sheet presents the results calculated with this routine to show the effects on the mixing of varying flow and geometric parameters. Comparisons are also made between results from the version of the empirical correlations implemented in the spreadsheet and the versions originally written in Applesoft BASIC (Apple Computer, Cupertino, CA) in the 1980's.
Suppose you are a city planner, regional water manager, or wildlife conservation specialist who is asked to include the potential impacts of climate variability and change in your risk management and planning efforts. What climate information would you use? The choice is often regional or local climate projections downscaled from global climate models (GCMs; also known as general circulation models) to include detail at spatial and temporal scales that align with those of the decision problem. A few years ago this information was hard to come by. Now there is Web-based access to a proliferation of high-resolution climate projections derived with differing downscaling methods.
A wave energy converter (WEC) and the power take-off (PTO) generator system can be represented by using a mass-spring-dampener model. By incorporating a negative stiffness spring within the PTO, the overall stiffness of the PTO can be lowered allowing the impedance of the PTO to be more closely matched with the WEC. By designing for impedance matching the WEC can greatly enhance its power generation capability. This project has involved the design, fabrication and testing of a new type of linear-stroke length and rotary stroke length adjustable negative stiffness magnetic springs for use within a wave energy converter (WEC). The magnetic springs were studied by using 3-D finite element analysis with the objective of creating high energy density and a long linear stroke length. After the construction and testing of both a proof-of-principle adjustable linear and rotary magnetic spring prototype the rotary (torsional) magnetic spring was selected for scaling up analysis. The selected scaled-up proof-of-principle magnetic spring had a peak torque of 850 Nm with a ±45 degree stroke length. By translating the inner rotor relative to the outer rotor, the stiffness could be adjusted to be either negative or positive stiffness. During this project a magnetic lead screw was also studied, and it was shown that by combining the magnetic lead screw with a linearly translating magnetic spring a very long rotary stroke length could be attained. However, as the magnetic lead screw increased complexity and reduced overall energy density relative to a rotary (torsional) spring, this design approach was not further pursed. Dynamometer testing of the variable stiffness magnetic springs was first completed by Portland State University and following this the magnetic spring performance was independently verified by Sandia National Laboratory (Sandia). A WEC analysis when using a variable stiffness magnetic spring was completed by using the WecOptTool. WecOptTool is an open-source WEC optimization software developed by Sandia that supports efficient power take-off (PTO) and control optimization. Wave condition data from the Oregon PacWave test-site was used in this study. The analysis showed that a WEC with a tunable stiffness value could consistently achieve about 80% of its maximum theoretical power production. The use of a tunable stiffness WEC, rather than zero-stiffness or a constant stiffness WEC was also shown to lead to a smaller maximum PTO force requirement. The variable stiffness magnetic spring was integrated into an experimental WEC developed by Sandia, called a Wave-Bot. Sandia successfully completed water-tank testing of the Wave-Bot at the Navy’s Carderock, Maryland, wave-basin test site. The wave-basin testing helped to experimentally demonstrate the operating capabilities and increased power generation capability of a WEC containing an integrated variable stiffness magnetic spring. A WEC capacity factor analysis was also completed. The capacity factor was defined as the ratio of annual average WEC generator power to the maximum (RMS) generated power. This capacity factor provided a means of identifying the ratio of potential revenue to cost. It was calculated that if a tunable variable stiffness magnetic spring has RMS constraints it could operate with a capacity factor above 30%. This is comparable to a wind turbine’s capacity factor.
Conservation tillage can reduce soil erosion, increase soil health, and decrease labor and fuel input costs. Despite these benefits, potential yield impacts remain an important concern for farmers considering adoption. Previous research suggests that conservation tillage is likely to have the largest yield benefits in more arid conditions, but a lack of field-level analyses across climatic, management and soil conditions limits confidence in such predictions. Satellite imagery provides the opportunity to monitor agricultural lands at sub-field resolution across large spatial scales and wide environmental gradients. Here we investigate the maize yield impacts of conservation tillage in the semi-arid western US Corn Belt, using sub-field resolution datasets on tillage practices and crop yields derived from satellite data spanning four states (Nebraska, Kansas, South Dakota, and North Dakota) between 2008 and 2020. On these datasets, we estimate heterogenous yield outcomes for several thousand maize fields across gradients in climate, soil quality and irrigation status by using a causal forests analysis, an adaptation of the random forests machine-learning algorithm for causal inference on observational data. We find that long-term adoption of conservation tillage increased rainfed maize yields by an average of 9.9% in the region. Impacts on irrigated yields were small and not statistically significant. These results, along with an analysis of variables related to greater than average yield benefits, indicate that improved water infiltration and retention are the primary reasons for conservation tillage benefits. Despite yield benefits, many fields estimated to see increased yields under long term low till have not adopted the practice. Therefore, we identify specific counties likely to benefit most from increased levels of adoption. Our results strengthen the understanding of the impacts of conservation agriculture on crop yields and help define environments and counties most likely to benefit from conservation tillage.
High-resolution IUE spectroscopy of the low-mass qWR star HD 45166, obtained at several epochs during 1980-1988, reveals a complex pattern of variability in its stellar wind emission lines, P Cygni profiles, and highly ionized photospheric absorption spectrum. The most intensive observations, obtained during a 36 hr continuous run in February 1988, show the presence of discrete absorption components (DACs) in the C IV 1550 resonance doublet. These DACs can blend to give the appearance of a well-developed P Cygni absorption profile seen at some other times, roughly doubling the column density of the ground state C(3+) ions in the wind. In the 1988 spectra, two principal features are seen, at about -950 km/s and -750 km/s, with column densities of about 14.0 and 14.7 dex/sq cm, respectively. Both features migrate in velocity with accelerations of about 140 cm/sq sec, implying a recurrence time scale of about 1.6 days and a lifetime of about 3 days for the DACs. A striking characteristic of the acceleration is its slowness. The pattern of DAC variability in HD 45166 is similar to that found for O-type stars and provides further evidence that the DACs are not mass-conserving features but rather that a given feature is formed by different material at different times. It is concluded that the C IV DAC variability observed in HD 45166 results from structural changes in the wind arising from radiative instabilities.
A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.
Background: In this comparative study we evaluate the performance of four software tools: DNAstar-D (DESeq2), DNAstar-E (edgeR), CLC Genomics and Partek Flow for identification of differentially expressed genes (DEGs) using a transcriptome of E. coli. The RNA-seq data are from the effect of below-background radiation 5.5 nGy total dose (0.2nGy/hr) on E. coli grown shielded from natural radiation 655 m below ground in a pre-World War II steel vault. The gene expression response to three supplemented sources of radiation designed to mimic natural background, 1952 – 5720 nGy in total dose (71–208 nGy/hr), are compared to this “radiation-deprived” treatment. In addition, RNA-seq data of Caenorhabditis elegans nematode from similar radiation treatments was analyzed by three of the software packages. Results: In E. coli, the four software programs identified one of the supplementary sources of radiation (KCl) to evoke about 5 times more transcribed genes than the minus-radiation treatment (69–114 differentially expressed genes, DEGs), and so the rest of the analyses used this KCl vs “Minus” comparison. After imposing a 30-read minimum cutoff, one of the DNAStar options shared two of the three steps (mapping, normalization, and statistic) with Partek Flow (they both used median of ratios to normalize and the DESeq2 statistical package), and these two programs identified the highest number of DEGs in common with each other (53). In contrast, when the programs used different approaches in each of the three steps, between 31 and 40 DEGs were found in common. Regarding the extent of expression differences, three of the four programs gave high fold-change results (15–178 fold), but one (DNAstar’s DESeq2) resulted in more conservative fold-changes (1.5–3.5). In a parallel study comparing three qPCR commercial validation software programs, these programs also gave variable results as to which genes were significantly regulated. Similarly, the C. elegans analysis showed exaggerated fold-changes in CLC and DNAstar’s edgeR while DNAstar-D was more conservative. Conclusions: Regarding the extent of expression (fold-change), and considering the subtlety of the very low level radiation treatments, in E. coli three of the four programs gave what we consider exaggerated fold-change results (15 – 178 fold), but one (DNAstar’s DESeq2) gave more realistic fold-changes (1.5–3.5). When RT-qPCR validation comparisons to transcriptome results were carried out, they supported the more conservative DNAstar-D’s expression results. When another model organism’s (nematode) response to these radiation differences was similarly analyzed, DNAstar-D also resulted in the most conservative expression patterns. Therefore, we would propose DESeq2 (“DNAstar-D”) as an appropriate software tool for differential gene expression studies for treatments expected to give subtle transcriptome responses.
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The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. Here, we introduce the stochastic finite volume method within the tensor-train framework to counteract this limitation. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing tensor-train techniques for hyperbolic systems and conservation laws involving shocks.
Here, this Letter introduces excited-state molecular dynamics in PYSEQM, a GPU-accelerated semiempirical quantum chemistry engine implemented in PyTorch. The new module enables Born–Oppenheimer molecular dynamics (BOMD) using configuration-interaction singles and random phase approximation for excited states, allowing long trajectories and large statistical ensembles to be simulated efficiently on a single GPU. We also implement an extended Lagrangian excited-state BOMD (XL-ESMD) scheme that propagates auxiliary electronic variables, enabling relaxed ground and excited-state convergence thresholds without compromising energy conservation. The excited-state BOMD implementation scales smoothly from small chromophores to a nearly 900-atom dendrimer (taking 6.5 s per MD step). PYSEQM also supports batched execution, allowing many geometries or trajectories to be evaluated in a single GPU launch, substantially increasing throughput and making ensemble-based protocols routine. As a demonstration, we compute absorption, emission, and infrared spectra from trajectories propagated on the ground and first excited states. The XL-ESMD scheme yields identical spectra at significantly lower computational cost, establishing the role of extended Lagrangian based dynamics for efficient excited-state BOMD simulations. Beyond raw performance, PYSEQM’s PyTorch foundation provides automatic differentiation for forces, efficient GPU batching, and seamless interfacing with machine learning models. These capabilities position PYSEQM as a practical platform for machine learning-augmented excited-state dynamics and lay the foundation for future data-driven nonadiabatic excited-state dynamics modeling of ultrafast spectroscopic probes.
Conservation of volume integrals of ratio of Rayleigh acoustic energy density to frequency variable in geometric acoustics in moving medium
Gasdynamic hyperbolic systems are treated by a novel conservative flux difference splitting upwind method which is applicable to explicit or implicit and iterative or direct schemes, for marching in time or space with the Euler or compressible Navier-Stokes equations. The method is able to capture sharp shocks correctly by maintaining global conservation. The embedded characteristics formulation is cast in the volumetric internal energy primitive variable, which is effective for real as well as perfect gases. Higher order upwind formulae are constructed from the distribution of pieces of the simple internal flux difference splitting, and the method reverts to first order at the appropriate points in order not to violate the domain of dependence by differencing across discontinuities. At insignificant computational overhead, switching is done by simple algebraic extensions of the truth functions that determine upwind direction for the first order scheme.
A new Liapunov stability condition is formulated for the shallow-water equations, using a gage-variable formalism. This sufficient condition is derived for the class of perturbations that conserve the total mass. It is weaker than existing stability criteria, i.e., it applies to a wider class of flows. Formal stability to infinitesimally small perturbations of arbitrary shape is obtained for two classes of large-scale geophysical flows: pseudo-eastward flow with constant shear, and localized coherent structures of modon type.
The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.
Energy models for vapor compression refrigeration in residential air conditioners have been developed through white-box, gray-box, and black-box methods in decades. However, existing white-box and gray-box models require complicated equations with detailed geometries while black-box models require substantial experimental data. Further, this paper aims to develop and validate a simple gray-box steady-state energy model without the need for detailed geometries, which can accurately predict the cooling capacity and electrical power input based on outdoor and indoor air conditions, and supply airflow rates. First three state variables, including the evaporation and condensation temperatures, and refrigerant mass flowrate, are applied to develop the energy model and are solved by three physical equations, including the energy conservations at the evaporator and condenser, and the refrigerant volume-mass flow correlation of the compressor. Secondly, seven performance property functions related to three state variables and three physical equations are identified and calibrated by simple temperature and power measurements. Finally, field experiments are conducted on a residential air conditioner to calibrate these performance property functions and validate the developed model. The validated results reveal the model can accurately predict the cooling capacity and electrical power input, with the normalized root mean square errors of 2.3% and 0.87% respectively.