Combined doping and geometry effects on transferred-electron bulk instabilities
Transferred electron bulk negative differential conductivity devices, analyzing combined doping and geometry effects on space charge and domain dynamics
Rabson, T. A.↗
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Black Holes in an Effective Field Theory Extension of General Relativity
Effective field theory methods suggest that some rather general extensions of general relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary. Thus, the tantalizing prospect to test the fundamental nature of gravity with gravitational-wave observations, in a systematic way, emerges naturally. Here, we build black hole solutions in such a framework and study their main properties. Once rotation is included, we find the first purely gravitational example of geometries without Z 2 symmetry. Despite the higher-order operators of the theory, we show that linearized fluctuations of such geometries obey second-order differential equations. We find nonzero tidal Love numbers. We study and compute the quasinormal modes of such geometries. These results are of interest to gravitational-wave science but also potentially relevant for electromagnetic observations of the galactic center or x-ray binaries.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Differential memory in the earth's magnetotail
The process of 'differential memory' in the earth's magnetotail is studied in the framework of the modified Harris magnetotail geometry. It is verified that differential memory can generate non-Maxwellian features in the modified Harris field model. The time scales and the potentially observable distribution functions associated with the process of differential memory are investigated, and it is shown that non-Maxwelllian distributions can evolve as a test particle response to distribution function boundary conditions in a Harris field magnetotail model. The non-Maxwellian features which arise from distribution function mapping have definite time scales associated with them, which are generally shorter than the earthward convection time scale but longer than the typical Alfven crossing time.
Burkhart, G. R.↗
Parallel computation of geometry control in adaptive truss structures
The fast computation of geometry control in adaptive truss structures involves two distinct parts: the efficient integration of the inverse kinematic differential equations that govern the geometry control and the fast computation of the Jacobian, which appears on the right-hand-side of the inverse kinematic equations. This paper present an efficient parallel implementation of the Jacobian computation on an MIMD machine. Large speedup from the parallel implementation is obtained, which reduces the Jacobian computation to an O(M-squared/n) procedure on an n-processor machine, where M is the number of members in the adaptive truss. The parallel algorithm given here is a good candidate for on-line geometry control of adaptive structures using attached processors.
Ramesh, A. V.↗
Multiscale geometric modeling of macromolecules I: Cartesian representation
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the polarized curvature, for the prediction of protein binding sites.
97 MATHEMATICS AND COMPUTING↗
Comparison of multigrid algorithms for high‐order continuous finite element discretizations
Summary We present a comparison of different multigrid approaches for the solution of systems arising from high‐order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev‐accelerated Jacobi, and the symmetric successive over‐relaxation smoothers, as well as elementwise block Jacobi smoothing. Three approaches for the multigrid hierarchy are compared: (1) high‐order h ‐multigrid, which uses high‐order interpolation and restriction between geometrically coarsened meshes; (2) p ‐multigrid, in which the polynomial order is reduced while the mesh remains unchanged, and the interpolation and restriction incorporate the different‐order basis functions; and (3) a first‐order approximation multigrid preconditioner constructed using the nodes of the high‐order discretization. This latter approach is often combined with algebraic multigrid for the low‐order operator and is attractive for high‐order discretizations on unstructured meshes, where geometric coarsening is difficult. Based on a simple performance model, we compare the computational cost of the different approaches. Using scalar test problems in two and three dimensions with constant and varying coefficients, we compare the performance of the different multigrid approaches for polynomial orders up to 16. Overall, both h ‐multigrid and p ‐multigrid work well; the first‐order approximation is less efficient. For constant coefficients, all smoothers work well. For variable coefficients, Chebyshev and symmetric successive over‐relaxation smoothing outperform Jacobi smoothing. While all of the tested methods converge in a mesh‐independent number of iterations, none of them behaves completely independent of the polynomial order. When multigrid is used as a preconditioner in a Krylov method, the iteration number decreases significantly compared with using multigrid as a solver. Copyright © 2015 John Wiley & Sons, Ltd.
Sundar, Hari↗
Symmetries of stochastic differential equations: A geometric approach
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Temperature distribution in a laser-heated diamond anvil cell as described by finite element analysis
Finite element analysis (FEA) is a powerful tool for numerically solving partial differential equations over complex geometries and is thus useful for analyzing heat transport in laser-heated diamond anvil cell (LHDAC) experiments. Our models expand on previously published simulations by calculating the volume-averaged temperatures of both the sample and insulation/pressure media under steady-state heating to determine the thermal pressure of the hot sample. Our goal is to produce an accurate relationship between the measured surface temperature of the absorbing sample and the temperature of the transparent insulating media, which is used to determine thermal pressure but susceptible to steep temperature gradients. We find that in doing so, our FEA models of temperature within the pressure/insulation media can differ from simplified estimates of temperature gradients by more than a factor of 2. We also explore temperature-dependent and temperature-independent thermal conductivity models and find that the volume-averaged temperatures differ by up to a factor of 1.3, forcing the predicted thermal pressures determined to also differ by up to a factor of 1.5 at a temperature of 2000 K at 50 GPa for neon. Higher temperatures exacerbate this difference. We also find that unintentional asymmetric sample insertion and sample heating, which are common in LHDAC experiments, do not have a first-order effect on volume-averaged temperatures. The FEA models, available in both Python and FlexPDE, are versatile across different sample geometries, materials, and heat source laser shapes.
Farah, Frederick↗
Geometric properties of commutative subalgebras of partial differential operators
We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k[u,t] is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.
97 MATHEMATICS AND COMPUTING↗
Programmable Phase Selection between Altermagnetic and Noncentrosymmetric Polymorphs of MnTe on InP via Molecular Beam Epitaxy
This dataset contains DFT input and output files supporting the theoretical modeling in the associated publication (ACS Appl. Mater. Interfaces 2026, 18, 15654-15664). The calculations model the interfacial energetics of two MnTe polymorphs — NiAs-MnTe (hexagonal, alpha phase) and ZnS-MnTe (cubic, gamma phase) — on InP(111) substrates with two surface terminations: In-terminated InP(111)A and P-terminated InP(111)B. This gives four interface configurations: NiAs on In-terminated (experimentally observed), NiAs on P-terminated (computed for comparison), ZnS on In-terminated (computed for comparison), and ZnS on P-terminated (experimentally observed). The dataset is organized into four calculation types, each covering all four polymorph/termination combinations: (i) Slabs: Pristine MnTe/InP heterostructure slabs used to compute total energies and interface energy densities (Eint) for all four configurations, as reported in Fig. 6 of the main text. (ii) Disorder: Same slab geometries with a P_Te + Te_P antisite defect pair introduced near the interface, used to assess chemical intermixing effects on interface stability (Fig. S8, SI). (iii) Strain: Pristine slab calculations with in-plane lattice parameters strained by -1% and +1% relative to the InP lattice constant, used to evaluate strain-dependent interface energetics (Fig. S9, SI). (iv) Charge_Density: Single-point calculations on the full heterostructure, the isolated InP slab, and the isolated MnTe slab at fixed geometry, used to compute differential charge density plots showing interfacial charge accumulation and depletion as a function of surface termination (Fig. S10, SI). Each calculation folder contains INCAR, KPOINTS, POSCAR, CONTCAR, OUTCAR, and POTCAR_info.txt (PAW potential information, excluding the full POTCAR due to VASP licensing restrictions). The calculations were performed using VASP 6.4.3 with PBE exchange-correlation, PAW potentials, a Hubbard correction of Ueff = 5 eV on Mn d-states, and A-type AFM spin initialization.
36 MATERIALS SCIENCE↗
Four lectures on Euler integrals
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.
Matsubara-Heo, Saiei-Jaeyeong↗
Challenge Solutions for a Significant Water Cut Reduction History Match on Heavy Oil Polymer EOR
Milne Point Field is conducting the first-ever active polymer flood pilot program designed to enhance oil recovery (EOR) of heavy oils on the Alaska North Slope (ANS). The experimental field program consists of two pairs of horizontal injection and production wells deployed in an isolated fault block in the Schrader Bluff reservoir. The EOR method combines polymer flooding and low salinity water flooding to improve recovery. Prior average water cut reduction in polymer EOR fields ordinarily ranges between 10% to 15% for most light oil and heavy oil reservoirs. When comparing other field applications, the long-lasting (24 months) and much lower water cut poses a challenge for numerical history matching when applying typical simulation methods. This abstract discusses two practical new approaches used for history matching of the long-lasting ultralow water cut. These new applications include 1) multiple relative permeability curves with J-function incorporation with low endpoints of relative permeability of water (Krw). This approach integrated the permeability differential adjustment in the geometries of horizontal and vertical directions based on geological review. 2) A specific permeability channel strips along with the horizontal or vertical planar assumption. The current history matching results indicate success in achieving an excellent agreement with the field observed low water-cut.
Namie, S.↗
A Survey of Some Current Research in Functional-differential Equations
Functional differential equation applications using geometric approach
DIFFERENTIAL EQUATION↗
Electron scattering by highly polar molecules. III - CsCl
Utilizing a crossed electron-beam-molecular-beam scattering geometry, relative values of differential electron scattering cross sections for cesium chloride at 5 and 20 eV electron impact energies and at scattering angles between 10 and 120 deg have been measured. These relative cross sections have been normalized to the cross section at 15 deg scattering angle calculated by the hybrid S-matrix technique. In the angular range between 0 and 10 deg and between 120 and 180 deg extrapolations have been made to obtain integral and momentum transfer cross sections. An energy-loss spectrum is also presented which gives various spectral features lying between the 4 and 10 eV regions in CsCl.
Vuskovic, L.↗
Algebraic grid generation
The numerical solution of partial differential equations about irregular geometries and with varying characteristic scales has created the need for coordinate systems and associated transformations which reflect both geometric and physical requirements. The process of finding coordinate transformations in discrete representations is called 'grid generation'. The present investigation is concerned with three algebraic grid generation methods. The methods include transfinite interpolation, the multisurface method, and the two-boundary technique. Interpolation formulas, in terms of homotopic mappings and constraints in terms of point positions and/or derivatives are the essential elements of the techniques. The methods are relatively simple to understand, they are explicit and do not require extensive computational effort, and they have a high degree of generality.
Smith, R. E.↗
Theory of idealized two-dimensional ballute in Newtonian hypersonic flow
A differential equation governing the geometry of a two-dimensional ballute in hypersonic flow and its constraining boundary conditions are derived under idealized assumptions. By solving these equations, the shape of the ballute is determined over a range of conditions. Lift, drag, pitching moment, and the allowed limit of center-of-gravity location for stability (meta-center) are then calculated using Newtonian hypersonic approximation. It is shown that the meta-center occurs near the forward end because of compliance of the ballute membrane to the shock layer pressures, especially at low free-stream densities. In order for the vehicle employing the ballute to be stable at all densities, the center of gravity must be within approximately the forward 20 percent of overall length of the vehicle. However, typical flight trajectories of an aeroassisted orbital transfer vehicle employing the ballute for aerobraking show that the vehicle may be able to complete its atmospheric flight without tumbling provided that the center of gravity is located within the forward 43 percent of the vehicle length because of the relatively short duration of flight through the destabilizing low-density regime.
Park, C.↗
Innovative design of composite structures: The use of curvilinear fiber format in structural design of composites
The influence is investigated of a curvilinear fiber format on load carrying capacity of a layered fiber reinforced plate with a centrally located hole. A curvilinear fiber format is descriptive of layers in a laminate having fibers which are aligned with the principal stress directions in those layers. Laminates of five curvilinear fiber format designs and four straightline fiber format designs are considered. A quasi-isotropic laminate having a straightline fiber format is used to define a baseline design for comparison with the other laminate designs. Four different plate geometries are considered and differentiated by two values of hole diameter/plate width equal to 1/6 and 1/3, and two values of plate length/plate width equal to 2 and 1. With the plates under uniaxial tensile loading on two opposing edges, alignment of fibers in the curvilinear layers with the principal stress directions is determined analytically by an iteration procedure. In-plane tensile load capacity is computed for all of the laminate designs using a finite element analysis method. A maximum strain failure criterion and the Tsai-Wu failure criterion are applied to determine failure loads and failure modes. Resistance to buckling of the laminate designs to uniaxial compressive loading is analyzed using the commercial code Engineering Analysis Language. Results indicate that the curvilinear fiber format laminates have higher in-plane tensile load capacity and comparable buckling resistance relative to the straightline fiber format laminates.
Charette, R. F.↗
Aerodynamic and Aerothermal Simulations of Mars Concept Vehicles Using Overset DPLR
NASA's Descent System Studies (DSS) Program is studying various concept vehicles to enable landing of heavy payloads on the surface of Mars. While it is desirable to run high-fidelity CFD simulations to accurately assess the aerodynamic and aerothermal effects of various design changes during EDL, it is usually difficult to quickly generate high-quality grids suitable for such analyses. One approach to address this bottleneck in mesh generation is through the use oversetting grids. Although the overset approach is efficient and powerful in solving partial differential equations on complex geometries, new users often find it challenging to apply overset concepts for their simulations. For example, generating hyperbolic grids with sufficient overlap; priority in hole-cutting on multiple overlapping grids; and fixes to assemble overlapping viscous grids at the body surface. The objective of this presentation is to introduce a simple process that combines the advantages of near-body, point-matched, structured grids with oversetting background grids suitable for grid alignment. This approach allows for grids that can be sequenced, reclustering of mesh spacing at the wall, and grid alignment with the bow shock. The current methodology is tested on a Mid-L/D configuration using the overset DPLR code.
Overset Grids↗