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The discovery of atomic monolayer magnetic materials has stimulated intense research activities in the two-dimensional (2D) van der Waals (vdW) materials community. The field is growing rapidly and there has been a large class of 2D vdW magnetic compounds with unique properties, which provides an ideal platform to study magnetism in the atomically thin limit. In parallel, based on tunneling magnetoresistance and magneto-optical effect in 2D vdW magnets and their heterostructures, emerging concepts of spintronic and optoelectronic applications such as spin tunnel field-effect transistors and spin-filtering devices are explored. While the magnetic ground state has been extensively investigated, reliable characterization and control of spin dynamics play a crucial role in designing ultrafast spintronic devices. Ferromagnetic resonance (FMR) allows direct measurements of magnetic excitations, which provides insight into the key parameters of magnetic properties such as exchange interaction, magnetic anisotropy, gyromagnetic ratio, spin-orbit coupling, damping rate, and domain structure. In this review article, we present an overview of the essential progress in probing spin dynamics of 2D vdW magnets using FMR techniques. Given the dynamic nature of this field, we focus mainly on broadband FMR, optical FMR, and spin-torque FMR, and their applications in studying prototypical 2D vdW magnets. We conclude with the recent advances in laboratory- and synchrotron-based FMR techniques and their opportunities to broaden the horizon of research pathways into atomically thin magnets. 

AWP-ODC is a 4th-order finite difference code used by the SCEC community for linear wave propagation, Iwan-type nonlinear dynamic rupture and wave propagation, and Strain Green Tensor simulation. We have ported and verified the CUDA-version of AWP-ODC-SGT, a reciprocal version used in the SCEC CyberShake project, to HIP so that it can also run on AMD GPUs. This code achieved sustained 32.6 Petaflop/s performance and 95.6% parallel efficiency at full scale on Frontier, a Leadership Computing Facility at Oak Ridge National Laboratory. The readiness of this community software on AMD Radeon Instinct GPUs and EPYC CPUs allows SCEC to take advantage of exascale systems to produce more realistic ground motions and accurate seismic hazard products. We have also deployed AWP-ODC to Azure to leverage the array of tools and services that Azure provides for tightly coupled HPC simulation on commercial cloud. We collaborated with Internet 2/Azure Accelerator supporting team, as part of Microsoft Internet2/Azure Accelerator for Research Fall 2022 Program, with Azure credits awarded through Cloudbank, an NSF-funded initiative. We demonstrate the AWP performance with a benchmark of ground motion simulation on various GPU based cloud instances, and a comparison of the cloud solution to on-premises bare-metal systems. AWP-ODC currently achieves excellent speedup and efficiency on CPU and GPU architectures. The Iwan-type dynamic rupture and wave propagation solver faces significant challenges, however, due to the increased computational workload with the number of yield surfaces chosen. Compared to linear solution, the Iwan model adds 10x-30x more computational time plus 5x-13x more memory consumption that require substantial code changes to obtain excellent performance. Supported by NSF’s Characteristic Science Applications (CSA) program for the Leadership-Class Computing Facility (LCCF) at Texas Advanced Computing Center (TACC), we are porting and improving the performance of this nonlinear AWP-ODC software, preparing for the next generation NSF LCCF system called Horizon, to be installed at TACC. During Texascale days on the current TACC’s Frontera, we carried out an Iwan-type nonlinear dynamic rupture and wave propagation simulation of a Mw7.8 scenario earthquake on the southern San Andreas fault. This simulation modeled 83 seconds of rupture with a grid spacing of 25 m to resolve frequencies up to 4 Hz with a minimum shear-wave velocity of 500 m/s. 

This paper develops a tree-topological local mesh refinement (TLMR) method on Cartesian grids for the simulation of bio-inspired flow with multiple moving objects. The TLMR nests refinement mesh blocks of structured grids to the target regions and arrange the blocks in a tree topology. The method solves the time-dependent incompressible flow using a fractional-step method and discretizes the Navier-Stokes equation using a finite-difference formulation with an immersed boundary method to resolve the complex boundaries. When iteratively solving the discretized equations across the coarse and fine TLMR blocks, for better accuracy and faster convergence, the momentum equation is solved on all blocks simultaneously, while the Poisson equation is solved recursively from the coarsest block to the finest ones. When the refined blocks of the same block are connected, the parallel Schwarz method is used to iteratively solve both the momentum and Poisson equations. Convergence studies show that the algorithm is second-order accurate in space for both velocity and pressure, and the developed mesh refinement technique is benchmarked and demonstrated by several canonical flow problems. The TLMR enables a fast solution to an incompressible flow problem with complex boundaries or multiple moving objects. Various bio-inspired flows of multiple moving objects show that the solver can save over 80% computational time, proportional to the grid reduction when refinement is applied. 

Equivariant representation is necessary for the brain and artificial perceptual systems to faithfully represent the stimulus under some (Lie) group transformations. However, it remains unknown how recurrent neural circuits in the brain represent the stimulus equivariantly, nor the neural representation of abstract group operators. The present study uses a one-dimensional (1D) translation group as an example to explore the general recurrent neural circuit mechanism of the equivariant stimulus representation. We found that a continuous attractor network (CAN), a canonical neural circuit model, self-consistently generates a continuous family of stationary population responses (attractors) that represents the stimulus equivariantly. Inspired by the Drosophila’s compass circuit, we found that the 1D translation operators can be represented by extra speed neurons besides the CAN, where speed neurons’ responses represent the moving speed (1D translation group parameter), and their feedback connections to the CAN represent the translation generator (Lie algebra). We demonstrated that the network responses are consistent with experimental data. Our model for the first time demonstrates how recurrent neural circuitry in the brain achieves equivariant stimulus representation. 

The activity of the grid cell population in the medial entorhinal cortex (MEC) of the mammalian brain forms a vector representation of the self-position of the animal. Recurrent neural networks have been proposed to explain the properties of the grid cells by updating the neural activity vector based on the velocity input of the animal. In doing so, the grid cell system effectively performs path integration. In this paper, we investigate the algebraic, geometric, and topological properties of grid cells using recurrent network models. Algebraically, we study the Lie group and Lie algebra of the recurrent transformation as a representation of self-motion. Geometrically, we study the conformal isometry of the Lie group representation where the local displacement of the activity vector in the neural space is proportional to the local displacement of the agent in the 2D physical space. Topologically, the compact abelian Lie group representation automatically leads to the torus topology commonly assumed and observed in neuroscience. We then focus on a simple non-linear recurrent model that underlies the continuous attractor neural networks of grid cells. Our numerical experiments show that conformal isometry leads to hexagon periodic patterns in the grid cell responses and our model is capable of accurate path integration. 

In this work, numerical simulations are employed to study hydrodynamic interactions in trout-like three-dimensional(3D) fish bodies arranged in vertical and horizontal planes. The fish body is modeled on a juvenile rainbow trout (Oncorhynchus mykiss) and is imposed on a traveling wave to mimic trout swimming. Three typical minimal schools are studied, including the in-line, the side-by-side, and the vertical school. A sharp interface immersed-boundary-based incompressible Navier-Strokes flow solver is then used to quantitively simulate the resulting flow and hydrodynamic performance of the schools. The results show that the hydrodynamic efficiency of the leading fish in the in-line school increases by 5.28%, and the thrust production and efficiency of the side-by-side school are enhanced by 2.28% and 3.86%, respectively. Besides, the thrust production of the vertical school increases by 21.6%. The results suggest great potential in exploiting the hydrodynamic benefits in fish schools arranged in three-dimensional space.