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At least 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Nonunique fraction of Fock exchange for defects in two-dimensional materials

By investigating the vacancy and substitutional defects in monolayer WS 2 with hybrid functionals, we find that there is no unique amount of Fock exchange that concurrently satisfies the generalized Koopmans' condition and reproduces the band-gap and band-edge positions. Fixing the mixing parameter of Fock exchange based on the band gap can lead to qualitatively incorrect defect physics in two-dimensional materials. Instead, excellent agreement is achieved with both experiment and many-body perturbation theory within the GW approximation once the mixing parameters are tuned individually for the defect species and the band edges. Here, we show the departure from a unique optimized mixing parameter is inherent to two-dimensional systems as the band edges experience a reduced screening while the localized defects are subject to bulklike screening.

2-dimensional systems↗
DOE OSTI2024

Multiparameter optical fiber sensing for energy infrastructure through nanoscale light–matter interactions: From hardware to software, science to commercial opportunities

Monitoring of energy infrastructure through robust yet economical sensing platforms is becoming an area of increased importance, with ubiquitous applications including the electrical grid, natural gas and oil transportation pipelines, H2 infrastructure (storage and transportation), carbon storage, power generation, and subsurface environments. Plasmonic and functional nanomaterial enabled fiber optic sensors show excellent promise for a wide range of sensing applications due to their versatility to be engineered for specific analytes of interest while retaining inherent advantages of the optical fiber sensor platform. Through the design of novel sensing layers, the optical transduction mechanism and wavelength dependence can also be tailored for ease of integration with low-cost interrogation systems enabling an inexpensive yet highly functional optical fiber sensing platform. In addition, recent advances in artificial intelligence and machine learning theoretical methods have been leveraged to simultaneously extract multiple parameters through multi-wavelength interrogation such that unique wavelengths can also serve as unique sensing elements, analogous to electronic nose sensor technologies. The concept of an optical fiber based “photonic nose” via multiple interrogation wavelengths and/or sensor nodes offers a compelling platform technology to realize multiparameter speciation of chemical analytes within complex gas mixtures. In this Perspective, we further generalize the notion of multiparameter sensing through the novel “photonic nervous system” concept based upon low-cost, functionalized optical fiber sensor probes monitoring a variety of distinct analyte classes (physical, chemical, electromagnetic, etc.) simultaneously to provide broad situational awareness via integrated sensors.

Su, Yang-Duan (ORCID:0000000214820902)↗
DOE OSTI2024

Observational benchmarks inform representation of soil organic carbon dynamics in land surface models

Abstract. Representing soil organic carbon (SOC) dynamics in Earth system models (ESMs) is a key source of uncertainty in predicting carbon–climate feedbacks. Machine learning models can help identify dominant environmental controllers and establish their functional relationships with SOC stocks. The resulting knowledge can be integrated into ESMs to reduce uncertainty and improve predictions of SOC dynamics over space and time. In this study, we used a large number of SOC field observations (n=54 000), geospatial datasets of environmental factors (n=46), and two machine learning approaches (namely random forest, RF, and generalized additive modeling, GAM) to (1) identify dominant environmental controllers of global and biome-specific SOC stocks, (2) derive functional relationships between environmental controllers and SOC stocks, and (3) compare the identified environmental controllers and predictive relationships with those in models used in Phase 6 of the Coupled Model Intercomparison Project (CMIP6). Our results showed that the diurnal temperature, drought index, cation exchange capacity, and precipitation were important observed environmental predictors of global SOC stocks. While the RF model identified 14 environmental factors that describe climatic, vegetation, and edaphic conditions as important predictors of global SOC stocks (R2=0.61, RMSE = 0.46 kg m−2), current ESMs oversimplify the relationships between environmental factors and SOC, with precipitation, temperature, and net primary productivity explaining > 96 % of the variability in ESM-modeled SOC stocks. Further, our study revealed notable disparities among the functional relationships between environmental factors and SOC stocks simulated by ESMs compared with observed relationships. To improve SOC representations in ESMs, it is imperative to incorporate additional environmental controls, such as the cation exchange capacity, and refine the functional relationships to align more closely with observations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Fresh look at the nuclear transparency using the generalized parton distributions

Color transparency (CT) is a fundamental phenomenon in QCD in which hadrons produced in high-energy exclusive processes traverse nuclear matter with minimal interactions. Nuclear transparency, which quantifies this attenuation suppression, is a quantity with high sensitivity to CT effects and provides critical insights into QCD dynamics in nuclear environments. In this study, we revisit nuclear transparency using the framework of generalized parton distributions (GPDs). By constructing nuclear GPDs (nGPDs) through the incorporation of nuclear parton distribution functions, we calculate the nuclear transparency 𝑇⁡(𝑄 2 ) for the carbon nucleus as a function of momentum transfer 𝑄 2 considering various definitions and compare the results obtained with available experimental data. Our finding highlights the importance of choosing a physically motivated definition of nuclear transparency. Moreover, we emphasize that a more reliable determination of nGPDs requires a dedicated global analysis incorporating nuclear data. Such an approach is essential for improving the theoretical understanding of CT and for achieving consistency with experimental observations in the high-𝑄 2 regime.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Neural-network model for force prediction in multi-principal-element alloys

Atomistic simulations can provide useful insights into the physical properties of multi-principal-element alloys. However, classical potentials mostly fail to capture key quantum (electronic-structure) effects. Here we present a deep 3D convolutional neural network (3D CNN) based framework combined with a voxelization technique to design interatomic potentials for chemically complex alloys. We highlight the performance of the 3D CNN model and its efficacy in computing potentials using the medium-entropy alloy TaNbMo. In order to provide insights into the effect of voxel resolution, we implemented two approaches based on the inner and outer bounding boxes. An efficient 3D CNN model, which is as accurate as the density-functional theory (DFT) approach, for calculating potentials will provide a promising schema for accurate atomistic simulations of structure and dynamics of general multi-principle element alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Optical functions of crystalline and amorphous TeO2

The optical functions of crystalline paratellurite (α-TeO2) and amorphous TeO2 were determined using several optical techniques: (1) standard spectroscopic two-modulator generalized ellipsometry (2-MGE) of paratellurite (200–850 nm, 6.2–1.46 eV), (2) near-normal-incidence two-modulator generalized ellipsometry microscopy (2-MGEM) of paratellurite (577 nm, 2.15 eV), (3) Mueller matrix transmission of paratellurite (320–798 nm, 3.87–1.55 eV), and (4) polarized transmission of paratellurite (323.6–334.3 nm, 3.83–3.71 eV). The 2-MGE measurements yielded highly accurate values of the dielectric functions and error estimates from 1.46 to 6.2 eV for both paratellurite and amorphous TeO2, whereas the polarization-dependent transmission yielded more accurate values of the absorption coefficient below the band edge of paratellurite. The 2-MGEM measured the diattenuation of paratellurite, which is related to the birefringence. Mueller matrix transmission measurements of paratellurite of a (001) cut crystal as a function of angle of incidence were used to determine both the birefringence and the rotary power as a function of photon energy.

Jellison Jr, Gerald [ORNL]↗
DOE OSTI2021

Scattering amplitudes for all masses and spins

We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an extra SU(2) little group index for massive particles, with the amplitudes for spin Sparticles transforming as symmetric rank 2S tensors. We systematically characterise all possible three particle amplitudes compatible with Poincare symmetry. Unitarity, in the form of consistent factorization, imposes algebraic conditions that can be used to construct all possible four-particle tree amplitudes. This also gives us a convenient basis in which to expand all possible four-particle amplitudes in terms of what can be called “spinning polynomials”. Many general results of quantum field theory follow the analysis of four-particle scattering, ranging from the set of all possible consistent theories for massless particles, to spin-statistics, and the Weinberg-Witten theorem. We also find a transparent understanding for why massive particles of sufficiently high spin cannot be “elementary”. The Higgs and Super-Higgs mechanisms are naturally discovered as an infrared unification of many disparate helicity amplitudes into a smaller number of massive amplitudes, with a simple understanding for why this can’t be extended to Higgsing for gravitons. We illustrate a number of applications of the formalism at one-loop, giving few-line computations of the electron (g - 2) as well as the beta function and rational terms in QCD. “Off-shell” observables like correlation functions and form-factors can be thought of as scattering amplitudes with external “probe” particles of general mass and spin, so all these objects — amplitudes, form factors and correlators, can be studied from a common on-shell perspective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Electrochemical, thermodynamic, and physical properties of tetradecyltrihexylphosphonium ([P 6,6, 6,14 ] + ) and methyl-propyl piperidinium containing ionic liquids and their propylene carbonate solutions

Here, the viscosity, conductivity, electrochemical window and related thermodynamic properties such as excess volume and dynamic viscosity deviation of two phosphonium ionic liquids were measured and calculated for “as-supplied” and dried neat liquids and also v/v mixtures of 99/1, 95/5, 90/10, 75/25, and 50/50 of the ionic liquids with propylene carbonate (PC). Tetradecyltrihexylphosphonium dicyanamide ([P 6,6,6,14 ] + dicyanamide), Cyphos 105, and tetradecyltrihexylphosphonium bis(trifluororomethanesulfonyl)imide (called bistriflimide) ([P 6,6,6,14 ] + bistriflimide), Cyphos 109, ionic liquids were studied. Generally speaking, there were slight differences in the measured properties of the wet and dried IL solutions which were reflected in differences if the calculated properties. The measured and calculated properties were compared with those collected and derived from a piperidinium-based ionic liquid, methyl-propyl piperidinium bistriflimide. Arrhenius plots for both the viscosity and conductivity were linear, with the linearity of the Litovitz plots being slightly higher. The viscosity and conductivity of the phosphonium solutions yielded Walden Plots that differed from Walden plots of piperidinium solutions and other ionic liquid solutions. For the phosphonium based ionic liquids, the ionicity was found to increase with increasing dilution in propylene carbonate. The electrochemical windows of the ionic liquids were determined as a function of the concentration of the ionic liquid present in the solution. The size of the window generally initially decreased and then increased with the addition of PC for the [P 6,6,6,14 ] + dicyanamide ionic liquid increasing from 3.4 V in the 95/5 v/v (volume Cyphos 105) to volume of PC solvent) to 3.7 in the 50/50 dried IL case. The electrochemical windows of the dried liquids were slightly larger 3.5 V for the 95/5 v/v and 4.2 V for the 50/50 v/v Cyphos 105/PC solutions. The electrochemical window was larger and the conductivity was higher for the piperidinium IL solutions, but since the ionicity increases with dilution, the phosphonium based IL solutions may prove favorable for processes such as electrochemical reduction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A divergent synthetic route to functional copolymer libraries via modular polymers

High-throughput polymer synthesis enables rapid exploration of chemical space but remains limited by batch-to-batch inconsistencies that can obscure structure–property relationship trends. To address this challenge, we developed a synthetic approach to produce multifunctional copolymers using post-polymerization modification of activated ester modular polymers with commercially available amines. Easily derivitized parent polymers—poly(tetrafluorophenyl acrylate) and poly(tetrafluorophenyl styrene sulfonate)—were synthesized by RAFT polymerization to yield single polymer batches containing highly reactive tetrafluorophenyl esters or sulfonate esters on each repeat unit. Tuning post-polymerization modification reaction conditions enabled the addition of sub-stoichiometric amounts of amines (relative to the repeat unit) to yield partially functionalized intermediates that could then be further derivatized. Reaction monitoring by 19 F NMR spectroscopy confirmed good control over these sequential post-polymerization modifications. This synthetic route produced a variety of copolymers with defined comonomer ratios while preserving the underlying polymer structure (degree of polymerization, dispersity, tacticity) for both the acrylate and styrene sulfonate backbones. We further applied this approach in a divergent manner to create a small library of structurally distinct copolymers from a single parent batch in three synthetic steps. This modular, divergent synthesis demonstrates a general route to structurally consistent copolymer libraries that enable systematic studies of structure–property relationships and can accelerate functional materials discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Energy barriers for Dy and H penetrating graphene on 6 H -SiC(0001) and freestanding bilayer graphene from first-principles calculations

Currently, intercalation of foreign guest atoms into two-dimensional (2D) layered van der Waals materials is an active research area motivated in part by the development of next-generation energy-storage technologies and optoelectronic devices. One such extensively studied 2D material is the graphene-on-SiC system. To realize and control the desired intercalated structures, it is fundamentally important to understand the kinetic process of intercalation. For the intercalation of a guest atom into graphene layers on SiC substrate, a critical kinetic parameter is the energy barrier of a guest atom penetrating the perfect graphene top layer into the gallery under it. However, accurate theoretical calculations for such penetration barriers are unavailable in literature. From our first-principles density functional theory calculations, we obtain the global energy barriers of 3.47 and 1.80 eV for single Dy and H atoms penetrating the graphene top layer on a graphene buffer layer supported by a Si-terminated 6H-SiC(0001) substrate, respectively. Furthermore, for comparison as well as for examining the lateral strain effects, we also obtain the global barriers of 5.05 and 1.50 eV for single Dy and H atoms penetrating freestanding bilayer graphene with a tensile strain of about 8.8% to match our model for supported graphene, as well as the global barriers of 7.21 and 4.18 eV for penetrating unstrained freestanding bilayer graphene, respectively. From corresponding minimum energy paths with multiple energy minima and saddle points, we can also obtain various local energy barriers and the global backward barrier from the graphene gallery back to the top surface.

2D materials↗
DOE OSTI2021

Semi-Analytic Functions to Calculate the Deposition Coefficients for Ice Crystal Vapor Growth in Bin and Bulk Microphysical Models

Numerical cloud models require estimates of the vapor growth rate for ice crystals. Current bulk and bin microphysical parameterizations generally assume that vapor growth is diffusion limited, though some parameterizations include the influence of surface attachment kinetics through a constant deposition coefficient. A parameterization for variable deposition coefficients is provided herein. The parameterization is an explicit function of the ambient ice supersaturation and temperature, and an implicit function of crystal dimensions and pressure. The parameterization is valid for variable surface types including growth by dislocations and growth by step nucleation. Deposition coefficients are predicted for the two primary growth directions of crystals, allowing for the evolution of the primary habits. Comparisons with benchmark calculations of instantaneous mass growth indicate that the parameterization is accurate to within a relative error of 1%. Parcel model simulations using Lagrangian microphysics as a benchmark indicate that the bulk parameterization captures the evolution of mass mixing ratio and fall speed with typical relative errors of less than 10%, whereas the average axis lengths can have errors of up to 20%. The bin model produces greater accuracy with relative errors often less that 10%. The deposition coefficient parameterization can be used in any bulk and bin scheme, with low error, if an equivalent volume spherical radius is provided.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Influence of Oxygen Uptake on Pitch Carbon Fiber

Carbon fiber precursor materials, such as polyacrylonitrile, pitch, and cellulose/rayon, require thermal stabilization to maintain structural integrity during conversion into carbon fiber. Thermal stabilization mitigates undesirable decomposition and liquification of the fibers during the carbonization process. Generally, the thermal stabilization of mesophase pitch consists of the attachment of oxygen-containing functional groups onto the polymeric structure. In this study, the oxidation of mesophase pitch precursor fibers at various weight percentage increases (1, 3.5, 5, 7.5 wt%) and temperatures (260, 280, 290 °C) using in situ differential scanning calorimetry and thermogravimetric analysis is investigated. The results are analyzed to determine the effect of temperature and weight percentage increase on the stabilization process of the fibers, and the fibers are subsequently carbonized and tested for tensile mechanical performance. Finally, the findings provide insight into the relationship between stabilization conditions, fiber microstructure, and mechanical properties of the resulting carbon fibers.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Field validation of isotropic analytical models for simulating fabric shades

Fabric roller shades are common shading materials used in commercial and residential buildings. Accurately characterizing and modeling shades helps practitioners select the appropriate product and its control strategy based on climate and occupants' priorities, such as visual comfort and view to outdoors. Previous studies established a generalized method for modeling complex fenestration systems using data-driven tabulated bidirectional scattering distribution functions. However, deploying such a method at scale to all fabric shading products on the market is too costly and time-consuming. Analytical models that are based on a limited set of measurements (e.g., normal-normal and normal-hemispherical visible transmittance and reflectance, and directional cut-off angles) can be used to model the wide variety of shading products on the market. This study evaluates the performance of two isotropic analytical models, Roos-Wienold and Modified-Kotey, for modeling fabric roller shades, with a focus on the model's ability to predict occupant visual comfort. The performance evaluation was conducted through laboratory and field measurements and simulations. The results showed that both models are sufficient for predicting vertical illuminance at seated eye-level. Roos-Wienold model was able to predict binary visual comfort classification (glare/no-glare) under a wide range of luminance conditions, while Modified-Kotey model did not perform as well under high-contrast low-adaptation conditions. Both models are insufficient in predicting visual comfort at a four-point scale (e.g., imperceptible, perceptible, disturbing, intolerable). The two isotropic models become less accurate when the fabric exhibits high anisotropy.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Krylov subspace recycling for evolving structures

Krylov subspace recycling is a powerful tool when solving a long series of large, sparse linear systems that change only slowly over time. In PDE constrained shape optimization, these series appear naturally, as typically hundreds or thousands of optimization steps are needed with only small changes in the geometry. In this setting, however, applying Krylov subspace recycling can be a difficult task. As the geometry evolves, in general, so does the finite element mesh defined on or representing this geometry, including the numbers of nodes and elements and element connectivity. This is especially the case if re-meshing techniques are used. As a result, the number of algebraic degrees of freedom in the system changes, and in general the linear system matrices resulting from the finite element discretization change size from one optimization step to the next. Changes in the mesh connectivity also lead to structural changes in the matrices. In the case of re-meshing, even if the geometry changes only a little, the corresponding mesh might differ substantially from the previous one. Obviously, this prevents any straightforward mapping of the approximate invariant subspace of the linear system matrix (the focus of recycling in this work) from one optimization step to the next; similar problems arise for other selected subspaces. In this paper, we present an algorithm to map an approximate invariant subspace of the linear system matrix for the previous optimization step to an approximate invariant subspace of the linear system matrix for the current optimization step, for general meshes. This is achieved by exploiting the map from coefficient vectors to finite element functions on the mesh, combined with interpolation or approximation of functions on the finite element mesh. We demonstrate the effectiveness of our approach numerically with several proof of concept studies for a specific meshing technique.

42 ENGINEERING↗
DOE OSTI2021

Effect of Temperature on the Pilot-Scale Catalytic Pyrolysis of Loblolly Pine

A pilot-scale biomass catalytic pyrolysis unit with a nominal throughput of one tonne of biomass per day (1TPD) has been in operation since 2013 to investigate the process parameters that have the largest influence on biocrude yield, oxygen content, and chemical composition. A parametric study was conducted to investigate the effect of pyrolysis temperature, ranging from 433 to 581 °C, on biocrude yield and quality. A locally sourced loblolly pine feedstock and a commercially available, spray dried, nonzeolitic γ-Al 2 O 3 catalyst were used in individual experiments conducted at each pyrolysis temperature to achieve a minimum of 4 h of steady-state continuous operation. Typically, 600–800 kg of biomass was fed over a 12-h period, with one experiment extended to almost 29 h (1144-kg biomass fed) and one experiment interrupted by a process upset after just 7 h (411-kg biomass fed). Comprehensive analysis of collected gas, liquid, and solid products were used to calculate carbon balances (77% to 107%) for each experiment. The biocrude yield ranged from 12 to 18 wt % C and, in general, decreased with increasing pyrolysis temperature. The average steady-state biocrude yield as a function of temperature translated to a biocrude production rate between 40 and 50 gallons per dry ton. The biocrude oxygen content varied between 21 and 31 wt %, on a dry basis, and as expected, decreased with increasing pyrolysis temperature. The identified components in the semivolatile biocrude products are mostly methoxyphenols and other multiphenolic compounds. The multiphenolic compounds are demethoxylated at pyrolysis temperatures above 500 °C, producing biocrudes with higher concentrations of monophenols and polycyclic aromatic hydrocarbons. The concentration of anhydrosugars, like levoglucosan in the biocrudes, decreased with increasing pyrolysis temperature from ∼15 to ∼1 vol %.

biofuels↗
DOE OSTI2024

Quarkonium transport in weakly and strongly coupled plasmas

We report on progress in the nonperturbative understanding of quarkonium dynamics inside a thermal plasma. The time evolution of small-size quarkonium is governed by two-point correlation functions of chromoelectric fields dressed with an adjoint Wilson line, known in this context as generalized gluon distributions (GGDs). The GGDs have been calculated in both weakly and strongly coupled plasmas by using perturbative and holographic methods. Strikingly, the results of our calculations for a strongly coupled plasma indicate that the quarkonium dissociation and recombination rates vanish in the transport descriptions that assume quarkonium undergoes Markovian dynamics. However, this does not imply that the dynamics is trivial. As a starting point to explore the phenomenological consequences of the result at strong coupling, we show a calculation of the Y(1 S ) formation probability in time-dependent perturbation theory. This is a first step towards the development of a transport formalism that includes non-Markovian effects, which, depending on how close the as of yet undetermined nonperturbative QCD result of the GGDs is to the strongly coupled N = 4 SYM result, could very well dominate over the Markovian ones in quark-gluon plasma produced at RHIC and the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Re-examining the silicon self-interstitial charge states and defect levels: A density functional theory and bounds analysis study

The self-interstitial atom (SIA) is one of two fundamental point defects in bulk Si. Isolated Si SIAs are extremely difficult to observe experimentally. Even at very low temperatures, they anneal before typical experiments can be performed. Given the challenges associated with experimental characterization, accurate theoretical calculations provide valuable information necessary to elucidate the properties of these defects. Previous studies have applied Kohn–Sham density functional theory (DFT) to the Si SIA, using either the local density approximation or the generalized gradient approximation to the exchange-correlation (XC) energy. The consensus of these studies indicates that a Si SIA may exist in five charge states ranging from -2 to +2 with the defect structure being dependent on the charge state. This study aims to re-examine the existence of these charge states in light of recently derived “approximate bounds” on the defect levels obtained from finite-size supercell calculations and new DFT calculations using both semi-local and hybrid XC approximations. We conclude that only the neutral and +2 charge states are directly supported by DFT as localized charge states of the Si SIA. Within the current accuracy of DFT, our results indicate that the +1 charge state likely consists of an electron in a conduction-band-like state that is coulombically bound to a +2 SIA. Furthermore, the -1 and -2 charge states likely consist of a neutral SIA with one and two additional electrons in the conduction band, respectively.

36 MATERIALS SCIENCE↗
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↗