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At least 937 records · Page 52

Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries

We give a characterization of complete strongly dually atomic lattices having unique irredundant decompositions which are also canonical. It is shown that all known characterizations of lattices with unique irredundant decompositions are a consequence of this result. In addition, upper continuous closure lattices of convex geometries with (unique) irredundant decompositions are characterized.

97 MATHEMATICS AND COMPUTING↗

Comparative DFT Computational Studies with Experimental Investigations for Novel Synthesized Fluorescent Pyrazoline Derivatives

A novel series of pyrazoline derivatives were synthesized and their spectral properties were characterized via FT-IR, {sup 1}H, and {sup 13}C NMR. The electronic transitions and fluorescence properties were tracked via UV-Vis and emission spectrometry. The density functional theory (DFT) calculations have been also computed to get spot onto the geometry, electronic transitions and spectroscopic properties theoretically that has been compared with the encountered experimental ones. Moreover, the dipole moment, optimized energy, HOMO - LUMO energies and band gaps were calculated for novel candidates pyrazoline derivatives with highly fluorescence quantum yield.

74 ATOMIC AND MOLECULAR PHYSICS↗

On Some Degenerate Elliptic Equations Arising in Geometric Problems

We consider some fully nonlinear degenerate elliptic operators and we investigate the validity of certain properties related to the maximum principle. In particular, we establish the equivalence between the sign propagation property and the strict positivity of a suitably defined generalized principal eigenvalue. Furthermore, we show that even in the degenerate case considered in the present paper, the well-known condition introduced by Keller–Osserman on the zero-order term is necessary and sufficient for the existence of entire weak subsolutions.

97 MATHEMATICS AND COMPUTING↗

Dedekind η-Function in Modern Research

In this paper, we describe properties of the Dedekind η-function, constructions arising from it, and their applications in various topics of the number theory and algebra. We discuss connections with the group representation theory and the study of the structure of spaces of modular forms. Special attention is paid to the special class of modular forms, namely, η-functions with multiplicative coefficients.

97 MATHEMATICS AND COMPUTING↗

Resonance Vibration and Dissipative Heating of a Flexible Viscoelastic Beam with Piezoactuators in the Presence of Shear Strains

We consider a problem of forced resonance vibration and dissipative heating of a hinged flexible viscoelastic beam with piezoactuators in the presence of transverse shear strains. The effects of geometric nonlinearities, in-plane shear strains, and the conditions of heat exchange on the surfaces on the amplitude and temperature-frequency characteristics of the forced vibration of the beam and the thermal failure of the system are investigated. The possibility of active damping of the mode of flexural vibrations by piezoactuators is analyzed.

97 MATHEMATICS AND COMPUTING↗

A hybrid of fractal image coding and fractal dimension for an efficient retrieval method

Fractal image coding (FIC) based on the inverse problem of an iterated function system plays an essential role in several areas of computer graphics and in many other interesting applications. Through FIC, an image can be transformed to compressed representative parameters and be expressed in a simple geometric way. Dealing with digital images requires storing a large number of images in databases, where searching such databases is time consuming. Therefore, finding a new technique that facilitates this task is a challenge that has received increasing attention from many researchers. In this study, a new method that combines fractal dimension (FD) which is an indicator of image complexity with the FIC scheme is proposed. Classifying images in databases according to their texture by using FD helps reduce the retrieval time of query images. The validity of the proposed method is evaluated using geosciences images. Result shows that the method is computationally attractive.

97 MATHEMATICS AND COMPUTING↗

Simulation of shading and algal growth in experimental raceways

Many algae research groups use elevated experimental raceways to characterize algal biomass productivity. Side walls and a relatively large paddlewheel shade the culture and lower productivity, particularly in winter and with low culture depth. This paper presents a methodology to calculate shading for a given raceway shape: (1) develop a mesh of the inner surface geometry of the raceway; (2) offset the mesh horizontally in the x and y directions on the water surface as a function of wall height, solar zenith angle, and solar azimuth angle; (3) calculate the shaded area for each projected mesh with the shoelace algorithm; (4) use regression to develop a response surface for shaded area as a function of horizontal x and y offset. For each time step, the shaded area is calculated with the regression equation based on the x and y offset at that time step. The shading model was added to the Huesemann Algae Biomass Growth (HABG) model, which predicts algae growth rate as a function of water temperature and light intensity in algae culture layers. The shading model was evaluated with biomass concentrations from three Regional Algal Feedstock Testbed (RAFT) experiments with three different species of algae. The shading algorithm reduced the HABG estimate of productivity and improved the agreement with observed productivities. In the model, productivity was sensitive to the assumed light distribution below the water surface. Averaging light in each layer resulted in higher calculated growth rate than calculating growth separately in shaded and unshaded areas. Shaded area was sensitive to raceway orientation, water depth, and time of year. A north-south raceway orientation had less average shading in winter but more average shading in summer than an east-west orientation.

59 BASIC BIOLOGICAL SCIENCES↗

LayTracks3D: A new approach for meshing general solids using medial axis transform

This study presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex-dominant meshes of general solids. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D have no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the Results section. Work is underway to extend LayTracks3D to generate all-hex meshes.

97 MATHEMATICS AND COMPUTING↗

A subzone reconstruction algorithm for efficient staggered compatible remapping

Staggered-grid Lagrangian hydrodynamics algorithms frequently make use of subzonal discretization of state variables for the purposes of improved numerical accuracy, generality to unstructured meshes, and exact conservation of mass, momentum, and energy. For Arbitrary Lagrangian–Eulerian (ALE) methods using a geometric overlay, it is difficult to remap subzonal variables in an accurate and efficient manner due to the number of subzone–subzone intersections that must be computed. This becomes prohibitive in the case of 3D, unstructured, polyhedral meshes. A new procedure is outlined in this paper to avoid direct subzonal remapping. The new algorithm reconstructs the spatial profile of a subzonal variable using remapped zonal and nodal representations of the data. The reconstruction procedure is cast as an under-constrained optimization problem. Enforcing conservation at each zone and node on the remapped mesh provides the set of equality constraints; the objective function corresponds to a quadratic variation per subzone between the values to be reconstructed and a set of target reference values. Numerical results for various pure-remapping and hydrodynamics tests are provided. Ideas for extending the algorithm to staggered-grid radiation-hydrodynamics are discussed as well as ideas for generalizing the algorithm to include inequality constraints.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

97 MATHEMATICS AND COMPUTING↗

Modulation of apparent optical properties using arrayed mesoscale structures

In this study, a method for using arrays of mesoscale structures to modify the apparent optical properties of an opaque composite surface has been theoretically demonstrated to both raise and lower the apparent emissivity as compared to the intrinsic properties of the constitutive materials. For design problems where thermomechanical and optical material properties are both of importance, mesoscale surface structuring can greatly expand the design space. Analysis via the net radiosity method herein illustrates the ability to achieve a wide range of spectral apparent optical properties. Notably, a hexagonal array of spheres on a planar surface can raise the apparent emissivity of a planar surface by 50%. Conversely, a hexagonal enclosure of reradiating surfaces, realized by thin adiabatic walls, can reduce the apparent emissivity of a blackbody by half. As this method of modifying apparent optical properties utilizes structures much larger than the wavelengths of interest, the relationship between intrinsic planar emissivity, geometry, and apparent emissivity can be computed semi-analytically at low computational expense. Passive solar cooling, thermophotovoltaic cells, aerodynamic surfaces exposed to intense heating, and solar absorbers are presented as case studies that could benefit from the use of mesoscale structures on opaque surfaces to modify the apparent optical properties.

42 ENGINEERING↗

Compositionally Tuning Electron Transfer from Photoexcited Core/Shell Quantum Dots via Cation Exchange

It is critical to find methods to control the thermodynamic driving force for photoexcited charge transfer from quantum dots (QDs) and explore how this affects charge transfer rates, since the efficiency of QD-based photovoltaic and photocatalysis technologies depends on both this rate and the associated energetic losses. In this work, we introduce a single-pot shell growth and Cu-catalyzed cation exchange method to synthesize Cd x Zn 1-x Se/Cd y Zn 1-y S QDs with tunable driving forces for electron transfer. Functionalizing them with two molecular electron acceptors—naphthalenediimide (NDI) and anthraquinone (AQ)—allowed us to probe nearly 1 eV of driving forces. For AQ, at lower driving forces, we find that higher Zn content results in a 130-fold increase of electron transfer rate constants. However, at higher driving forces electron transfer dynamics are unaltered. Here, the data are understood using an Auger-assisted electron transfer model and analyzed with computational work to determine approximate binding geometries of these electron acceptors. Our work provides a method to tune QD reducing power and produces useful metrics for optimizing QD charge transfer systems that maximize rates of electron transfer while minimizing energetic losses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nutrient transport suggests an evolutionary basis for charged archaeal surface layer proteins

Surface layers (S-layers) are two-dimensional, proteinaceous, porous lattices that form the outermost cell envelope component of virtually all archaea and many bacteria. Despite exceptional sequence diversity, S-layer proteins (SLPs) share important characteristics such as their ability to form crystalline sheets punctuated with nano-scale pores, and their propensity for charged amino acids, leading to acidic or basic isoelectric points. However, the precise function of S-layers, or the role of charged SLPs and how they relate to cellular metabolism is unknown. Nano-scale lattices affect the diffusion behavior of low-concentration solutes, even if they are significantly smaller than the pore size. Here, we offer a rationale for charged S-layer proteins in the context of the structural evolution of S-layers. Using the ammonia-oxidizing archaea (AOA) as a model for S-layer geometry, and a 2D electrodiffusion reaction computational framework to simulate diffusion and consumption of the charged solute ammonium (NH 4 + ), we find that the characteristic length scales of nanoporous S-layers elevate the concentration of NH 4 + in the pseudo-periplasmic space. Our simulations suggest an evolutionary, mechanistic basis for S-layer charge and shed light on the unique ability of some AOA to oxidize ammonia in environments with nanomolar NH 4 + availability, with broad implications for comparisons of ecologically distinct populations.

59 BASIC BIOLOGICAL SCIENCES↗

Preservation of kinetics parameters generated by Monte Carlo calculations in two-step deterministic calculations

The generation of accurate kinetic parameters such as mean generation time Λ and effective delayed neutron fraction β eff via Monte Carlo codes is established. Employing these in downstream deterministic codes warrants another step to ensure no additional error is introduced by the low-order transport operator when computing forward and adjoint fluxes for bilinear weighting of these parameters. Another complexity stems from applying superhomogenization (SPH) equivalence in non-fundamental mode approximations, where reference and low-order calculations rely on a 3D full core model. In these cases, SPH factors can optionally be computed for only part of the geometry while preserving reaction rates and K-effective, but the impact of such approximations on kinetics parameters has not been thoroughly studied. This paper aims at studying the preservation of bilinearly-weighted quantities in the Serpent–Griffin calculation procedure. Diffusion and transport evaluations of IPEN/MB-01, Godiva, and Flattop were carried out with the Griffin reactor physics code, testing available modeling options using Serpent-generated multigroup cross sections and equivalence data. Verifying Griffin against Serpent indicates sensitivities to multigroup energy grid selection and regional application of SPH equivalence, introducing significant errors; these were demonstrated to be reduced through the use of a transport method together with a finer energy grid.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Kinetic solutions for electrons in multi-cusp ion source

Some analytical kinetic solutions are obtained for the primary and plasma electrons in multi-cusp ion source. The characteristics based on these solutions are discussed, such as frictional coefficient, collision frequency, electron current, electron diffusion, electron density, and electrical conductivity. A code based on one of these solutions is developed to discuss the plasma electrons diffusion; the simulation results are qualitatively consistent with our current experiences.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

How many invariant polynomials are needed to decide local unitary equivalence of qubit states?

Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Treating the effect of interface reflections on superdiffusive spin transport in multilayer samples (invited)

Femtosecond laser-induced magnetization dynamics has recently been related to superdiffusive spin transport. With the aim to accurately compute spin superdiffusion in the complex geometries of layered heterostructures and free standing layers, we develop here a dedicated numerical scheme. We introduce a discretization technique to solve the superdiffusive equation numerically on a time and space grid. The discretization scheme facilitates an explicit treatment of the total reflection at the vacuum-material surfaces as well as of partial reflections at the interfaces between two different materials. The advantages of the numerical technique are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗