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At least 19 records

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Collinear ferromagnetism with reduced moment length in kagome magnet Nd 3 ⁢Ru 4 ⁢Al 12

Here, we determine the magnetic ground state of the kagome lattice magnet Nd 3 ⁢Ru 4⁢ Al 12 by single-crystal neutron diffraction, supported by experiments with polarized neutrons. We identify this material as a collinear ferromagnet (“hex-FM”) with uniform moment length and ordering vector 𝑸 = 0, in contrast to a previous, seminal report that proposed unequal moment lengths on two Nd sites, here called the “ortho-FM” state. Our analysis of the flipping ratio in polarized neutron scattering is consistent with the hex-FM state. The results provide a microscopic basis for understanding the large fluctuation-induced Hall and Nernst responses near 𝑇 C ≈ 41K, as previously reported for Nd 3 ⁢Ru 4 ⁢Al 12 .

RKKY interaction↗

Correlation between complex spin textures and the magnetocaloric and Hall effects in Eu⁢(Ga 1−𝑥 ⁢Al 𝑥 ) 4 (𝑥=0.9, 1)

Determining the electronic phase diagram of a quantum material as a function of temperature (𝑇) and applied magnetic field (𝐻) forms the basis for understanding the microscopic origin of transport properties, such as the anomalous Hall effect (AHE) and topological Hall effect (THE). For many magnetic quantum materials, including Eu⁢Al 4 , a THE arises from a topologically protected magnetic skyrmion lattice with a nonzero scalar spin chirality. We identified a square skyrmion lattice (sSkL) peak in Eu⁢(Ga 1−𝑥 ⁢Al 𝑥 ) 4 (𝑥=0.9) identical to the peak previously observed in Eu⁢Al 4 by performing neutron-scattering measurements throughout the phase diagram. Here, comparing these neutron results with transport measurements, we found that in both compounds the maximal THE does not correspond to the sSkL area. Instead of the maximal THE, the maximal magnetocaloric-effect boundaries better identify the sSkL lattice phase observed by neutron-scattering measurements. The maximal THE therefore arises from interactions of itinerant electrons with frustrated spin fluctuations in a topologically trivial magnetic state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

On the Onset of Plasticity: Determination of Strength and Ductility

The analysis of the work hardening variation with stress reveals insight to operative stress-strain mechanisms in material systems. The onset of plasticity can be assessed and related to ensuing plastic deformation up to the structural instability using one constitutive relationship that incorporates both behaviors of rapid work hardening (Stage 3) and the asymptotic leveling of stress (Stage 4). Results are presented for the mechanical behavior analysis of Ti-6Al-4V wherein the work hardening variation of Stages 3 and 4 are found to: be dependent through a constitutive relationship; be useful in a Hall-Petch formulation of yield strength; and provide the basis for a two point-slope fit method to model the experimental work hardening and stress-strain behavior.

36 MATERIALS SCIENCE↗

Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. Finally, this manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The IEA Wind Task 49 Reference Floating Wind Array Design Basis

International Energy Agency Wind Technology Collaboration Programme (IEA Wind) Task 49 on Integrated Design of Floating Wind Arrays is an international collaboration aiming to advance the development of large-scale floating wind farms by providing open-access resources to the research and development and planning communities. The work of Task 49 focuses on array-level challenges related to the colocation of many floating wind turbines; their layouts, mooring systems, and cabling systems; failure risks; logistical considerations; marine spatial planning needs; and future research needs and innovation directions. This report provides a general design basis for the development of reference floating wind farm designs. These reference array designs will extend the scope of existing reference floating wind turbine designs to facilitate research on array-level floating wind technology challenges and innovations. The design basis promotes coordination and consistency in developing the reference array designs.

17 WIND ENERGY↗

Spin reorientations in structurally metastable, disordered, and hexagonal Cr 7 ⁢Te 8

Vapor deposited two-dimensional Cr 7 ⁢Te 8 displays unusual temperature dependent Hall effect properties, including a room-temperature anomalous Hall effect, sign reversals of the Hall resistivity on cooling, and a peak in the Hall resistivity at low temperatures. The two-dimensional Cr 7⁢ Te 8 heterostructures that form the basis of these measurements are hexagonal in structure. We study the magnetic and structural properties of bulk Cr 7 ⁢Te 8 synthesized by quenching from 1000⁢°C with the goal of relating the magnetic, structural, and electronic properties. This quenched phase is metastable, hexagonal, and displays different magnetic properties from the slow-cooled and more thermodynamically stable monoclinic phase. High-resolution x-ray diffraction of the quenched hexagonal phase finds a first-order transition to a lower symmetry monoclinic phase on heating above ∼550 K. Magnetic susceptibility measurements of the quenched hexagonal phase reveal ferromagnetic ordering above room temperature, along with the two distinct transitions at ∼220 K and ∼70 K. Through neutron diffraction studies, we find the ∼220 K anomaly is a spin reorientation transition of the ferromagnetically aligned magnetic moments and the ∼70K feature represents a transition from a high-temperature ferromagnet to a low-temperature antiferromagnet. We suggest that these magnetic transitions are related to changes in the unit-cell dimensions and are connected to the temperature-dependent Hall resisitivity studied in two-dimensional heterostructures. This implies a link between structural, magnetic, and electronic properties in the “pseudo” two-dimensional chromium tellurides.

Chemical synthesis↗

Frequency-domain modeling of floating wind arrays with shared mooring lines

A frequency-domain model for floating wind turbine dynamics has been extended to model floating wind farms with couplings from shared mooring systems. The model, called RAFT, could previously calculate the mean offsets and wave-induced response spectra for single floating wind turbines. Now, the model supports multiple floating wind turbines, each with their own properties and responses, along with mooring lines that run directly between floating wind turbines in the array, meaning that shared mooring lines or fully suspended dynamic power cables can be included. This capability is achieved by setting up an array-level solution of the system mean offsets and assembling the full system matrices for solving the dynamic response. The quasi-static mooring model MoorPy is used to linearize the mooring system properties. To compute the floating wind turbine relative motions, phase offsets are applied to each turbine's response as a function of wave frequency based on the wavelength and relative positions in the array. These differential motions are then applied to mooring system tension Jacobians to compute the tension loads in the shared mooring lines. Overall, the capability provides a frequency-domain analog to the modeling capabilities of the floating support structure in FAST.Farm. Mean offsets and power spectral density plots of responses are compared between RAFT and FAST.Farm to verify the implementation. The results indicate good agreement within the expectations of a frequency-domain modeling approach and suggest correct implementation of the shared mooring aspects. Additionally, a unique comb-like frequency response in the shared mooring line tensions has been observed. This phenomenon has a clear physical basis and may be an important design consideration for future shared mooring systems.

17 WIND ENERGY↗

Exact Landau Level Description of Geometry and Interaction in a Flatband

Flatbands appear in many condensed matter systems, including the two-dimensional electron gas in a high magnetic field, correlated materials, and moiré heterostructures. They are characterized by intrinsic geometric properties such as the Berry curvature and Fubini-Study metric. The influence of the band geometry on electron-electron interaction is difficult to understand analytically because the geometry is in general nonuniform in momentum space. In this work, we study the topological flatband of Chern number C = 1 with a momentum-dependent but positive definite Berry curvature that fluctuates in sync with Fubini-Study metric. We derive an exact correspondence between such ideal flatbands and Landau levels and show that the band geometry fluctuation gives rise to a new type of interaction in the corresponding Landau levels that depends on the center of mass of two particles. We characterize such interactions by generalizing the usual Haldane pseudopotentials. This mapping gives exact zero-energy ground states for short-ranged repulsive generalized pseudopotentials in flatbands, in analogy to fractional quantum Hall systems. Driving the center-of-mass interactions beyond the repulsive regime leads to a dramatic reconstruction of the ground states towards gapless phases. The generalized pseudopotential could be a useful basis for future numerical studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electronic hydrodynamics in graphene

Highlights: Electrons in ultra-clean graphene at high enough temperatures behave hydrodynamically. Unconventional hydrodynamics in graphene can be derived from the kinetic theory. Kinetic coefficients include the quantum conductivity and shear and Hall viscosities. -- Abstract: In this paper I report a pedagogical derivation of the unconventional electronic hydrodynamics in graphene on the basis of the kinetic theory. While formally valid in the weak coupling limit, this approach allows one to derive the unconventional hydrodynamics in the system which is neither Galilean- nor Lorentz-invariant, such that hydrodynamic equations cannot be inferred from symmetry arguments. I generalize earlier work to include external magnetic fields and give explicit expressions for dissipative coefficients, the shear viscosity and electrical conductivity. I also compare the resulting theory with relativistic hydrodynamics.

79 ASTRONOMY AND ASTROPHYSICS↗

First CLAS12 Double-Pion (Npp) Electroproduction Analysis

The N* program aims to explore strong interaction dynamics of the three-valence quark distance-dependent structure. The electroproduction and photoproduction studies provide insight into the nucleon resonance structure. One of the primary objectives of N* is to extract the electroexcitation amplitudes, which are crucial in determining the inner structure of various nucleon excitation states and their underlying degrees of freedom. Studying them on the nucleon length scale reveals also parts of the complex nature of the universe and its origin at their most fundamental level. The extraction of these amplitudes is mostly based on the single-pion, and particularly at higher invariant masses W, on the double-pion electroproduction channels, because nucleon resonance dominantly couple to them. CLAS has produced mostly all of the world data on charged double-pion electroproduction in the nucleon resonance region for photon virtualities Q2 up to 5 GeV2. The kinematic range can be extended with CLAS12, which can explore these amplitudes in the still almost unexplored range of Q2 > 5.0 GeV2. This will offer opportunities to understand the resonance structure at distances where the three-bound quark degree of freedom dominates and pave the way towards perturbative Quantum Chromodynamics (pQCD). This dissertation presents new double-pion electroproduction cross sections in the W range [1.4, 2.10] GeV and the Q2 range [2.0, 8.0] GeV2, using the Run Group A Fall-2018 dataset. This data was taken with the CLAS12 detector in Hall B at Thomas Jefferson National Laboratory (JLab) at an electron beam energy of 10.6 GeV. These cross sections are the basis for the extraction of resonance electroexcitation amplitudes using the phenomenological JLab- Moscow State University (JM) model.

Neupane, Krishna↗

Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures

We highlight recent advances in the theory, materials fabrication, and experimental characterization of strongly correlated and topological states in [111] oriented transition metal oxide thin films and heterostructures, which are notoriously difficult to realize compared to their [001] oriented counterparts. We focus on two classes of complex oxides, with the chemical formulas ABO 3 and A 2 B 2 O 7 , where the B sites are occupied by an open-shell transition metal ion with a local moment and the A sites are typically a rare earth element. The [111] oriented quasi-two-dimensional lattices derived from these parent compound lattices can exhibit peculiar geometries and symmetries, namely, a buckled honeycomb lattice, as well as kagome and triangular lattices. These lattice motifs form the basis for emergent strongly correlated and topological states expressed in exotic magnetism, various forms of orbital ordering, topological insulators, topological semimetals, quantum anomalous Hall insulators, and quantum spin liquids. For transition metal ions with high atomic number, spin–orbit coupling plays a significant role and may give rise to additional topological features in the electronic band structure and in the spectrum of magnetic excitations. We conclude this perspective by articulating open challenges and opportunities in this actively developing field.

36 MATERIALS SCIENCE↗

A new and alternative look at nonlinear Alfvénic states

The formulation for studying nonlinear Alfvenic states, sustainable in Hall Magnetohydrodynamics (HMHD), becomes considerably simpler and more tractable when circularly polarized Beltrami vectors (the eigenstates of linear HMHD) are used as the basis functions. Nonlinear HMHD is, then, reduced to a rather simple looking set of scalar equations from which a model problem of three interacting Beltrami modes is formulated and analytically solved. The triplet interactions span a variety of familiar nonlinear processes leading to a redistribution as well as periodic exchange of energy. The energy exchange processes (whose strength is measured by an energy exchange/depletion time) will, perhaps, play a dominant role in determining the spectral content of an eventual Alfvenic state. All nonlinearities (sensitive functions of the interacting wave vectors) operate at par, and none is dominant over any substantial region of k-space; their intricate interplay prevents a “universal” picture from emerging; few generalizations on the processes that may, for instance, lead to a turbulent state, are possible. However, the theory can definitely claim: (1) the energy tends to flow from lower to higher k and (2) the higher k z (in the direction of the ambient magnetic field) components of a mode with a given k are depleted/oscillate faster—in some cases much faster. It is noteworthy that the mode coupling is the strongest (with the shortest depletion time) when the participating wave vectors are nearly perpendicular; perhaps, an expected consequence of the curl (cross product) nonlinearities. Numerical simulations will be necessary to help create a fully reliable picture.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetic and electron transport properties of Co 2 Si nanomagnets

In this study, magnetotransport and ferromagnetism in thin films of Co 2 Si nanoclusters are investigated experimentally and theoretically. The nanoclusters are fabricated by an inert-gas condensation-type cluster-deposition method and have an average size of 11.3 nm. Unlike the bulk Co 2 Si that exhibits a very weak net magnetic moment only below 10 K, the nanoclusters exhibit room-temperature ferromagnetism with a substantial saturation magnetization. Key features of the system are its closeness to the Stoner transition, magnetic moments induced by spin polarization starting from surface atoms, and nonuniaxial anisotropy associated with the orthorhombic crystal structure of Co 2 Si . A method is introduced to determine the effective anisotropy using the experimental magnetization data of this complex system and its relationship with the two lowest-order nonuniaxial anisotropy constants. On decreasing temperature from 300 K, the nanoclusters show electron-transport properties unusual for a ferromagnetic metal, including an increase of Hall resistivity and a nonmonotonic change of negative magnetoresistance with a peak at around 100 K. The underlying physics is explained on the basis of the large polarization of surface spins and variation in the degree of their misalignments due to temperature-dependent effective anisotropy.

36 MATERIALS SCIENCE↗

Competition between excitonic insulators and quantum Hall states in correlated electron–hole bilayers

Excitonic insulators represent a unique quantum phase of matter that enables the study of exotic quantum bosonic states. Strongly coupled electron–hole bilayers, which host stable dipolar exciton fluids with an exciton density that can be adjusted electrostatically, offer an ideal platform to investigate correlated excitonic insulators. On the basis of electron–hole bilayers made of MoSe2/hexagonal boron nitride/WSe2 heterostructures, here we study the behaviour of excitonic insulators in a perpendicular magnetic field. We report the observation of excitonic quantum oscillations in both Coulomb drag signals and electrical resistance at low to medium magnetic fields. Under a strong magnetic field, we identify multiple quantum phase transitions between the excitonic insulator phase and the bilayer quantum Hall insulator phase. These findings underscore the interplay between the electron–hole interactions and Landau-level quantization, and enable further exploration of quantum phenomena in composite bosonic insulators.

Qi, Ruishi↗

Time-reversal symmetry breaking in the Fe-chalcogenide superconductors

Significance In the Fe-chalcogenide superconductors, topology, superconductivity, and magnetism all come together to provide a platform for a range of exotic quantum phenomena. Topology and superconductivity can interact to give topological superconductivity capable of supporting Majorana fermions that could prove to be the basis of future qubit technology. The large spin–orbit interaction associated with the topological phenomena combined with magnetism can potentially result in the quantum anomalous Hall effect although the superconductivity will work against such. It is important that we understand the relevant roles of the different phenomena. Here we provide evidence of time-reversal symmetry breaking and associated mass acquisition in a topological surface state at the superconducting transition, an observation highly suggestive of the formation of surface ferromagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A hierarchical evaluation framework for assessing climate simulations relevant to the energy-water-land nexus (Final Report)

The overarching goal was to construct a hierarchy of new and well-tested metrics and analysis tools that support both fundamental and use-inspired research. Motivating this goal was a convergence of needs from climate scientists and stakeholders alike for a systematic, robust framework of model evaluation and diagnosis to provide scientific insights, inform model development, support best practices for the use of climate model outputs, and facilitate communication of climate information in the evolving landscapes of multi-model, multi-resolution, and large ensemble simulations that generate terabytes of data for any single climate run. Steps toward attaining these goals benefited from expertise and established capability of the project team, which included leadership of the North American Regional Climate Change Assessment Program (NARCCAP) and the Coordinated Regional Downscaling Experiment (CORDEX), development of hierarchical model evaluation approaches, and successful research in the analysis and diagnosis of climate model skill, as well as the understanding and modeling of regional climate processes in North America. As part of the overarching goal, the project worked to disseminate a suite of methodologies, algorithms, and software components that the wider community can employ to advance climate science and applications. With rigorous demonstration, the evaluation framework and the mix of standard and high risk / high reward approaches helped form the basis for future development of a computationally enabled user-friendly system for community use.

17 WIND ENERGY↗

Composing preconditioners for multiphysics PDE systems with applications to Generalized MHD

New patch smoothers or relaxation techniques are developed for solving linear matrix equations coming from systems of discretized partial differential equations (PDEs). One key linear solver challenge for many PDE systems arises when the resulting discretization matrix has a near null space that has a large dimension, which can occur in generalized magnetohydrodynamic (GMHD) systems. Patch-based relaxation is highly effective for problems when the null space can be spanned by a basis of locally supported vectors. The patch-based relaxation methods that we develop can be used either within an algebraic multigrid (AMG) hierarchy or as stand-alone preconditioners. These patch-based relaxation techniques are a form of well-known overlapping Schwarz methods where the computational domain is covered with a series of overlapping sub-domains (or patches). Patch relaxation then corresponds to solving a set of independent linear systems associated with each patch. In the context of GMHD, we also reformulate the underlying discrete representation used to generate a suitable set of matrix equations. In general, deriving a discretization that accurately approximates the curl operator and the Hall term while also producing linear systems with physically meaningful near null space properties can be challenging. Unfortunately, many natural discretization choices lead to a near null space that includes non-physical oscillatory modes and where it is not possible to span the near null space with a minimal set of locally supported basis vectors. Further discretization research is needed to understand the resulting trade-offs between accuracy, stability, and ease in solving the associated linear systems.

97 MATHEMATICS AND COMPUTING↗