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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 55 records · Page 3

Covariant formulation of spinodal decomposition in rapidly expanding quark gluon plasma

Quantum chromodynamics (QCD) is expected to have a first order phase transition between the confined hadron gas and the deconfined quark gluon plasma at high baryon densities. This will result in phase boundary effects in the metastable and unstable regions. It is important to include these effects in phenomenological models of heavy ion collisions to identify experimental signatures of a phase transition. This requires building intuition on phase separation in rapidly expanding fluids. In this work we present the covariant equations of relativistic hydrodynamics with a phase boundary, provide prescriptions to extend the equation of state to metastable and unstable regions, and show the effects of spinodal separation in a Bjorken flow. Published by the American Physical Society 2024

Kapusta, Joseph I. (ORCID:0000000259429835)↗

Securing 3D NAND Without Density Loss via In-Situ Encryption Using a Single Transistor XOR Cell

In this article, we push lightweight XOR-based in-situ encryption to extreme density by proposing a singletransistor XOR memory cell and applying it to 3D NAND, enabling secure data storage without density loss. Using a ferroelectric field-effect transistor (FeFET) as an example technology, we demonstrate that: i) a single-transistor memory can realize the XOR function by exploiting the ability to charge the source and drain separately and control current flow direction, eliminating the need for conventional encrypted cells that rely on complementary devices; ii) with a XOR-based cipher, encryption and decryption can be mapped to in-situ array operations, where ciphertext is stored as the threshold voltage (VTH) states of FeFETs in a NAND string, and decryption is achieved through read operations using key-dependent complementary source/drain bias; iii) the proposed technique is scalable to multi-level cell (MLC) storage by encrypting and decrypting data bit by bit; iv) using an integrated NAND FeFET array, we experimentally demonstrate encryption and decryption operations for both single-level cell (SLC) and MLC storage; v) systemlevel benchmarking shows that the proposed technique achieves 48× and 278× improvements in encryption and decryption throughput, respectively, compared to AES.

36 MATERIALS SCIENCE↗

Active Fluids Form System-Spanning Filamentary Networks

Recent experimental realizations of liquid-liquid phase separation of active liquid crystals have offered an insight into the interaction between phase separation, ubiquitous in soft matter and biology, and chaotic active flows. Here, in this Letter, we use continuum theory to examine phase separation of an active liquid crystal and a passive fluid and report two new results. First, we provide an analytical derivation of the activity-induced suppression of the phase boundary of the coexistence region—a result first reported in simulations and experiments. We show that the shift in the critical point is a result of the balance between self-stirring active flows and phase-separating diffusive fluxes. Second, we show that this same balance is responsible for dramatically changing the morphology of the phase separated state, resulting in the emergence of a new mixed active phase consisting of a dynamical filamentous active network that invades the entire system area, trapping droplets of passive material. This structure exists even for very low volume fractions of active material. Our work provides an important step towards the goal of understanding how to use activity as a new handle for sculpting interfaces.

active nematics↗

Implementation and evaluation of multi-dual mode counter-current chromatography in the CUP Modeler software

Counter-current chromatography (CCC) is a separation technique that utilizes immiscible solvent pairs as stationary and mobile phases, which imparts numerous benefits compared to solid-liquid chromatography including the ability to treat either the more-dense or less-dense solvent layer as the mobile phase. Multi-dual mode (MDM) is a CCC elution mode capable of improving the separation of closely eluting compounds by alternating upper- and lower-layer solvent flows in opposing directions within the same separation. While some effort has been made to model MDM, implementation of these models in experimental design has yet to be widely adopted. Accordingly, we further developed our previously published cell utilized partitioning (CUP) model to include MDM predictions with CCC and packaged the full suite of CUP modeling capabilities into a user-friendly, open-source tool called the CUP Modeler. The mathematical model for MDM CCC was derived and validated with experimental separation of ethyl guaiacol (EG) and ethyl phenol (EP), two compounds that co-elute in our previously demonstrated reductive catalytic fractionation (RCF) lignin monomer isolation method. The developed MDM model provided insights into the effect of multiple operating parameters - including stationary phase retention, flow rate, column efficiency, feed concentration ratio, selectivity factor, and solute distribution ratios - on the separation yields, productivity, and purities. Our model agreed with prevailing understanding of MDM but also revealed new insights including that the ideal distribution ratios for co-eluting solutes to be separated by MDM is between 1.1 and 1.5, with the lower value ideally close to 1.25. Overall, this work provides fundamental insights for MDM process design and enables broader adoption of general liquid-liquid chromatography with a new, open-source user-friendly interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Preliminary Testing of a Continuous Cryopump for Primary Fusion Device Pumping and Direct Internal Recycling

Here, the concept of directly recirculating fusion machine exhaust gas, bypassing the tritium plant, to make fuel pellets was proposed in the 1990s and later termed direct internal recycling (DIR). In the DIR concept, the residual fusion fuel in the machine exhaust stream is separated from impurities locally and diverted directly to the fueling systems, bypassing isotopic separation and other processing equipment, and therefore significantly reducing the required size of the fuel processing plant, reducing plant inventory, and thus increasing the economic viability of fusion as an energy source. One concept for DIR consists of a series of cryogenic pumps to separate the impurities from the machine exhaust gas using different triple point temperatures and saturation curves of exhaust constituents. In this concept, the plasma exhaust is initially passed through an impurity trap operating at ~25–30 K to desublimate impurities such as hydrocarbons, argon, oxygen, and nitrogen. The resulting process stream will consist of DT fuel and helium. The process stream is then pumped by a continuous cryopump known as a “snail pump.” This pump is a steady-state continuous cryopump that desublimates all remaining exhaust gas constituents while allowing helium, a byproduct of the fusion reaction, to pass through. The helium is pumped to the tritium plant for processing while the desublimated material is continuously scraped off, heated up, and transported to the fueling system. This article will present the cryogenic DIR concept and outline the design and operation of the snail pump, along with results from preliminary testing. Tests to assess pumping and separation efficiency found that at D2 flows below 50.7 Pa ⋅ m3/s with 1% helium, the pump is capable of pumping and separating the gas with a resulting DIR fraction of >99%, with no helium entrained in the primary fuel exhaust stream. The main limitation is due to the thermal performance of the cryogenic circuits of the pump, which will be addressed in future testing.

Gebhart III, Trey E. [Oak Ridge National Laborator↗

Bridging the Gap Between Pure and Mixed-Gas Performance of Thin-Film Composite Membranes

This study examines the influence of cell design on mixed-gas testing with PolyActive™ TFC membranes, featuring pure-gas CO₂ permeance of 1700–3100 GPU, representative of state-of-the-art CO₂/N₂ separation membranes. By designing and 3D-printing a counter-current permeation cell with optimized flow efficiency, we achieved a 33–41% increase in mixed-gas CO₂ permeance compared to traditional cells. Additionally, a comparison of sweep-gas and vacuum permeation methods revealed that vacuum operation mitigates downstream polarization, enhancing mixed-gas CO₂ permeance by 41%. These results underscore the critical role of permeation cell design and testing methods in accurately evaluating membrane performance, with significant implications for scaling up TFC membranes and optimizing industrial processes.

3D printing↗

Recovery of Oxpure 612C-50 Coconut Carbon Particles Using Bump Arrays

Cyanide is used to leach gold from crushed ore (solid matrix) into a gold cyanide solution. The gold is extracted from the cyanide solution by adsorption onto activated carbon. The gold extraction process occurs when the activated coconut carbon is placed into tanks that contain the gold cyanide solution either in a batch process or into a continuous flow circuit. The coconut carbon is then removed from the solution for gold recovery. The use of the mesofluidic separation system (a deterministic lateral displacement system) can significantly reduce costs and waste generated from the process of removing the coconut carbon from the solution. In the coconut carbon recovery process used at many gold mines in Nevada, the gold is attached to carbon particles that are still in the cyanide liquor. The mesofluidic system can rapidly remove the gold bearing carbon particles from the cyanide liquor quickly and with no operating costs. The benefits include: • Reduce operational costs related to filtration and hydro-cyclones • Reduced acid usage for the elution gold stripping phase as only 25% of the fluids will follow the carbon particles to the final express lane when two mesofluidic systems are used in series This alternative particle removal techniques would be advantageous. A promising technique for removing larger particles from slurries is mesofluidic separation, similar to deterministic lateral displacement arrays or “bump” arrays [1] but operates at much larger flow rates. As described by Pease, et al. [2], “Bump arrays in deterministic lateral displacement devices separate large particles from small particles using arrays of staggered posts. Large particles, defined as those with radii larger than the distance between the edge of a post and the stagnation streamline from the next downstream post, must bump toward one side of the device, whereas particles smaller than this distance slalom from entrance to exit without net lateral displacement.” Unlike filters or sieves, the posts in the arrays that cause separation do not block or occlude particle flow but work because particles go around the posts. Unlike hydrocyclones separation, separation is not driven by particle density, because gravitational forces are unimportant to mesofluidic separation. Burns, et al., and Pease, et al., have shown that particles may be separated from complex suspensions, under turbulent flow conditions, and at industrially important flow rates [3-5]. They have also recently shown that mesofluidic devices may be arranged in series to increase separation performance [6]. In this paper, we evaluate the mesofluidic system for the separation of commercial OxPure GR 612 Charred Coconut shell particles as a proof of principle test for the rapid separation using the 1500 micron cut mesofluidic separator. We first describe the experimental system and conditions. We then present the experimental results. [1] Huang, L.R., E.C. Cox, R.H. Austin, J.C. Sturm. 2004. Continuous particle separation through deterministic lateral displacement. Science, 304, 987–990. https://doi.org/10.1126/science.1094567. [2] Pease L.F., J.A. Bamberger, C.A. Burns, and M.J. Minette. 2021. Large Particle Separation from Non-Newtonian Slurries using Bump Arrays. In Proceedings of the ASME 2021 Fluids Engineering Division Summer Meeting FEDSM2021-65904, V003T08A023. New York, New York: ASME. doi:10.1115/FEDSM2021-65904 [3] Burns C.A., T.G. Veldman, J. Serkowski, R.C. Daniel, X.-Y. Yu, M.J. Minette, L.F. Pease. 2021. Mesofluidic separation versus dead-end filtration. Separation and Purification Technology, 254, 117256. https://doi.org/10.1016/j.seppur.2020.117256. [4] Pease L.F., J.E. Serkowski, T.G. Veldman, J. Williams, X.-Y. Yu, M.J. Minette, J.A. Bamberger, C.A. Burns. 2021. Can Bump Arrays Separate Particles from Turbulent Flows?. In Proceedings of the ASME 2021 Fluids Engineering Division Summer Meeting FEDSM2021-67696, V003T08A024. New York, New York: ASME. doi:10.11

mesofluidic separation, slurry, bump array↗

Modeling and Optimization of a Rotating Packed Bed Contactor with a Tetraamine-Appended Metal−Organic Framework for CO 2 Capture

A potential contactor technology for sorbent-based CO 2 capture is the rotating packed bed that contains separate sections for continuous adsorption and desorption. A heat exchanger can be embedded to remove heat in the adsorption section and add heat in the desorption section. In this work, we develop a two-dimensional (2D) model of a rotating packed bed for use in CO 2 capture applications. Mass and energy balances for the model are developed based on a Ljungström-type air preheater, which accounts for the counter-current axial flow of gas phases in separate sections of the bed and the rotation of a solid sorbent, which cycles between adsorption and desorption sections. The sorbent used for this analysis is the tetraamine-appended metal−organic framework Mg 2 (dobpdc)(3−4− 3), chosen for its stability and affinity for CO 2 at low partial pressures, such as those from a natural gas power plant source. An optimization problem is solved that considers the trade-off between maximizing the productivity of the bed and minimizing energy consumption. Maximum productivity and minimum energy are found to be 8.53 kg/h/m 3 and 3.84 MJ/kg, respectively, when these objectives are optimized independently. It is observed that the flue gas pressure and bed rotational speed are the desired operating variables to vary for model-based design of experiments to reduce uncertainty in parameter estimation, as these two variables yielded the most information content based on the Fisher information matrix.

20 FOSSIL-FUELED POWER PLANTS↗

Manufacturing of Continuous Microporous Polymeric Fibers for Separation Applications

Polyolefin plastic waste, particularly polypropylene, is one of the most prevalent components in the plastic waste stream generated globally. However, only a small fraction of this waste is recycled and reintegrated into second applications. These materials have significant embedded energy that could be used for additional productivity if recycled properly. Therefore, there is a critical need to develop scalable processing techniques with high throughput to effectively recycle it. We report the continuous manufacturing of microporous fibers using waste polypropylene plastic and melt-processable lignin, a plant biomass constituent produced as a byproduct in paper mills or biorefineries, as a template to create pores. Further, these filaments with hierarchical porosity─created by controlled microphase separation during high-speed extensional flow followed by removal of lignin─exhibit exceptional capillary action for hydrophobic liquids. The resulting porous fibers can be used for various separation applications. For example, the oil uptake of the fibers is 9.59 ± 0.82 g/g for applications in oil recovery in bodies of water. In addition, polyethylenimine infiltration within these nanoporous fibers introduces cyclic room temperature sorption and thermal desorption potential of acidic gases such as CO 2 in a bench-scale experiment. The fibers exhibit multiple cycles of CO 2 absorption, with a range of 0.15 to 0.17 mmol/g. Thus, these polyethylenimine-infiltered nanoporous polypropylene fibers can also be used in removing acidic gases from a gas mixture.

36 MATERIALS SCIENCE↗

Reinforced AEM Separators Based on Triblock Copolymers for Electrode-decoupled RFBs

Washington University in St. Louis (WUSTL), in collaboration with The University of Texas at San Antonio (UTSA) and Giner Inc. developed highly selective anion exchange membranes (AEMs) and a novel electrode-decoupled redox flow battery (RFB) for grid scale energy storage as part of the ARPA-E IONICS program (with connections to the DAYS program in the later part of the project). RFBs exhibit the crucial characteristic of system-level decoupled scaling of energy and power which makes them cost effective for the multi-GWh scales envisioned for grid-scale energy storage solutions. This has led to extensive (and deserved) research interest and attention. This project aimed to enhance the design space available for redox-flow batteries (RFBs) by enabling the long-term separation of disparate cationic (elemental) actives using a highly selective membrane separator, while concurrently permitting the transport of anions to balance charge. The approach proposed was to design and develop a highly selective anion-exchange membrane (AEM), which would in turn permit the design and development of electrode-decoupled RFBs. Pairs of (different element) cationic species with redox reactions exhibiting a large difference in their standard electrode potentials were identified to develop high voltage, high power RFBs while disrupting the existing paradigm of using a single element which can ionize to more than two soluble oxidation states (e.g.: Vanadium).

25 ENERGY STORAGE↗

SPE-CZE-MS Quantifies Zeptomole Amounts of Phosphorylated Peptides

Capillary zone electrophoresis (CZE) is gaining attention in the field of single-cell proteomics for its ultralow-flow and high-resolution separation abilities. Even more sample-limited yet rich in biological information are phosphoproteomics experiments, as the phosphoproteome composes only a fraction of the whole cellular proteome. Rapid analysis, high sensitivity, and maximization of sample utilization are paramount for single-cell analysis. Some challenges of coupling CZE analysis with mass spectrometry analysis (MS) of complex mixtures include 1. sensitivity due to volume loading limitations of CZE and 2. incompatibility of MS duty cycles with electropherographic time scales. Here, we address these two challenges as applied to singlecell- equivalent phosphoproteomics experiments by interfacing a microchip-based CZE device integrated with a solid-phaseextraction (SPE) bed with the Orbitrap Astral mass spectrometer. Using 225 phosphorylated peptide standards and phosphorylated peptide-enriched mouse brain tissue, we investigate microchip-based SPE-CZE functionality, quantitative performance, and complementarity to nano-LC-MS (nLC-MS) analysis. We highlight unique SPE-CZE separation mechanisms that can empower fitfor- purpose applications in single-cell-equivalent phosphoproteomics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Collective behavior of “flexicles”

In recent years the functionality of synthetic active microparticles has edged even closer to that of their biological counterparts. However, we still lack the understanding needed to recreate at the microscale key features of autonomous behavior exhibited by microorganisms or swarms of macroscopic robots. In this study, we propose a model for a three-dimensional deformable cellular composite particle consisting of self-propelled rod-shaped colloids confined within a flexible vesicle—representing a superstructure we call a “flexicle” that couples particle deformation to the internal dynamics of the internal active components. Using molecular dynamics simulations, we investigate the collective behavior of dense systems composed of many flexicles. We show that individual flexicles exhibit shape changes upon collisions with other flexicles that lead to rearrangements of the internal active rods, which slows flexicle motion. This shape deformability gives rise to a diverse set of motility-induced phase separation phenomena and the spontaneous flow of flexicles reminiscent of the migration of cells in dense tissues. Our findings establish a foundation for designing responsive, cell-like active particles and developing strategies for controlling swarm migration and other autonomous swarm behaviors at cellular and colloidal scales.

Science & Technology - Other Topics↗

MPACT Safeguards Modeling: FY25 Update

Sandia National Laboratories develops and maintains several open-source software packages to support material accountancy analyses. This includes the Material Accountancy Performance Indicator Toolkit (MAPIT), the Fissile Facility Flow Modeler (F3M) and the Separation and Safeguards Performance Model Library (SSPM-L). MAPIT is responsible for performing statistical safeguards analyses on bulk and itemized data from nuclear fuel cycle facilities and can operate on real or synthetic data. MAPIT is the only open-source software for such analyses. F3M is a library of modules, built in MATLAB Simulink, that contain pre made blocks to represent different generic fuel cycle processes. These blocks can be used together in a modular fashion to represent and simulate nuclear fuel cycle processes with the goal of improving facility-level accountancy during the design phase. F3M is also an open-source library. Finally, the SSPM-L library is a series of completed models built from F3M. The library includes facility models such as a generic PUREX facility and a fuel fabrication facility. The SSPM-L library is not open source, but is available to collaborators with a relevant use case. These tools include modeling and simulation pipelines to simulate nuclear fuel cycle facilities and the underlying software needed to simulate measurement uncertainty and perform statistical analyses. Together, these tools can perform end-to-end nuclear material accountancy analyses. This report documents the various improvements made to these tools in FY25. Specifically, we added new statistical test, new statistical modeling capabilities, new fuel cycle facility models, and launched a new open-source model component library.

97 MATHEMATICS AND COMPUTING↗

INFUSE:FLARED (Final Technical Report)

This report summarizes the final outcomes of the INFUSE:FLARED collaboration between Tokamak Energy (TE), the University of Illinois Urbana-Champaign (UIUC), and the Department of Energy (DOE). The project aimed to experimentally determine and model the pumping, absorption, and separation behavior of deuterium in flowing liquid lithium under gas and plasma exposure conditions. The work supports the development of lithium-based plasma-facing components (PFCs) and tritium management strategies for next-generation fusion plants.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Validation of SPH code Spheral to model interacting solid bodies in a supersonic flow

Contemporary discussions of planetary defense involve analyzing the risks posed by smaller sized, 20 to 200 m diameter, asteroids which are capable of breaking up in the atmosphere and generating a blast wave. Consequence assessments for this size class of asteroids are performed through fast-running analytic or semi-analytic models which are informed by high-fidelity hydrocode simulations of asteroid entry and breakup. However, insufficient historical data necessitates validating the independent physical processes which dominate airburst events. Here, the Fluid Solid Interface Smoothed Particle Hydrodynamics solver was previously used by Pearl et al. in 2023 to model the Chelyabinsk airburst and is used here to perform a series of validation simulations. The first effort involves modeling a cylinder in a hypersonic flow and comparing the bow shock geometry to that predicted by analytic theory. The second effort involves modeling the separation of two spherical bodies in supersonic flow and validating against experimental footage. Combined, these exercises demonstrate the ability of the code to model the flight-path of interacting solid bodies in a hypersonic flow.

Airburst↗

Recovery of Natural Gas Equipment Emissions into Gas Compression Engines for the Reduction of Potential Greenhouse Gas Emissions

Since the turn of the millennium, the United States (U.S.) oil and natural gas (ONG) industry has nearly doubled its natural gas production rate. As a result, the ONG industry has recently come under increasing scrutiny for its contributions to greenhouse gas (GHG) emissions. Consequently, various solutions to this problem have been proposed and formulated to reduce the impacts of GHG emissions on the environment. West Virginia University (WVU) have found it important to research the impacts of recovering vented gas streams into prime-mover engines. The U.S. Department of Energy (DOE) and National Energy Technology Laboratory (NETL) have granted WVU funding to research and develop a “Methane Mitigator” (M2) - a “Scalable Vent Mitigation Strategy to Simultaneously Reduce Methane Emissions and Fuel Consumption from the Compression Industry.” One of the main areas of interest for this research was the collection of emissions from natural gas equipment into a Caterpillar G3508J natural gas compression engine. The parameters being analyzed from the engine were brake-specific emissions and power output. The emissions sources considered for this research were pneumatic controllers (PCs), reciprocating compressor vents, and the engine’s open crankcase breather. The compressor vent and PC emissions were simulated using a mass flow controller (MFC) and flowed into the engine using two separate methods: (1) directly into the air intake, and (2) through a retrofitted closed crankcase ventilation system (CCV), serving as a buffer volume. The crankcase emissions were quantified without the CCV, and the impact on exhaust emissions from circulating the crankcase gases into the intake was measured. The simulated compressor vent and PC flows from the MFC had limited effect on the steady state operation of the engine and resulting performance. When the simulated flows were fed directly into the engine’s air intake, the changes within the engine’s continuous performance and emission parameters were larger but lasted for shorter durations. Conversely, when the simulated flows were fed into the CCV before entering the air intake, the changes in the engine’s performance and emission parameters were less pronounced for continuous analysis but lasted for longer durations. In either case, the continuous emission changes in both emissions and performance varied in size depending on the test scenario being run, but the cycle average changes in emissions and performance showed little impact overall compared to the engine’s baseline operation. As a result, the inclusion of a CCV shows a decrease in baseline carbon dioxide equivalent (CO2-eq.) engine emissions (from combined exhaust and open crankcase) of almost 4%. Likewise, the CCV inclusion reduced baseline total methane (CH4) from combined exhaust and open crankcase by upwards of 16%. These atmospheric emissions only decreased further with the inclusions of collected PC and compressor vent flows. The resulting changes in time-averaged rated exhaust behavior (or lack thereof) prove that the proposed M2 system could likely be deployed at sites with modern lean-burn natural gas engines as a viable option for reducing and eliminating potential GHG sources that would have otherwise been unutilized as energy sources.

03 NATURAL GAS↗

Stress Corrosion Cracking of NaSICON Membranes in Aqueous Electrolytes for Redox-Flow Batteries

The sodium super-ionic conductor (NaSICON) has versatile applications as a ceramic electrolyte for energy storage, where it can serve as an impermeable separator in solid-state batteries and redox flow systems. In particular, NaSICON systems have been proposed to be relatively stable in contact with water, making them compatible with aqueous battery chemistries. However, owing to their brittle nature and metal oxide constituents, stress-corrosion cracking (SCC) is an important failure mechanism that has not been previously explored. In this study, we assess the fracture toughness of NaSICON membranes in contact with aqueous solutions that are relevant to redox flow systems. Microindentation was performed to generate visible surface cracks and residual stress, which were observed to grow in length after exposure to aqueous solutions. This allows for a quantitative measurement of fracture toughness, which decreases after exposure to water. To contextualize these results, we develop a simplified model of the fracture behavior in aqueous redox-flow batteries that incorporate NaSICON membranes, illustrating the importance of SCC in cell design. This work provides quantitative insights into SCC as a failure mode in NaSICON, enhancing our understanding of the chemo-mechanical behavior of ceramic electrolytes in contact with aqueous solutions.

Zhang, Mengyao↗

Phase separation, edge currents, and Hall effect for active matter with Magnus dynamics

Here we examine run-and-tumble disks in two-dimensional systems where the particles also have a Magnus component to their dynamics. For increased activity, we find that the system forms a motility-induced phase-separated (MIPS) state with chiral edge flow around the clusters, where the direction of the current is correlated with the sign of the Magnus term. The stability of the MIPS state is non-monotonic as a function of increasing Magnus term amplitude, with the MIPS region first extending down to lower activities followed by a break up of MIPS at large Magnus amplitudes into a gel-like state. We examine the dynamics in the presence of quenched disorder and a uniform drive and find that the bulk flow exhibits a drive-dependent Hall angle. This is a result of the side jump effect produced by scattering from the pinning sites and is similar to the behavior found for skyrmions in chiral magnets with quenched disorder.

97 MATHEMATICS AND COMPUTING↗