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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Thermodynamic controls on the synthesis, structure and reactivity of materials for energy (Final Report)

The major objectives have been: a) to advance and use unique calorimetric capabilities to determine the energetics of oxide and other materials having possible energy applications, with an emphasis on new materials for batteries, fuel cells and solar energy conversion, b) to understand, in terms of both macroscopic energetics and microscopic structure and bonding, the interplay of defect chemistry, oxidation-reduction, and size effects at the bulk and nanoscale in determining materials properties. This project emphasizes mixed ionic-electronic conduction materials containing transition metals of variable valence, especially perovskites and lithium containing phases, with M = Mn, Fe, Co, Ni. The thermochemistry of new families of complex halide, chalcogenide, nitride and hybrid (organic-inorganic) perovskite materials were explored. The major and unique technique employed is high temperature oxide melt solution calorimetry, with careful attention given to materials synthesis and characterization. The thermochemical studies will be coupled with structural studies, especially to characterize order-disorder phenomena by in situ high temperature diffraction techniques.

14 SOLAR ENERGY↗
DOE OSTI2024

High-resolution ion mobility based on traveling wave structures for lossless ion manipulation resolves hidden lipid features

Abstract High-resolution ion mobility (resolving power > 200) coupled with mass spectrometry (MS) is a powerful analytical tool for resolving isobars and isomers in complex samples. High-resolution ion mobility is capable of discerning additional structurally distinct features, which are not observed with conventional resolving power ion mobility (IM, resolving power ~ 50) techniques such as traveling wave IM and drift tube ion mobility (DTIM). DTIM in particular is considered to be the “gold standard” IM technique since collision cross section (CCS) values are directly obtained through a first-principles relationship, whereas traveling wave IM techniques require an additional calibration strategy to determine accurate CCS values. In this study, we aim to evaluate the separation capabilities of a traveling wave ion mobility structures for lossless ion manipulation platform integrated with mass spectrometry analysis (SLIM IM-MS) for both lipid isomer standards and complex lipid samples. A cross-platform investigation of seven subclass-specific lipid extracts examined by both DTIM-MS and SLIM IM-MS showed additional features were observed for all lipid extracts when examined under high resolving power IM conditions, with the number of CCS-aligned features that resolve into additional peaks from DTIM-MS to SLIM IM-MS analysis varying between 5 and 50%, depending on the specific lipid sub-class investigated. Lipid CCS values are obtained from SLIM IM ( TW(SLIM) CCS) through a two-step calibration procedure to align these measurements to within 2% average bias to reference values obtained via DTIM ( DT CCS). A total of 225 lipid features from seven lipid extracts are subsequently identified in the high resolving power IM analysis by a combination of accurate mass-to-charge, CCS, retention time, and linear mobility-mass correlations to curate a high-resolution IM lipid structural atlas. These results emphasize the high isomeric complexity present in lipidomic samples and underscore the need for multiple analytical stages of separation operated at high resolution. Graphical abstract

Reardon, Allison R. (ORCID:0000000165830134)↗
DOE OSTI2021

Analytical solution for the cumulative wake of wind turbines in wind farms

This paper solves an approximate form of conservation of mass and momentum for a turbine in a wind farm array. The solution is a fairly simple explicit relationship that predicts the streamwise velocity distribution within a wind farm with an arbitrary layout. As this model is obtained by solving flow-governing equations directly for a turbine that is subject to upwind turbine wakes, no ad hoc superposition technique is needed to predict wind farm flows. A suite of large-eddy simulations (LES) of wind farm arrays is used to examine self-similarity as well as validity of the so-called conservation of momentum deficit for turbine wakes in wind farms. The simulations are performed with and without the presence of some specific turbines in the wind farm. This allows us to systematically study some of the assumptions made to develop the analytical model. A modified version of the conservation of momentum deficit is also proposed to provide slightly better results at short downwind distances, as well as in the far wake of turbines deep inside a wind farm. Model predictions are validated against the LES data for turbines in both full-wake and partial-wake conditions. While our results highlight the limitation in capturing the flow speed-up between adjacent turbine columns, the model is overall able to acceptably predict flow distributions for a moderately sized wind farm. Finally, the paper employs the new model to provide insights on the accuracy of common wake superposition methods.

17 WIND ENERGY↗
DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗
DOE OSTI2021

Uranium corrosion characterization by handheld laser-induced breakdown spectroscopy

In this study, a commercial-off-the-shelf handheld laser-induced breakdown spectroscopy system was modified, calibrated and tested for discrimination between uranium oxide and uranium hydride when assessing uranium corrosion products. Operating parameters, system modifications, and onboard data analysis were developed to accomplish the analytical task. This work represents the first laser-induced breakdown spectroscopy analysis of bulk uranium hydride, a pyrophoric material, within an inert glovebox. Finally, the work shown here illustrates a rapid identification technique for uranium corrosion types from pure UO 2 or U 3 O 8 to pure UH 3 .

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2024

Fluorescent, phosphorescent, magnetic resonance contrast and radioactive tracer labelling of extracellular vesicles

This review focusses on the significance of fluorescent, phosphorescent labelling and tracking of extracellular vesicles (EVs) for unravelling their biology, pathophysiology, and potential diagnostic and therapeutic uses. Various labeling strategies, such as lipid membrane, surface protein, luminal, nucleic acid, radionuclide, quantum dot labels, and metal complex-based stains, are evaluated for visualizing and characterizing EVs. Direct labelling with fluorescent lipophilic dyes is simple but generally lacks specificity, while surface protein labelling offers selectivity but may affect EV-cell interactions. Luminal and nucleic acid labelling strategies have their own advantages and challenges. Here, each labelling approach has strengths and weaknesses, which require a suitable probe and technique based on research goals, but new tetranuclear polypyridylruthenium(II) complexes as phosphorescent probes have strong phosphorescence, selective staining, and stability. Future research should prioritize the design of novel fluorescent probes and labelling platforms that can significantly enhance the efficiency, accuracy, and specificity of EV labeling, while preserving their composition and functionality. It is crucial to reduce false positive signals and explore the potential of multimodal imaging techniques to gain comprehensive insights into EVs.

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

Evidence of excited-state lifetime enhancement in dimyristoyl-phosphocholine nanodiscs by ultraviolet absorption spectroscopy

Ultraviolet absorption spectroscopy is an analytical tool that is commonly utilized to determine protein concentrations, primarily due to characteristic absorption of tryptophan and tyrosine at 280 nm. Accurate concentration determination is essential to the accuracy of many biophysical techniques, and ultraviolet absorption provides a convenient and rapid method to assess protein concentration. However, the widespread usage of this method assumes that ultraviolet absorption is the same for individual amino acids in aqueous solution (where the molar extinction coefficient was measured) as for the amino acid in the conformational environment of the protein of interest. We demonstrate that additional considerations may be necessary for the membrane scaffold protein in dimyristoyl-phosphocholine nanodiscs through ultraviolet absorption spectroscopy of nanodiscs, liposomes, the membrane scaffold protein, and a mixture of liposomes and the non-nanodisc-associated protein. The aromatic amino acids of the membrane scaffold protein absorb significantly less light at 280 nm when associated with lipids in a lipoprotein assembly, which we plausibly attribute to an enhancement of chromophore excited-state lifetimes due to reduced intramolecular motion in the nanodisc. We caution that using the molar absorptivity of the membrane scaffold protein alone to determine nanodisc concentrations may not yield accurate results. Instead, the molar absorptivity of each nanodisc formulation should be explored independently to account for the unique conformational environment of each nanodisc.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Machine Learning–Augmented Laser-Induced Breakdown Spectroscopy for Spectral Discrimination of Iron Oxalates

Enhanced characterization and phase identification of post-PUREX Pu Oxalates (PuOXA) are pivotal for nonproliferation and pre-detonation nuclear forensics. Despite significant advances in the characterization of PuO 2 samples, little is known about the impact of both the chemical structure and oxidation states of PuOXA (i.e., Pu(III) and Pu(IV)) have on optical emission signatures. Here, we demonstrate the analytical capabilities of laser-induced breakdown spectroscopy (LIBS) applied to Fe(II) and Fe(III) oxalate samples as surrogates for PuOXA, highlighting the discriminating features in the LIBS emission spectra arising from differences in the oxidation states within mixed FeOXA samples. We report the enhancement of spectral feature selection using Principal Component Analysis (PCA), which enables the analytical superiority of machine learning algorithms such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Partial Least Squares Regression (PLSR), Support Vector Regression (SVR), and Random Forest Regression (RFR) over conventional univariate techniques for phase discrimination and chemometric analysis. Cluster analysis revealed how both matrix effects and laser ablation influence cluster separability by introducing spectral artifacts that misdirect the maximization of variance. PCA-selected emission lines were used in the regression models, demonstrating that both univariate and multivariate linear regression models (i.e., PLSR and SVR) can achieve acceptable performance, with machine learning models outperforming conventional calibration regressions. Furthermore, the application of non-linearly activated PCA-selected emission lines illustrates how simplifying the data while retaining captured variance enables the use of less complex and more computationally efficient models. Furthermore, this is particularly evident in the underperformance of RFR, which suffers from increased computational costs and overfitting owing to its high complexity.

Oxalates↗
DOE OSTI2022

3DBFSVBF (3D BatFinder Smart Video BioFilter and Multi-class BatFinder Smart Video BioFilter) [SWR-22-88]

Bats are notoriously difficult to study, therefore, identifying specific behavioral trends and the precise environmental conditions at the time of collision requires a monitoring solution that can reliably collect relevant data. To date, thermal infrared video surveillance has been extensively applied to study bats and has proven to be a powerful yet cumbersome tool. Current analytical approaches are time consuming because data processing data has not been fully automated. In the past, steps have been taken to record avian and bat activity in conjunction with complicated image processing techniques that separate species from other moving objects within the field of view (i.e. clouds and portions of the wind turbine). Once the videos are collected, the post-processing does not allow real time monitoring and identification, leading to a delay in both studying the behavior of these species and determining the effectiveness of any impact reduction strategy being studied. Moreover, object identification capability is lacking, thus limiting the usefulness of video data. To resolve these issues, we are using open source 3D computer vision and machine learning techniques allowing for automatic detection of objects in real-time with the ability to correlate these objects with environmental variables and recording the flight paths of each object. The machine learning has been trained on 3D data and allows for automated real-time data collection, identification and tracking, thereby eliminating the need for long and tedious post-analysis processing of the videos. This machine learning model is an added feature to the previous BatFinder Smart Video BioFilter and increases the accuracy of that systems classification by increasing the accuracy of identifying bats (90% accuracy) and insects (69% accuracy) to a 97% accuracy. There are two object classifier machine learning models, Binary and multi-classification. Binary object classifier labeled BatFinder_Smart_Video_BioFilter.h5 distinguishes between biological objects and non-biological objects. The main goal of this object classifier is to ignore the turbine blades while detecting biological object flying withing the rotor swept area of the turbine. Non-biological objects have a probability of 0 and biological objects have a probability of 1. Multi-classifier labeled Multiclass_BatFinder_Smart_Video_BioFilter.h5 distinguishes between bats, birds, insects and non-biological.

Yarbrough, John↗
DOE OSTI2024

Rapid measurement of soluble xylo-oligomers using near-infrared spectroscopy (NIRS) and multivariate statistics: calibration model development and practical approaches to model optimization

Rapid monitoring of biomass conversion processes using techniques such as near-infrared (NIR) spectroscopy can be substantially quicker and less labor-, resource-, and energy-intensive than conventional measurement techniques such as gas or liquid chromatography (GC or LC) due to the lack of solvents and preparation methods, as well as removing the need to transfer samples to an external lab for analytical evaluation. The purpose of this study was to determine the feasibility of rapid monitoring of a biomass conversion process using NIR spectroscopy combined with multivariate statistical modeling, and to examine the impact of (1) subsetting the samples in the original dataset by process location and (2) reducing the spectral range used in the calibration model on model performance. We develop multivariate calibration models for the concentrations of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids at multiple points in a biomass conversion process which produces and then purifies XOS compounds from sugar cane bagasse. A single model using samples from multiple locations in the process stream showed acceptable performance as measured by standard statistical measures. However, compared to the single model, we show that separate models built by segregating the calibration samples according to process location show improved performance. We also show that combining an understanding of the sample spectra with simple multivariate analysis tools can result in a calibration model with a substantially smaller spectral range that provides essentially equal performance to the full-range model. We demonstrate that real-time monitoring of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids concentration at multiple points in a process stream using NIR spectroscopy coupled with multivariate statistics is feasible. Segregation of sample populations by process location improves model performance. Models using a reduced spectral range containing the most relevant spectral signatures show very similar performance to the full-range model, reinforcing the importance of performing robust exploratory data analysis before beginning multivariate modeling.

09 BIOMASS FUELS↗
DOE OSTI2025

Edge ML for CAN bus intrusion detection in AVs

Autonomous Vehicles (AVs) are revolutionizing transportation, but their reliance on interconnected cyber-physical systems exposes them to unprecedented cybersecurity risks. This study addresses the critical challenge of detecting real-time cyber intrusions in self-driving vehicles by leveraging a dataset from the Udacity self-driving car project. We simulate four high-impact attack vectors, Denial of Service (DoS), spoofing, replay, and fuzzy attacks, by injecting noise into spatial features (e.g., bounding box coordinates) to replicate adversarial scenarios. We develop and evaluate two lightweight neural network architectures (NN-1 and NN-2) alongside a logistic regression baseline (LG-1) for intrusion detection. The models achieve exceptional performance, with NN-2 attaining an AUC score of 93.15% and 93.15% accuracy, demonstrating their suitability for edge deployment in AV environments. Through explainable AI techniques, we uncover unique forensic fingerprints of each attack type, such as spatial corruption in fuzzy attacks and temporal anomalies in replay attacks, offering actionable insights for feature engineering and proactive defense. Visual analytics, including confusion matrices, ROC curves, and feature importance plots, validate the models' robustness and interpretability. This research sets a new benchmark for AV cybersecurity, delivering a scalable, field-ready toolkit for Original Equipment Manufacturers (OEMs) and policymakers. By aligning intrusion fingerprints with SAE J3061 automotive security standards, we provide a pathway for integrating machine learning into safety-critical AV systems. Our findings underscore the urgent need for security-by-design AI, ensuring that AVs not only drive autonomously but also defend autonomously. This work bridges the gap between theoretical cybersecurity and life-preserving engineering, offering a leap toward safer, more secure autonomous transportation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

BFSVBF (BatFinder Smart Video BioFilter) [SWR-22-87] and Multi-class BatFinder Smart Video BioFilter Keras

Bats are notoriously difficult to study, therefore, identifying specific behavioral trends and the precise environmental conditions at the time of collision requires a monitoring solution that can reliably collect relevant data. To date, thermal infrared video surveillance has been extensively applied to study bats and has proven to be a powerful yet cumbersome tool. Current analytical approaches are time consuming because data processing data has not been fully automated. In the past, steps have been taken to record avian and bat activity in conjunction with complicated image processing techniques that separate species from other moving objects within the field of view (i.e. clouds and portions of the wind turbine). Once the videos are collected, the post-processing does not allow real time monitoring and identification, leading to a delay in both studying the behavior of these species and determining the effectiveness of any impact reduction strategy being studied. Moreover, object identification capability is lacking, thus limiting the usefulness of video data. To resolve these issues, we are using open source computer vision and machine learning techniques allowing for automatic detection of objects in real-time with the ability to correlate these objects with environmental variables and recording the flight paths of each object. The code has gone through five rounds of development with images used to train the models. This advancement allows for automated real-time data collection, identification, and tracking, thereby eliminating the need for long and tedious post-analysis processing of the videos. We will discuss the two open source and publicly available machine learning models developed within this scope of this work: 1) a binary model with a 97.5% accuracy in identifying the difference between an object and an empty scene, including wind turbine and clouds; and 2) a multiple classification model with the capability of identifying the type of object detected: bats (90% accuracy), birds (83% accuracy), insects (69% accuracy) and non-biological (99% accuracy).

Yarbrough, John↗
DOE OSTI2022

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

EDX ClaiMM

EDX ClaiMM is a centralized data & analytical platform designed to revolutionize U.S. critical minerals and materials (CMM) activities. By providing a robust digital infrastructure, ClaiMM will accelerate the combination, leveraging, and rapid utilization of vital data, advanced tools, and cutting-edge research advancements in CMM. This adaptive digital research hub connects the CMM community to essential knowledge products and offers access to interoperable datasets, databases, models, software, and tools from the National Energy Technology’s (NETL’s) Energy Data eXchange (EDX) and other authoritative sources, serving both public and private sectors. EDX ClaiMM delivers AI-informed solutions to address fundamental knowledge gaps and fosters the innovation of new techniques for enhanced characterization and recovery of CMMs within the U.S. By leveraging cloud-hosted, scalable digital infrastructure, ClaiMM meets public–private applied energy needs. It equips the CMM community with priority digital resources that harness on-site and cloud compute capabilities, enabling big data storage, advanced processing, analytics, and visualization.

Critical Materials; Critical Minerals; Rare Earth ↗
DOE OSTI2026

Investigation of nonlinear mechanical behavior of two superfine-grained graphites with DIC assisted disc splitting test

Using standardized uniaxial tensile test specimens is not practical due to the limited volumes in irradiation capsules, molten salt degradation facilities, or oxidation apparatus. The ASTM International Standard Test Method for Tensile Strength Estimate by Disc Compression of Manufactured Graphite (ASTM D8289) was developed to provide a convenient way for estimating tensile strength. Unlike the traditional uniaxial tensile test in ASTM C749 (International Standard Test Method for Tensile Stress–Strain of Carbon and Graphite), which uses dog-bone shaped specimens larger than 12.95 mm × 120.65 mm, the ASTM D8289 standard uses smaller discs with diameters of 6–12.7 mm. A digital image correlation (DIC) system, which uses a full-field noncontact surface displacement measurement technique, was applied along with the ASTM D8289 disc splitting test on IG-110 samples and compared with previous measurements from Mersen 2114 samples. Results confirmed that the DIC technique can measure the surface displacement/strain on these small (Ø6 mm × 3 mm) graphite specimens with good repeatability. However, Mersen 2114 and IG-110 samples exhibited strain discrepancies when DIC measurements were compared with analytical and finite element simulation values. The loading history and strain results also indicated different mechanical behaviors between Mersen 2114 and IG-110, particularly the nonlinear behavior of the IG-110 samples. Good agreement was observed by comparing the splitting tensile strengths of two superfine-grained grades with results from other work. The specimen size effect is discussed when comparing the splitting tensile strength with corresponding uniaxial tensile strength of these two graphite grades.

Lin, Lianshan [ORNL] (ORCID:0000000203399219)↗
DOE OSTI2022

A machine learning inversion scheme for determining interaction from scattering

Small angle scattering techniques have now been routinely used to quantitatively determine the potential of mean force in colloidal suspensions. However the numerical accuracy of data interpretation is often compounded by the approximations adopted by liquid state analytical theories. To circumvent this long standing issue, here we outline a machine learning strategy for determining the effective interaction in the condensed phases of matter using scattering. Via a case study of colloidal suspensions, we show that the effective potential can be probabilistically inferred from the scattering spectra without any restriction imposed by model assumptions. Comparisons to existing parametric approaches demonstrate the superior performance of this method in accuracy, efficiency, and applicability. This method can effectively enable quantification of interaction in highly correlated systems using scattering and diffraction experiments.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Carbon nanotube substrates enhance SARS-CoV-2 spike protein ion yields in matrix-assisted laser desorption–ionization mass spectrometry

Nanostructured surfaces enhance ion yields in matrix-assisted laser desorption–ionization mass spectrometry (MALDI-MS). The spike protein complex, S1, is one fingerprint signature of Sars-CoV-2 with a mass of 75 kDa. Here, we show that MALDI-MS yields of Sars-CoV-2 spike protein ions in the 100 kDa range are enhanced 50-fold when the matrix–analyte solution is placed on substrates that are coated with a dense forest of multi-walled carbon nanotubes, compared to yields from uncoated substrates. Nanostructured substrates can support the development of mass spectrometry techniques for sensitive pathogen detection and environmental monitoring.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗