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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

X-ray Energy-Dispersive Spectrometry During In Situ Liquid Cell Studies Using an Analytical Electron Microscope

The use of analytical spectroscopies during scanning/transmission electron microscope (S/TEM) investigations of micro- and nano-scale structures has become a routine technique in the arsenal of tools available to today's materials researchers. Essential to implementation and successful application of spectroscopy to characterization is the integration of numerous technologies, which include electron optics, specimen holders, and associated detectors. While this combination has been achieved in many instrument configurations, the integration of X-ray energy-dispersive spectroscopy and in situ liquid environmental cells in the S/TEM has to date been elusive. In this work we present the successful incorporation/modifications to a system that achieves this functionality for analytical electron microscopy.

Zaluzec, Nestor J.↗
DOE OSTI2025

Ionic Liquids in Analytical Chemistry: Fundamentals, Technological Advances, and Future Outlook

The development of new analytical methods most often focus on novel materials used to impart selectivity or sensitivity to the protocol. Ionic liquids (ILs) are a class of solvents that have been extensively explored as promising materials for various applications and continue to be explored due to their tunable physicochemical properties. These materials possess melting temperatures below 100 °C and can interact with analytes through a multitude of interactions afforded by their readily tunable chemical structure. These interactions include electrostatic, dispersive, hydrogen bonding, π–π, and dipolar interactions and can be modulated or strengthened based on the functional groups present within the chemical structure. ILs consist predominately of organic cations and either inorganic or organic anions, both of which can be functionalized with desired moieties. Common cation and anions found in IL chemical structures are presented in Figure 1. The unique polarity afforded by the ionic structure has also led to their increasing use in areas including sample preparation, chemical separations, electrochemistry, mass spectrometry, and spectroscopy.

Zeger, Victoria R. [Iowa State Univ., Ames, IA (Un↗
DOE OSTI2019

Online, real-time analysis of highly complex processing streams: Quantification of analytes in Hanford tank sample

Processing of hazardous materials is a crucial example of where on-line monitoring can significantly reduce operation risk, cost, and time. This is particularly true in the case of the Hanford site, where nuclear materials from the cold war era are being processed for environmental cleanup efforts. In exceedingly complex streams such as those at Hanford, on-line and real-time monitoring can be a challenge due to complexity of signals. Further obstacles are imposed by the caustic nature of processing streams as well as the radiation damage inflicted on instruments and probes. On-line monitoring based on Raman spectroscopy enables the detection of many Hanford tank species of interest, and was demonstrated here on nine chemical species that comprise the majority of tank waste by volume, including Al(OH)4-, C2O42-, CO32-, CrO42-, NO32-, NO3-, OH-, PO43-, SO42-. Real-time analysis of Raman signal allows for immediate quantification of target analytes and was successfully accomplished through the use of chemometric models. Furthermore, irradiation tests reveal Raman monitoring systems can effectively continue to operate even after receiving 1·107 Rad of gamma dose. The on-line, real-time monitoring system developed here was successfully used to simultaneously quantify nine target analytes in a real samples collected from Hanford tank AP-105.

Lines, Amanda M.↗
DOE OSTI2026

Analytic Nuclear Gradients Including Oriented External Electric Fields in a Molecule-Fixed Frame

Electric-field-assisted chemistry has attracted much attention in recent years, particularly in the context of oriented external electric fields for controlling molecular structure and reactivity. Such fields have been explored in a wide range of applications, including switching materials, nanoparticles, controllable catalysts, medicines, and clinical therapies. However, the determination of fixed fields in the laboratory frame becomes ineffective for flexible molecules, as conformational changes can significantly alter the relative orientation between the applied field and molecular structure. In this work, we propose two molecular reference frames─the principal axis frame and the local reference frame─to define oriented electric fields within the molecular framework. These coordinate systems powerfully eliminate ambiguities in the relative orientation between the applied field and the molecule. Analytic nuclear gradients in the presence of external electric fields are derived and implemented, with an initial application to field-dependent geometry optimizations of cis - and trans -formanilide. Analysis of the resulting field-induced equilibrium structures reveals distinct structural responses, validating the accuracy and robustness of the proposed formalism. The analytic gradient framework enables systematic investigations of molecular properties and reactivity under arbitrarily oriented electric fields, opening new opportunities for computational modeling and rational design in electric-field-controlled chemistry.

electric fields↗
DOE OSTI2018

Analytical Model to Detect Fault Permeability Alteration Induced by Fault Reactivation in Compartmentalized Reservoirs

Underground fluid injection induces changes in in situ stress condition of the target formation and local faults that can potentially lead to fault reactivation, which may result in the leakage of injected and/or native fluids into neighboring formations. In this paper, we introduce an analytical method to detect fault reactivation caused by fluid injection into deep faulted aquifers considering across-fault leakage. The fundamental assumption made in our model is that fault permeability will be altered upon fault slip. Therefore, we model fault reactivation as a sudden change in fault permeability at the onset of fault slip. The fault is modeled as a linear interface between two permeable formations with equal rock and fluid properties. The governing equations are coupled through the fault interface and are solved using the Laplace-Fourier integral transform technique. Based on the analytical solution, we find the characteristic bottomhole pressure and pressure derivative responses that enable detecting fault reactivation using diagnostic plots. We observe that pressure derivative undergoes a rapid change at the onset of fault slip followed by a late-time trend to attain a new equilibrium governed by the altered fault permeability. Furthermore, we discuss the evolution of the across-fault leakage rate upon and after fault slippage. Here, the results from this study are presented in the form diagnostic plots and type curves that may be used for reservoir and fault characterization purposes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

Infiltration processes in fractured-porous media remain a crucial, yet not very well understood component of recharge and vulnerability assessment. Under partially-saturated conditions flows in fractures, percolating fracture networks, and fault zones contribute to the fastest spectrum of infiltration velocities via preferential pathways. Specifically, the partitioning dynamics at fracture intersections determine the magnitude of flow fragmentation into vertical and horizontal components and hence the bulk flow velocity and dispersion of fracture networks. In this work, we derive an approximate analytical solution for the partitioning process and validate it using smoothed particle hydrodynamics simulations. The developed transfer function is conceptually based on simulation results and laboratory experiments carried out in previous works. It allows to efficiently simulate flow through fracture networks with simple cubic structure and arbitrary number of fractures and aperture sizes via linear response theory and convolution of a given input signal. We derive a non-dimensional bulk flow velocity ($\widetilde{v}$) and dispersion coefficient ($\widetilde{D}$) to characterize fracture networks in terms of dimensionless horizontal and vertical time scales $\tau_m$ and $\tau_0$. The dispersion coefficient is shown to strongly depend on the horizontal time scale and converges towards a constant value of $0.08$ within reasonable fluid and geometrical parameter ranges, while the non-dimensional velocity exhibits a characteristic $\widetilde{v} \sim \tau_m^{-1/2}$ scaling. Given that hydraulic information is often only available at limited places within (fractured-porous) aquifer system, such as boreholes or springs, our study intends to provide a rudimentary analytical concept to potentially reconstruct internal fracture network geometries from external boundary information, e.g., the dispersive properties of discharge (groundwater level fluctuations).

42 ENGINEERING↗
DOE OSTI2022

Leakage From Coexisting Geologic Forcing and Injection‐Induced Pressurization: A Semi‐Analytical Solution for Multilayered Aquifers With Multiple Wells

Abstract Abnormal fluid pressures (above or below hydrostatic pressure) can develop and persist in sedimentary basins. The common occurrence of abnormal pressures may cause challenges for project permitting of geological carbon sequestration (GCS), particularly in reservoirs with pre‐injection overpressure. The leaky wells that may exist in some sedimentary basins can provide flow paths between deep brine aquifers and shallower freshwater aquifers. Pre‐injection relative overpressures can cause brine leakage through leaky wells even before any injection occurs. The tendency for flow through leaky wells is coupled with the process of pressure dissipation that occurs through aquitards. Specifically, with non‐zero permeability, aquitards can dissipate pressure over large areal extents and thereby reduce leakage rates through leaky wells. This study presents development of a semi‐analytical solution for hydraulic head and brine leakage in multilayered aquifer–aquitard systems with geologic pressure forcing. The geologic forcing that causes abnormal pressures in the multilayered system can coexist with any number of injection, extraction, and leaky wells that also affect fluid pressure. The semi‐analytical model is applied to explore how leakage through leaky wells varies as functions of pressurization rate, along with aquitard and leaky well properties in an overpressured multilayered system. The results show that although injection‐induced pressures can dissipate rapidly through suitably permeable aquitards, coexisting geologic forcing may create sustained rates of brine leakage into freshwater aquifers through leaky wells. In GCS, a very low‐permeability aquitard with high capillary entry pressure to free‐phase CO 2 is desired to serve as the caprock to prevent leakage of CO 2 from the storage reservoir. Nevertheless, the results from this study show that the brine leakage impact to shallow freshwater aquifers through leaky wells might substantially decrease with increasing aquitard permeability values, as long as small aquitard permeability and high capillary entry pressure serve to prevent CO 2 leakage.

Cihan, A.↗
DOE OSTI2023

One-Parameter Analytical Derivation in Modified Budyko Framework for Unsteady-State Streamflow Elasticity in Humid Catchments

The changes in climate and catchment properties have altered the hydrological processes significantly at different spatiotemporal scales around the world. In particular for finer time scales, changes in water storage, which has been commonly neglected for long-term temporal scales, may play an important role on hydrological processes. Nevertheless, few studies addressed this question in modifying the Budyko framework, with most of them remaining a steady-state assumption on catchment characteristics. Here, in this work, we derive new analytical formulas of unsteady-state streamflow elasticity in a modified Budyko framework, incorporating both storage change and one specific parameter for catchment properties. We study 78 humid catchments in the USA with simulation data of daily hydrological processes from a probability-distribution-based hydrological model (the modified HyMOD). As indicated by results, the annual storage change ratio is linearly correlated with the annual aridity index, and this relationship can be used to estimate elasticity coefficients with our formulas. The estimated elasticity coefficients perform well in simulating the annual streamflow with the power-law model. For different catchments, variability of the unsteady-state elasticity is higher than that of the steady-state elasticity. Unsteady-state streamflow coefficients show significant linear correlation with catchment properties, such as the average slope, average elevation, and catchment area. This study provides a new analytical approach to investigate the interannual stability of catchments with varying climate and catchment properties.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Analytical Model for the Higher Order Moments of Midlatitude Atmospheric Temperature Distributions

Observed distributions of atmospheric temperature are non-Gaussian. Therefore, moments beyond variance are necessary in determining the frequency of extreme temperature events. Here we propose a simple kinematic model for atmospheric mid-latitude temperature variability based on symmetric advection from a non-symmetric background temperature profile. We then use this model to derive analytical expressions for the higher order moments of temperature distributions. Our results show that nonzero skewness and kurtosis arise due to the nonlinearity of the time-mean meridional temperature profile. The analytical model matches an idealized Held-Suarez atmospheric model, indicating nonlinearity of time-mean temperature in latitude is the dominant contribution to nonzero skewness and kurtosis in synoptic temperature variations. Model analysis further shows decrease in higher order moments due to climate change come roughly equally from changes in mixing length and changes in the background temperature profiles.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Analytical and numerical modeling of optical second harmonic generation in anisotropic crystals using #SHAARP package

Electric-dipole optical second harmonic generation (SHG) is a second-order nonlinear process that is widely used as a sensitive probe to detect broken inversion symmetry and local polar order. Analytical modeling of the SHG polarimetry of a nonlinear optical material is essential to extract its point group symmetry and the absolute nonlinear susceptibilities. Current literature on SHG analysis involves numerous approximations and a wide range of (in)accuracies. We have developed an open-source package called the Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP.si) which derives analytical and numerical solutions of reflection SHG polarimetry from a single interface (.si) for bulk homogeneous crystals with arbitrary symmetry group, arbitrary crystal orientation, complex and anisotropic linear dielectric tensor with frequency dispersion, a general SHG tensor and arbitrary light polarization. #SHAARP.si enables accurate modeling of polarimetry measurements in reflection geometry from highly absorbing crystals or wedge-shaped transparent crystals. The package is extendable to multiple interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A Simple Analytical Model for Magnetization and Coercivity of Hard/Soft Nanocomposite Magnets

Here, we present a simple analytical model to estimate the magnetization (σ s ) and intrinsic coercivity (Hci) of a hard/soft nanocomposite magnet using the mass fraction. Previously proposed models are based on the volume fraction of the hard phase of the composite. But, it is difficult to measure the volume of the hard or soft phase material of a composite. We synthesized Sm 2 Co 7 /Fe-Co, MnAl/Fe-Co, MnBi/Fe-Co, and BaFe 12 O 19 /Fe-Co composites for characterization of their σs and Hci. The experimental results are in good agreement with the present model. Therefore, this analytical model can be extended to predict the maximum energy product (BH) max of hard/soft composite.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Analytical model for the motion and interaction of two-dimensional active nematic defects

Here, we develop an approximate, analytical model for the velocity of defects in active nematics by combining recent results for the velocity of topological defects in nematic liquid crystals with the flow field generated from individual defects in active nematics. Importantly, our model takes into account the long-range interactions between defects that result from the flows they produce as well as the orientational coupling between defects inherent in nematics. Our work complements previous studies of active nematic defect motion by introducing a linear approximation that allows us to treat defect interactions as two-body interactions and incorporates the hydrodynamic screening length as a tuning parameter. We show that the model can analytically predict bound states between two +1/2 winding number defects, effective attraction between two –1/2 defects, and the scaling of a critical unbinding length between ±1/2 defects with activity. The model also gives predictions for the trajectories of defects, such as the scattering of +1/2 defects by –1/2 defects at a critical impact parameter that depends on activity. In the presence of circular confinement, the model predicts a braiding motion for three +1/2 defects that was recently seen in experiments, as well as stable and ergodic trajectories for four or more defects.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quantum sensing of paramagnetic analytes by nanodiamonds in levitated microdroplets and aqueous solutions

Nanodiamonds (ND) hosting negatively charged nitrogen-vacancy (NV-) color centers have received attention for applications in magnetic field, electric field, chemical, and bio-sensing. The versatility of these probes is their excellent room-temperature optical and spin properties, along with their small size, functionalized surfaces and resistance to bleaching, making them ideal as nanoscopic sensors in picoliter volumes (e.g. single cells, but also microcompartments and aerosols). For quantitative ND-NV- sensing of paramagnetic analytes in such contexts, however, there remains an incomplete understanding of how factors related to the aqueous phase environment control detection efficiency. To address this, optically detected magnetic resonance (ODMR) is measured in bulk macroscale solutions and single levitated microdroplets as a function of Gd+3 concentration (340 nM to 1.5 mM), nanodiamond size, pH, competitor ions, and ligands. The ODMR response to [Gd+3] is found to be nonlinear, and pH, ND and sample volume dependent; indicating the detection of Gd+3 requires efficient adsorption of the analyte to the diamond surface. Langmuir adsorption isotherms embedded in a quantitative photophysical model links the ODMR response to adsorption thermodynamics of Gd+3. The equilibrium constant for Gd+3 adsorption to a carboxylated ND surface is determined to be (1 ± 0.5) x 105 M-1 corresponding to a free energy of adsorption of (-28 ± 1) kJ mol-1. These results provide general insight into how complex aqueous and microscale environments impact nanodiamond based quantum sensing modalities, and portend their application as quantitative chemical sensors in microenvironments.

Brown, Emily K↗
DOE OSTI2025

Analytical Identification Method of Generalized Short‐Circuit Ratio Using Phasor Measurement Units

This paper introduces a novel analytical approach for the identification of the admittance matrix and the generalized short-circuit ratio (gSCR) in power systems integrated with renewable energy sources. The proposed method leverages voltage and current measurements from phasor measurement units (PMUs) to construct a least squares objective function, which is then solved using matrix calculus and partial derivatives. Unlike conventional optimization algorithms, this approach provides an analytical solution that substantially reduces data requirements, enabling the efficient and accurate identification of the gSCR with smaller datasets. Additionally, its fixed computational complexity allows for real-time updates as new data are collected, ensuring continuous refinement of the system of equations and enabling rapid, precise gSCR calculations. The method also exhibits strong robustness against measurement noise, making it well-suited for practical applications in dynamic power systems. The combination of reduced data requirements, real-time adaptability, noise robustness and fixed computational load establishes this method as a highly efficient and reliable tool for real-time power system stability analysis. Case studies on an EPRI 36-bus system demonstrate the method's effectiveness, highlighting its accuracy in closely matching true gSCR values, even under diverse disturbances and noisy conditions.

Han, Zelei [Hohai University, Nanjing (China)] (OR↗
DOE OSTI2020

Guest Editorial: Advanced Data-Analytics for Power System Operation, Control, and Enhanced Situational Awareness

Along with the smart grid development, modern power systems are entering a ‘data-intensive’ era. A vast volume of data from power grids is being collected through advanced sensing and communication technologies, such as smart metering data, phasor measurement data, as well as meteorological data (e.g., wind speed and solar irradiance) related to renewable power generation. Such data contains comprehensive information about the power system covering equipment's health status, power grid's static and dynamic characteristics, renewable power generation, customers’ electricity usage pattern, etc. Therefore, advanced data-analytics techniques are needed to convert such data to knowledge for practical applications. In line with the trend of widespread data-driven applications in power systems, this Special Issue aims to present state-of-the-art research works on advanced data-analytics for power system's operation, control, and situational awareness. There are in total twenty-six papers accepted for publication in this Special Issue through careful peer reviews and revisions. Under the overarching theme of data-driven applications in power systems, the selected papers are broadly categorised into five topics. The summary of every topic is given below. You are, however, strongly encouraged to read the full paper if interested.

Xu, Yan↗
DOE OSTI2013

Evaluation of Analytical and Numerical Techniques for Defining the Radius of Influence for an Open-Loop Ground Source Heat Pump System

In an open-loop groundwater heat pump (GHP) system, groundwater is extracted, run through a heat exchanger, and injected back into the ground, resulting in no mass balance changes to the flow system. Although the groundwater use is non-consumptive, the withdrawal and injection of groundwater may cause negative hydraulic and thermal impacts to the flow system. Because GHP is a relatively new technology and regulatory guidelines for determining environmental impacts for GHPs may not exist, consumptive use metrics may need to be used for permit applications. For consumptive use permits, a radius of influence is often used, which is defined as the radius beyond which hydraulic impacts to the system are considered negligible. In this paper, the hydraulic radius of influence concept was examined using analytical and numerical methods for a non-consumptive GHP system in southeastern Washington State. At this location, the primary hydraulic concerns were impacts to nearby contaminant plumes and a water supply well field. The results of this study showed that the analytical techniques with idealized radial flow were generally unsuited because they over predicted the influence of the well system. The numerical techniques yielded more reasonable results because they could account for aquifer heterogeneities and flow boundaries. In particular, the use of a capture zone analysis was identified as the best method for determining potential changes in current contaminant plume trajectories. The capture zone analysis is a more quantitative and reliable tool for determining the radius of influence with a greater accuracy and better insight for a non-consumptive GHP assessment.

GHPs↗
DOE OSTI2013

Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from ±1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincaré iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation with respect to the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Physical properties and analytical models of band-to-band tunneling in low-bandgap semiconductors

Low-bandgap semiconductors, such as InAs and InSb, are widely considered to be ideal for use in tunnel field-effect transistors to ensure sufficient on-current boosting at low voltages. This work elucidates the physical and mathematical considerations of applying conventional band-to-band tunneling models in low-bandgap semiconductors, and presents a new analytical alternative for practical use. The high-bandgap tunneling generates most at maximum field region with shortest tunnel path, whereas the low-bandgap generations occur dispersedly because of narrow tunnel barrier. The local electrical field associated with tunneling-electron numbers dominates in low-bandgap materials. This work proposes decoupled electric-field terms in the pre-exponential factor and exponential function of generation-rate expressions. Without fitting, the analytical results and approximated forms exhibit great agreements with the sophisticated forms both in high- and low-bandgap semiconductors. Neither nonlocal nor local field is appropriate to be used in numerical simulations for predicting the tunneling generations in a variety of low- and high-bandgap semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗