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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Nonlinear power flow control for networked AC/DC microgrids

A method for designing feedforward and feedback controllers for integration of stochastic sources and loads into a nonlinear networked AC/DC microgrid system is provided. A reduced order model for general networked AC/DC microgrid systems is suitable for HSSPFC control design. A simple feedforward steady state solution is utilized for the feedforward controls block. Feedback control laws are provided for the energy storage systems. A HSSPFC controller design is implemented that incorporates energy storage systems that provides static and dynamic stability conditions for both the DC random stochastic input side and the AC random stochastic load side. Transient performance was investigated for the feedforward/feedback control case. Numerical simulations were performed and provided power and energy storage profile requirements for the networked AC/DC microgrid system overall performance. The HSSPFC design can be implemented in the Matlab/Simulink environment that is compatible with real time simulation/controllers.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Self-consistent simulation of resistive kink instabilities with runaway electrons

A new fluid model for runaway electron simulation based on fluid description is introduced and implemented in the magnetohydrodynamics code M3D-C1, which includes self-consistent interactions between plasma and runaway electrons. The model utilizes the method of characteristics to solve the continuity equation for the runaway electron density with large convection speed, and uses a modified Boris algorithm for pseudo particle pushing. The model was employed to simulate magnetohydrodynamics instabilities happening in a runaway electron final loss event in the DIII-D tokamak. Nonlinear simulation reveals that a large fraction of runaway electrons get lost to the wall when kink instabilities are excited and form stochastic field lines in the outer region of the plasma. Plasma current converts from runaway electron current to Ohmic current, and get pinched at the magnetic axis. Here, given the good agreement with experiment, the simulation model provides a reliable tool to study macroscopic plasma instabilities in existence of runaway electron current, and can be used to support future studies of runaway electron mitigation strategies in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A Stochastic Calculus Approach to Boltzmann Transport

Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. Here, we make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.

Boltzmann transport↗
DOE OSTI2022

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Stochastic parametric skeletal dosimetry model for humans: General approach and application to active marrow exposure from bone-seeking beta-particle emitters

The objective of this study is to develop a skeleton model for assessing active marrow dose from bone-seeking beta-emitting radionuclides. This article explains the modeling methodology which accounts for individual variability of the macro- and microstructure of bone tissue. Bone sites with active hematopoiesis are assessed by dividing them into small segments described by simple geometric shapes. Spongiosa, which fills the segments, is modeled as an isotropic three-dimensional grid (framework) of rod-like trabeculae that “run through” the bone marrow. Randomized multiple framework deformations are simulated by changing the positions of the grid nodes and the thickness of the rods. Model grid parameters are selected in accordance with the parameters of spongiosa microstructures taken from the published papers. Stochastic modeling of radiation transport in heterogeneous media simulating the distribution of bone tissue and marrow in each of the segments is performed by Monte Carlo methods. Model output for the human femur at different ages is provided as an example. The uncertainty of dosimetric characteristics associated with individual variability of bone structure was evaluated. An advantage of this methodology for the calculation of doses absorbed in the marrow from bone-seeking radionuclides is that it does not require additional studies of autopsy material. The biokinetic model results will be used in the future to calculate individual doses to members of a cohort exposed to 89,90 Sr from liquid radioactive waste discharged to the Techa River by the Mayak Production Association in 1949–1956. Further study of these unique cohorts provides an opportunity to gain more in-depth knowledge about the effects of chronic radiation on the hematopoietic system. In addition, the proposed model can be used to assess the doses to active marrow under any other scenarios of 90 Sr and 89 Sr intake to humans.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Automated Antenna Design with Evolutionary Algorithms

Current methods of designing and optimizing antennas by hand are time and labor intensive, and limit complexity. Evolutionary design techniques can overcome these limitations by searching the design space and automatically finding effective solutions. In recent years, evolutionary algorithms have shown great promise in finding practical solutions in large, poorly understood design spaces. In particular, spacecraft antenna design has proven tractable to evolutionary design techniques. Researchers have been investigating evolutionary antenna design and optimization since the early 1990s, and the field has grown in recent years as computer speed has increased and electromagnetic simulators have improved. Two requirements-compliant antennas, one for ST5 and another for TDRS-C, have been automatically designed by evolutionary algorithms. The ST5 antenna is slated to fly this year, and a TDRS-C phased array element has been fabricated and tested. Such automated evolutionary design is enabled by medium-to-high quality simulators and fast modern computers to evaluate computer-generated designs. Evolutionary algorithms automate cut-and-try engineering, substituting automated search though millions of potential designs for intelligent search by engineers through a much smaller number of designs. For evolutionary design, the engineer chooses the evolutionary technique, parameters and the basic form of the antenna, e.g., single wire for ST5 and crossed-element Yagi for TDRS-C. Evolutionary algorithms then search for optimal configurations in the space defined by the engineer. NASA's Space Technology 5 (ST5) mission will launch three small spacecraft to test innovative concepts and technologies. Advanced evolutionary algorithms were used to automatically design antennas for ST5. The combination of wide beamwidth for a circularly-polarized wave and wide impedance bandwidth made for a challenging antenna design problem. From past experience in designing wire antennas, we chose to constrain the evolutionary design to a monopole wire antenna. The results of the runs produced requirements-compliant antennas that were subsequently fabricated and tested. The evolved antenna has a number of advantages with regard to power consumption, fabrication time and complexity, and performance. Lower power requirements result from achieving high gain across a wider range of elevation angles, thus allowing a broader range of angles over which maximum data throughput can be achieved. Since the evolved antenna does not require a phasing circuit, less design and fabrication work is required. In terms of overall work, the evolved antenna required approximately three person-months to design and fabricate whereas the conventional antenna required about five. Furthermore, when the mission was modified and new orbital parameters selected, a redesign of the antenna to new requirements was required. The evolutionary system was rapidly modified and a new antenna evolved in a few weeks. The evolved antenna was shown to be compliant to the ST5 mission requirements. It has an unusual organic looking structure, one that expert antenna designers would not likely produce. This antenna has been tested, baselined and is scheduled to fly this year. In addition to the ST5 antenna, our laboratory has evolved an S-band phased array antenna element design that meets the requirements for NASA's TDRS-C communications satellite scheduled for launch early next decade. A combination of fairly broad bandwidth, high efficiency and circular polarization at high gain made for another challenging design problem. We chose to constrain the evolutionary design to a crossed-element Yagi antenna. The specification called for two types of elements, one for receive only and one for transmit/receive. We were able to evolve a single element design that meets both specifications thereby simplifying the antenna and reducing testing and integration costs. The highest performance antenna found using a getic algorithm and stochastic hill-climbing has been fabricated and tested. Laboratory results correspond well with simulation. Aerospace component design is an expensive and important step in space development. Evolutionary design can make a significant contribution wherever sufficiently fast, accurate and capable software simulators are available. We have demonstrated successful real-world design in the spacecraft antenna domain; and there is good reason to believe that these results could be replicated in other design spaces.

Hornby, Gregory S.↗
DOE OSTI2020

Distribution Development for the RDX Regional Model at Los Alamos National Laboratory - 20385

Representing uncertainty in model inputs often means finding a balance between uncertainty and physical reality. Developing wide distributions may seem conservative in principle, but this approach may lead to unrealistic model results. Characterizing the current state of knowledge of stochastic inputs presents many challenges, especially if the data available are limited or have limited relevance to the site. Relationships among these inputs may also be important to represent but are typically complex or difficult to define. Often special adjustments must be made to account for reduced credibility in particular data. If parameters are strongly related to one another, a correlation structure may be developed for input to the model. Other techniques such as regression models may be used to incorporate relationships between the information available and the desired parameters. The process of developing distributions must consider details of the model in terms of what the distribution is meant to represent. This paper uses the example of a probabilistic fate and transport model for hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) in the regional aquifer at Los Alamos National Laboratory (LANL). For many parameters, a single draw is applied to all space and time over which the model is run, for a single iteration. This simplification is often made for many reasons, and can often be beneficial, but also adds additional complexity in the distribution development process. Defining the distributional goals as they relate to the modeling process is an important step, which should take place prior to evaluation of the data. Usually, the distributions developed are meant to characterize the average value of the parameter over the spatial and temporal domain of the model. Distribution development requires consideration of many sources of information on the parameter where available, ideally from multiple references. Examples of different sources include data from different references but also from different conditions, measurement methods, or experimental types. Depending on these conditions and the reliability or relevance of particular references, different sources of data may each contribute valuable information but have varying relevance to the site. In these cases, weighting data unequally is a useful way to incorporate this information. As an example, aqueous dispersivity data are available for a variety of rock types. Only a few values are available for the desired rock type, and this is not enough to develop a distribution. Therefore, dispersivity values from other rock types are included in distribution development but are down-weighted such that the best data have the most influence on the distribution developed. In another case, K{sub d} distributions in the model are meant to represent a known composition of multiple soil types. Data from these materials are weighted accordingly to develop a distribution for the weighted average K{sub d} across soil types. Other cases include varying reliability of different sources, and weighting data according to the confidence in these sources. In some cases, input parameters are correlated with one another. An example is advective porosity, which is positively correlated with total porosity and must be less than total porosity. Paired data with both parameters must exist to discern the relationship between the two parameters and if it is necessary to build a correlation structure into the model. In general, correlated parameters may be represented in the model by a multivariate distribution, or perhaps more desirably, capturing the correlation within the developed distributions which may be treated as independent from one another. In the example of porosity, this can be done by transforming advective porosity into a proportion of total porosity which may be drawn independently from the distribution of total porosity. This paper explores how complex data and correlations can be incorporated to meet the distributional goals of the model, using the RDX regional model as a detailed example. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Reconstruction of effective potential from statistical analysis of dynamic trajectories

The broad incorporation of microscopic methods is yielding a wealth of information on the atomic and mesoscale dynamics of individual atoms, molecules, and particles on surfaces and in open volumes. Analysis of such data necessitates statistical frameworks to convert observed dynamic behaviors to effective properties of materials. Here, we develop a method for the stochastic reconstruction of effective local potentials solely from observed structural data collected from molecular dynamics simulations (i.e., data analogous to those obtained via atomically resolved microscopies). Using the silicon vacancy defect in graphene as a model, we apply the statistical framework presented herein to reconstruct the free energy landscape from the calculated atomic displacements. Evidence of consistency between the reconstructed local potential and the trajectory data from which it was produced is presented, along with a quantitative assessment of the uncertainty in the inferred parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Comparing (stochastic-selection) ab initio multiple spawning with trajectory surface hopping for the photodynamics of cyclopropanone, fulvene, and dithiane

Ab Initio Multiple Spawning (AIMS) simulates the excited-state dynamics of molecular systems by representing nuclear wavepackets in a basis of coupled traveling Gaussian functions, called trajectory basis functions (TBFs). New TBFs are spawned when nuclear wavepackets enter regions of strong nonadiabaticity, permitting the description of non-Born–Oppenheimer processes. The spawning algorithm is simultaneously the blessing and the curse of the AIMS method: it allows for an accurate description of the transfer of nuclear amplitude between different electronic states, but it also dramatically increases the computational cost of the AIMS dynamics as all TBFs are coupled. Recently, a strategy coined stochastic-selection AIMS (SSAIMS) was devised to limit the ever-growing number of TBFs and tested on simple molecules. In this work, we use the photodynamics of three different molecules—cyclopropanone, fulvene, and 1,2-dithiane—to investigate (i) the potential of SSAIMS to reproduce reference AIMS results for challenging nonadiabatic dynamics, (ii) the compromise achieved by SSAIMS in obtaining accurate results while using the smallest average number of TBFs as possible, and (iii) the performance of SSAIMS in comparison to the mixed quantum/classical method trajectory surface hopping (TSH)—both in terms of its accuracy and computational cost. We show that SSAIMS can accurately reproduce the AIMS results for the three molecules considered at a much cheaper computational cost, often close to that of TSH. We deduce from these tests that an overlap-based criterion for the stochastic-selection process leads to the best agreement with the reference AIMS dynamics for the smallest average number of TBFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Galactic Bar Resonances with Diffusion: An Analytic Model with Implications for Bar–Dark Matter Halo Dynamical Friction

Abstract The secular evolution of disk galaxies is largely driven by resonances between the orbits of “particles” (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari, and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies—effects that have, with few exceptions, been previously explored only with complex N -body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles’ slow actions. We solve this equation for various values of the dimensionless diffusion strength Δ, and then apply our theory to the calculation of bar–halo dynamical friction. For Δ = 0, we recover the classic result of Tremaine and Weinberg that friction ultimately vanishes, owing to the phase mixing of resonant orbits. However, for Δ > 0, we find that diffusion suppresses phase mixing, leading to a finite torque. Our results suggest that stochasticity—be it physical or numerical—tends to increase bar–halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

The Effect of Stochastic Acceleration on the Dynamics of Solar Energetic Particles in the Heliosphere

Solar Energetic Particles (SEPs) are crucial in space weather phenomena, impacting space-based technologies and human activities in space. Understanding the dynamics of SEPs, including their acceleration and transport mechanisms, is essential for improving predictive models and mitigating adverse effects. This study investigates the impact of stochastic acceleration (SA) on the dynamics of SEPs within the heliosphere. By integrating stochastic acceleration into a SEP transport model, we assess its impact relative to diffusive shock acceleration (DSA). The investigation utilizes the Adaptive Mesh Particle Simulator (AMPS) within the Space Weather Modeling Framework (SWMF) to simulate SEP dynamics, incorporating solar wind parameters and turbulence from the Alfven Wave Solar Model (AWSoM). To do this, we solve the focused transport equation to model the propagation of SEPs along magnetic field lines, extending these lines to 5 AU to incorporate the potential effects of pitch angle scattering beyond 1 AU. This aspect could notably impact the decay phase of a SEP event. Modeling the transport of SEPs is coupled with the simulation of solar wind dynamics, the interplanetary magnetic field, and the characteristics of Alfven wave turbulence. This presentation covers the modeling approach used in this research, the characterization of the impact of the stochastic acceleration, and the role of pitch angle scattering at various heliocentric distances on the dynamics of the SEP events' decay phase.

SEP↗
DOE OSTI2026

Image Distinguishability Analysis Testing Through Principal Components and Its Application to Hot Spot Scale Invariance

Hot spots are spatial regions of intense energy localization that govern initiation of secondary high explosives. Studies that characterize or compare simulated hot spots are frequently either qualitatively descriptive or resort to quantitative distribution functions that neglect stochastic variations and spatial correlations—effects that are also neglected in common comparison tests like the Kolmogorov–Smirnov test. To this end, we develop an image distinguishability analysis (IDA) test based on principal component (PC) analysis that makes pixel-by-pixel comparisons between small, for example, O(<10), image data sets. The IDA test makes comparisons through a generalized distance metric in the PC space and a test statistic that is derived to calculate mathematical equation-values. Here, we derive a statistical distribution and criticality criterion to determine whether images are distinguishable from established baselines. We apply the IDA test on images generated from molecular dynamics simulations of hot spots from pore collapse in TATB to assess scale invariance in the complex patterns of hot spots that form in a representative high explosive crystal. The IDA test shows that TATB hot spot spatial temperature fields and their derived temperature histograms exhibit scale-invariant features over specific intervals of shock orientation, strength, and initial pore diameter. However, the IDA test also shows that qualitatively different conclusions regarding invariance can be reached depending on whether the hot spot is treated as a spatially correlated field as opposed to a distribution function that lacks spatial information.

organic↗
DOE OSTI2025

Discrete fracture network model benchmarks developed and applied in a DECOVALEX-2023 repository performance assessment study

This study presents newly developed benchmarks for modeling flow and transport within discrete fracture networks (DFNs) and useful methods for analyzing the results. The new benchmarks are designed to test modeling approaches for use in probabilistic performance assessment models of deep geologic repositories in fractured rock. The benchmarks simulate flow and transport through a 1 km 3 block of fractured rock. The first simulates migration of a short pulse of tracer through a simple network of four intersecting fractures. The second adds 1089 stochastically generated fractures. The third changes the pulse to a continuous point source. Evaluation of model performance relies on moment analysis and comparison of the results of different models. The expected nondimensional first moment of the conservative tracer for each benchmark is 1. The benchmarks were simulated by teams from Canada, Czechia, Germany, Korea, Sweden, Taiwan, and the United States as part of a DECOVALEX-2023 study (decovalex.org). The teams used various approaches, including explicit DFN modeling, DFN upscaling to an equivalent continuous porous medium (ECPM), and a combination of both methods. Transport mechanisms are modeled using either the advection-dispersion equation or particle tracking. Results demonstrate strong agreement among the models in breakthrough behavior up to the 75th percentile. Significant deviations in first moments and well-clustered outputs led to the identification of inaccuracies in several models. Such findings exemplify the benefit of exercising these benchmarks and using the presented methods to test DFN flow and transport models.

Benchmark↗
DOE OSTI2022

Shape‐Dependent Multi‐Weight Magnetic Artificial Synapses for Neuromorphic Computing

Abstract In neuromorphic computing, artificial synapses provide a multi‐weight (MW) conductance state that is set based on inputs from neurons, analogous to the brain. Herein, artificial synapses based on magnetic materials that use a magnetic tunnel junction (MTJ) and a magnetic domain wall (DW) are explored. By fabricating lithographic notches in a DW track underneath a single MTJ, 3–5 stable resistance states that can be repeatably controlled electrically using spin‐orbit torque are achieved. The effect of geometry on the synapse behavior is explored, showing that a trapezoidal device has asymmetric weight updates with high controllability, while a rectangular device has higher stochasticity, but with stable resistance levels. The device data is input into neuromorphic computing simulators to show the usefulness of application‐specific synaptic functions. Implementing an artificial neural network (NN) applied to streamed Fashion‐MNIST data, the trapezoidal magnetic synapse can be used as a metaplastic function for efficient online learning. Implementing a convolutional NN for CIFAR‐100 image recognition, the rectangular magnetic synapse achieves near‐ideal inference accuracy, due to the stability of its resistance levels. This work shows MW magnetic synapses are a feasible technology for neuromorphic computing and provides design guidelines for emerging artificial synapse technologies.

Leonard, Thomas↗
DOE OSTI2024

A New Simple-to-Configure Self-Perturbing Multivariable Extremum-Seeking Controller

This paper presents a new stochastic relay-based extremum-seeking controller (ESC) for multi-input-single-output (MISO) systems. The algorithm was developed with the goal of simplifying configuration to enable easier deployment to real-world problems. A solution is developed first for a static map and then adapted for a general class of dynamic systems. The number of configurable parameters is one per input channel for the static case and only one additional parameter is needed for the dynamic version. The problem of gradient identifiability is solved via the use of stochastic relay gains and a simple stability proof for the static case is presented. Simulation tests demonstrate the performance of the strategy for optimizing both static and dynamic systems.

Salsbury, Timothy [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2023

Predicting rare events using neural networks and short-trajectory data

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. Additionally, we illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Oscillation-like diffusion of two-dimensional liquid dusty plasmas on one-dimensional periodic substrates with varied widths

The long-time diffusion of two-dimensional dusty plasmas on a one-dimensional periodic substrate with varying widths is investigated using Langevin dynamical simulations. When the substrate is narrow and the dust particles form a single row, the diffusion is the smallest in both directions. In this study, we find that as the substrate width gradually increases to twice its initial value, the long-time diffusion of the two-dimensional dusty plasmas first increases, then decreases, and finally increases again, giving an oscillation-like diffusion with varying substrate widths. When the width increases to a specific value, the dust particles within each potential well arrange themselves in a stable zigzag pattern, greatly reducing the diffusion and leading to the observed oscillation in the diffusion with the increase in the width. In addition, the long-time oscillation-like diffusion is consistent with the number of dust particles that are hopping across the potential wells of the substrate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗