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At least 1,765 records · Page 98

Spectral methods in the presence of discontinuities

Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and L 2 -norm. However, for non-smooth problems, convergence is significantly worse—the L 2 -norm of the error for a discontinuous problem will converge at a sub-linear rate and the infinity norm will not converge at all. We explore and improve upon a post-processing technique—optimally convergent mollifiers—to recover exponential convergence from a poorly-converging spectral reconstruction of non-smooth data. Furthermore this is an important first step towards using these techniques for simulations of realistic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Numerical schemes for 3-wave kinetic equations: A complete treatment of the collision operator

In our previous work Walton and Tran (2023), numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dynamics of the equation given the multiple blow-up time phenomenon. In this second work in the series, we propose numerical treatments for the complete 3-wave kinetic equations, in which the complete, much more complicated collision operators are fully considered based on a novel conservative form of the equation. Here we then derive an implicit finite volume scheme to solve the equation. The new discretization uses an adaptive time-stepping method which allows for the simulations to be carried to very long times. Our computed solutions are compared with previously derived long-time asymptotic estimates for the decay rate of total energy of time-dependent solutions of 3-wave kinetic equations and found to be in excellent agreement.

97 MATHEMATICS AND COMPUTING↗

Hardware acceleration for HPS algorithms in two and three dimensions

We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU; in three dimensions, we modify and extend the adaptive discretization technique of Geldermans and Gillman [1] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems.

Fast direct solvers↗

Electronic density of states as the descriptor of elastic bond strength, ductility, and local lattice distortion in BCC refractory alloys

Although electronic density of states (DOS) is fundamental to materials properties, its general relationship to mechanical properties of alloys is not well established. In this paper, using density functional theory (DFT) calculations, we show that the electronic occupancy at the Fermi level, N(E f ), obtained from DOS is a key descriptor of alloy strength and ductility. Our comprehensive analysis of numerous body centered cubic (BCC) refractory high entropy alloys (RHEAs) shows an overwhelming correlation that low N(E f ) indicates strong bonds that have high stiffness resulting in high elastic constants. High bond stiffness indicates presence of covalent nature of bonds that are directional in nature resulting in resistance to deformation leading to high bulk (B) and shear (G) moduli. Consequently, N(E f ) provides a direct correlation to the tendency of alloy ductility evidenced in the Pugh ratio (G/B). As stiffer bonds result in lower local lattice distortion (LLD), N(E f ) are LLD are also found to be corelated which opens up a correlation to solid solution strengthening and yield strength. Thus, this work unveils fundamental correlations between N(E f ) and (1) elastic bond strength, (2) ductility, and (3) LLD. These correlations open opportunities for the design of high strength high ductile RHEAs.

36 MATERIALS SCIENCE↗

Recent advances in combustion science related to hydrogen safety

Hydrogen is a key pillar in the global Net Zero strategy. Rapid scaling up of hydrogen production, transport, distribution and utilization is expected. This entails that hydrogen, which is traditionally an industrial gas, will come into proximity of populated urban areas and in some situations handled by the untrained public. To realize all their benefits, hydrogen and its technologies must be safely developed and deployed. The specific properties of hydrogen involving wide flammability range, low ignition energy and fast flame speed implies that any accidental release of hydrogen can be easily ignited. Comparing with conventional fuels, combustion systems fueled by hydrogen are also more prone to flame instability and abnormal combustion. This paper aims to provide a comprehensive review about combustion research related to hydrogen safety. It starts with a brief introduction which includes some overview about risk analysis, codes and standards. The core content covers ignition, fire, explosions and deflagration to detonation transition (DDT). Considering that DDT leads to detonation, and that detonation may also be induced directly under special circumstances, the subject of detonation is also included for completeness. The review covers laboratory, medium and large-scale experiments, as well as theoretical analysis and numerical simulation results. While highlights are provided at the end of each section, the paper closes with some concluding remarks highlighting the achievements and key knowledge gaps.

08 HYDROGEN↗

The role of geographical spreaders in infectious pattern formation and front propagation speeds

The pattern formation and spatial spread of infectious populations are investigated using a kernel-based Susceptible–Infectious–Recovered (SIR) model applicable across a wide range of basic reproduction numbers R O . The goal is to examine the role of geographical spreaders on transient spatial pattern formation of infectious populations and the associated maximum invasive front speeds c max . In the simulations conducted here, geographical spreaders are defined as a portion of the infected population Φ experiencing high mobility between identical communities. The spatial organization of the infected population and c max are determined when the infections are randomly initiated in space within multiple communities. For small but finite , scaling analysis and numerical simulations in 1-dimension suggest that when the spreading kernel is Gaussian-shaped, where is the inverse of the infectious duration. This finding for agrees with a diffusion-based representation of mobility in 1-D. Numerical simulations in 2-D across wide-ranging suggest that , the variance of the spatial kernel describing mobility of long-distance geographical spreaders across communities, determines the spatial organization of infections across communities. When (long-distance mobility, where is the minimum spatial extent defining adjacent communities), the infectious population will experience a transient but spatially coherent pattern with a wavelength that can be derived from the spreading kernel properties. Moreover, the 2-D simulations for the bounded kernel suggest that attainment of is also dictated by but the magnitude is not sensitive to unlike diffusion-based models.

60 APPLIED LIFE SCIENCES↗

Assessing the relative importance of flame regimes in Raman/Rayleigh line measurements of turbulent lifted flames

Understanding and quantifying the relative importance of premixed and non-premixed reaction zones within turbulent partially premixed flames is an important issue for multi-regime combustion. The recently-developed method of gradient-free regime identification (GFRI) is applied to instantaneous 1D Raman/Rayleigh measurements of temperature and major species from two turbulent lifted methane/air flames. Local premixed and non-premixed reaction zones are identified using criteria based on the mixture fraction, the chemical explosive mode, and the heat release rate, the latter two being calculated from an approximation of the full thermochemical state of each measured sample. A chemical mode (CM) zero-crossing is a previously documented marker for a premixed reaction zone. Results from the lifted flames show strong correlations among the mixture fraction at the CM zero-crossing, the magnitude of the change in CM at the zero-crossing, and the local heat release rate at the CM zero-crossing compared to the maximum heat release rate. The trends are confirmed through a comparable analysis of numerical simulations of two laminar triple flames. These newly documented trends are associated with the transition from dominantly premixed flame structures to dominantly non-premixed flames structures. The methods introduced for assessing the relative importance of local premixed and non-premixed reactions zones have potential for application to a broad range of turbulent flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-cell, triple pane, vacuum insulated glazing

A novel Triple Pane Vacuum Insulated Glazing (TPVIG) architecture consisting of three panes of glass separated by two offset grids is described. The grids are made of frit-coated fibers fused with the glass panes in a vacuum to create many independent hermetic cells. Unlike traditional VIGs, which are separated by support pillars, these cells significantly increase the redundancy in sealing, and the additional bonds formed by the grid lines reduce the stresses on the edge bonds thereby increasing VIG reliability. A numerical thermal analysis was conducted to determine the thermal performance of the VIG and suggested U-values below 0.5 W/m 2 -K (greater than R=11.4 hr-ft 2 -°F/Btu) can be obtained. A prototype of the VIG unit consisting of three glass panes (5.7 mm, 1.1 mm and 5.7 mm thick with low-e coating on two surfaces) was fabricated and tested for thermal performance using the hot box method. The experimental center of glass U-value for the VIG was found to be 0.42 W/m 2 K (R=13.2 hr-ft 2 -°F/Btu). Furthermore, this U-value is about four times lower than a typical Argon filled double pane window.

14 SOLAR ENERGY↗

How equation of state selection impacts accuracy near the critical point: Forced convection supercritical CO 2 flow over a cylinder

Increasing application of supercritical fluids leads to increased use of numerical simulations to guide designs. However, the impact of Equations of State (EoS) selection on computational cost and accuracy is not well understood. Laminar flow around a heated cylinder is used as a test case. A robust matrix of 99-simulations is used to analyze the flow of carbon dioxide just above the critical point at the isobaric condition of 8 MPa and temperatures between 305 and 390 K. Four EoS were studied: Ideal Gas Law, cubic EoS’s Peng-Robinson and Soave-Redlich-Kwong, and the Span-Wagner EoS. Results were identical for isothermal cases, but for heated or cooled cases, the high-fidelity Span-Wagner EoS simulations presented drastically different wake structures. Compared to the high-fidelity SW EoS, cEoS’s underestimated Nu values by up to 38% and cEoS’s underestimated CD values by 18–42%. In conclusion, the Span-Wagner EoS required only 17% more computation time then the cubic EoS simulations, making the Span-Wagner EoS recommended for engineering design.

42 ENGINEERING↗

Numerical study of radiation effect on the municipal solid waste combustion characteristics inside an incinerator

Highlights: • A 3-D model for the MSW incinerator with preheated air was developed. • Gas radiative properties were obtained from a statistical narrow-band model. • Non-gray body radiation model can provide more accurate simulation results. - Abstract: Due to its advantages of high degree volume reduction, relatively stable residue, and energy reclamation, incineration becomes one of the best choices for Municipal Solid Waste (MSW) disposal. However, detailed measurements of temperature and gas species inside a furnace are difficulty by conventional experimental techniques. Therefore, numerical simulation of MSW incineration in the packed bed and gas flow field was applied. In this work, a three dimensional (3-D) model of incinerator system, including flow, heat transfer, detailed chemical mechanisms, and non-gray gas models, was developed. Radiation from the furnace wall and the flame formed above the bed is of importance for drying and igniting the waste. The preheated air with high temperature is used for the MSW combustion. Under the conditions of high temperature and high pressure, MSW combustion produces a variety of radiating gases. The wavelength-depend radiative properties of flame adopted in non-gray radiation model were obtained from a statistical narrow-band model. The influence of radiative heat transfer on temperature, flow field is researched by adiabatic model (without considering radiation), gray radiation model, and non-gray radiation model. The simulation results show that taking into account the non-gray radiation is essential.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Electroconvection near an ion-selective surface with Butler–Volmer kinetics

We study the effects of interfacial kinetics on the electro-hydrodynamics of ion transport near an ion-selective surface using a combination of linear stability analysis and numerical simulation. The finite kinetics of the electrolyte–electrode interface affects the ion transfer and electroconvection in many ways. On a surface of fixed topography, such as a metal surface of slow and stable ion deposition or covered by a polymer membrane, the finite kinetics reduces the current in one-dimensional ion diffusion/migration, increases the critical voltage for the onset of the electroconvective instability, changes the dynamics of the electroconvection and the overlimiting current, and enhances the lateral ion diffusion within the interfacial layer. The first three effects are indirectly caused by the reaction kinetics and can be characterized by an effective voltage difference across the liquid electrolyte. In comparison, the last effect is controlled by a direct interplay between kinetics and nonlinear electroconvection. Scaling laws for ion transport and features of electroconvection are proposed. We also analyse the linear stability of a surface which evolves under ion deposition and find that the finite kinetics decreases the growth rate of both electroconvective and morphological instabilities and therefore modifies the wavenumber of the most unstable mode.

Mechanics↗

Why scientists should learn to program in Python

Scientists have been central to the historical development of the computer industry, but the importance of software only continues to grow for all areas of scientific research and in particular for powder diffraction. Knowing how to program a computer is a basic and useful skill for scientists. The article introduces the three types of programming languages and why scripting languages are now preferred for scientists. Of them, the authors assert Python is the most useful and easiest to learn. Python is introduced. Also presented is an overview to a few of the many add-on packages available to extend the capabilities of Python, for example, for numerical computations, scientific graphics and graphical user interface programming.

97 MATHEMATICS AND COMPUTING↗

Comparing Sensor Fusion and Multimodal Chemometric Models for Monitoring U(VI) in Complex Environments Representative of Irradiated Nuclear Fuel

Optical sensors and chemometric models were leveraged for the quantification of uranium(VI) (0–100 μg mL –1 ), europium (0–150 μg mL –1 ), samarium (0–250 μg mL –1 ), praseodymium (0–350 μg mL –1 ), neodymium (0–1000 μg mL –1 ), and HNO 3 (2–4 M) with varying corrosion product (iron, nickel, and chromium) levels using laser fluorescence, Raman scattering, and ultraviolet–visible–near-infrared absorption spectra. In this paper, an efficient approach to developing and evaluating tens of thousands of partial least-squares regression (PLSR) models, built from fused optical spectra or multimodal acquisitions, is discussed. Each PLSR model was optimized with unique preprocessing combinations, and features were selected using genetic algorithm filters. The 7-factor D-optimal design training set contained just 55 samples to minimize the number of samples. The performance of PLSR models was evaluated by using an automated latent variable selection script. PLS1 regression models tailored to each species outperformed a global PLS2 model. PLS1 models built using fused spectra data and a multimodal (i.e., analyzed separately) approach yielded similar information, resulting in percent root-mean-square error of prediction values of 0.9–5.7% for the seven factors. Further, the optical techniques and data processing strategies established in this study allow for the direct analysis of numerous species without measuring luminescence lifetimes or relying on a standard addition approach, making it optimal for near-real-time, in situ measurements. Nuclear reactor modeling helped bound training set conditions and identified elemental ratios of lanthanide fission products to characterize the burnup of irradiated nuclear fuel. Leveraging fluorescence, spectrophotometry, experimental design, and chemometrics can enable the remote quantification and characterization of complex systems with numerous species, monitor system performance, help identify the source of materials, and enable rapid high-throughput experiments in a variety of industrial processes and fundamental studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Ion Pairing and Molecular Orientation at Liquid/Liquid Interfaces: Self-Assembly and Function

We report that molecular orientation plays a pivotal role in defining the functionality and chemistry of interfaces, yet accurate measurements probing this important feature are few, due, in part, to technical and analytical limitations in extracting information from molecular monolayers. For example, buried liquid/liquid interfaces, where a complex and poorly understood balance of inter- and intramolecular interactions impart structural constraints that facilitate the formation of supramolecular assemblies capable of new functions, are difficult to probe experimentally. Here, we use vibrational sum-frequency generation spectroscopy, numerical polarization analysis, and atomistic molecular dynamics simulations to probe molecular orientations at buried oil/aqueous interfaces decorated with amphiphilic oligomers. We show that the orientation of self-assembled oligomers changes upon the addition of salts in the aqueous phase. The evolution of these structures can be described by competitive ion effects in the aqueous phase altering the orientations of the tails extending into the oil phase. These specific anionic effects occur via interfacial ion pairing and associated changes in interfacial solvation and hydrogen-bonding networks. These findings provide more quantitative insight into orientational changes encountered during self-assembly and pave the way for the design of functional interfaces for chemical separations, neuromorphic computing applications, and related biomimetic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Local Electronic Structure Changes in Polycrystalline CdTe with CdCl 2 Treatment and Air Exposure

Postdeposition CdCl 2 treatment of polycrystalline CdTe is known to increase the photovoltaic device efficiency. However, the precise chemical, structural, and electronic changes that underpin this improvement are still debated. In this work, spectroscopic photoemission electron microscopy was used to spatially map the vacuum level and ionization energy of CdTe films, enabling the identification of electronic structure variations between grains and grain boundaries (GBs). In vacuo preparation and inert transfer of oxide-free CdTe surfaces isolated the separate effects of CdCl 2 treatment and ambient oxygen exposure. Qualitatively, grain boundaries displayed lower work function and downward band bending relative to grain interiors, but only after air exposure of CdCl 2 -treated CdTe. Analysis of numerous space charge regions at grain boundaries showed an average depletion width of 290 nm and an average band bending magnitude of 70 meV, corresponding to a GB trap density of 10 11 cm –2 and a net carrier density of 10 15 cm –3 . Finally, these results suggest that both CdCl 2 treatment and oxygen exposure may be independently tuned to enhance the CdTe photovoltaic performance by engineering the interface and bulk electronic structure.

36 MATERIALS SCIENCE↗

Apparent Activation Energies in Complex Reaction Mechanisms: A Simple Relationship via Degrees of Rate Control

The apparent activation energy of chemical reactions previously played a central role in the field of chemical kinetics and has served as an important tool for analyzing and understanding reaction rates, mechanistic details of complex reaction mechanisms, elementary-step energetics, catalytic activity and reaction selectivity. In this work, we derive a general expression which shows that the apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all the species (intermediates, transition states and products) in the reaction mechanism, each weighted by its generalized degree of rate control (DRC). Since the DRC is zero for most of these species, even in very complex mechanisms, the weighted average includes only a few terms. This simplicity provides deep insight into the connection between the reaction energy diagram and the apparent activation energy. We prove both this and the quantitative validity of this equation by analysis of numerous reaction mechanisms. We also show the failures or weaknesses of previous equations for the apparent activation energy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗