Multi-dimensional summation-by-parts operators for general function spaces: Theory and construction
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Atomic-Level Understanding of Surface Reconstruction Based on Li[Ni x Mn y Co 1–x–y ]O 2 Single-Crystal Studies
The stability of cathode particle surfaces that are directly exposed to the electrolyte is one of the most crucial and determining factors for cathode performance at high operating voltages. Theory has predicted a strong dependence of surface stability on chemical compositions as well as surface facets of layered oxides, yet conflicting results on the correlations exist as most experimental studies focus on cycled secondary particles recovered from composite electrodes. Here, we synthesize well-formed Li[Ni x Mn y Co 1–x–y ]O 2 (NMC) single-crystal samples, carefully define pristine surface properties, and then monitor their evolution with cycling. Atomic-resolution scanning transmission electron microscopy (STEM) imaging and electron energy loss spectroscopy (EELS) analysis show the formation of a surface reconstruction layer (SRL) as well as an extended surface reduction layer on pristine, Li-permeable non-(001) surfaces, even before cycling. We reveal a transition region with chemical gradient, in which the layered structure gradually densifies and eventually transforms into the SRL on the top surface. Contrary to these observations, no SRL is observed on pristine, Li-impermeable (001) surfaces, revealing the facet-dependent nature of surface reconstructions during particle synthesis. Upon electrochemical cycling, significant composition-and facet-dependent SRL growth is observed. The driving force and mechanism for surface reconstruction are further discussed. The present study provides insights into the origin as well as the nature of SRLs, highlighting the significance of surface engineering in cathode material optimization.
25 ENERGY STORAGE↗
Methods of high current magnetic field generator for transcranial magnetic stimulation application
This paper describes the design procedures and underlying concepts of a novel High Current Magnetic Field Generator (HCMFG) with adjustable pulse width for transcranial magnetic stimulation applications. This is achieved by utilizing two different switching devices, the MOSFET and insulated gate bipolar transistor (IGBT). Results indicate that currents as high as ±1200 A can be generated with inputs of +/−20 V. Special attention to tradeoffs between field generators utilizing IGBT circuits (HCMFG{sub 1}) and MOSFET circuits (HCMFG{sub 2}) was considered. The theory of operation, design, experimental results, and electronic setup are presented and analyzed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
High-resolution vacuum-ultraviolet photoabsorption spectra of 1-butyne and 2-butyne
The absolute photoabsorption cross sections of 1- and 2-butyne have been recorded at high resolution by using the vacuum-ultraviolet Fourier-Transform spectrometer at the SOLEIL Synchrotron. Both spectra show more resolved structure than previously observed, especially in the case of 2-butyne. In this work, we assess the potential importance of Rydberg states with higher values of orbital angular momentum, l, than are typically observed in photoabsorption experiments from ground state molecules. We show how the character of the highest occupied molecular orbitals in 1- and 2-butyne suggests the potential importance of transitions to such high-l (l = 3 and 4) Rydberg states. Furthermore, we use theoretical calculations of the partial wave composition of the absorption cross section just above the ionization threshold and the principle of continuity of oscillator strength through an ionization threshold to support this conclusion. The new absolute photoabsorption cross sections are discussed in light of these arguments, and the results are consistent with the expectations. This type of argument should be valuable for assessing the potential importance of different Rydberg series when sufficiently accurate direct quantum chemical calculations are difficult, for example, in the n ≥ 5 manifolds of excited states of larger molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Output power of a quantum dot laser: Effects of excited states
A theory of operating characteristics of quantum dot (QD) lasers is discussed in the presence of excited states in QDs. We consider three possible situations for lasing: (i) ground-state lasing only; (ii) ground-state lasing at first and then the onset of also excited-state lasing with increasing injection current; (iii) excited-state lasing only. The following characteristics are studied: occupancies of the ground-state and excited-state in QDs, free carrier density in the optical confinement layer, threshold currents for ground- and excited-state lasing, densities of photons emitted via ground- and excited-state stimulated transitions, output power, internal and external differential quantum efficiencies. Under the conditions of ground-state lasing only, the output power saturates with injection current. Under the conditions of both ground- and excited-state lasing, the output power of ground-state lasing remains pinned above the excited-state lasing threshold while the power of excited-state lasing increases. There is a kink in the light-current curve at the excited-state lasing threshold. The case of excited-state lasing only is qualitatively similar to that for single-state QDs—the role of ground-state transitions is simply reduced to increasing the threshold current.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
General expressions and physical origin of the coupling coefficient of arbitrary tuned coupled electromagnetic resonators
The theory and operation of various devices and systems, such as wireless power transfer via magnetic resonant coupling, magneto-inductive wave devices, magnetic resonance spectroscopy probes, and metamaterials can rely on coupled tuned resonators. The coupling strength is usually expressed in terms of the coupling coefficient κ, which can have electrical κ{sub E} and/or magnetic κ{sub M} components. In the current article, general expressions of κ are derived. The relation between the complex Poynting equation in its microscopic form and κ is made and discussed in detail. It is shown that κ can be expressed in terms of the interaction energy between the resonators' modes. It thus provides a general form that combines the magnetic and electric components of κ. The expressions make it possible to estimate the frequencies and fields of the coupled modes for arbitrarily oriented and spaced resonators. Thus, enabling the calculation of system specific parameters such as the transfer efficiency of wireless power transfer systems, resonator efficiency for electron spin resonance probes, and dispersion relations of magneto-inductive and stereo-metamaterials structures.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Electron parallel closures for various ion charge numbers
Electron parallel closures for the ion charge number Z = 1 [J.-Y. Ji and E. D. Held, Phys. Plasmas 21, 122116 (2014)] are extended for 1 ≤ Z ≤ 10. Parameters are then computed for various Z with the same form of the Z = 1 kernels adopted. The parameters are smoothly varying in Z and hence can be used to interpolate parameters and closures for noninteger, effective ion charge numbers.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Ionic versus metallic bonding in Al n Na m and Al n Mg m (m ≤ 3, n + m ≤ 15) clusters
First principles electronic structure studies on the ground state geometries, stability, and the electronic structure of Al n Na m and Al n Mg m (m ≤ 3, n + m ≤ 15) clusters have been carried out to examine the nature of bonding between Na or Mg and Al. Identifying whether the bonding is ionic or metallic in bulk materials is typically straightforward; however, in small clusters where quantum confinement is important, the nature of bonding may become unclear. Here, we have performed a critical analysis of the bonding in these bimetallic clusters using charge analysis, electrical dipole moments, hybridization of the atomic orbitals, the Laplacian of the charge density at the bond critical points, and the change in the bonding energy between neutral and anionic forms of the cluster. For Na n Al m clusters, we find that the Na binding is primarily ionic, while the bonding in Al n Mg m is primarily metallic. We find that the Mulliken population of the 3 p orbital of Na and Mg can provide a rapid assessment of the nature of bonding. We also find that the Hirshfeld charge and dipole moments are effective indicators, when placed in context. We found that the Laplacian of the charge density at the bond critical points can be misleading in identifying whether the bonding is ionic or metallic in small clusters.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Two species drag/diffusion model for energetic particle driven modes
A nonlinear bump-on-tail model for the growth and saturation of energetic particle driven plasma waves has been extended to include two populations of fast particles—one dominated by dynamical friction at the resonance and the other by velocity space diffusion. The resulting temporal evolution of the wave amplitude and frequency depends on the relative weight of the two populations. The two species model is applied to burning plasma with drag-dominated alpha particles and diffusion-dominated ICRH accelerated minority ions, showing the stabilization of bursting modes. Further, the model also suggests an explanation for the recent observations on the TJ-II stellarator, where Alfvén Eigenmodes transition between steady state and bursting as the magnetic configuration varied.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Properties of coupled-cluster equations originating in excitation sub-algebras
In this paper we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of nilpotent sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending concepts behind actives-spaces and seniority numbers to provide more accurate description of electron correlation effects. Moreover, new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for though cases defined by the presence of strong static and dynamic correlation effects. We will also explore invariance properties associated with the nilpotent sub-algebras to define a new class of CC approximations referred in this paper to as the nilpotent-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.
Kowalski, Karol↗
Electron parallel closures for the 3 + 1 fluid model
Linear closures are obtained for arbitrary collisionality for the 3 + 1 fluid model which includes the evolution of density, flow velocity, and pressure both parallel and perpendicular to a preferred direction, usually a magnetic field. A large set of 6400 moment equations is solved to provide closures that are accurate in the collisional regime and well into the collisionless regime. The closures in the collisionless limit are determined by solving the kinetic equation with a model collision operator. Simple fits for the kernel functions that define the closures are obtained for arbitrary collisionality in wave number space. The results are linearly accurate to within 3% across the entire range of collisionality.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation
We present a modified approach for simulating electronically nonadiabatic dynamics based on the Nakajima-Zwanzig generalized quantum master equation (GQME). The modified approach utilizes the fact that the Nakajima-Zwanzig formalism does not require casting the overall Hamiltonian in system-bath form, which is arguably neither natural nor convenient in the case of the Hamiltonian that governs nonadiabatic dynamics. Within the modified approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density operator is fully captured by a memory kernel super-operator. A methodology for calculating the memory kernel from projection-free inputs is developed. Simulating the electronic dynamics via the modified approach, with a memory kernel obtained using exact or approximate methods, can be more cost effective and/or lead to more accurate results than direct application of those methods. The modified approach is compared to previously proposed GQME-based approaches, and its robustness and accuracy are demonstrated on a benchmark spin-boson model with a memory kernel which is calculated within the Ehrenfest method.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The microscopic Einstein-de Haas effect
The Einstein-de Haas (EdH) effect, where the spin angular momentum of electrons is transferred to the mechanical angular momentum of atoms, was established experimentally in 1915. While a semiclassical explanation of the effect exists, modern electronic structure methods have not yet been applied to model the phenomenon. In this paper, we investigate its microscopic origins by means of a noncollinear tight-binding model of an O2 dimer, which includes the effects of spin-orbit coupling, coupling to an external magnetic field, and vector Stoner exchange. By varying an external magnetic field in the presence of spin-orbit coupling, a torque can be generated on the dimer, validating the presence of the EdH effect. The avoided energy level crossings and the rate of change of magnetic field determine the evolution of the spin. We also find that the torque exerted on the nuclei by the electrons in a time-varying B field is not only due to the EdH effect. In conclusion, the other contributions arise from field-induced changes in the electronic orbital angular momentum and from the direct action of the Faraday electric field associated with the time-varying magnetic field.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Combining the mapping Hamiltonian linearized semiclassical approach with the generalized quantum master equation to simulate electronically nonadiabatic molecular dynamics
The generalized quantum master equation (GQME) provides a powerful framework for simulating electronically nonadiabatic molecular dynamics. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. In this paper, we consider two different procedures for calculating the memory kernel of the GQME from projection-free inputs obtained via the combination of the mapping Hamiltonian (MH) approach and the linearized semiclassical (LSC) approximation. Here, the accuracy and feasibility of the two procedures are demonstrated on the spin-boson model. We find that although simulating the electronic dynamics by direct application of the two LSC-based procedures leads to qualitatively different results that become increasingly less accurate with increasing time, restricting their use to calculating the memory kernel leads to an accurate description of the electronic dynamics. Comparison with a previously proposed procedure for calculating the memory kernel via the Ehrenfest method reveals that MH/LSC methods produce memory kernels that are better behaved at long times and lead to more accurate electronic dynamics
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Anti-symmetric representation of the extended magnetohydrodynamic equations
We introduce the anti-symmetric representation of the extended magnetohydrodynamic (MHD) equations. In this representation, the use of the anti-symmetric flux operator (∇·ν+ν·∇) results in conservation theorems with discrete analogs. Inherently robust numerical applications are achieved with little effort, and conservation to machine precision is possible with simple numerical schemes. Starting from the two-fluid equations, we construct a single-fluid MHD model based on generalized center-of-mass variables for the mass (√ρ), momentum (√ρν), and pressure (√ p ). This model is shown to possess identical conservation properties to the two-fluid system, with the only restriction being the use of a single temperature. Common approximations to the Braginskii heat fluxes and to the gyroviscous stress tensor are cast into our representation for convenience. The discrete conservation properties are verified using the classic Orszag–Tang vortex problem. In addition to the favorable mass, momentum, and energy conservation properties, the time reversibility of the simulations is demonstrated.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Charge-state independent anomalous transport for a wide range of different impurity species observed at Wendelstein 7-X
Here, the plasma volume averaged impurity confinement of selected charge states and impurity species has been characterized for the Stellarator Wendelstein 7-X (W7-X), covering a wide range of atomic charges (Z = 12–44) and atomic masses (M = 28–184). A comparison of the experimental findings to theoretical neoclassical and turbulent transport expectations suggests, aside from/in addition to the neoclassical transport, an additional significant anomalous transport mechanism, which is not inconsistent with the predictions of a turbulence dominated impurity transport and is in agreement with the experimental results from recent transport studies based on the direct measurements of impurity diffusion profiles, performed at W7-X.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A comprehensive conductivity model for drift and micro-tearing modes
The parallel electrical conductivity is a crucial parameter in the study of the linear stability of drift-modes like the micro-tearing mode (MTM). The conductivity enters by closing the electromagnetic tearing layer equations. Recent progress in the understanding of the pedestal suggests that the MTM could play an important role in its structure and evolution. For this reason, we revisit and improve previous model conductivities. This parameter is generally derived from the linearized drift kinetic equation. In the past literature, it has been computed using either simplified collision operators or neglecting the spatial dependence away from the rational surface. Here, a fully consistent expression for the conductivity that would accurately model the pedestal has not been available. By applying a novel variational procedure and with the full Fokker Plank collision operator, including electron–electron collisions, we compute a closed expression for the parallel electrical conductivity in the form of a rational function.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗