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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows

Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.

Sjoegreen, B.↗
DOE OSTI2025

Exploring Data Set Bias and Decision Support with Predictive Uncertainty Through Bayesian Approximations and Convolutional Neural Networks

Individual seismic catalogs can contain multiscale observations from fault level to global scales and associated waveforms from discrete events reflect crustal structure across many different scales and locations. Seismic network aperture, geographic location, and observation distance may not provide informative guidance or intuition on how different catalogs will behave across models trained under different conditions. We rely on uncertainty to provide guardrails for when to trust model decisions, but understanding when our uncertainty is trustworthy is an open challenge. Here, in this work, we explore Bayesian approximation methods for assigning predictive uncertainty in seismic event classification problems. We find that computationally expensive Bayesian approximations do not outperform simple ensemble methods. We also find that when exploiting multiple seismic event catalogs, joint training with data from all the catalogs combined with Bayesian approximations and supervised training for classification can obscure bias and result in less robust uncertainty while also not providing substantial performance benefits compared to training individual models for each catalog.

58 GEOSCIENCES↗
NASA NTRS2005

The SMART Theory and Modeling Team: An Integrated Element of Mission Development and Science Analysis

When targeting physical understanding of space plasmas, our focus is gradually shifting away from discovery-type investigations to missions and studies that address our basic understanding of processes we know to be important. For these studies, theory and models provide physical predictions that need to be verified or falsified by empirical evidence. Within this paradigm, a tight integration between theory, modeling, and space flight mission design and execution is essential. NASA's Magnetospheric MultiScale (MMS) mission is a pathfinder in this new era of space research. The prime objective of MMS is to understand magnetic reconnection, arguably the most fundamental of plasma processes. In particular, MMS targets the microphysical processes, which permit magnetic reconnection to operate in the collisionless plasmas that permeate space and astrophysical systems. More specifically, MMS will provide closure to such elemental questions as how particles become demagnetized in the reconnection diffusion region, which effects determine the reconnection rate, and how reconnection is coupled to environmental conditions such as magnetic shear angles. Solutions to these problems have remained elusive in past and present spacecraft missions primarily due to instrumental limitations - yet they are fundamental to the large-scale dynamics of collisionless plasmas. Owing to the lack of measurements, most of our present knowledge of these processes is based on results from modern theory and modeling studies of the reconnection process. Proper design and execution of a mission targeting magnetic reconnection should include this knowledge and have to ensure that all relevant scales and effects can be resolved by mission measurements. The SMART mission has responded to this need through a tight integration between instrument and theory and modeling teams. Input from theory and modeling is fed into all aspects of science mission design, and theory and modeling activities are tailored to SMART needs during mission development and science analysis. In this presentation, we will present an overview of SMART theory and modeling team activities. In particular, we will provide examples of science objectives derived from state-of-the art models, and of recent research results that continue to be utilized in SMART mission development.

Hesse, Michael↗
DOE OSTI2025

Materials Engineering for High Performance and Durability Proton Exchange Membrane Water Electrolyzers

Proton exchange membrane water electrolyzers (PEMWEs) are expected to play a crucial role in the global green energy transition during the 21st century. They provide a versatile and sustainable solution for generating hydrogen with very high purity in combination with renewable energies, such as solar and wind. Despite their promise, PEMWEs face several critical problems, including high costs, performance limitations, and durability challenges, particularly at low iridium (Ir) loading on the anode. Advancing next-generation PEMWEs requires extensive work on materials engineering of all cell components, including the catalyst layer (CL), membrane, porous transport layer (PTL), bipolar plate (BPP), and gasket. This task must be performed with the complementary contribution of different modeling and characterization techniques. This review presents a critical perspective from academia, research centers, and industry, mapping main developments, remaining gaps, and strategic pathways to advance PEMWE technology. A focus is devoted to key aspects, such as operation at low Ir loading, membrane durability, multiscale transport layers, porous and non-porous flow fields, multiphysics modeling, and multipurpose characterization techniques, which are thoroughly discussed. By unifying these topics, this review provides readers with the essential knowledge to grasp current developments and tackle tomorrow's challenges in PEMWE engineering.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.

Yee, H. C.↗
NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗
NASA NTRS2003

Fractals and Spatial Methods for Mining Remote Sensing Imagery

The rapid increase in digital remote sensing and GIS data raises a critical problem -- how can such an enormous amount of data be handled and analyzed so that useful information can be derived quickly? Efficient handling and analysis of large spatial data sets is central to environmental research, particularly in global change studies that employ time series. Advances in large-scale environmental monitoring and modeling require not only high-quality data, but also reliable tools to analyze the various types of data. A major difficulty facing geographers and environmental scientists in environmental assessment and monitoring is that spatial analytical tools are not easily accessible. Although many spatial techniques have been described recently in the literature, they are typically presented in an analytical form and are difficult to transform to a numerical algorithm. Moreover, these spatial techniques are not necessarily designed for remote sensing and GIS applications, and research must be conducted to examine their applicability and effectiveness in different types of environmental applications. This poses a chicken-and-egg problem: on one hand we need more research to examine the usability of the newer techniques and tools, yet on the other hand, this type of research is difficult to conduct if the tools to be explored are not accessible. Another problem that is fundamental to environmental research are issues related to spatial scale. The scale issue is especially acute in the context of global change studies because of the need to integrate remote-sensing and other spatial data that are collected at different scales and resolutions. Extrapolation of results across broad spatial scales remains the most difficult problem in global environmental research. There is a need for basic characterization of the effects of scale on image data, and the techniques used to measure these effects must be developed and implemented to allow for a multiple scale assessment of the data before any useful process-oriented modeling involving scale-dependent data can be conducted. Through the support of research grants from NASA, we have developed a software module called ICAMS (Image Characterization And Modeling System) to address the need to develop innovative spatial techniques and make them available to the broader scientific communities. ICAMS provides new spatial techniques, such as fractal analysis, geostatistical functions, and multiscale analysis that are not easily available in commercial GIS/image processing software. By bundling newer spatial methods in a user-friendly software module, researchers can begin to test and experiment with the new spatial analysis methods and they can gauge scale effects using a variety of remote sensing imagery. In the following, we describe briefly the development of ICAMS and present application examples.

Lam, Nina↗
DOE OSTI2025

Multiscale Modeling Framework Using Element‐Based Galerkin Methods for Moist Atmospheric Limited‐Area Simulations

This paper presents a multiscale modeling framework (MMF) to model moist atmospheric limited-area weather. The MMF resolves large-scale convection using a coarse grid while simultaneously resolving local features through numerous fine local grids and coupling them seamlessly. Both large- and small-scale processes are modeled using the compressible Navier-Stokes equations within the Nonhydrostatic Unified Model of the Atmosphere (NUMA), and are discretized using a continuous element-based Galerkin method (spectral elements) with high-order basis functions. Consequently, the large-scale and small-scale models share the same dynamical core but have the flexibility to be adjusted individually. The proposed MMF method is tested in 2D and 3D idealized limited-area weather problems involving storm clouds produced by squall line and supercell simulations. Numerical results from the MMF showed enhanced representation of cloud processes compared to the coarse model.

Kang, Soonpil [Naval Postgraduate School, Monterey↗
NASA NTRS2006

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.↗
NASA NTRS2007

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis-Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.↗
DOE OSTI2025

Uncovering multiscale structure-property correlations via active learning in scanning tunneling microscopy

Atomic arrangements and local sub-structures fundamentally influence emergent material functionalities. These structures are conventionally probed using spatially resolved studies and the property correlations are deciphered by a researcher based on sequential explorations, thereby limiting the efficiency and scope. Here we demonstrate a multi-scale Bayesian deep-learning based framework that automatically correlates material structure with its electronic properties using scanning tunneling microscopy (STM) measurements in real-time. Its predictions are used to autonomously direct exploration toward regions of the sample that optimize a given material property. This method is deployed on a low-temperature ultra-high vacuum STM to understand the structure-property relationship in a europium-based semimetal, EuZn 2 As 2 , a promising candidate relevant to magnetism-driven topological phenomena. The framework employs a sparse-sampling approach to efficiently construct the scalar-property space using minimal measurements, about 1–10% of the data required in standard hyperspectral methods. Moreover, we formulate the problem hierarchically across length scales, implementing autonomous workflow to locate mesoscopic and atomic structures that correspond to a target material property. This framework offers the choice to design scalar-property from the spectroscopic data to steer sample exploration. Our findings reveal correlations of the electronic properties unique to surface terminations, local defect density, and point defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2017

Conjunction Assessment Techniques and Operational Results from the Magnetospheric Multiscale Mission

This paper will describe the results that have been obtained to date during the MMS mission concerning conjunction assessment. MMS navigation makes use of a weak-signal GPS-based system: this allows signals to be received even when MMS is flying above the GPS orbits, producing a highly accurate determination of the four MMS orbits. This data is downlinked to the MMS Mission Operations Center (MOC) and used by the Flight Dynamics Operations Area (FDOA) for both maneuver design and conjunction assessment. The MMS fly in tetrahedron formations around apogee, in order to collect simultaneous particles and fields science data. The original plan was to fly tetrahedra between 10 and 160 km in size; however, after Phase 1a of the mission, the science team requested that smaller sizes be flown if feasible. After analysis (to be detailed in a companion paper), a new minimum size of 7 km was decided upon. Flying at this reduced scale size makes conjunction assessment between the MMS spacecraft even more important: the methods that are used by the MMS FDOA to address this problem will be described in the paper, and a summary given of the previous analyses that went into the development of these techniques. Details will also be given of operational experiences to date. Finally, two CA mitigation maneuver types that have been designed (but never yet required to actually be performed) will also be outlined.

conjunction Assessment↗
NASA NTRS2016

Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix and Polymer Matrix Composite Structures

Stochastic-based, discrete-event progressive damage simulations of ceramic-matrix composite and polymer matrix composite material structures have been enabled through the development of a unique multiscale modeling tool. This effort involves coupling three independently developed software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/ Life), and (3) the Abaqus finite element analysis (FEA) program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating unit cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC. Abaqus is used at the global scale to model the overall composite structure. An Abaqus user-defined material (UMAT) interface, referred to here as "FEAMAC/CARES," was developed that enables MAC/GMC and CARES/Life to operate seamlessly with the Abaqus FEA code. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events, which incrementally progress and lead to ultimate structural failure. This report describes the FEAMAC/CARES methodology and discusses examples that illustrate the performance of the tool. A comprehensive example problem, simulating the progressive damage of laminated ceramic matrix composites under various off-axis loading conditions and including a double notched tensile specimen geometry, is described in a separate report.

composite structures↗
DOE OSTI2025

Openpronghorn

OpenPronghorn is a simulation tool specifically tailored for modeling thermal-hydraulic phenomena in advanced nuclear reactors. It is built on the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source platform that facilitates the development of high-performance scientific computing applications. OpenPronghorn solves the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in fluid flows, using the finite volume numerical method. The code supports a wide range of fluid flow conditions that are applicable to nuclear reactors, including incompressible and weakly compressible flows, as well as single-phase and multiphase flows. It is capable of modeling diverse flow regimes, including laminar and turbulent flows, using various turbulence models such as the standard k-epsilon models, the v2f model, and the mixing length model. For multiphase flows, OpenPronghorn employs a mixture a Eulerian modeling approach with mixture, drift-flux, and full Eulerian models, and includes open-sourced interfacial transfer correlations for drag, exchange, and heat transfer coming from the scientific literature. OpenPronghorn's modular design allows it to handle multiscale simulations, ranging from detailed Reynolds-Averaged Navier Stokes (RANS) simulations to coarse-mesh and lumped parameter models. This flexibility enables users to perform high-fidelity simulations of specific reactor components as well as system-level analyses of entire reactor circuits. The code can be coupled with other MOOSE-based tools using the MultiApp system, allowing for the transfer of coupling quantities such as mass flow rates, heat fluxes, and boundary conditions between different simulation scales. One of the main features of OpenPronghorn is the it includes built-in validation cases from the open-source scientific literature and supports the implementation of user-defined models and correlations through MOOSE's FunctorMaterial system. OpenPronghorn is designed to be computationally efficient, leveraging the SIMPLE projection method for large-scale problems, and can be run on high-performance computing systems to handle the extensive computational demands of detailed reactor simulations. Overall, OpenPronghorn is a versatile and robust tool that provides critical insights into the thermal-hydraulic behavior of advanced nuclear reactors, supporting the design, safety, and optimization of next-generation nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗
DOE OSTI2025

Streaming Data in HPC Workflows Using ADIOS

The “IO Wall” problem, in which the gap between computation rate and data access rate grows continuously, poses significant problems to scientific workflows which have traditionally relied upon using the filesystem for intermediate storage between workflow stages. One way to avoid this problem in scientific workflows is to stream data directly from producers to consumers and avoiding storage entirely. However, the manner in which this is accomplished is key to both performance and usability. This paper presents the Sustainable Staging Transport, an approach which allows direct streaming between traditional file writers and readers with few application changes. SST is an ADIOS “engine”, accessible via standard ADIOS APIs, and because ADIOS allows engines to be chosen at run-time, many existing file-oriented ADIOS workflows can utilize SST for direct application-to-application communication without any source code changes. This paper describes the design of SST and presents performance results from various applications that use SST, for feeding model training with simulation data with substantially higher bandwidth than the theoretical limits of Frontier’s file system, for strong coupling of separately developed applications for multiphysics multiscale simulation, or for in situ analysis and visualization of data to complete all data processing shortly after the simulation finishes.

Podhorszki, Norbert [ORNL] (ORCID:000000019647542X↗
NASA NTRS2009

Multiscale Computer Simulation of Tensile and Compressive Strain in Polymer- Coated Silica Aerogels

While the low thermal conductivities of silica aerogels have made them of interest to the aerospace community as lightweight thermal insulation, the application of conformal polymer coatings to these gels increases their strength significantly, making them potentially useful as structural materials as well. In this work we perform multiscale computer simulations to investigate the tensile and compressive strain behavior of silica and polymer-coated silica aerogels. Aerogels are made up of clusters of interconnected particles of amorphous silica of less than bulk density. We simulate gel nanostructure using a Diffusion Limited Cluster Aggregation (DLCA) procedure, which produces aggregates that exhibit fractal dimensions similar to those observed in real aerogels. We have previously found that model gels obtained via DLCA exhibited stress-strain curves characteristic of the experimentally observed brittle failure. However, the strain energetics near the expected point of failure were not consistent with such failure. This shortcoming may be due to the fact that the DLCA process produces model gels that are lacking in closed-loop substructures, compared with real gels. Our model gels therefore contain an excess of dangling strands, which tend to unravel under tensile strain, producing non-brittle failure. To address this problem, we have incorporated a modification to the DLCA algorithm that specifically produces closed loops in the model gels. We obtain the strain energetics of interparticle connections via atomistic molecular statics, and abstract the collective energy of the atomic bonds into a Morse potential scaled to describe gel particle interactions. Polymer coatings are similarly described. We apply repeated small uniaxial strains to DLCA clusters, and allow relaxation of the center eighty percent of the cluster between strains. The simulations produce energetics and stress-strain curves for looped and nonlooped clusters, for a variety of densities and interaction parameters.

Good, Brian↗
DOE OSTI2024

SQMS Quantum R&D in Machine Learning, Optimization and Sensing beyond Fundamental Physics Applications

This newly formed team at SQMS under the Ecosystem Thrust is looking to develop capabilities impacting societal advances outside the core domain of HEP and condensed matter physics. We explicitly leverage the experimental and algorithmic innovations developed across all groups as well as connect to broad-scope external projects of the diverse team of PIs. As the inaugural set of projects, we are studying numerically quantum machine learning models inspired by efficiently trainable echo-state and orthogonal neural networks and developing designs for related experiments to be performed on quantum processors based on SQMS SRF cQED technology and Rigetti s transmon arrays. Investigated models exploit ideas and lessons learned from multiple prior work by SQMS team members in a variety of internal and external activities [R1]. Target initial applications include noisy signal processing, potentially captured by quantum sensors or noisy QPUs, as well as simulation and classification of healthcare data. For instance, image reconstruction of the brain s electrical properties by solving the inverse Maxwell equation problem with uncertainty [R2] through a hybrid quantum-classical physics-informed architecture for time-dependent processes [R3]. The group is also investigating the application and development of novel quantum sensors based on magnetic levitation of a superconducting sphere coupled to a superconducting qubit. This coupling enables high-precision measurements of the position of the sphere, which can be used for sensitive detection of forces, enabling practical applications such as gravimetry for geophysics analysis, or accelerometry for GPS-denied navigation [R4] [R1] Rieffel, Eleanor G., Ata Akbari Asanjan, M. Sohaib Alam, Namit Anand, David E. Bernal Neira, Sophie Block, Lucas T. Brady et al. "Assessing and advancing the potential of quantum computing: A NASA case study." Future Generation Computer Systems (2024). [R2] Yu, X., Serrall s, J.E., Giannakopoulos, I.I., Liu, Z., Daniel, L., Lattanzi, R. and Zhang, Z., 2023. Pifon-ept: Mr-based electrical property tomography using physics-informed fourier networks. IEEE Journal on Multiscale and Multiphysics Computational Techniques. [R3] Wudarski, Filip, Daniel OConnor, Shaun Geaney, Ata Akbari Asanjan, Max Wilson, Elena Strbac, P. Aaron Lott, and Davide Venturelli. "Hybrid quantum-classical reservoir computing for simulating chaotic systems." arXiv preprint arXiv:2311.14105 (2023). [R4] Higgins, Gerard, Saarik Kalia, and Zhen Liu. "Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors." Physical Review D 109.5 (2024): 055024.

Venturelli, Davide↗
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↗