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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2020

Analytical solution for partial heating on the exterior of the pipe with application to measuring fluid flow rate

An analytical model using Green’s functions for partial external heating of a pipe is developed, which results in an exact mathematical solution for the radial and axial temperature distribution in the pipe wall. Partial heating consists of a constant heat flux function imposed over a small section of the exterior of a pipe and for a limited time duration. The solution comprises steady-state and transient parts, and an algebraic identity is used to decrease the number of summation terms in the slowly-converging steady- state part. Intrinsic verification principles are used to verify the solution. As an example application, this transient solution is applied toward the development of a simple, noninvasive method for in-field measurement of the flow rate in pipes. Furthermore, to simulate this application, a pulse of energy is imposed to the wall of the pipe, and the developed mathematical solution is used to find the flow rate of the fluid inside the pipe. An optimal experiment is designed to find the best measurement location and time.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Bifurcation Analysis Reveals Solution Structures of Phase Field Models

The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, in this study, we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models. Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions. To elucidate the idea, we apply this analytical approach to three representative phase field equations: the Allen-Cahn equation, the Cahn-Hilliard equation, and the Allen-Cahn-Ohta-Kawasaki system. The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

State-of-the-art short-term electricity market operation with solar generation: A review

With the accelerating penetration of solar energy in energy systems, market operations concerning the solar-associated intermittency are widely discussed. How to correctly model the solar generation in the market and solve the uncertainty-based operation problems call for solutions. Unlike other renewable resources, solar power can be more easily applied to the demand side through behind-the-meter installations in a distributed manner with significant future extensibility. The corresponding operational rules in the markets are largely being revised. Over the past two decades, with the development of deregulated power markets, numerous studies related to uncertainty-based market operations tend to transform the market from a deterministic and centralized framework to a stochastic and decentralized one. As the relevant literature is most recent, this paper reviews their contributions to electricity market operations with solar integration and underlines the research directions of this topic and ongoing industry practices. A thorough review of the electricity markets worldwide with solar energy is provided. A variety of proposed mathematical solutions to the problem are also addressed.

14 SOLAR ENERGY↗
DOE OSTI2022

Effects of internal swelling on residual elasticity of a quasi-brittle material through a composite sphere model

This work describes the development of a micromechanical-based constitutive model accounting for the effect of internal expansion on the residual elasticity of a Hashin composite material. This material is made of spherical inclusions that are subjected to gradual swelling within a quasi-brittle matrix. The main focus of this work is to describe and analyze the material mechanical response, with an additional focus on the internal swelling’s effect on the stress–strain response and residual elasticity. Microstructural features and parameters of major importance for the mechanical responses were identified. The innovative characteristics of the proposed approach are summarized as follows: (1) a full determination of the physics of a complete-damage problem throughout the whole process of inclusion swelling with upscaling techniques, which transfers the microcrack-related properties from the lower scale to upper scale; and (2) an evolution of the mechanical fields and the corresponding residual elasticity for various inclusion swelling levels. Concerning the matrix–inclusion composite, it was hypothesized that only the matrix was susceptible to cracking, with varied degrees of damage, whereas the inclusions behave elastically and the elastic modulus of the expanding inclusions remains constant. It is to emphasize that the gradual swelling of inclusions is modeled by an increasing strain in the current micromechanical-based constitutive model, and the microcracks are represented by a set of randomly oriented penny-shaped microcracks with identical radii (namely, closed cracks). The main contribution of the current research is to establish the exact mathematical solutions for the mechanical fields (stress, strain) caused by the swelling of the inclusions (mechanical loading) and derive the effective residual elasticity of a composite (structural response) subject to internal expansion and quasi-brittle damage. Based on the assumption of closed cracks that could be extended to open cracks in the upcoming work, the results proposed by the present paper help to understand the non-linear mechanical behavior of quasi-brittle materials subject to microcracking and provide a theoretical framework to be used as academical benchmark for numerical simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Modeling the electrical double layer at solid-state electrochemical interfaces

Models of the electrical double layer (EDL) at electrode/liquid-electrolyte interfaces no longer hold for all-solid-state electrochemistry. Here we show a more general model for the EDL at a solid-state electrochemical interface based on the Poisson–Fermi–Dirac equation. By combining this model with density functional theory predictions, the interconnected electronic and ionic degrees of freedom in all-solid-state batteries, including the electronic band bending and defect concentration variation in the space-charge layer, are captured self-consistently. Along with a general mathematical solution, the EDL structure is presented in various materials that are thermodynamically stable in contact with a lithium metal anode: the solid electrolyte Li 7 La 3 Zr 2 O 12 (LLZO) and the solid interlayer materials LiF, Li 2 O and Li 2 CO 3 . Here, the model further allows design of the optimum interlayer thicknesses to minimize the electrostatic barrier for lithium ion transport at relevant solid-state battery interfaces.

25 ENERGY STORAGE↗
DOE OSTI2020

Numerical methods for nonlocal and fractional models

Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to adequately model observed phenomena or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis, and specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference, and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modeling and algorithmic extensions which serve to show the wide applicability of nonlocal modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Numerical methods for nonlocal and fractional models

Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. Here, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Using Complex Probability Amplitudes to Simulate Solute Transport in Composite Porous Media

Probability amplitudes are fundamental to quantum mechanics and offer robust descriptions of complicated systems, which have allowed physicists to explain behaviors inaccessible to classical physics. This article ponders how some of the same conceptual underpinnings of the mathematics used for modeling quantum systems might be applied to subsurface water resources problems and speculates how these tools could facilitate applications on quantum computers. A probability amplitude-based model for describing advective-dispersive transport in porous media using linear operators is investigated. The proposed complex valued model decomposes spreading into two “sub-continuum partial dispersion” coefficients, and this recovers classical spreading when the sum of these coefficients is the Fickian dispersion coefficient. However, the probability amplitudes have a manyto-one relationship to a probability distribution, so it embeds a level of heterogeneity into seemingly equivalent functions. Two propagators with different sub-continuum coefficients may have the same macroscopic behavior when either is considered in isolation, but when they act on the other the system’s behavior changes. Additionally, differences in the amplitudes cause a reduction in spreading as velocity correlations are disrupted, despite both propagators having identical dispersion coefficients, and this cannot be achieved using classical methods without changing the dispersion coefficient. The main point is that these amplitude-based models offer a way to embed information about the system into the propagators, instead of just “averaging it out” when making an upscaled model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

New results on asymmetric thick branes

This work deals with the presence and stability of thick brane solutions in the warped five dimensional braneworld scenario with a single extra spatial dimension of infinite extent. We combine two distinct procedures that give rise to new possibilities, allowing that we describe models of asymmetric thick branes, with the asymmetry being controlled by a single real parameter. We illustrate the main results with some distinct models, which show that the method works for both standard and generalized models, and the solutions are gravitationally stable against small perturbations of the metric.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

The exact discontinuity of a partial wave along the left-hand cut and the exact N∕D method in non-relativistic scattering

We first deduce the analytical continuation in the complex planes of the initial and final three-momenta of the Lippmann–Schwinger equation in coupled or uncoupled partial-wave amplitudes. This result allows us to deduce a master equation whose solution is the exact discontinuity of the on-shell partial-wave amplitudes along the left-hand cut. This equation is always a linear non-singular integral equation whose solution is fixed exclusively by the knowledge of the potential, applicable to either regular or singular potentials. The capability of calculating exactly this discontinuity allows one to settle the exact N∕D method in two-body non-relativistic scattering for coupled and uncoupled waves. We exemplify this new advance in scattering theory by explicitly checking the agreement between the Lippmann–Schwinger equation with the corresponding solutions of the exact N∕D method for some examples that involve regular and singular potentials, either attractive or repulsive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Electromagnetic waves in an optical photonic lattice

Laser light propagation in a photonic lattice consisting of two parallel waveguide arrays is theoretically studied using the coupled mode method, with the interaction of each waveguide with the nearest neighbours and between the waveguides of the arrays being taken into account. Analytical expressions are obtained that make it possible to accurately predict the presence of localisation of light depending on the coupling constants. Particular solutions of a system of coupled waves are found, which describe strongly localised light propagating without transverse diffraction along the entire lattice at certain values of the coupling constants. The emergence of spatially limited transverse diffraction of light is predicted. (integral optics)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Control of the optical properties of gum and dentin tissue of a human tooth at laser spectral lines in the range of 200 – 800 nm

A change in the optical properties of the tissue of the gums and dentin of a human tooth is experimentally investigated in vitro with the application of a 99.5 % glycerol solution. The kinetics of the total transmittance in the spectral range of 200 – 800 nm on characteristic laser lines is studied. It is shown that the effectiveness of optical clearing, expressed as a relative increase in the total transmittance, for gum tissue in the laser radiation range of 200 – 800 nm can vary significantly (by an order of magnitude). In this case, the absolute values of optical transmittance in the UV region are relatively small due to the strong absorption by the endogenous chromophores of the studied tissues, and in the visible and NIR regions, on the contrary, they are significant, which is due to the absence of strongly absorbing chromophores. The effectiveness of dentin clearing in the entire visible and NIR spectral regions is on average 25 % for 300 minutes of immersion of the sample in a 99.5 % glycerol solution. The presented results are necessary for increasing the efficiency of laser therapy and methods for optical monitoring of morphological changes in biological tissues for the purpose of early diagnosis of diseases. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Extending the operation range of a phase-sensitive optical time-domain reflectometer by using fibre with chirped Bragg gratings

>A record long external-disturbance detection distance of 140 km without employing optical amplifiers in the fibre line is demonstrated by a phase-sensitive optical time-domain reflectometer (Φ-OTDR) using a fibre section with inscribed chirped fibre Bragg gratings (CFBGs). This solution provides simultaneous operation of Φ-OTDR with a standard single-mode fibre at a distance of up to 100 km and with a CFBG fibre section located from the fibre line input point by at least 140 km. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

The Improved Orbit Solution and Component Masses of bet LMi

bet LMi is a double-lined visual binary with an orbital period of ∼39 yr. Via a simultaneous fitting to both astrometric and radial velocity measurements, we give a complete and improved orbit solution with high precision. Then, the component masses are precisely determined as 2.98 ± 0.10 M {sub ⊙} and 1.92 ± 0.04 M {sub ⊙} with a relative precision of ∼3%, respectively. The orbital parallax is determined to be 19.6 ± 0.2 mas, which is two times more precise than Hipparcos parallax. With the known apparent magnitudes and magnitude difference of the components, we derive the luminosity of the components as 50.7 ± 1.8 L {sub ⊙} and 9.1 ± 4.1 L {sub ⊙}. The estimated radii of the components are 9.4 ± 0.3 R {sub ⊙} and 3.7 ± 1.5 R {sub ⊙}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Relating the depth of the water table to the depth of weathering

Weathering of bedrock creates and occludes permeability, affecting subsurface water flow. Often, weathering intensifies above the water table. On the other hand, weathering can also commence below the water table. To explore relationships between weathering and the water table, a simplified weathering model for an eroding hillslope was formulated that takes into account both saturated and unsaturated subsurface water flow (but does not fully account for changes in dissolved gas chemistry). The phreatic line was calculated using solutions to mathematical treatments for both zones. In the model, the infiltration rate at the hill surface sets both the original and the eventual steady-state position of the water table with respect to the weathering reaction front. Depending upon parameters, the weathering front can locate either above or below the water table at steady state. Erosion also affects the water table position by changing porosity and permeability even when other hydrological conditions (e.g. hydraulic conductivity of parent material, infiltration rate at the surface) do not change. The total porosity in a hill (water storage capacity) was found to increase with infiltration rate (all else held constant). Furthermore, this effect was diminished by increasing the erosion rate. We also show examples of how the infiltration rate affects the position of the water table and how infiltration rate affects weathering advance.

58 GEOSCIENCES↗
DOE OSTI2022

It’s Not What You Take Up, It’s What You Keep: How Discoveries from Diverse Disciplines Directed the Development of the FDG PET/CT Scan

Although imaging glucose metabolism with positron emission tomography combined with X-ray CT (FDG-PET/CT) has become a standard diagnostic modality for the discovery and surveillance of malignant tumors and inflammatory processes, its origins extend back to more than a century of notable discoveries in the fields of inorganic and organic chemistry, nuclear physics, mathematics, biochemistry, solute transport physiology, metabolism, and imaging, accomplished by pioneering and driven investigators, of whom at least ten were recipients of the Nobel Prize. These tangled and diverse roots eventually coalesced into the FDG-PET/CT method, that through its many favorable characteristics inherent in the isotope used ( 18 F), the accurate imaging derived from coincidence detection of positron annihilation radiation combined with computed tomography, and the metabolic trapping of 2-deoxy-2-[ 18 F] fluoro-d-glucose (FDG) in tissues, provides safety, sensitivity, and specificity for tumor and inflammation detection. Here, the authors hope that this article will increase the appreciation among its readers of the insight, creativity, persistence, and drive of the many investigators who made this technique possible. This article is followed by a review of the many applications of FDG-PET/CT to the gastrointestinal tract and hepatobiliary system (Mandelkern in Dig Dis Sci 2022)

2-DG↗