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At least 253 records · Page 14

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗

Frustration- and doping-induced magnetism in a Fermi–Hubbard simulator

Geometrical frustration in strongly correlated systems can give rise to a plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids. Promising candidate materials for such phases can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions U/t ≈ 9, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120° spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. Furthermore, this work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices and realizing t–t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials.

74 ATOMIC AND MOLECULAR PHYSICS↗

Multiquanta flux jumps in superconducting fractal

We study the magnetic field response of millimeter scale fractal Sierpinski gaskets (SG) assembled of superconducting equilateral triangular patches. Directly imaged quantitative induction maps reveal hierarchical periodic filling of enclosed void areas with multiquanta magnetic flux, which jumps inside the voids in repeating bundles of individual flux quanta Φ 0 . The number N s of entering flux quanta in different triangular voids of the SG is proportional to the linear size s of the void, while the field periodicity of flux jumps varies as 1/s. We explain this behavior by modeling the triangular voids in the SG with effective superconducting rings and by calculating their response following the London analysis of persistent currents, J s , induced by the applied field H a and by the entering flux. With changing H a , J s reaches a critical value in the vertex joints that connect the triangular superconducting patches and allows the giant flux jumps into the SG voids through phase slips or multiple Abrikosov vortex transfer across the vertices. The unique flux behavior in superconducting SG patterns, may be used to design tunable low-loss resonators with multi-line high-frequency spectrum for microwave technologies.

36 MATERIALS SCIENCE↗

Evolution of magnetic interactions in Sb-substituted MnBi 2 Te 4

The Mn(Bi 1–x Sb x ) 2 Te 4 series is purported to span from an antiferromagnetic (AF) topological insulator at x = 0 to a trivial AF insulator at x = 1. Here we report on neutron diffraction and inelastic neutron scattering studies of the magnetic interactions across this series. All compounds measured possess ferromagnetic (FM) triangular layers and we find a crossover from AF to FM interlayer coupling near x = 1 for our samples. The large spin gap at x = 0 closes rapidly and the average FM exchange interactions within the triangular layer increase with Sb substitution. Similar to a previous study of MnBi 2 Te 4 , we find severe spectral broadening which increases dramatically across the compositional series. In addition to broadening, we observe an additional sharp magnetic excitation in MnSb 2 Te 4 that may indicate the development of local magnetic modes originating from antisite disorder between Mn and Sb sublattices. Here, the results suggest that both substitutional and antisite disorder contribute substantially to the magnetism in Mn(Bi 1–x Sb x ) 2 Te 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Possible octupole deformation of 208 Pb and the ultracentral v 2 to v 3 puzzle

Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of nonspherical nuclei. In the case of 129 Xe collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In 208 Pb collisions a discrepancy exists in similar centralities, where either elliptic flow is overpredicted or triangular flow is underpredicted by hydrodynamic models; this is known as the v 2 -to-v 3 puzzle in ultracentral collisions. Motivated by low-energy nuclear structure calculations, we consider the possibility that 208Pb nuclei could have a pear-shape deformation (octupole), which has the effect of increasing triangular flow in central PbPb collisions. Using the recent data from ALICE and ATLAS, we reexamine the v 2 -to-v 3 puzzle in ultracentral collisions, including new constraints from recent measurements of the triangular cumulant ratio v 3 {4}/v 3 {2} and comparing two different hydrodynamic models. We find that while an octupole deformation would slightly improve the ratio between v 2 and v 3 , it is at the expense of a significantly worse triangular flow cumulant ratio. In fact, the latter observable prefers no octupole deformation, with β 3 ≲ 0.0375 for 208 Pb, and is therefore consistent with the expectation for a doubly-magic nucleus even at top collider energies. Furthermore, the v 2 -to-v 3 puzzle remains a challenge for hydrodynamic models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Shaped Beams from Diamond Field-Emitter Array Cathodes

Diamond field-emitter arrays (DFEAs) are arrays of diamond pyramids with exquisitely sharp tips and micrometer-scale bases that produce high current densities. These arrays can be fabricated in arbitrary shapes, ranging from single tips to many millions of tips, so that they produce an inherently shaped electron beam. Each tip emits a modest current, but the large dense array can produce many Amps. We are investigating these cathodes for use in dielectric wakefield accelerators; however, they may also be applicable to vacuum microwave tubes. Recently, shaped beam production and transport have been demonstrated in the 1.3-GHz RF gun at the Argonne Cathode Test Stand at the Argonne National Laboratory. The charge was measured on a Faraday cup and the beam imaged on a YAG screen with peak electric field gradients on the cathode ranging from 12 to 35 MV/m. Three cathode geometries were tested: one 1-mm equilateral triangle with 7-mu m base pyramids and 10-mu m pitch, one 1-mm equilateral triangle with 10-mu m base and 25-mu m pitch, and one sparse 5 x 5 square array with 20-mu m base and 400-mu m pitch. The two triangular arrays emitted 35 nC in an RF macropulse at 35 MV/m and 13-nC charge at 27 MV/m, respectively, while the sparse array emitted 0.060-nC charge at 15 MV/m. This article presents the results of the triangular array experiments, including damage due to breakdown in the RF gun and initial models of tip-to-tip shielding.

Cathodes↗

Temperature-Dependent Structural Transition in Cu-Intercalated Trigonal CuYbSe 2

Rare-earth delafossites, ARCh 2 ; A = alkali metal, R = rare-earth, Ch = chalcogen which consist of intercalated rare-earth metal dichalcogenides, host frustrated triangular lattices that are fertile ground for exotic phenomena. In most cases, the triangular rare-earth sublattice arises from R-3m (No. 166) structures with three layers of rare-earth metal dichalcogenide octahedra or P6 3 /mmc (No. 194) structures with two such layers, analogous to those found in transition metal dichalcogenides. Substituting the alkali metal with Cu + yields a distinct trigonal crystal symmetry P-3m1 (No. 164) in these structures. This symmetry change alters the coordination environment from ASe 6 octahedra in R-3m AYbSe 2 to CuSe 4 tetrahedra in CuYbSe 2 , resulting in shortened rare-earth to rare-earth separations and significantly reduced interlayer distances. Using X-ray single-crystal diffraction, powder neutron diffraction, resistance, and specific heat measurements, a structural transition slightly below room temperature (258 K) is observed. The low-temperature structure is a lower-symmetry I2/m structure, accompanied by partial Cu-site vacancy ordering. The combination of Cu disorder and the triangular lattice geometry in CuYbSe 2 provides a promising platform for investigating frustrated magnetism and unconventional transport phenomena.

Chemical structure↗

Shaping effects on scrape-off layer plasma turbulence: A rigorous validation of three-dimensional simulations against TCV measurements

The effect of plasma shaping on scrape-off layer (SOL) plasma turbulence is investigated through a rigorous validation exercise. Two- and three-dimensional simulations of the SOL plasma dynamics in three TCV limited discharges are carried out with the GBS code. These discharges realize an almost circular magnetic equilibrium, an elongated equilibrium, and an elongated equilibrium with negative triangularity. For the three plasma discharges, three simulations are performed, considering (i) a three-dimensional model with an explicit dependence on elongation, triangularity, and the inverse aspect ratio; (ii) a circular three-dimensional model in the infinite aspect ratio limit; and (iii) a two-dimensional model, which assumes a circular magnetic equilibrium in the infinite aspect ratio limit, cold ions, and interchange driven turbulence in the sheath limited regime. Ten validation observables common to simulations and experimental measurements from a reciprocating probe located at the TCV outer midplane are identified, and the agreement between experimental and numerical results relative to each observable is evaluated. The composite metric introduced by Ricci et al. [Phys. Plasmas 18, 032109 (2011)] is then used to assess the overall agreement between simulations and experimental measurements. It is found that the shaping model implemented in GBS improves the description of SOL plasma turbulence, taking into account the impact of elongation and triangularity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗