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At least 1,135 records · Page 63

Multisublattice cluster expansion study of short-range ordering in iron-substituted strontium titanate

Owing to the challenges in obtaining realistic atomic configurations in large chemical phase spaces, it is not straightforward to describe structure–property relations in materials exhibiting configurational disorder. One example is iron-substituted strontium titanate (SrTi 1–x Fe x O 3–d , STF), a promising perovskite-derivative cathode material in solid oxide fuel cells that exhibits full solid solubility 0 ≤ x ≤ 1 and a tendency to exhibit short-range order. Here we demonstrate a multisublattice cluster expansion (CE) framework and apply it to STF across the full composition range. The CE approach is distinct from more traditional CE formulations in that clusters are defined explicitly by the chemical species distributed among multiple sublattices, rather than via cluster functions of occupation variables with decoration. The modified CE approach makes it easy to distinguish meaningful chemical interactions that are harder to extract from conventional CE, since for the latter chemical identity in a cluster is expressed as a product of site occupations. The least absolute shrinkage and selection operator (LASSO) is implemented as a regression analysis tool to select key clusters and avoid overfitting. We demonstrate this formulation on STF, and show that it can accurately predict configurational energies in comparison to conventional CE. From the key clusters, we identify that short-range ordering between substitutional Fe and oxygen vacancies (V O ) results in the formation of Fe–VO strings. In addition, we consider the stability of STF through CE-based Monte Carlo (MC) simulations and confirm the presence of superstructures that were previously observed in transmission electron microscopy. In this work, analysis of atomic configurations from MC samples reveals variations in the oxidation state of Fe atoms, which can be explained by the ordering tendency of Fe and V O . The cluster description and selection formalism described here may be applied to other disordered multisublattice systems for accurate and efficient material modeling.

36 MATERIALS SCIENCE↗

Investigation of the Self-Assembly Behavior of Statistical Bottlebrush Copolymers via Self-Consistent Field Theory Simulations

Bottlebrush copolymers, a class of high-density side-chain-grafted copolymers with high molecular weights, have recently attracted extensive research attention due to the dramatic reduction of chain entanglement in these copolymers, unique self-assembly behaviors, and distinctive physical properties. In this study, we employ self-consistent field theory simulations to systemically investigate the phase behavior of statistical bottlebrush copolymers A-stat-B, an intriguing subclass of bottlebrush copolymers with random or alternating sequences of A and B side chains. We find that a broader variety of ordered mesophases can be stabilized in the melts of these copolymers relative to the more extensively studied bottlebrush block copolymers. In particular, we observe that these statistical copolymers can stabilize sphere phases over a larger range of species volume fractions than their diblock and tetrablock counterparts but require much higher segregation strength to achieve this. The sphere and hexagonally packed cylinder phases formed by conformationally symmetric statistical bottlebrush copolymers possess interesting discrete core–shell structures with the backbone and lower volume fraction side-chain species forming shells and cores, respectively. Moreover, we uncover a new strategy of stabilizing the Frank–Kasper phase A15 by introducing conformational asymmetry through different side-chain lengths and also observe deflection of order–order phase boundaries and significant mixing between the backbones and short side chains as conformational asymmetry is introduced.

36 MATERIALS SCIENCE↗

Using Convolutional Neural Network to Emulate Seasonal Tropical Cyclone Activity

Abstract It has been widely recognized that tropical cyclone (TC) genesis requires favorable large‐scale environmental conditions. Based on these linkages, numerous efforts have been made to establish an empirical relationship between seasonal TC activities and large‐scale environmental favorability in a quantitative way, which lead to conceptual functions such as the TC genesis index. However, due to the limited amount of reliable TC observations and complexity of the climate system, a simple analytic function may not be an accurate portrait of the empirical relationship between TCs and their ambiences. In this research, we use convolution neural networks (CNNs) to disentangle this complex relationship. To circumvent the limited amount of seasonal TC observation records, we implement transfer‐learning technique to train ensemble of CNNs first on suites of high‐resolution climate model simulations with realistic seasonal TC activities and large‐scale environmental conditions, and then on a state‐of‐the‐art reanalysis from 1950 to 2019. The trained CNNs can well reproduce the historical TC records and yields significant seasonal prediction skills when the large‐scale environmental inputs are provided by operational climate forecasts. Furthermore, by inputting the ensemble CNNs with 20th century reanalysis products and Phase 6 of the Coupled Model Intercomparison Project (CMIP6) simulations, we investigated TC variability and its changes in the past and future climates. Specifically, our ensemble CNNs project a decreasing trend of global mean TC activity in the future warming scenario, which is consistent with our future projections using high‐resolution climate model.

Meteorology & Atmospheric Sciences↗

An Integrated Modeling Framework for Sediment Dynamics During Urban Flooding: Application to Hurricane Harvey in Houston

Floodwater can mobilize and redistribute large volumes of sediment from upland to downstream urban areas, threatening infrastructure, water quality, and ecosystem health. However, existing modeling approaches often fail to capture sediment dynamics in urban floodplains due to the lack of integration between upland hydrological processes and riverine sediment transport. This study presents the first integrated modeling framework that couples the Energy Exascale Earth System Model (E3SM) land component, which simulates runoff and hillslope erosion, with TELEMAC-GAIA, a two-dimensional hydrodynamic and sediment transport model. This framework enables the fully distributed, process-based simulation of high-resolution (as fine as 30 m) sediment dynamics from hillslopes to floodplains. Applied to a highly urbanized watershed in Houston during Hurricane Harvey, this framework reproduced observed water levels at 16 USGS gauges (median R 2 = 0.83 and KGE = 0.78), key sediment dynamics such as sediment transport and deposition processes, and reproduced spatial deposition patterns consistent with LiDAR-derived data. Based on the simulation, we estimate 8.0 million m 3 of event-scale sediment deposition, including 5.7 million m 3 trapped in the flood-control reservoirs and 2.3 million m 3 deposited along major channels and floodplains. Using a representative unit removal cost, this corresponds to an estimated dredging cost of $581 million for total deposition. These results provide a first-order, physically based quantification of Harvey-scale sediment impacts. This study provides a valuable tool for the holistic analysis of sediment dynamics triggered by extreme urban flooding, supporting flood-resilience planning. More broadly, it highlights the importance of integrating physically based hydrological processes for urban flooding and sediment research.

Hurricane Harvey↗

Investigation of mode activity in NBI-heated experiments of Wendelstein 7-X

The 2018 operation phase (OP 1.2b) of the stellarator Wendelstein 7-X (W7-X) included, for the first time, neutral beam injection (NBI) to heat the plasma. Since the injection geometry at W7-X is not parallel, this generates both passing and trapped fast particles. During longer phases of NBI injection, with the primary purpose to study the heating efficiency of this system, Alfvén eigenmodes (AEs) were observed by a number of diagnostics, including the phase contrast imaging (PCI) system, the magnetic pick-up coils (Mirnov coils), and the soft x-ray multi-camera tomography system (XMCTS). Alfvén eigenmodes are of great interest for future fusion reactors as it has been shown that the resonant interaction of fast ions with self-excited AEs can lead to enhanced transport of fast ions and potentially to energy losses. This is especially true for so-called gap-modes, Alfvén eigenmodes with frequencies in gaps of the continuous spectrum, since they lack continuum damping. These modes are commonly known to be excited by fast ions, but other destabilizing mechanisms, e.g. the electron-pressure gradient are also possible. In this article we present a first analysis of the experimentally observed frequencies from the theoretical side. The calculation of shear Alfvén wave continua for selected cases and the assignment of observed frequencies to the gaps of the continuous spectra are presented. Using the ideal-MHD code CKA (Könies A. 2007 10th IAEA TM on Energetic Particles in Magnetic Confinement System), we find gap modes that match the experimental measurements in terms of the observed frequencies. We emphasize the crucial roles played by the coupling of sound and Alfvén waves as well as of the Doppler shift arising as a consequence of the radial electric field in W7-X. We employ the perturbative gyrokinetic code CKA-EUTERPE (Feh´er 2013 Simulation of the interaction between Alfv´en waves and fast particles), using a slowing-down distribution function for the fast ions as calculated by the Monte-Carlo particle following code ASCOT (Hirvijoki et al 2014 Comput. Phys. Commun. 185 1310–21) to assess the fast-ion drive. Here we find that the fast-ion drive is insufficient to overcome the background-plasma damping. The fact that unstable modes were observed experimentally may point to problems with the modelling or indicate the existence of other destabilizing mechanisms, e.g. associated with the electron-pressure gradient (Windisch et al 2017 Plasma Phys. Control. Fusion 59 105002) that sensitively depend on the profiles of the background plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comparing multi-source urban flood indicators: satellite, simulation, and citizen-reported data

Urban flooding arises from complex mechanisms, making it challenging to capture accurately with a single detection method. This study evaluates three complementary approaches to detect flooding across three Chicago neighborhoods: (i) Sentinel-1 synthetic aperture radar (SAR), offering weather-independent, high-resolution (10 m) imagery of surface inundation; (ii) the storm water management model (SWMM), simulating combined sewer overflow and drainage performance; and (iii) citizen-generated 311 service requests, capturing observed flooding impacts. By analyzing six storms ranging from severe to mild, we examine how each source uniquely contributes to identifying urban flood events. SAR imagery effectively identifies standing water but can miss brief flooding due to satellite revisit constraints. SWMM provides detailed insights into system-wide drainage behavior yet may underestimate localized street-level flooding. Meanwhile, 311 calls reflect real-world flooding impacts but are vulnerable to underreporting. Statistical overlap analysis highlights chronic flood hotspots repeatedly identified across multiple detection methods, indicating persistent infrastructure and topographic vulnerabilities. Temporal analysis further reveals that while SWMM flooding aligns closely with rainfall peaks, 311 calls typically precede or persist beyond these peaks. Our findings emphasize the value of using satellite observations, hydrological modeling, and resident-reported data in a complementary manner to better interpret patterns in flood timing, severity, and spatial distribution—providing insights that can inform targeted infrastructure improvements and contribute to urban flood resilience planning.

311↗

Using Density-Corrected DFT to Understand Density-Driven and Functional-Dependent Errors in Ab Initio Simulations of the Hydrated Electron

The hydrated electron, an excess electron in liquid water, plays a crucial role in a plethora of chemical processes, motivating extensive research efforts to characterize its structure, dynamics, and reactivity in solution. Recent theoretical approaches to understanding this intriguing object have involved ab initio simulations based on density functional theory (DFT). Although DFT allows for the study of hydrated electron reactivity and quantum mechanical behavior, it is well-known that anionic systems can suffer from significant density-driven errors (DDEs). Density-corrected DFT (DC-DFT) provides a framework to mitigate such errors; the method reduces DDEs by replacing the self-consistent (SC) density associated with a given density functional with the Hartree–Fock (HF) density. Since HF densities tend to be more localized than DFT SC densities, the DC-DFT scheme significantly improves errors in calculations where the SC density is spuriously delocalized. Here, we investigate how the use of density correction affects the calculated properties of the DFT-simulated (PBEh) hydrated electron, a particularly challenging diffuse anionic system to simulate. First, we analyze charge delocalization in a system consisting of a model octahedral hydrated electron water cluster (the so-called Kevan structure) along with a spatially separated sulfur atom. We show that the use of density correction indeed reduces DDEs in comparison to a standard DFT global hybrid functional. We then propagate molecular dynamics trajectories of the hydrated electron using DC-DFT, where we find that DC further localizes electron density in the cavity region, a signature of reduced charge delocalization. Unfortunately, the decreased radius of gyration of the spin density and corresponding tightening of the local solvation structure from density correction causes predicted observables to deviate further from experimental measurements than when density correction is not employed. Here, we argue that DC’s worse agreement with experiment results from the removal of a fortuitous cancellation of errors that is intrinsic to the PBEh functional. This indicates that the difficulties with DFT to simulate hydrated electrons are primarily due to the inherent approximations in DFT rather than to density-driven errors.

Density functional theory↗

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗

Evidence for Bootstrap Percolation Dynamics in a Photoinduced Phase Transition

Upon intense femtosecond photo-excitation, a many-body system can undergo a phase transition through a non-equilibrium route, but understanding these pathways remains an outstanding challenge. Here, we use time-resolved second harmonic generation to investigate a photo-induced phase transition in Ca 3 Ru 2 O 7 and show that mesoscale inhomogeneity profoundly influences the transition dynamics. We observe a marked slowing down of the characteristic time τ that quantifies the transition between two structures. τ evolves non-monotonically as a function of photo-excitation fluence, rising from below 200 fs to ~1.4 ps, then falling again to below 200 fs. To account for the observed behavior, we perform a bootstrap percolation simulation that demonstrates how local structural interactions govern the transition kinetics. Finally, our work highlights the importance of percolating mesoscale inhomogeneity in the dynamics of photo-induced phase transitions and provides a model that may be useful for understanding such transitions more broadly.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantifying the line-of-sight halo contribution to the dark matter convergence power spectrum from strong gravitational lenses

Galaxy-galaxy strong gravitational lenses have become a popular probe of dark matter (DM) by providing a window into structure formation on the smallest scales. In particular, the convergence power spectrum of subhalos within lensing galaxies has been suggested as a promising observable to study DM. However, the distances involved in strong-lensing systems are vast, and we expect the relevant volume to contain line-of-sight (LOS) halos that are not associated with the main lens. We develop a formalism to calculate the effect of LOS halos as an effective convergence power spectrum. Here, the multilens plane equation couples the angular deflections of consecutive lens planes, but by assuming that the perturbations due to the LOS halos are small, we show that they can be projected onto the main-lens plane as effective subhalos. We test our formalism by simulating lensing systems using the full multiplane lens equation and find excellent agreement. We show how the relative contribution of LOS halos and subhalos depends on the source and lens redshift, as well as the assumed halo and subhalo mass functions. For a fiducial system with fraction of DM halo mass in substructure f sub = 0.4% for subhalo masses [10 5 –10 8 ]M ⊙ , the interloper contribution to the power spectrum is at least several times greater than that of subhalos for source redshifts z s ≳ 0.5. Furthermore, it is likely that for the SLACS and BELLS lenses the interloper contribution dominates: f sub ≳ 2% (4%) is needed for subhalos to dominate in SLACS (BELLS), which is higher than current upper bounds on f sub for our mass range. Since the halo mass function is better understood from first principles, the dominance of interlopers in galaxy-galaxy lenses with high-quality imaging can be seen as a significant advantage when translating this observable into a constraint on DM.

79 ASTRONOMY AND ASTROPHYSICS↗

Terrace‐Edge‐Induced Domain Nucleation in Room‐Temperature 2D Magnetic Van Der Waals Heterostructures

Abstract Terrace‐edges, which are step‐like height discontinuities formed during layer stacking or exfoliation, can locally modify magnetic characteristics. Magnetic domain behavior and its structural dependence in a 2D van der Waals (vdW) heterostructure composed of two distinct room‐temperature ferromagnets: Fe 3 GaTe 2 , an intrinsic vdW ferromagnet, and vanadium‐doped WSe 2 , a transition metal dichalcogenide exhibiting defect‐induced magnetism, is investigated. Using magnetic transmission X‐ray microscopy, the formation and annihilation of magnetic domains are directly observed and it is found that domains preferentially form at terrace‐edges of the heterostructure. Micromagnetic simulations reveal that in‐plane magnetization tilting near the terrace‐edge results in a localized maximum in total magnetic energy that promotes domain formation. The findings highlight the significant role of structural edge features and interfacial magnetic interactions in determining domain formation in hybrid 2D vdW magnetic systems, offering a new route to spatially controlled magnetization at room temperature.

Lee, Jieun↗

A parallel p ‐adaptive discontinuous Galerkin method for the Euler equations with dynamic load‐balancing on tetrahedral grids

Abstract A novel p ‐adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three‐dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order and is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p ‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p ‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p ‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p ‐adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p ‐adaptation.

97 MATHEMATICS AND COMPUTING↗

Total experimental uncertainty in hydrodynamic testing of a semisubmersible wind turbine, considering numerical propagation of systematic uncertainty

Quantifying the uncertainty in experimental results is a vital step in properly validating numerical simulation tools for designing floating wind turbines; without a good understanding of the experimental uncertainties, it is impossible to confirm if numerical simulation tools can capture the physics with acceptable accuracy. Recent validation studies suggest that the wave-induced, low-frequency surge and pitch motions of semisubmersible-type floating wind turbines are consistently underpredicted by numerical simulations, but it has not been possible to state whether or not this underprediction is within the level of experimental error. Here, previously assessed systematic uncertainty components in hydrodynamic tests of the OC5-DeepCwind semisubmersible are propagated to response metrics of interest using numerical simulation tools, and combined with the system's random uncertainty to obtain the total experimental uncertainty. The uncertainty in the low-frequency response metrics is found to be most sensitive to the system properties (e.g., mooring stiffness and center of gravity), and also the wave elevation. The results of the present study suggest that the underprediction of the low-frequency response behavior observed in previous validation studies is larger than the experimental uncertainty.

17 WIND ENERGY↗

Interface magnetism in vanadium-doped MoS 2 /graphene heterostructures

Magnetism in two-dimensional materials is of great importance in discovering new physical phenomena and developing new devices at the nanoscale. In this paper, first-principles simulations are used to calculate the electronic and magnetic properties of heterostructures composed of graphene and MoS 2 considering the influence of point defects and vanadium doping. It is found that the concentration of the dopants and the types of defects can result in induced magnetic moments leading to ferromagnetically polarized systems with sharp interfaces. This provides a framework for interpreting the experimental observations of enhanced ferromagnetism in both MoS 2 /graphene and V-doped MoS 2 /graphene heterostructures. The computed electronic and spin polarizations give a microscopic understanding of the origin of ferromagnetism in these systems and illustrate how doping and defect engineering can lead to targeted property tunability. Our work has demonstrated that through defects engineering, ferromagnetism can be achieved in V-doped MoS2/graphene heterostructures, providing a potential way to induce magnetization in other TMDC/graphene materials and opening new opportunities for their applications in nano-spintronics.

36 MATERIALS SCIENCE↗

Machine learning approaches for structural and thermodynamic properties of a Lennard-Jones fluid

Predicting the functional properties of many molecular systems relies on understanding how atomistic interactions give rise to macroscale observables. However, current attempts to develop predictive models for the structural and thermodynamic properties of condensed-phase systems often rely on extensive parameter fitting to empirically selected functional forms whose effectiveness is limited to a narrow range of physical conditions. Here, we illustrate how these traditional fitting paradigms can be superseded using machine learning. Specifically, we use the results of molecular dynamics simulations to train machine learning protocols that are able to produce the radial distribution function, pressure, and internal energy of a Lennard-Jones fluid with increased accuracy in comparison to previous theoretical methods. The radial distribution function is determined using a variant of the segmented linear regression with the multivariate function decomposition approach developed by Craven et al. [J. Phys. Chem. Lett. 11, 4372 (2020)]. The pressure and internal energy are determined using expressions containing the learned radial distribution function and also a kernel ridge regression process that is trained directly on thermodynamic properties measured in simulation. The presented results suggest that the structural and thermodynamic properties of fluids may be determined more accurately through machine learning than through human-guided functional forms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kinetic simulations comparing quasi-parallel and quasi-perpendicular piston-driven collisionless shock dynamics in magnetized laboratory plasmas

Magnetized collisionless shocks are common in astrophysical systems, and scaled versions can be created in laboratory experiments by utilizing laser-driven piston plasmas to create these shocks in a magnetized background plasma. A key parameter for these experiments is the angle θB between the shock propagation direction and the background magnetic field. We performed quasi-1D piston-driven shock simulations to explore shock formation, evolution, and key observables relevant to laboratory experiments for a range of shock angles between θB=90° to θB=30°. Our results show that the spatial and temporal scales of shock formation for all angles considered are similar when expressed in terms of the perpendicular component of the magnetic field. In a steady state, ion and electron temperatures become more isotropic, and the electron-to-ion temperature ratio is higher for smaller θB. At θB=30°, ion heating parallel to the magnetic field becomes dominant, associated with more ions being reflected at one discontinuity and subsequently trapped by the next discontinuity due to shock reformation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Local models of two-temperature accretion disc coronae – II. Ion thermal conduction and the absence of disc evaporation

We use local stratified shearing-box simulations with magnetic field-aligned thermal conduction to study an idealized model of the coupling between a cold, radiatively efficient accretion disc, and an overlying, hot, two-temperature corona. Evaporation of a cold disc by conduction from the hot corona has been proposed as a means of mediating the soft-to-hard state transitions observed in X-ray binary systems. We model the coronal plasma in our local disc patch as an MHD fluid subject to both free-streaming ion conduction and a parametrized cooling function that captures the collisional transfer of energy from hot ions to colder, rapidly cooling leptons. In all of our models, independent of the initial net vertical magnetic flux (NF) threading the disc, we find no evidence of disc evaporation. The ion heat flux into the disc is radiated away before conduction can heat the disc’s surface layers. When an initial NF is present, steady-state temperature, density, and outflow velocities in our model coronae are unaffected by conduction. Instead of facilitating disc evaporation, thermal conduction is more likely to feed the disc with plasma condensing out of the corona, particularly in flows without NF. Our work indicates that uncertainties in the amount of NF threading the disc hold far greater influence over whether or not the disc will evaporate into a radiatively inefficient accretion flow compared to thermal conduction. We speculate that a change in net flux mediates disc truncation/evaporation.

79 ASTRONOMY AND ASTROPHYSICS↗

Shapiro steps and stability of skyrmions interacting with alternating anisotropy under the influence of ac and dc drives

Here we use atomistic simulations to examine the sliding dynamics of a skyrmion in a two-dimensional system containing a periodic one-dimensional stripe pattern of variations between low and high values of the perpendicular magnetic anisotropy. The skyrmion changes in size as it crosses the interface between two anisotropy regions. On applying combined dc and ac driving in either parallel or perpendicular directions, we observe a wide variety of Shapiro steps, Shapiro spikes, and phase-locking phenomena. The phase-locked orbits have two-dimensional dynamics due to the gyrotropic or Magnus dynamics of the skyrmions and are distinct from the phase-locked orbits found for strictly overdamped systems. Along a given Shapiro step when the ac drive is perpendicular to the dc drive, the velocity parallel to the ac drive is locked while the velocity in the perpendicular direction increases with increasing drive to form Shapiro spikes. At the transition between adjacent Shapiro steps, the parallel velocity jumps up to the next step value, and the perpendicular velocity drops. The skyrmion Hall angle shows a series of spikes as a function of increasing dc drive, where the jumps correspond to the transition between different phase-locked steps. At high drives, the Shapiro steps and Shapiro spikes are lost. When both the ac and dc drives are parallel to the stripe periodicity direction, Shapiro steps appear, while if the dc drive is parallel to the stripe periodicity direction and the ac drive is perpendicular to the stripe periodicity, then there are only two locked phases, and the skyrmion motion consists of a combination of sliding along the interfaces between the two anisotropy values and jumping across the interfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗