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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Hydrothermal solubility of Dy hydroxide as a function of pH and stability of Dy hydroxyl aqueous complexes from 25 to 250 °C

The rare earth elements (REE) have important applications in green energy technologies. The formation of mineral deposits in geologic systems commonly involves hydrothermal fluids which can mobilize the REE. However, the REE speciation is not well known as a function of pH. The thermodynamic properties of REE hydroxyl complexes used in geochemical models are based on the Helgeson-Kirkham-Flowers (HKF) equation of state parameters which were derived by extrapolation of low temperature experimental and estimated data. In this study, Dy hydroxide solubility experiments are combined with available literature data to improve these models from 25 to 250 °C and optimize the thermodynamic properties of Dy 3+ and Dy hydroxyl complexes using GEMSFITS. Batch-type solubility experiments were conducted from 150 to 250 °C and at saturated water vapor pressure in perchloric acid solutions with initial pH values of 2 to 5 in 0.5 pH unit increments. The measured solubility of Dy hydroxide is retrograde with temperature and decreases with pH. The logarithm of total dissolved Dy molality ranges from –2.3 to –5.3 at 150 °C (pH 4.7–5.5), from –2.4 to –5.6 at 200 °C (pH 3.9–5.1), and from –3.7 to –6.9 at 250 °C (pH of 3.4 and 5.0). The optimized standard partial molal Gibbs energies of formation (Δ f G° T ) derived for Dy 3+ and DyOH 2+ display a close to linear relationship with temperature, fitting with previous optimizations based on DyPO 4 solubility data in the literature. A comparison of the optimized ΔfG°T values for aqueous Dy species with predictions from available HKF parameters indicates significant differences ranging from +11 to –26 kJ/mol between 25 and 250 °C. The experimental fits are used to derive the Dy hydroxide solubility products (K s0 ) and formation constants for the hydrolysis of Dy (β n with n = 1 to 3; Dy 3+ + nOH – = DyOH n 3-n ) as a function of temperature. The optimization method presented yields accurate thermodynamic properties for the Dy 3+ aqua ions and the DyOH 2+ species at the acidic to mildly acidic pH studied whereas more experimental work is needed at near-neutral and alkaline conditions to better constrain the other hydroxyl complexes. Furthermore, the optimized thermodynamic data have a significant impact on geochemical modeling of the mobility and solubility of REE minerals in acidic hydrothermal fluids.

58 GEOSCIENCES↗
DOE OSTI2025

Thermal Performance of Triply Periodic Minimal Surface Lattice Structures in Single-Phase Dielectric Fluid Cooling of Power Electronics

Additive manufacturing has transformed thermal management by enabling the production of complex, optimized geometries that conventional manufacturing methods cannot achieve. This study investigates the single-phase convective heat transfer performance of gyroid triply periodic minimal surface (TPMS) lattice structures with functional porosity. TPMS structures provide high surface area to volume ratios and are amenable to 3D printing. A gyroid numerical model was created and validated against an existing experimental study with a similar feature size to the investigated geometries. The TPMS structure has a periodic width of 1.6 mm, a length of 10 mm, and a height of 4 mm, with a functional porosity ranging from 0.5 to 0.8, decreasing with distance from the heated surface. Three different flow configurations were examined for an inlet fluid temperature of 70 °C. The inlet velocities range from 0.01 to 1.2 m/s, corresponding to a Reynolds number range of 10–900 with a heat flux of 50 W/cm 2 applied at the base. AmpCool ® AC-110 dielectric fluid (Prandtl number 59.5) was used as the coolant. Thermal performance and friction characteristics were studied for the three flow orientations. The parallel flow configuration was identified as the most efficient for heat removal. A detailed analysis of the numerical results highlights the underlying physics behind the thermal performance differences among the flow configurations.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2026

Near-Infrared Photoluminescence from Spin-Flip Excited States of π-Conjugated Tris(quinolinolate) Chromium(III) Complexes

Tuning metal–ligand covalency offers promising design strategies to tailor the photoluminescence (PL) emission energies of metal-centered, spin-flip excited states. Herein, we report a series of tris(quinolinolate) chromium(III) complexes that exhibit record-low near-infrared II emission energies in a fluid solution at room temperature, afforded by their strong metal–ligand covalencies. Appending π-conjugated arylethynyl substituents to quinolinolate ligands resulted in minimal changes to metal–ligand bond lengths, facilitating nearly indiscriminate metal–ligand covalencies for each tris(quinolinolate) chromium(III) complex. As a result, near-infrared II emission was observed across the series, while simultaneously affording careful tuning of the 4 LMCT/ 4 ( 1 ILCT) electronic transition energies across the visible region. Here, detailed analyses of ground-state electronic structures and excited-state electronic transitions revealed that PL arises from a ligand-field, 2 E excited state, admixed with charge-transfer character. This assignment was supported by solvent-dependent near-infrared emission energies and long excited-state lifetimes, consistent with spin-forbidden relaxation (ranging from 115 ± 5 to 123 ± 1 ns across the series). Utilizing spectroscopic data, ligand-field parameters were quantified, further rationalizing the role of strong metal–ligand covalency in enabling near-infrared II emission. Supported by these results, this study presents a new class of ligands that enable room-temperature near-infrared II emission in chromium(III)-based spin-flip excited states.

Absorption spectroscopy↗
DOE OSTI2024

Implementation of Detailed Polyethylene Pyrolysis Kinetics into CFD Simulations using Machine Learning

Municipal solid waste (MSW) and waste plastics have received significant attention due to the issues of waste generation and storage, as well as their potential as an energy resource. High-density polyethylene (HDPE) makes up a large portion of plastic waste and has been the subject of several conversion studies. However, the mechanisms associated with converting HDPE through pyrolysis and gasification are extensive and complex making them difficult to implement into high-fidelity computational fluid dynamic (CFD) simulations. For this project, a primary pyrolysis mechanism containing 42 unique species and 737 heterogeneous reactions was used to generate kinetic data over a range of operating conditions. A machine learning (ML) model was developed to replicate the results of the detailed pyrolysis mechanism while significantly increasing the computational efficiency. A deep operator network (DeepONet) architecture was adopted to train the model using time steps relevant to CFD simulations. The ML used physics-based loss functions to ensure mass conservation. The ML model has been deployed in simple MFiX CFD simulations, single particle, and an experimental drop tube reactor, and has shown promising performance compared to the original scheme.

Houston, Ross↗
DOE OSTI2024

Accelerating transients with NekRS: GPU overlapping domain implementation and multi-rate timestepping

The simulation of nuclear transients using Computational Fluid Dynamics (CFD) presents significant computational challenges due to the inherent complexity and the wide separation in temporal scales between various flow physical phenomena. These disparities lead to high computational costs, often making the simulation of transients impractical without advanced techniques. Consequently, multiple research initiatives are being pursued by the NEAMS thermal-hydraulic area, some driven by academic institutions and some by national laboratories. Overall, they are exploring novel methods to make transient simulations more feasible and efficient. This report delves into recent advancements within the CFD code NekRS, specifically those achieved in Fiscal Year 2024 under the CONNECT effort, aimed at improving the performance and feasibility of transient simulations. The first major advancement involves the porting of NekRS to Aurora, one of the Department of Energy’s (DOE) most powerful supercomputers. Additionally, the report discusses the implementation of an overlapping domain capability within NekRS. This novel GPU-accelerated capability allows different spatial regions of the domain to be solved independently, enhancing the code’s efficiency, particularly when running large-scale simulations in complex domains. The scalability of this approach is demonstrated, highlighting its potential to transform how transients are approached in CFD simulations. Lastly, the report focuses on how this overlapping domain capability specifically accelerates transient simulations through multi-rate timestepping. By decoupling different regions and facilitating faster computations, this method offers a promising pathway to making nuclear transient simulations more computationally feasible, addressing one of the critical bottlenecks in the field. Together, these advancements represent a significant leap forward in transient simulation technology, bringing closer the possibility of handling highly complex nuclear scenarios with greater efficiency and accuracy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗
DOE OSTI2025

Modeling hydraulic fracture opening and closure with proppant transport and settlement

Hydraulic fracturing is a widely used reservoir stimulation technique for improving fluid circulation in rock formations with extremely low permeability, particularly in enhanced geothermal systems (EGS). To better understand the complex processes involved and improve hydraulic stimulation performance, we have developed ELK (ELectrical fracKing), a MOOSE-based 3D finite element application designed to model the behavior of proppant-fluid mixtures in propagating fractures. ELK integrates both the fluid and proppant components, incorporating particle-driven processes such as gravity settling, particle-particle interactions, and strong density and viscosity contracts, in addition to conventional fluid-driven fracture propagation. In this contribution, we extend ELK to model propped fracture closure, which occurs after the injection phase due to a dramatic drop in the effective stress on the fracture plane. During the shut-in, flowback, and production periods, the fracture width decreases, with the closure behavior depending on proppant concentration.. At low concentrations, closure follows a nonlinear joint law linked to the stiffness of asperities in the fracture walls. While at high concentrations, it is controlled by the properties of packed proppant bed. The extended ELK application is validated against several benchmark examples, including the propagation of an inclined frictional crack, fracture opening and sliding in response to fluid injection, and flowback analysis. We believe that ELK’s enhanced capabilities can serve as a valuable tool for the design and optimization of EGS deployment.

15 - GEOTHERMAL ENERGY↗
DOE OSTI2024

Development & Experimental Validation of a Generalized Resistance-Capacitance Model for Numerical Simulation of Phase-Change Material Embedded Heat Exchangers

Latent heat thermal energy storage (LHTES) using phase change material (PCM) has attracted increased attention as a viable solution for overcoming the mismatch between energy supply and demand for renewable energy-based systems. PCM-embedded heat exchangers (PCM-HX) have the potential to significantly improve thermal performance due to high storage capacity and low temperature variation during the phase change process. Most models for simulating LHTES heat transfer use Computational Fluid Dynamics (CFD) simulations, which have high computational costs resulting from considering the complex and time-dependent physics relevant to PCM-HXs. In this paper, a Generalized Resistance Capacitance-based Model (GRCM) was developed to predict the thermal performance of arbitrary PCM-HXs in a computationally efficient manner without compromising modeling accuracy. The GRCM is exercised for three case studies: (i) verification for a single-slabbed finned PCM-HX, (ii) verification and validation for a copper foam/paraffin composite PCM-HX, and (iii) validation for a straight tube annular finned PCM-HX. The copper foam PCM-HX uses an electric heater at the top of HX, while the other two configurations utilize water as heat transfer fluid. For the single-slabbed finned PCM-HX melting case, the mean deviation in average PCM temperature predicted by the GRCM compared to the CFD model was between 0.56 – 0.73 K, with maximum temperature deviation of 2.68 K. For the HTF outlet temperature, the validation results showed that GRCM prediction matches very well with experimental data, with mean temperature deviation of 0.24 K during melting case, while for solidification case was 0.34 K. These results showcase the GRCM’s capability for accurately reproducing the thermal characteristics of PCM-HXs with considerably lower computational effort.

42 ENGINEERING↗
DOE OSTI2025

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗
DOE OSTI2025

CaptureFOAM

CaptureFOAM provides utilities for fast and accurate direct air capture (DAC) contactor simulations, based on the OpenFOAM framework. At the core, CaptureFOAM is a suite of mass transfer and chemistry models built upon the OpenFOAM thin film model, which allows coarser mesh resolution and less constrictive time step requirements when compared to a traditional volume of fluid approach. This allows CaptureFOAM to conduct device-scale simulations for complex geometries including commercial packing materials and novel contactor shapes, matching experimental results in a wide variety of applications.

Kincaid, Kellis [Oak Ridge National Laboratory (OR↗
DOE OSTI2025

Development for Integrated System-Level Analysis Capabilities in SAM for Molten Salt Reactors

In recent years, there has been renewed interest in Molten Salt Reactors (MSRs) for their potential advantages compared to reactors that rely on solid fuel. In response to such interest, many methods and codes have been developed to capture the unique features of MSRs. Among them, the System Analysis Module (SAM) is a modern system analysis tool that provides fast-running, modest-fidelity, whole-plant transient analysis capabilities, essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. For liquid-fuel MSRs, the complex physics and chemistry involved in MSR operation—such as reactor kinetics, fluid flow, heat transfer, and salt composition dynamics—pose significant challenges for system-level modeling. Specific modeling capabilities are needed for system-level transient simulation. This paper presents recent advancements in SAM capability enhancements for system-level modeling of MSRs, focusing on improved simulation fidelity, computational efficiency, and multi-physics integration. Key enhancements include the development of species transport, Delayed Neutron Precursor (DNP) drift, modified Point Kinetics Equations (PKE), decay heat modeling, key fission product behavior, salt corrosion, and thermal-hydraulic coupling, as well as code robustness and performance enhancements for MSR applications. The code enhancement allows for better predictive accuracy in safety analysis, transient behavior, and operational optimization, thus supporting the design and licensing of next-generation MSRs. Results from case studies are presented to demonstrate the benefits of these enhancements in accurately capturing key reactor transient behaviors.

Hu, Rui (ORCID:0000000237712920)↗
DOE OSTI2024

Reversible Electron-Beam Patterning of Colloidal Nanoparticles at Fluid Interfaces

The directed self-assembly of colloidal nanoparticles (NPs) using external fields guides the formation of sophisticated hierarchical materials but becomes less effective with decreasing particle size. As an alternative, electron-beam-driven assembly offers a potential avenue for targeted nanoscale manipulation, yet remains poorly controlled due to the variety and complexity of beam interaction mechanisms. Here, we investigate the beam–particle interaction of silica NPs pinned to the fluid–vacuum interface of ionic liquid droplets. In these experiments, scanning electron microscopy of the droplet surface resolves NP trajectories over space and time while simultaneously driving their reorganization. With this platform, we demonstrate the ability to direct particle transport and create transient, reversible colloidal patterns on the droplet surface. By tuning the beam voltage, we achieve precise control over both the strength and sign of the beam–particle interaction, with low voltages repelling particles and high voltages attracting them. This response stems from the formation of well-defined solvent flow fields generated from trace radiolysis of the ionic liquid, as determined through statistical analysis of single-particle trajectories under varying solvent composition. Altogether, electron-beam-guided assembly introduces a versatile strategy for nanoscale colloidal manipulation, offering new possibilities for the design of dynamic, reconfigurable systems with applications in adaptive photonics and catalysis.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Development of a conduction-based model for analyzing frozen startup of alkali-metal heat pipes

One key area of interest in heat pipe modeling/simulation is to analyze the startup behavior of the liquid-metal heat pipes (LMHPs) from a frozen state. This so-called ‘frozen startup’ process involves a complex set of nonlinear mass and heat transport phenomena, including phase transitions from solid to liquid and vapor, multiphase interactions, microporous wick flow, and compressible vapor dynamics. The complexity of these processes makes it challenging to simulate LMHP’s frozen startup using conventional numerical methods or commercial computational fluid dynamics (CFD) software. This paper presents a simplified conduction-based modeling approach that can provide practical insights into the entire LMHP frozen startup process, while alleviating the challenges of modeling its complex physics. The theoretical foundation and physical assumptions of the proposed model are based solely on heat-conduction equation, allowing for a more tractable simulation without sacrificing essential physical accuracy. The proposed model was implemented in a commercial CFD software, and its prediction was compared with the experimental data obtained from sodium heat-pipe startup experiments. The comparison highlights the proposed model's ability to capture the transient thermal behavior of LMHP during frozen startup. This study not only validates the conduction-based frozen startup modeling method but also shows its potential as a practical and efficient tool for understanding the startup performance of the LMHP systems.

Microreactor↗
DOE OSTI2026

Mesh-based multiphysics coupling acceleration for fusion neutronics through clustering for fusion blanket applications

Accurate modeling of particle transport within fusion blankets is essential for predicting performance metrics such as heat deposition and the tritium breeding ratio (TBR). However, high-fidelity coupling of thermal fluids from computational fluid dynamics (CFD) to neutronics simulations often incurs significant computational costs due to the complexity of surface intersection calculations in Monte Carlo codes. This paper presents an accelerated multiphysics coupling method for neutronics that utilizes hierarchical agglomerative clustering to map complex material property distributions to a neutronics model. Implemented within the fusion reactor design and assessment (FREDA) framework, the method leverages existing Python packages to automate the creation of clustered geometries for OpenMC. The approach is demonstrated on a sector model of an ARC-class tokamak with an immersion molten salt blanket, and an simple geometry with varying isotopic concentrations. Results show that the clustering method significantly reduces computational burden without compromising fidelity, providing a foundation for agile iteration of neutronics simulations involving multiple coupled material properties.

Bae, Jin Whan [ORNL] (ORCID:0000000326548907)↗
DOE OSTI2024

Application of Modified Meshgraphnets for Subsurface Prediction during CO2 Sequestration

In the face of the increasingly dire consequences of anthropogenic climate change, capturing and storing carbon dioxide is paramount. However, several impediments exist to the safe and effective subsurface storage of CO2, such as cost of transport, identification of suitable sites for subsurface storage, and assessment of long-term risk from storage in subsurface aquifers. Accurate subsurface modeling is necessary to ensure that CO2 storage is both safe and effective. Still, such modeling has traditionally required either substantial time and computational power (numerical simulation) or a substantial amount of pre-existing data for training (machine learning models). Additionally, these models lack flexibility in dealing with both changes in discretization of the input data and generalizability beyond the data on which they are trained. In order to address these issues, this research applies graph neural networks (GNNs) to predict subsurface saturation and pressure during CO₂ injection in a model of the Illinois Basin-Decatur Project (IBDP). GNNs provide a flexible, intuitive method for representing and manipulating complex unstructured data, which is often found in many practical domain problems such as fluid flow and subsurface characterization. These unstructured grids are easily represented in GNNs by representing spatially-localized features such as permeability, porosity, saturation, and pressure as nodes in a graph and relationships between these properties as edges connecting these nodes. This research applies a specific GNN model called MeshGraphNets (MGN) to model the change in CO2 saturation and pressure over a 50-month time period (36 months of injection, 14 months post-injection). The MGN model leverages a message passing process that allows the network to learn both the spatial and temporal dynamics of this system simultaneously. Additionally, training on a limited dataset (64 realizations, 20 time points each) resulted in a high degree of accuracy in saturation prediction both within the same timeframe as the training (20 months, 0.039 average RMSE) and when projecting out to the end of injection (36 months, 0.053 average RMSE). Temporal predictions such as those generated by MGNs and other similar models are prone to accumulated error over time; in order to address this, a multi-step rollout (MSR) training process was applied to calculate training loss. This method mimics the forward prediction during inference by “rolling out” multiple time points in a single training step using the previous prediction as input to the MGN model. By calculating the loss several time steps forward from the current prediction, the model is forced to find a more stable state over time. Application of MSR to the MGN model resulted in an average 15% reduction in inference error over time during forward prediction. This study showcases the immense potential of GNNs as a game-changing methodology for predicting pressure and saturation evolution in CCS projects, ultimately paving the way for more sustainable and effective carbon storage solutions. Presentation prepared for the 2024 AiChE Annual Meeting, October 27 to November 1 2024, San Diego, CA.

Holcomb, Paul↗
DOE OSTI2024

Developing a remediation framework

When harmful contaminants are detected in soil, sediment, or groundwater (or suspected due to industrial activities), remediation efforts may be required to protect human health and the environment. This chapter will introduce and discuss the steps in the general site remediation process that are key when approaching any remediation strategy, regardless of the site complexity. While these steps are described in a linear fashion, in most cases, the approach is more fluid and iterative depending on the desired outcomes and success of each progressive clean-up effort along the way. This chapter will additionally articulate some key considerations which may be important to the overall remediation strategy depending on the particular needs and desired outcomes. From these more general discussions, the chapter will branch into a case-study of the remediation approach, or process steps, previously/currently/in the future taking place at the Hanford Site, as one example of a complex waste sites in the United States. As indicated earlier, while a remediation strategy can be more simply described by a progression of general process steps, it is far more likely to observe fluidity and strategy evolution over time from the first conceived strategy as remediation progress occurs. The chapter concludes with a brief discussion of how the strategy at the Hanford Site has evolved to provide a singular example of what this evolution might look like for other complex waste sites.

Muller, Katherine A.↗
DOE OSTI2026

Nanorod Pair Complexes Manipulated via Magnetic Casimir Forces

Here, we demonstrate a route to modulate Casmir–Lifshitz interactions between anisotropic nanoparticles and magnetic fluids. By semiclassical quantum electrodynamics, we study ground state dispersion forces for cylindrical dielectric nanorods made of polystyrene (PS) and zinc oxide (ZnO) embedded in toluene-based host media with gold-coated magnetite nanoparticles and also predict magnetic contributions to the fully retarded excited state interaction. The variation in magnetic permeability enables tuning between repulsive and attractive interactions, and measurable magnetic Casimir traps are predicted between a pair of ZnO–PS nanoparticles whose equilibrium position can be modulated over an order of magnitude with a small variation in the size of the magnetite nanoparticle. This provides an alternative magnetic Casimir-effect pathway to reversibly tune quantum electromagnetic forces at the nanoscale for the assembly and enhancement of colloidal stability.

Excited-state interaction↗
DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗