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The results of a recent paper by A. V. Vasin, S. V. Kislyakov, and the author on the relationship between the local boundary smoothness of an analytic function and local boundary smoothness of its modulus are extended to the case of generalized pointwise Hölder type conditions of order between one and two.
We study a pair of surfaces associated with a function analytic in a domain G, establish relations between the coefficients of the first (second) fundamental quadratic forms of these surfaces and prove theorems on their invariance under conformal transformations.
The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric {sub 2}F{sub 1}, {sub 1}F{sub 1} and {sub 0}F{sub 1} functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins. In this paper I will apply three term recurrence formula (Y.S. Choun, (arXiv:1303.0806), 2013) to the power series expansion in closed forms of Heun function (infinite series and polynomial) including all higher terms of A{sub n}’s. Section 3 contains my analysis on applying the power series expansions of Heun function to a recent paper (R.S. Maier, Math. Comp. 33 (2007) 811–843). Due to space restriction final equations for the 192 Heun functions are not included in the paper, but feel free to contact me for the final solutions. Section 4 contains two additional examples using the power series expansions of Heun function. This paper is 3rd out of 10 in series “Special functions and three term recurrence formula (3TRF)”. See Section 5 for all the papers in the series. The previous paper in series deals with three term recurrence formula (3TRF). The next paper in the series describes the integral forms of Heun function and its asymptotic behaviors analytically. -- Highlights: •Power series expansion for infinite series of Heun function using 3 term rec. form. •Power series for polynomial which makes B{sub n} term terminated of Heun function. •Applicable to areas such as the Teukolsky equation in Kerr–Newman–de Sitter geometries.
The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.
An automated separation–direct analysis scheme has been developed to determine both the concentration and isotopic composition of a suite of elements down to the low picogram level in a complex silicon-based matrix. With the ultimate goal of performing rapid analysis of materials with non-natural isotopic compositions, RAPID (Rapid Analysis of Post-Irradiation Debris) consists of a high-pressure ion chromatography system directly coupled to an inductively coupled plasma mass spectrometer. The RAPID method achieves matrix exclusion and direct online analysis of the elementally separated components, yielding precise isotopic compositions for up to 40 elements in less than one hour per sample. When combined with isotope dilution, this approach shows the potential to yield elemental concentrations with low uncertainties, providing a rapid analytical method that encompasses group I and II metals, transition metals, refractory metals, platinum group metals, lanthanides, and actinides. Furthermore, the method development, robustness, sensitivity, uncertainties, and potential applications in nuclear and environmental measurements will be discussed in this paper.
Numerical simulation of an electrodynamic system in empty space requires the implementation of open boundary conditions (BC) to terminate the solution of Maxwell’s equations on the boundaries of the computational domain. The Perfectly Matched Layer (PML) has become the method of choice for open BC with wave equations, as it is straightforward and relatively easy to implement, and offers very efficient and user-adjustable absorption rates. PMLs are most often employed with the Finite-Difference Time-Domain (FDTD) algorithm, which in its most common implementation offers second-order accuracy in space and time on Cartesian grids. Yet, simulations (including some class of electromagnetic Particle-In-Cell simulations) that require higher precision may resort to higher-order Maxwell solvers employing extended finite-difference stencils, or even to pseudo-spectral Maxwell solvers, for which a general, versatile and efficient formulation of the PML has been missing so far. Here we propose a novel “two-step” formulation of the PML that is simple, very versatile and can be used as is with any Maxwell solver. In particular, it is applicable to a large class of Maxwell solvers including the arbitrary-order Pseudo-Spectral Analytical Time-Domain (PSATD) solver, which offers arbitrarily low numerical dispersion when increasing solver order and becomes dispersion-free at infinite order. Analysis and numerical simulations demonstrate that the new formulation is as efficient as the standard PML formulation, both for the FDTD and the PSATD implementations.
An analytical and empirical-based 1-D, non-isothermal, steady-state model for anion exchange membrane fuel cell capable of capturing two-phase phenomena is presented in this study. Coupled multi-physics including mass and charge transport, electrochemical reactions, heat transfer, and two-phase water transport are considered in the model and the simulated results are compared to experimental data. To better represent actual material properties and localized conditions, the model applies multilayer discretization in the gas diffusion electrode to enhance prediction accuracy. The model successfully predicts the baseline performance at 70 °C, 131 kPa abs., 92% RH with pure H 2 /O 2 gas as well as the limiting current at 10% H 2 . The robust simulation approach allows for simplistic and accurate estimation of cell performance without the complications of applying two-phase parameters and expensive computational need for numerical models. In addition, the results from the sensitivity studies of material properties and operating conditions provide valuable insights on water management strategies and optimal component design for advancing anion exchange membrane fuel cell technology.
Recent advances in information, communication, and environmental monitoring technologies have increased the availability, spatiotemporal resolution, and quality of water-related data, thereby leading to the emergence of many innovative big data applications. Among these applications, visualization and visual analytics, also known as the visual computing techniques, empower the synergy of computational methods (e.g., machine learning and statistical models) with human reasoning to improve the understanding and solution toward complex science and engineering problems. These approaches are frequently integrated with geographic information systems and cyberinfrastructure to provide new opportunities and methods for enhancing water resources management. Here, we present a comprehensive review of recent hydroinformatics applications that employ visual computing techniques to (1) support complex data-driven research problems, and (2) support the communication and decision-makings in the water resources management sector. Then, we conduct a technical review of the state-of-the-art web-based visualization technologies and libraries to share our experiences on developing shareable, adaptive, and interactive visualizations and visual interfaces for water resources management applications. We close with a vision that applies the emerging visual computing technologies and paradigms to develop the next generation of hydroinformatics applications.
Agglomeration of wet particles, i.e., particles coated with a thin liquid layer, is a common phenomenon in many processes like fluidized bed combustion of low rank fuels. The availability of an agglomeration model that can evaluate the outcome of a binary collision between wet particles differing in solid particle properties, liquid layer thicknesses, and initial collision (impact) speeds is essential for obtaining a comprehensive understanding on the existing processes experiencing wet particle agglomeration or for a successful development of new processes with high chances of wet particle agglomeration. This study presents a generalized agglomeration model on the basis of energy conservation before and after collision when colliding wet particles may differ in solid particle properties, liquid layer thicknesses, and impact speeds. The model was established based on the approximate values of energy losses that may happen during the collision. It incorporates body forces, solid-solid contacting, liquid capillary, and viscous contributions, as well as the liquid bridge volume effect. Predictions of the new model for collision outcomes of identical wet particles were like those from an analytical energy balance model developed recently by the group for identical wet particles. We also validated the new model by experimental data from literature. The results of a collision direction analysis indicated that the direction often has a minimal effect on the collision outcome in many practical scenarios. The results of Monte Carlo uncertainty analyses with the new model revealed that proper estimations of impact speed, under capillary limiting conditions, and thickness of coating layers and asperity heights, under viscous limiting conditions, are critical for the realistic prediction of collision outcomes at impact speeds close to critical impact speed, i.e., the minimum particle speed required for the particles to rebound.
Reaction–diffusion equations describe a number of physical, chemical, and biological phenomena, many of which occur in composite environments with piece-wise constant diffusion coefficients. In this work, we develop semi-analytical solutions of axisymmetric reaction–diffusion equations with first-order reaction kinetics and continuous transient boundary conditions. These solutions are directly applicable to heat conduction in composite media with transient boundary conditions and heat generation. The solutions lose their robustness in the long time regime, when the Laplace variable tends to zero. Lastly, this limitation is overcome by the use of corresponding steady-state solutions.
This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.
Here, an analytic model of the evolution of dislocation density in fcc polycrystals is described. The evolution equations approximately account for most known dislocation storage, dynamic recovery, and dislocation generation mechanisms in fcc polycrystals. Specifically, the model incorporates network (forest) and grain boundary storage, mobile-network and mobile–mobile annihilation, screw–screw annihilation via athermal and thermal single cross-slip, generation by double cross-slip (Koehler mechanism, including dipole formation), Frank-Read sources, grain boundary nucleation, and mobile–immobile dislocation nucleation due to shock loading. Single cross-slip is assumed to proceed through the Friedel–Escaig (FE) mechanism; the corresponding activation energy is calculated using a modified FE model. The activation energy for double cross-slip is calculated for the first time by extending the FE model. The exact evolution equations are integro-differential equations, and as such are difficult to implement in a code; hence, the evolution equations are simplified by making several approximations. Preliminary results on copper are presented, including comparisons to experimental data.
In this study, we are interested in an interface reconstruction method for 3D arbitrary convex cells that could be used in multi-material flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volume-matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction. We follow the same approach as in the recent authors' publication for 2D arbitrary convex cells in planar and axisymmetrical geometries, namely we derive an analytical formula for the volume of the specific prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes. This formula is used to bracket the interface plane constant such that the volume-matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution. Finally, the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster.
We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter–Gummel scheme to non-Boltzmann (e.g. Fermi–Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.
A predictive analytical model is presented for the electrical conductivity of multi-principal-element alloys (MPEAs), including those containing aluminum, transition metals, and refractory metals. Given that the lattice parameter of the Wigner-Seitz cell of an MPEA is similarly variable to a bulk metallic glass, it is postulated that electron scattering can be approximated by a series of two-level systems. Here, the resulting reduced-order model enabled an accurate determination of electrical resistivity and electron thermal conductivity based on the scattering of electrons in a two-level system across a Bloch-potential-based virtual crystal approximation. Model results are compared to experimental four-point probe electrical resistivity measurements between 300 K and 700 K for Al 0.3 CoCrCuFeNi, CoCrFeMnNi, (CoCrFeMnNi) 0.98 W 0.02 , (CoCrFeMnNi) 0.95 W 0.05 , and Nb 4 Ta 4 V 3 Ti, for model validation.
Abstract Artificial intelligence (AI) promises to reshape scientific inquiry and enable breakthrough discoveries in areas such as energy storage, quantum computing, and biomedicine. Scanning transmission electron microscopy (STEM), a cornerstone of the study of chemical and materials systems, stands to benefit greatly from AI-driven automation. However, present barriers to low-level instrument control, as well as generalizable and interpretable feature detection, make truly automated microscopy impractical. Here, we discuss the design of a closed-loop instrument control platform guided by emerging sparse data analytics. We hypothesize that a centralized controller, informed by machine learning combining limited a priori knowledge and task-based discrimination, could drive on-the-fly experimental decision-making. This platform may unlock practical, automated analysis of a variety of material features, enabling new high-throughput and statistical studies.
Crystalline silicotitanate (CST) inorganic ion exchanger is a candidate material for remediation of highly alkaline (pH > 14) aqueous nuclear waste streams containing high sodium concentrations (>5 M). In this work, ion exchange column testing with wastes from Hanford tanks AP-105, AP-107, and AW-102 was carried out to study the uptake of 137 Cs to estimate the decontamination factor (DF) value. Additionally, DF values for uptake of Al, Ca, Pb, Np, Pu, U, and Sr were determined and the ion exchange capacity of CST toward these analytes was estimated. Limited data is available on the load behavior of other minor and trace elements with recent CST production lots and this characterization will help improve understanding of the behavior of CST and assist in identifying potential disposition pathways as well as assessing removal capabilities of CST for other components.
Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear–electronic coupling in addition to accurately predicting Franck–Condon vertical excitations. Here, in this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.