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Vector bundles of rank 2 on the projective line over ℤ are considered. It is assumed that such a bundle E is trivial on a generic fiber, and its restriction to any special fiber is isomorphic either to O{sup 2} or to O(−1)⊕O(1). Under these assumptions it is proved that an exact sequence of the form 0→O(−2) → E →O(2) → 0 exists.
First-principles density functional theory (DFT) calculations for the electronic structure problem require a solution of the Kohn–Sham equation, which requires one to solve a nonlinear eigenvalue problem. Solving the eigenvalue problem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshev-filtered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors and results in a significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original formulation of the CheFSI method utilizes a sparse iterative diagonalization at the first SCF step to provide initial vectors for subspace filtering at latter SCF steps. This diagonalization is expensive for large scale problems. We develop a new initial filtering step to avoid completely this diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps. Our new approach saves memory usage and can be two to three times faster than the original CheFSI method.
Considering a 3 + 1 dimensional lattice quantum chromodynamics (QCD) model defined with the improved Wilson action, three flavors, and 4 × 4 Dirac spin matrices, in the strong coupling regime, we reanalyze the question of the existence of the eightfold way baryons and complete our previous work where the existence of isospin octet baryons was rigorously solved. Here, we show the existence of isospin decuplet baryons which are associated with isolated dispersion curves in the subspace of the underlying quantum mechanical Hilbert space with vectors constructed with an odd number of fermion and antifermion basic quark and antiquark fields. Moreover, smoothness properties for these curves are obtained. The present work deals with a case for which the traditional method to solve the implicit equation for the dispersion curves, based on the use of the analytic implicit function theorem, cannot be applied. We do not have only one but two solutions for each one-baryon decuplet sector with fixed spin third component. Instead, we apply the Weierstrass preparation theorem, which also provides a general method for the general degenerate case. This work is completed by analyzing a spectral representation for the two-baryon correlations and providing the leading behaviors of the field strength normalization and the mass of the spectral contributions with more than one-particle. These are needed results for a rigorous analysis of the two-baryon and meson-baryon particle spectra.
In this work, we discuss the relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that the criterion for studying the violation of Lorentz symmetry is preserving the gauge symmetry. -- Highlights: •Two new possible scenarios of studying Lorentz symmetry breaking effects. •Coulomb-like potential induced by the Lorentz symmetry breaking effects. •Relativistic Landau–He–McKellar–Wilkens quantization. •Exact solutions of the Dirac equation.
Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in configuration space. The immense computational cost of evolving high-dimensional variables, and their large number of degrees of freedom, often limits the utility of continuum kinetic simulations and presents a challenge when it comes to accurately simulating real-world physical phenomena. To address this challenge, we present techniques that accelerate and minimize the computational work required for a scalable Vlasov-Poisson solver. We show theoretical hardware compute and communication bounds for solving a fourth-order finite-volume Vlasov-Poisson system. These bounds are then used to inform and evaluate the design of performance portable algorithms for a multiple graphics processing unit (GPU) accelerated version of the Vlasov-Poisson solver VCK-CPU [1]. We demonstrate that the multi-GPU Vlasov solver implementation, VCK-GPU, simultaneously minimizes required inter-process data transfer while also being bounded by the machine network performance limits. This results in an overall strong scaling speedup per timestep of up to 40x in three-dimensional phase space (one position, two velocity coordinates) and 54x in four dimensional phase space (two position, two velocity coordinates) and a 341x increase in simulation throughput of the GPU accelerated code over the existing CPU code. The GPU code is also able to weak scale up to 256 compute nodes and 1024 GPUs. In conclusion, we demonstrate that the improved compute performance enables exploring configurations which were previously computationally infeasible, including resolving fine-scale distribution function filamentation and multi-species dynamics with realistic electron-proton mass ratios.
In this article, we treat G{sub 2}-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G{sub 2}-structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G{sub 2}-structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry.
Properties of magnetic loop antennas for exciting electron whistler modes have been investigated in a large laboratory plasma. The parameter regime is that of large plasma frequency compared to the cyclotron frequency and signal frequency below half the cyclotron frequency. The antenna diameter is smaller than the wavelength. Different directions of the loop antenna relative to the background magnetic field have been measured for small amplitude waves. The differences in the topology of the wave magnetic field are shown from measurements of the three field components in three spatial directions. The helicity of the wave magnetic field and of the hodogram of the magnetic vector in space and time are clarified. The superposition of wave fields is used to investigate the properties of two antennas for small amplitude waves. Standing whistler waves are produced by propagating two wave packets in opposite directions. Directional radiation is obtained with two phased loops separated by a quarter wavelength. Rotating antenna fields, produced with phased orthogonal loops at the same location, do not produce directionality. The concept of superposition is extended in a Paper II to generate antenna arrays for whistlers. These produce nearly plane waves, whose propagation angle can be varied by the phase shifting the currents in the array elements. Focusing of whistlers is possible. These results are important for designing antennas on spacecraft or diagnosing and heating of laboratory plasmas.
In two-dimensional artificial crystals with large real-space periodicity, the nonlinear current response to a large applied electric field can feature a strong angular dependence, which encodes information about the band dispersion and Berry curvature of isolated electronic Bloch minibands. Within the relaxation-time approximation, we obtain analytic expressions up to infinite order in the driving field for the current in a band-projected theory with time-reversal and trigonal symmetry. For a fixed field strength, the dependence of the current on the direction of the applied field is given by rose curves whose petal structure is symmetry constrained and is obtained from an expansion in real-space translation vectors. We illustrate our theory with calculations on periodically buckled graphene and twisted double bilayer graphene, wherein the discussed physics can be accessed at experimentally relevant field strengths.
The concept of a Fermi surface, the constant-energy surface containing all the occupied electron states in momentum, or wave-vector (k), space plays a key role in determining electronic properties of conductors. In two-dimensional (2D) carrier systems, the Fermi surface becomes a contour which, in the simplest case, encircles the occupied states. In this case, the area enclosed by the contour, which we refer to as the Fermi sea (FS), is a simple disk. In this work, we report the observation of an FS with a new topology, namely, an FS in the shape of an annulus. Such an FS is expected in a variety of 2D systems where the energy band dispersion supports a ring of extrema at finite k, but its experimental observation has been elusive. Our study provides (1) theoretical evidence for the presence of an annular FS in 2D hole systems confined to wide GaAs quantum wells and (2) experimental signatures of the onset of its occupation as an abrupt rise in the sample resistance, accompanied by a sudden appearance of Shubnikov–de Haas oscillations at an unexpectedly high frequency whose value does not simply correspond to the (negligible) density of holes contained within the annular FS.
A true understanding of the properties of pnictide superconductors requires the development of high-quality materials and performing measurements designed to unravel their intrinsic properties and short-range nematic correlations which are often obscured by extrinsic effects such as poor crystallinity, inhomogeneity, domain formation, and twinning. Here, in this paper, we report the systematic growth of high-quality Na-substituted BaFe 2 As 2 single crystals and their characterization using pulsed magnetic fields x-ray diffraction and x-ray diffuse scattering. Analysis of the properties and compositions of the highest-quality crystals shows that their actual Na stoichiometry is about 50-60% of the nominal content and that the targeted production of crystals with specific compositions is accessible. We derived a reliable equation to estimate the Na stoichiometry based on the measured superconducting T c of these materials. Attempting to force spin reorientation and induce tetragonality, orthorhombic Ba 1-x Na x Fe 2 As 2 single crystals subjected to out-of-plane magnetic fields up to 31.4T are found to exhibit strong in-plane magnetic anisotropy demonstrated by the insufficiency of such high fields in manipulating the relative population of their twinned domains or in suppressing the orthorhombic order. Broad x-ray diffuse-intensity rods observed at temperatures between 30 and 300 K uncover short-range structural correlations. Local structure modeling together with 3D-Δ pair-distribution function mapping of real-space interatomic vectors show that the diffuse scattering arises from in-plane short-range chemical correlations of the Ba and Na atoms coupled with short-range atomic displacements within the same plane due to an effective size difference between the two atomic species.
This paper studies a dual inverter supplied by a DC-link and a floating capacitor (FC), emerged as a promising inverter topology for motor drive applications. For this type of inverter, the voltage ratio between the DC-link and the FC can be actively controlled. This ratio design is crucial as it essentially defines both the DC-link voltage utilization and the inverter output quality. Several voltage ratios have previously been discussed to enhance the dual inverter performance, but only one aspect, either the voltage utilization or the output quality, is investigated. As a result, although one performance aspect can be improved, the other aspect has been adversely affected. In this work, a comparative study considering both aspects is carried out for all the possible voltage ratios. Based on this analysis, the optimal ratios for different inverter modulation indices are identified. This is followed by proposing a ratio selection strategy to double the voltage utilization without degrading the output quality. Furthermore, this strategy enables an electric drive to work at a higher maximum speed without flux weakening for a given DC-link voltage. The claimed advantages have been proved by experimental tests on an open-end windings induction motor drive.
The steady states of cells affect their response to perturbation. Indeed, diagnostic markers for predicting the response to therapeutic perturbation are often based on steady state measurements. In spite of this, no method exists to systematically characterize the relationship between steady state and response. Mathematical models are established tools for studying cellular responses, but characterizing their relationship to the steady state requires that it have a parametric, or analytical, expression. For some models, this expression can be derived by the King-Altman method. However, King-Altman requires that no substrate act as an enzyme, and is therefore not applicable to most models of signal transduction. For this reason we developed py-substitution, a simple but general method for deriving analytical expressions for the steady states of mass action models. Where the King-Altman method is applicable, we show that py-substitution yields an equivalent expression, and at comparable efficiency. We use py-substitution to study the relationship between steady state and sensitivity to the anti-cancer drug candidate, dulanermin (recombinant human TRAIL). First, we use py-substitution to derive an analytical expression for the steady state of a published model of TRAIL-induced apoptosis. Next, we show that the amount of TRAIL required for cell death is sensitive to the steady state concentrations of procaspase 8 and its negative regulator, Bar, but not the other procaspase molecules. This suggests that activation of caspase 8 is a critical point in the death decision process. Finally, we show that changes in the threshold at which TRAIL results in cell death is not always equivalent to changes in the time of death, as is commonly assumed. Our work demonstrates that an analytical expression is a powerful tool for identifying steady state determinants of the cellular response to perturbation.
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This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.
Thrifty Array Foram (TAF) files store numeric data in a binary format, minimizing storage requirements while preserving quick read access. Real data of any size and dimensionality can be stored in this format at varying degrees of numeric precision. Implicit array are associated with each dimension, eliminating the need to explicitly store uniformly-spaced grid vectors. Unlimited text comments may be included with the array for user documentation, and every file begins with a text synopsis of the binary structure. The format is deliberately designed for memory mapping, where portions of the array can be read without loading the entire file at once.
We discuss boundary-value problems for the system of equations of the spatial theory of elasticity in the class of double-periodic functions and obtain a general solution of the system. We distinguish six types of elementary Floquet waves and examine their energy characteristics. We consider fundamental boundary-value problems in the half-space in the vector form. The diffraction problem for an elastic wave on a periodic system of defects in the vector form is reduced to the paired summator functional equation.
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
We recently presented an algorithm for state-averaged complete active space self-consistent field (SA-CASSCF) orbital optimization that capitalizes on sparsity in the atomic orbital basis set to reduce the scaling of computational effort with respect to molecular size. Here, we extend those algorithms to calculate the analytic gradient and nonadiabatic coupling vectors for SA-CASSCF. Combining the low computational scaling with acceleration from graphical processing units allows us to perform SA-CASSCF geometry optimizations for molecules with more than 1000 atoms. The new approach will make minimal energy conical intersection searches and nonadiabatic dynamics routine for molecular systems with O(10{sup 2}) atoms.