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Complex Dynamics in Argyrodite Solid-State Ion Conductors
Argyrodites are a compositionally diverse family of materials that exhibit remarkable ion transport properties. While the average crystal structures of argyrodites have been extensively studied, ion transport in these materials is governed by a confluence of dynamic processes spanning the cation, anion, and polyanionic sublattices. This Perspective synthesizes recent advances in understanding the role of dynamics in structural behavior and ion transport properties. We examine the compositional and structural motifs that govern order−disorder transitions within the argyrodite family and further explore how ion hopping is facilitated by lattice dynamics, from long-range phonons to local rotational dynamics of polyanionic species. Through the lens of dynamics spanning multiple time and length scales, we establish guiding principles that govern transport phenomena and highlight avenues of future study for the argyrodite family of ion conductors.
The scientific case for concurrent neutron and X-ray scattering and spectroscopy
The interrogation of materials with X-rays or neutrons to determine structure, energetics, and dynamics is fundamental to advancing physical and chemical materials science and enabling innovative material technologies. A persistent challenge in materials development is that progress depends on understanding structure and dynamics across multiple length and time scales in increasingly complex, multicomponent systems featuring interfaces, heterogeneity, and hierarchical organization. Despite rapidly growing demands on materials characterization, current experimental approaches are almost exclusively based on isolated X-ray or neutron scattering and spectroscopy, reflecting a paradigm largely unchanged for decades. To assess the scientific need for a new experimental paradigm, a 3-day workshop sponsored by the U.S. National Science Foundation (NSF) was held at the SpringHill Suites, San Jose, California, from June 2 to 4, 2022. The workshop brought together 70 national and international experts who critically evaluated opportunities enabled by concurrent neutron and X-ray (NeX) scattering, spectroscopy, and imaging experiments. The participants reached a clear consensus that establishing NeX capabilities is crucial for advancing the science of complex materials in the United States. This report illustrates the scientific drivers for NeX experiments through representative examples spanning biomaterials, energy materials, soft matter, nanomaterials, quantum materials, geoscience, and applied materials research. The complementarity of neutrons and X-rays is essential for robust model development and refinement, particularly in multiphase and multicomponent systems. While joint refinement of data from separate experiments is valuable, concurrent measurements uniquely eliminate uncertainties arising from sample evolution, environmental drift, and irreproducibility associated with experiments performed at different locations and times. Realizing NeX capabilities will require the development of new instrumentation, data analysis frameworks, and robust sample environments compatible with both neutron and X-ray probes. Addressing these challenges will enable unambiguous interpretation of complex materials behavior and open new frontiers in materials research.
The Scientific Case for Concurrent Neutron and X-ray Scattering and Spectroscopy
The interrogation of materials with X-rays or neutrons to determine the structure, energetics, and dynamics of materials is fundamental to advancing materials' physical and chemical science and developing innovative material technologies. A transcending challenge in developing novel materials is that progress hinges on understanding the structure and dynamics across multiple time and length scales in complex materials that feature multiple components, interfaces, and compositions. Despite the ever-growing demands on materials’ characterization, existing approaches are almost exclusively based on isolated X-ray or neutron scattering, i.e., an approach commensurate with the more narrowly defined needs of fifty years ago. A three-day workshop sponsored by the U.S. National Science Foundation (NSF) analyzed the demand for concurrent neutron and X-ray (NeX) experiments. It was held at the Spring Hill Suites, San Jose, California, from June 2 to 4, 2022. In this workshop, 70 national and international experts ascertained the crucial need to establish NeX capabilities to advance the science of complex materials and systems in the US. Here, we illustrate the need for NeX scattering and spectroscopy experiments by showcasing examples that span areas as diverse as biomaterials, energy science, soft matter, and nanomaterials. To provide NeX capability will require new instrumentation that enables concurrent experiments. Affected areas include chemistry, soft matter, quantum materials, pure and applied chemistry, bioscience, geoscience, and applied materials. NeX benefits research outcomes due to the complementarity of the two techniques, which is essential for better model refinement. While joint refinement of data from separate neutron and X-ray experiments is critical to avoid ambiguities, especially in multiphase-multicomponent materials, concurrent experiments overcome scientific and technical barriers associated with single measurements, separated by location and, thus, time. Among all the examples, these factors introduce uncertainties in the results that complicate data analysis. [1,2] [3] While models are strongly sample-dependent, the principles of joint refinement are generally applicable to these disciplines, including the development of advanced parameterization, modeling, and analysis techniques that also consider the temporal and spatial resolutions of the two methods, leading to unambiguous data interpretation. Solutions for technical barriers must be found to realize NeX experiments, including developing robust sample environments that meet the optical requirements of neutrons and X-rays.
An on-board near-optimal climb-dash energy management
On-board real time flight control is studied in order to develop algorithms which are simple enough to be used in practice, for a variety of missions involving three dimensional flight. The intercept mission in symmetric flight is emphasized. Extensive computation is required on the ground prior to the mission but the ensuing on-board exploitation is extremely simple. The scheme takes advantage of the boundary layer structure common in singular perturbations, arising with the multiple time scales appropriate to aircraft dynamics. Energy modelling of aircraft is used as the starting point for the analysis. In the symmetric case, a nominal path is generated which fairs into the dash or cruise state. Feedback coefficients are found as functions of the remaining energy to go (dash energy less current energy) along the nominal path.
On-board near-optimal climb-dash energy management
On-board real time flight control is studied in order to develop algorithms which are simple enough to be used in practice, for a variety of missions involving three dimensional flight. The intercept mission in symmetric flight is emphasized. Extensive computation is required on the ground prior to the mission but the ensuing on-board exploitation is extremely simple. The scheme takes advantage of the boundary layer structure common in singular perturbations, arising with the multiple time scales appropriate to aircraft dynamics. Energy modelling of aircraft is used as the starting point for the analysis. In the symmetric case, a nominal path is generated which fairs into the dash or cruise state.
On-board near-optimal climb-dash energy management
On-board real time flight control is studied in order to develop algorithms which are simple enough to be used in practice, for a variety of missions involving three-dimensional flight. The intercept mission in symmetric flight is emphasized. Extensive computation is required on the ground prior to the mission but the ensuing on-board exploitation is extremely simple. The scheme takes advantage of the boundary layer structure common in singular perturbations, arising with the multiple time scales appropriate to aircraft dynamics. Energy modelling of aircraft is used as the starting point for the analysis. In the symmetric case, a nominal path is generated which fairs into the dash or cruise state. Previously announced in STAR as N84-16116
Optimization of Supersonic Transport Trajectories
This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.
Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft
This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.
Understanding and Manipulating Counterion Condensation within Charged Polymer Electrolytes for Selective and Low Resistant Membrane Separations
Polymeric ion-exchange membranes are found at the heart of numerous electrochemical systems spanning separations (electrodialysis and membrane capacitive deionization) and energy conversion and storage (flow batteries, fuel cells, and electrolyzers). The ion-exchange membrane separators need to be ion conducting but electron insulating, and in many scenarios selective for a particular ion to conduct. Because of their polymeric nature, the molecular architectures of ion-exchange membranes lack the molecular precision found in many inorganic materials. Plus, they contain numerous structural defects that impede ionic transport. As a result of their poor structure, it has been difficult to carefully probe the underlying physics that governs ion transport in ion-exchange membranes. We investigated counterion condensation phenomena in ion-exchange membranes and correlated it to bulk ionic charge transport and selectivity in precisely defined and long-range ordered materials afforded through the principles of directed self-assembly. A multi-faceted approach spanning i.) advanced metrology, two-dimensional atomic force microscopy, x-ray scattering, and ion-exchange equilibria, and ii.) molecular simulations (classical molecular dynamics and ab-inito molecular dynamics) that bridge multiple time and length scales, were employed to correlate the extent of counterion condensation to ionic conductivity and selectivity. After uncovering the extent of the condensation phenomena in this project, new macromolecular chemistries were employed to manipulate the ion pairing interactions of the condensed counterions to tethered ions on the polymer backbone so more facile and selective conduction rates can be attained. The research has aided in the rational design of polymeric ion-exchange membrane separators with high current density for electrochemical systems and subsequently better energy efficiency.
Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update
INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.
Satellite attitude prediction by multiple time scales method
An investigation is made of the problem of predicting the attitude of satellites under the influence of external disturbing torques. The attitude dynamics are first expressed in a perturbation formulation which is then solved by the multiple scales approach. The independent variable, time, is extended into new scales, fast, slow, etc., and the integration is carried out separately in the new variables. The theory is applied to two different satellite configurations, rigid body and dual spin, each of which may have an asymmetric mass distribution. The disturbing torques considered are gravity gradient and geomagnetic. Finally, as multiple time scales approach separates slow and fast behaviors of satellite attitude motion, this property is used for the design of an attitude control device. A nutation damping control loop, using the geomagnetic torque for an earth pointing dual spin satellite, is designed in terms of the slow equation.
Data-driven time-scale separation of ODE right-hand sides using dynamic mode decomposition and time delay embedding
Multi-physics simulation often involves multiple different scales. The ARKODE ODE solver package in the SUNDIALS library addresses multi-scale problems with a multi-rate time-integrator that can work with a right-hand side that has fast scale and slow scale components. In this report, we use dynamic mode decomposition and time delay embedding to extract the fast and slow components of the right-hand sides of a simple ODE from data. We then use the extracted components to solve the ODE with ARKODE. Finally, to move towards a real-world use case, we attempt to extract fast and slow scale dynamics from synthetic seismic modeling data.
Electron Precipitation Parameters and Ionospheric Conductances Inferred from Auroral Images Acquired by the Visible Imaging Systems (VIS) on the Polar Spacecraft
The Visible Imaging System (VIS) on the polar spacecraft provided time sequences of auroral images at multiple wavelengths that yield information of auroral dynamics on a global scale with a spatial resolution of - 20 km and temporal resolution of approx. 1 minute. Time sequences of VIS images in which the aurora was highly dynamic are used to infer global maps for the electron precipitation parameters, energy flux and characteristic energies, and ionospheric conductances. The maps are inferred from the corresponding VIS images using an auroral model (Lumerzheim et al., 1987). The temporal and spatial resolution of the VIS inferred patterns are unprecedented. The inferred patterns are highly structured and vary significantly on a time scale of less than 5 minutes. These patterns can be very beneficial for global physics-based numerical models for the high-latitude ionosphere which previously had to rely on statistical models for the electron precipitation and ionospheric conductance.
Developing ML/AI Methods for High-Throughput Characterization of Multiple-Sensor Streams of Tokamak Dynamics for High-Speed Control (Final Report)
This project evaluated and developed new mathematical and algorithmic techniques capable of handling (in real-time) the growing amounts of data generated by modern fusion research. While existing numerical linear algebra (NLA) methods provide the backbone to classical data analysis and algorithms, these methods fundamentally do not port to distributed architectures nor do they allow low-latency data reduction for control. Motivated by the needs for modern fusion reactors, this project explored and implemented new numerical methods to characterize plasma dynamics, respond in real-time to discharge evolution, and to process massive-scale data accurately and rapidly more fully. This project links expertise in multiple-sensor diagnostics of tokamak plasma dynamics from Columbia University’s Plasma Physics Laboratory with expertise in massive-scale data reduction and extreme data control algorithms at Columbia University’s Data Science Institute. This interdisciplinary project (i) applied machine learning methods, (ii) implemented a properly-trained neural-network for very fast processing of high-speed plasma videography, and (ii) developed the applied mathematical methods, based on randomized-NLA (rNLA) routines, for data analysis, reduction, and real-time control. The Columbia University High Beta Tokamak-Extended Pulse (HBT-EP) facility provided data to test new algorithms and partnership with Columbia University's Data Sciences Institute evaluated the broader use of new algorithms for many challenging control applications.
Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi
Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i.e., resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time scales of days, and multiple constituents per species with fortnightly filters. It outputs astronomical phase lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s), and reconstruction(s); confidence limits; and signal-to-noise ratios. Artificial data and water levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1 , S 1 , and P 1 ) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1 ) on water levels in the LCRE. CWT_Multi also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWT_Multi, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWT_Multi is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.
Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes
With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.
A new approach to the design of time-varying control systems with application to the Space Shuttle Boost
A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.