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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

HERO WEC V1.0 2024 - WEC-Sim Detailed Simulation Runs and Summary Data

This dataset includes results from simulations of NREL's hydraulic and electric reverse osmosis wave energy converter (HEREO WEC). Simulation runs include 135 wave cases that were based on the updated WEC-Sim model, which is linked below. The data represented in this repository is based on an updated WEC-Sim model using laboratory data to tune and refine the original WEC-Sim model for the V1.0 HERO WEC. The 135 wave cases represent waves with the following wave height and wave period ranges: - Significant Wave Height: 0.25 - 3.75m in 0.25m increments - Wave Period: 5 - 13 sec in 1 sec increments Each run was simulated using a Pierson-Moskowitz irregular wave spectrum with a 100 second ramp time, a total simulation time of 3,100 seconds, and a simulation time-step of 0.005s. A reference table has been included to map each multi condition run (MCR) case with each wave condition. Summary data set includes a spreadsheet and image files with matrices that are associated with data from simulation runs. All matrices cover the same significant wave height and wave periods from the simulation runs, in the same increments. The following matrices are included: - Power Abs: The average absorbed power from the WEC (calculated from anchor reaction force and heave velocity) - Power Hyd: The average hydraulic power output at pump (calculated from pump output flow and pressure) - Power - Hyd ROi: The average hydraulic power measured at the RO system inlet (calculated from RO system pressure and flow (pre-accumulator)) - Flow - Pump out: The average flowrate measured at the pump outlet - Flow - Perm: The average permeate (clean water) production - Flow - RO (pre): The average flowrate measured at the inlet of the RO system before the accumulators - Flow - RO (post): The average flowrate measured after the accumulator bank in the RO system - Pressure - RO: The average pressure measured at the inlet of the RO system This data set has been developed by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Water Power Technologies Office.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

HERO WEC V1.0 - WEC-Sim Detailed Simulation Runs and Summary Data

Data sets from simulation runs include 144 wave cases that were run based on the WEC-Sim model (https://mhkdr.openei.org/submissions/483). The 144 wave cases represent waves with the following wave height and wave period ranges: - Significant Wave Height: 0.25 - 4.0m in 0.25m increments - Wave Period: 5 - 13 sec in 1 sec increments Each run was simulated using a Pierson-Moskowitz irregular wave spectrum with a 200 second ramp time and a total simulation time of 2,200 seconds. Summary data set includes a spreadsheet and image files with matrices that are associated with data from simulation runs. All matrices cover the same significant wave height and wave periods from the sim runs, in the same increments. The following matrices are included: - Mechanical Power Input: Absorbed power calculated using linear input velocity at PTO (power take-off) multiplied by winch tension. - Mechanical Power Output: The hydraulic power calculated at the pump output prior to the pressure relief valve dump. - Feed Pressure: Average pressure at RO (reverse osmosis) input prior to pre-filters - RO Power Input: The hydraulic power calculated at the RO system inlet, accounts for flow loss due to pressure relief valve - Water Production: Average clean water flow at RO output

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Spatially quasi-periodic water waves of finite depth

We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and travelling wave settings. We adopt a quasi-periodic conformal mapping formulation of the Euler equations, where one-dimensional quasi-periodic functions are represented by periodic functions on a higher-dimensional torus. We compute the time evolution of free surface waves in the presence of a background flow and a quasi-periodic bottom boundary and observe the formation of quasi-periodic patterns on the free surface. Two types of quasi-periodic travelling waves are computed: small-amplitude waves bifurcating from the zero-amplitude solution and larger-amplitude waves bifurcating from finite-amplitude periodic travelling waves. We derive weakly nonlinear approximations of the first type and investigate the associated small-divisor problem. We find that waves of the second type exhibit striking nonlinear behaviour, e.g. the peaks and troughs are shifted non-periodically from the corresponding periodic waves due to the activation of quasi-periodic modes.

Science & Technology - Other Topics↗
DOE OSTI2021

Spatially Quasi-Periodic Water Waves of Infinite Depth

Abstract We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of the equations of motion in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on a torus. We adopt a conformal mapping formulation and employ a quasi-periodic version of the Hilbert transform to determine the normal velocity of the free surface. Two methods of time-stepping the initial value problem are proposed, an explicit Runge–Kutta (ERK) method and an exponential time-differencing (ETD) scheme. The ETD approach makes use of the small-scale decomposition to eliminate stiffness due to surface tension. We perform a convergence study to compare the accuracy and efficiency of the methods on a traveling wave test problem. We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential. As time evolves, each wave peak evolves differently, and only some of them overturn. Beyond water waves, we argue that spatial quasi-periodicity is a natural setting to study the dynamics of linear and nonlinear waves, offering a third option to the usual modeling assumption that solutions either evolve on a periodic domain or decay at infinity.

Wilkening, Jon (ORCID:0000000327827596)↗
DOE OSTI2020

Optimum power analysis of a self-reactive wave energy point absorber with mechanically-driven power take-offs

This paper studies a self-reactive ocean wave energy converter (WEC) where energy is absorbed through the relative motion between a floating buoy on the ocean surface and a submerged body. Two types of direct-drive power take off (PTO) systems are examined. One adopts a ball screw system in inverse driving mode with mechanical motion rectifier (MMR) that converts the oscillating bi-directional input heave motion into unidirectional rotation to drive an electromagnetic generator, and another one uses a ball screw system to directly drive the generator (called non-MMR). Dynamic models for both types of PTOs are established and integrated with the overall WEC system model in both the time and frequency domains. Numerical simulation is used to investigate the dynamic performance of both PTOs. The influences of the PTO inerter, which is from the rotational inertia of the flywheel and generator, and the WEC drag damping coefficient are discussed and explored. The analytical closed-form solution for the optimum condition of the non-MMR system is derived based on the criterion of maximum power absorption, and numerical simulation yields the optimum condition for the MMR system. Overall, the results under regular and irregular waves show that the PTO inerter in the MMR system can improve the power absorption for small wave periods and maintain the same performance for large wave periods. The PTO inerter in the non-MMR system shifts the peak frequency. The WEC drag damping negatively influences the power absorption in both PTO systems, especially at large wave periods.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Open-Loop Control of Adjustable Tuned Mass Dampers for Floating Wind Turbine Platforms

In this study, we demonstrate the ability of adjustable tuned mass dampers (TMDs) to reduce the platform motion of floating offshore wind turbines (FOWTs). The TMDs are located in the hull and provide control authority by varying the amount of water ballast and compressed air in a reservoir over time. The optimal TMD settings depend on the wind and wave conditions of the FOWT. We present an open-loop control scheme that changes the TMD natural frequency based on sea state and a simple method for estimating the peak wave period and significant wave height. The performance of this open-loop control is compared to ideal control of the TMDs (set knowing the exact sea state), a TMD with a constant natural frequency targeting the design load case with the greatest platform motion, and a baseline set of simulations of the platform without TMDs. The constant natural frequency case performs nearly as effectively as the actively controlled case, suggesting that the TMDs can be simply designed for extreme load conditions and provide consistent control over a range of environments; however, the methods used to find the optimal TMD parameters and estimate sea state statistics could be used in other aspects of FOWT control and design.

artificial intelligence↗
DOE OSTI2020

Investigating the Impact of Power-Take-Off System Parameters and Control Law on a Rotational Wave Energy Converter’s Peak-to-Average Power Ratio Reduction

Due to the irregular nature of real waves, the power captured in a wave energy converter (WEC) system is highly variable. This is an important barrier to the effective use of WECs. To address this challenge, this study focuses on a rotational WEC power-take-off system in which high-speed and high-efficiency generators along with a torque/power smoothing inertia element can be effectively utilized. In the first phase of this study, the U.S. Department of Energy’s reference model 3 (WEC-Sim RM3; two-body point absorber), along with a slider-crank WEC, were integrated for linear to rotational conversion. Relative motion between the float and spar in RM3 was the driving force for this slider-crank WEC, which is connected to a motor/generator set through a gearbox. RM3 geometry was scaled down by 25 times to work within the limits of the physical motor/generator set used in the experimentation. Once the integration in a hardware-in-the-loop simulation environment was successfully completed, data on the peak-to-average power ratio was collected for various wave conditions including regular and irregular waves. The control algorithm designed to keep the system in resonance with waves was able to maintain relatively high speed depending on the specific gear ratio and wave period. Initial results with hardware-in-the-loop simulations reveal that gear ratio and crank radius have a strong impact on the peak-to-average power ratio. In addition, it was found that output power from the generator was maximized at a larger gear ratio, as the crank radius was increased.

50 EE - Wind and Water Power Program - Water (EE-4↗
DOE OSTI2022

WUS256: An Adjoint Waveform Tomography Model of the Crust and Upper Mantle of the Western United States for Improved Waveform Simulations

Abstract We report a new model (WUS256) of radially anisotropic seismic wavespeeds of the crust and upper mantle of the western United States (WUS) obtained from adjoint waveform tomography for the purpose of improving synthetic waveform fits to observed data. WUS256 is based on inversion of over 94,000 waveforms from 72 earthquakes recorded by nearly 3,400 stations. We started with the SPiRaL global model (Simmons et al., 2021, https://doi.org/10.1093/gji/ggab277 ) and waveforms in the period band of 50–120 s. We followed a conservative multiscale inversion approach with eight stages and 256 total inversion iterations which enabled monotonic misfit reduction to 20‐s minimum‐period waves. WUS256 relied on time‐frequency (TF) phase misfits and a trust region limited memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) optimization. Hessian‐vector products were used to qualitatively assess model resolution. Results indicate that WUS256 has good coverage of the continental regions to depths of about 150 km and is able to resolve features on lateral scales of about 200 km. We quantify waveform fits by the reduction in TF and normalized amplitude difference misfits between WUS256 and the SPiRaL starting model. WUS256 significantly improves waveform fits with misfit reduction 64% for both inversion and validation data sets compared to the SPiRaL starting model and shows even better fits compared to other models. Waveform fits illustrate that WUS256 reproduces body‐waves, fundamental mode surface waves as well as late arriving dispersed and/or scattered short period surface waves. The improvement in waveform fit indicates that WUS256 can be used to reproduce path effects on regional complete waveforms and moment tensor inversions.

58 GEOSCIENCES↗
DOE OSTI2022

Global wave energy resource classification system for regional energy planning and project development

Efforts to streamline and codify wave energy resource characterization and assessment for regional energy planning and wave energy converter (WEC) project development have motivated the recent development of resource classification systems. Given the unique interplay between WEC absorption and resource attributes, viz, available wave power frequency, directionality, and seasonality, various consensus resource classification metrics have been introduced. However, the main international standards body for the wave energy industry has not reached consensus on a wave energy resource classification system designed with clear goals to facilitate resource assessment, regional energy planning, project site selection, project feasibility studies, and selection of WEC concepts or archetypes that are most suitable for a given wave energy climate. In this work, a primary consideration of wave energy generation is the available energy that can be captured by WECs with different resonant frequency and directional bandwidths. Therefore, the proposed classification system considers combinations of three different wave power classifications: the total wave power, the frequency-constrained wave power, and the frequency-directionally constrained wave power. The dominant wave period bands containing the most wave power are sub-classification parameters that provide useful information for designing frequency and directionally constrained WECs. The bulk of the global wave energy resource is divided into just 22 resource classes representing distinct wave energy climates that could serve as a common language and reference framework for wave energy resource assessment if codified within international standards.

16 TIDAL AND WAVE POWER↗
DOE OSTI2020

A global ensemble of ocean wave climate projections from CMIP5-driven models

This dataset, produced through the Coordinated Ocean Wave Climate Project (COWCLIP) phase 2, represents the first coordinated multivariate ensemble of 21st Century global wind-wave climate projections available (henceforth COWCLIP2.0). COWCLIP2.0 comprises general and extreme statistics of significant wave height (H S ), mean wave period (T m ), and mean wave direction (θ m ) computed over time-slices 1979–2004 and 2081–2100, at different frequency resolutions (monthly, seasonally and annually). The full ensemble comprising 155 global wave climate simulations is obtained from ten CMIP5-based state-of-the-art wave climate studies and provides data derived from alternative wind-wave downscaling methods, and different climate-model forcing and future emissions scenarios. The data has been produced, and processed, under a specific framework for consistency and quality, and follows CMIP5 Data Reference Syntax, Directory structures, and Metadata requirements. Technical comparison of model skill against 26 years of global satellite measurements of significant wave height has been undertaken at global and regional scales. This new dataset provides support for future broad scale coastal hazard and vulnerability assessments and climate adaptation studies in many offshore and coastal engineering applications.

Science & Technology - Other Topics↗
DOE OSTI2024

WEC-Sim Modeling of Laminar Scientific's Patented Seesaw Wave Energy Converter: Preprint

Laminar Scientific's patented seesaw wave energy converter was modeled in WEC-Sim to predict performance. The device operates by utilizing ocean surface waves to rotate a truss in pitch about a pivot. The pivot is located at the top of two pylons, which are embedded in the seafloor. The seesaw has a float on either end, and the buoyancy forces from each float cause the system to rise or fall with passing waves. Device performance relies upon seesaw length and ocean wavelength creating an antiphase effect. The seesaw truss has an adjustable length intended to achieve this effect. The operation method enforces a narrow band of wavelengths which induce the largest rotational motion from the device. The hydrodynamic analysis of the device was performed using Capytaine, and the results confirmed that the device operates best in a narrow frequency band. Four float-to-float spacing cases and three pylon radii were examined. The hydrodynamic results indicate a match between the model and the physical expectations for the device, and that varying the pylon radii by 0.1-m increments for three instances creates minimal changes in hydrodynamic properties. Power matrices for three float spacing cases of the device were simulated with Joint North Sea Wave Project spectra waves and optimal power take-off damping in WEC-Sim. The maximum average power production for the 15-m spacing case was 14.1 kW with a 5.0-s peak wave period and 4-m significant wave heights. Plots of capture-width ratios indicated that the device performance was linear and confirmed that the device is optimal in a narrow frequency band. The maximum percentage of the available wave power produced by the 15-m device was approximately 16%. Simulations of the device in regular waves were used to produce plots of average power compared to a ratio of float spacing to wavelength. These plots indicate that the power production is maximized at a ratio of 0.5, and further confirm that the device has a narrow frequency response. The device was simulated at an example field location, where the device produced an annual average power rating of 1.6 kW given an average omnidirectional wave climate of 10.3 kW m-1 and an optimal, linearized power take-off model. While the maximum predicted device performance is reliant upon a narrow band of wave frequencies, the conducted analysis provides an opportunity to improve device design prior to prototyping and testing. Modifying the design to respond to a broader frequency range would improve device performance.

numerical modeling↗
DOE OSTI2020

Dominant Wave Energy Systems and Conditional Wave Resource Characterization for Coastal Waters of the United States

Opportunities and constraints for wave energy conversion technologies and projects are evaluated by identifying and characterizing the dominant wave energy systems for United States (US) coastal waters using marginal and joint distributions of the wave energy in terms of the peak period, wave direction, and month. These distributions are computed using partitioned wave parameters generated from a 30 year WaveWatch III model hindcast, and regionally averaged to identify the dominant wave systems contributing to the total annual available energy ( A A E ) for eleven distinct US wave energy climate regions. These dominant wave systems are linked to the wind systems driving their generation and propagation. In addition, conditional resource parameters characterizing peak period spread, directional spread, and seasonal variability, which consider dependencies of the peak period, direction, and month, are introduced to augment characterization methods recommended by international standards. These conditional resource parameters reveal information that supports project planning, conceptual design, and operation and maintenance. The present study shows that wave energy resources for the United States are dominated by long-period North Pacific swells (Alaska, West Coast, Hawaii), short-period trade winds and nor’easter swells (East Coast, Puerto Rico), and wind seas (Gulf of Mexico). Seasonality, peak period spread, and directional spread of these dominant wave systems are characterized to assess regional opportunities and constraints for wave energy conversion technologies targeting the dominant wave systems.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Oceanographic Conditions. 2007 - 2040. North Slope Alaska.

Complete representations of oceanographic conditions require spatial and temporal information about the significant wave height (Hs), peak wave period (Tp), wind speed, wind direction, wave direction, water level, salinity, and temperature. This data develops location-independent typologies to reduce the number of boundary conditions needed to assess nearshore oceanographic environments in both a Historical (2007-2019) and Future (2020-2040) timespan along the Alaskan North Slope. Wave information for both time spans were generated from WaveWatch III, Delft3D-FLOW, and Delft3D-WAVE simulations forced by wind conditions from reanalysis data (e.g., ASRv2 and ERA5) for the historical simulations while projected conditions were obtained from downscaled GFDL-CM3 forced under RCP8.5 conditions. Salinity was generated from GOFS 3.1 for the years between 2008-2015 and skin temperature of the ocean was obtained from ASRv2 reanalysis data for the years between 2007-2016. To identify generalized oceanographic typologies, K-means clustering was applied to the energy-weighted joint-probability distribution of Hs and Tp at six sites along the North Slope of Alaska. Distributions of wave and wind direction, wind speed, and water level associated with locaiton-indepndent centroids were assigned single values to describe a reduced order, typological rendition of offshore oceanographic conditions. These final typologies and their constituent data are provided here and can be used to evaluate the change in ocean energy over the next two decades in response to climate change and provide insight into expected consequences such as coastal erosion and flooding. A full assessment of the findings and techniques developed can be found in: Eymold, W.K., Flanary, C., Erikson, L., Nederhoff, K., Chartrand, C.C., Jones, C., Kasper, J., and Bull, D.L. Typological Representation of the Offshore Oceanographic Environment along the Alaskan North Slope. Continental Shelf Research (2022). 10.1016/j.csr.2022.104795

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Parametric Instability of Alfvén Waves and Wave Packets in Periodic and Open Systems

The parametric decay instability of Alfvén waves has been widely studied, but few investigations have examined wave packets of finite size and the effect of different boundary conditions on the growth rate. In this paper, we perform a linear analysis of circular and arc-polarized wave trains and wave packets in periodic and open boundary systems in a low- β plasma. We find that both types of wave are 3–5 times more stable in open boundary conditions compared to periodic. Additionally, once the wave packet width ℓ becomes smaller than the system size L , the growth rate decreases nearly with a power law γ ∝ ℓ / L . This study demonstrates that the stability of a pump wave cannot be separated from the laboratory settings, and that the growth rate of daughter waves depends on the conditions downstream and upstream of the pump wave and on the fraction of volume it fills. Our results can explain simulations and experiments of localized Alfvén waves. They also suggest that Alfvénic fluctuations in the solar wind, including sharp impulses known as switchbacks, can be more stable than traditional theory suggests depending on wind conditions.

Alfven waves↗
DOE OSTI2024

Force-free Wave Interaction in Magnetar Magnetospheres: Computational Modeling in Axisymmetry

Abstract Crustal quakes of highly magnetized neutron stars can disrupt their magnetospheres, triggering energetic phenomena like X-ray and fast radio bursts. Understanding plasma wave dynamics in these extreme environments is vital for predicting energy transport across scales to the radiation length. This study models relativistic plasma wave interaction in magnetar magnetospheres with force-free electrodynamics simulations. For propagation along curved magnetic field lines, we observe the continuous conversion of Alfvén waves to fast magnetosonic (FMS) waves. The conversion efficiency can be up to three times higher when counter-propagating Alfvén waves interact in the equatorial region. Alfvén waves generate FMS waves of twice their frequency during their first crossing of the magnetosphere. After the initial transient burst of FMS waves, Alfvén waves convert to FMS waves periodically, generating variations on timescales of the magnetospheric Alfvén wave crossing time. This decaying FMS wave tail carries a significant portion (half) of the total energy emitted. Plastic damping of “bouncing” Alfvén waves by the magnetar crust has minimal impact on the FMS efficiency. We discuss the implications of the identified wave phenomena for magnetar observations. Outgoing FMS waves can develop electric zones, potential sources of coherent radiation. Long wavelength FMS waves could generate FRBs through reconnection beyond the light cylinder.

Astronomy & Astrophysics↗
DOE OSTI2023

Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values

We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent root-bracketing techniques or Chebyshev interpolation to locate bifurcation points. Only positive singular values have to be computed, though the method relies on the existence of an analytic or smooth singular value decomposition (SVD). The sign of the determinant of the Jacobian, computed as part of the bidiagonal reduction in the SVD algorithm, eliminates slope discontinuities at the zeros of the smallest singular value. We use the method to search for spatially quasi-periodic traveling water waves that bifurcate from large-amplitude periodic waves. The water wave equations are formulated in a conformal mapping framework to facilitate the computation of the quasi-periodic Dirichlet-Neumann operator. We find examples of pure gravity waves with zero surface tension and overhanging gravity-capillary waves. In both cases, the waves have two spatial quasi-periods whose ratio is irrational. We follow the secondary branches via numerical continuation beyond the realm of linearization about solutions on the primary branch to obtain traveling water waves that extend over the real line with no two crests or troughs of exactly the same shape. The pure gravity wave problem is of relevance to ocean waves, where capillary effects can be neglected. Such waves can only exist through secondary bifurcation as they do not persist to zero amplitude. The gravity-capillary wave problem demonstrates the effectiveness of using the signed smallest singular value as a test function for multi-parameter bifurcation problems. This test function becomes mesh independent once the mesh is fine enough.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Validating simulated mountain wave impacts on hub-height wind speed using SoDAR observations

The ascent of stably stratified air over a mountain barrier can trigger the generation of mountain waves. Mountain waves occur frequently over the Columbia River Gorge in western North America and can impact wind power generation over the area. Therefore, predicting the details of mountain waves events (e.g., dominant wavelength, timing, and duration) can be very valuable for the wind energy community. In this study, the ability of the Weather Research and Forecasting (WRF) model to simulate mountain waves and their impact on hub-height wind speed is investigated. Our results suggest that the WRF model has moderate skill in simulating observed mountain wave. Further, given WRF predictions of wavelength range and wave period, the Fast Fourier Transform can calculate the simulated mountain wave impact on hub-height wind speed. The resulting wind speeds agree well with SoDAR observations in terms of both magnitude and pattern. Finally, for the simulated cases, WRF consistently predicts impacts of significant mountain wave events about an hour earlier than the actual observations. Overall, in this work, the sensitivities as well as uncertainties associated with our methodology are discussed in detail.

17 WIND ENERGY↗
DOE OSTI2021

Matter-wave stripe solitons induced by helicoidal spin–orbit coupling

Highlights: • Four kinds of exact stripe soliton solutions in Bose–Einstein condensates with helicoidal spin–orbit coupling (SOC) are represented. • The influence of helicoidal SOC on the structure of stripe solitons are described in detail. • The corresponding spin polarization is expressed on the Bloch sphere. • The formation mechanism of stripe solitons and the interaction properties of moving stripe solitons are discussed. We present the exact analytical solution of stripe solitons on different backgrounds in Bose–Einstein condensates with helicoidal spin–orbit coupling (SOC). They are divided into two categories, one is stationary stripe soliton on zero background or period-wave background, the other is moving stripe soliton on zero background or plane-wave background. The period of stripe is determined by both strength and frequency of helicoidal SOC, and the oscillation amplitude of stripe is adjustable in the case of fixed total density. The corresponding spin polarization is expressed on Bloch sphere. For stationary soliton, the spin density vector take values in three directions, which is different from the Rashba–Dresslhaus coupling scheme. The spin density vectors display more complicated spatial distribution for moving stripe solitons. Meanwhile, the formation mechanism of stripe soliton and the interaction properties of moving stripe solitons are discussed. Our work enhances the understanding of stripe solitons, and is helpful for the observation of stripe phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗