Results for “Differential Geometry” — Page 22

DOE OSTI2024

Thermal and hydraulic performance of volumetrically heated triply periodic minimal surface heaters

Advanced heat transfer surfaces, mainly Triply Periodic Minimal Surfaces (TPMSs) have great potential to increase heat transfer performance over traditional heat transfer surfaces due to their tortuous flow path and higher surface area-volume ratio. The emergence of additive manufacturing of nuclear fuel motivates experimental investigation of such advanced geometries in the context of a nuclear reactor core. Here, this study employed a novel method to explore the performance of gyroid and diamond TPMS geometries. Volumetrically heated heaters were additively manufactured from conductive polymer filament, and airflow was used to simulate the convective heat transfer from the core within a nuclear reactor. The mass flow and volumetric generation rates were varied, local Nusselt number correlations were obtained using embedded thermocouples to measure the solid and fluid temperature, and friction factor correlations were developed using differential pressure measurements. The gyroid TPMS presented a friction factor 1.5 times higher than the diamond TPMS and 90 times that of the rod bundle. TPMS geometries showed Nusselt numbers 8–10 times higher than that of the rod bundle, also maintaining colder internal temperatures, which suggested that they could sustain 250–275 % higher power density than the rod bundle for a given centerline temperature. Hence, having the potential to greatly increase the safety margins and power output of a nuclear reactor core with similar volume.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Differential equations from unitarity cuts: nonplanar hexa-box integrals

We compute ϵ-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is presented. For 5-point planar topologies, Gram determinants which vanish in 4 dimensions are used to build compact expressions for pure integrals. Using unitarity cuts and computational algebraic geometry, we obtain a compact IBP system which can be solved in 8 hours on a single CPU core, overcoming a major bottleneck for deriving the differential equations. Alternatively, assuming prior knowledge of the alphabet of the nonplanar hexa-box, we reconstruct analytic differential equations from 30 numerical phase-space points, making the computation almost trivial with current techniques. We solve the differential equations to obtain the values of the master integrals at the symbol level. Full results for the differential equations and solutions are included as supplementary material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10{sup −4} so the Fourier-Bessel series can be approximated by elementary functions. The time development of the system is characterized by two time constants, τ{sub c} and τ{sub g}. The constant τ{sub c} describes the approach to the stationary state of the total charge and the potential. τ{sub c} is several orders of magnitude smaller than the geometry-dependent constant τ{sub g}, which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Kinematical vortices in double photoionization of helium by attosecond pulses

Two-armed helical vortex structures are predicted in the two-electron momentum distributions produced in double photoionization (DPI) of the He atom by a pair of time-delayed elliptically polarized attosecond pulses with opposite helicities. These predictions are based upon both a first-order perturbation theory analysis and numerical solutions of the two-electron, time-dependent Schrödinger equation in six spatial dimensions. The helical vortex structures originate from Ramsey interference of a pair of ionized two-electron wave packets, each having a total angular momentum of unity, and appear in the sixfold differential DPI probability distribution for any energy partitioning between the two electrons. The vortex structures are exquisitely sensitive to the time delay between the two pulses, their relative phase, their ellipticity, and their handedness; moreover, they occur in a variety of electron detection geometries. However, the vortex structures only occur when the angular separation β = cos -1 (ˆ p 1 ∙ ˆ p 2 ) between the electron momenta p 1 and p 2 is held fixed. The vortex structures can also be observed in the fourfold differential DPI probability distribution obtained by averaging the sixfold differential probability over the emission angles of one electron. Such kinematical vortices are a general phenomenon that may occur in any ionization process, initiated by two time-delayed short pulses with opposite ellipticities, for particular detection geometries.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1977

Three-dimensional elastic stress and displacement analysis of finite geometry solids containing cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement fields in finite geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in finite solids.

Kring, J.↗

NASA NTRS1977

Three-dimensional elastic stress and displacement analysis of finite geometry solids containing cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement fields in finite geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in finite solids.

Kring, J.↗

NASA NTRS1975

Application of differential game theory to role-determination in aerial combat

The development of criteria which specify the roles of pursuer and evader as functions of the relative geometry and of the important parameters of the problem are discussed. A reduced-order model of the relative motion is derived and discussed. In this model, the two aircraft move in the same plane at unequal but constant speeds, and with different maximum turn rates. The equations of relative motion are of third order, the dependent variables being the relative range, bearing, and heading of the two aircraft. Termination of the pursuit-evasion game is defined by either the heading-limited or the range-limited end condition. These are geometric conditions for which the evading aircraft is in front of the other, with the relative heading and relative range satisfying certain inequalities. Retrograde solutions to the equations of relative motion were used with the derived optimal terminal maneuvers to find where an assumed set of end conditions could have begun.

Merz, A. W.↗

DOE OSTI2019

Nature of Electronically Excited States of Furocoumarins

A comprehensive study of spectral-luminescent and photophysical properties of coumarin sensitizers is performed using the methods of quantum chemistry, electron spectroscopy, and fluorescence. A comparative study of photophysical processes occurring in 8-methoxypsoralen (8-MOP) and 4,9-dimethoxy-7-methylfuro [3,2-g][1] benzofuran-5-1 (khellin) is performed using the quantum-chemical software package based on the semi-empirical method of intermediate neglect of differential overlap with original spectroscopic parameterization. The dependences of the fluorescent properties and reactivity of the compounds on the geometry and composition of the solvation shell of molecules are established. It is shown that incorporation of additional methoxy groups in the structure of molecules has the strongest effect on the spectral-luminescent characteristics of khellin compared with 8-MOP.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Eigenvector centrality for geometric and topological characterization of porous media

Solving flow and transport through complex geometries such as porous media is computationally difficult. Such calculations usually involve the solution of a system of discretized differential equations, which could lead to extreme computational cost depending on the size of the domain and the accuracy of the model. Geometric simplifications like pore-networks, where the pores are represented by nodes and pore throats by edges connecting pores, have been proposed. These models, despite their ability to preserve the connectivity of the medium, have difficulties in capturing preferential paths (high velocity) and stagnation zones (low velocity) as they do not consider the specific relations between nodes. Nonetheless, network theory approaches, where a complex network is a graph, can help to simplify and better understand fluid dynamics and transport in porous media. Here we present a novel method to address these issues based on eigenvector centrality, which has been corrected to overcome the centralization problem, and modified to introduce a bias in the centrality distribution along a particular direction to address the flow and transport anisotropy in porous media. We compare the model predictions with millifluidic transport experiments, which shows that, albeit simple, this technique is computationally efficient and has potential for predicting preferential paths and stagnation zones for flow and transport in porous media. We propose to use eigenvector centrality probability distribution to compute entropy as an indicator of the ‘mixing capacity’ of the system.

58 GEOSCIENCES↗

NASA NTRS1980

Stereo radar for mapping and interpretation

The use of terrain imaging radar to extract elevation information by stereo viewing and measurement is discussed. Either a three dimensional visual model or elevation measurements may be obtained by simultaneous viewing or differential measurement of images obtained by a side-looking radar from two different flightpaths. Expressions describing radar image geometry, model vertical exaggeration, and stereo measurement accuracy are derived. The dependence of the exaggeration and accuracy on system parameters and key system errors is derived, discussed, and illustrated by application to several airborne and spaceborne systems and system concepts, and the results of some preliminary measurements of imagery from two airborne and one spaceborne system are given.

Graham, L.↗

NASA NTRS1990

Effect of interleaves on fracture of laminated composites. I - Analysis. II - Solution and results

The effect of interleaves placed between the fiber-reinforced plies of multilayered composite laminates is investigated analytically, with the composite approximated by linearly elastic isotropic media consisting of half-planes separated from a finite-width layer by thin interleaves of low extensional and shear moduli. Integral equations are derived which describe the effect of interleaves on damage growth. Numerical solutions are then developed which are based on Gaussian integration techniques and Hadamard's concept of differentiation of Cauchy integrals. Critical stresses and displacements are calculated to investigate the influence of relative elastic properties and geometry of the interleafed composite on interface debonding, extent and suppression and delamination, and stress relieving in the undamaged plies.

Kaw, A. K.↗

NASA NTRS1998

Design Considerations for Lightweight Space Radiators Based on Fabrication and Test Experience with a Carbon-Carbon Composite Prototype Heat Pipe

This report discusses the design implications for spacecraft radiators made possible by the successful fabrication and Proof-of-concept testing of a graphite-fiber-carbon-matrix composite (i.e., carbon-carbon (C-C)) heat pipe. The proto-type heat pipe, or space radiator element, consists of a C-C composite shell with integrally woven fins. It has a thin-walled furnace-brazed metallic (Nb-1%Zr) liner with end caps for containment of the potassium working fluid. A short extension of this liner, at increased wall thickness beyond the C-C shell, forms the heat pipe evaporator section which is in thermal contact with the radiator fluid that needs to be cooled. From geometric and thermal transport properties of the C-C composite heat pipe tested, a specific radiator mass of 1.45 kg/m2 can be derived. This is less than one-fourth the specific mass of present day satellite radiators. The report also discusses the advantage of segmented space radiator designs utilizing heat pipe elements, or segments, in their survivability to micro-meteoroid damage. This survivability is further raised by the use of condenser sections with attached fins, which also improve the radiation heat transfer rate. Since the problem of heat radiation from a fin does not lend itself to a closed analytical solution, a derivation of the governing differential equation and boundary conditions is given in appendix A, along with solutions for rectangular and parabolic fin profile geometries obtained by use of a finite difference computer code written by the author.

Juhasz, Albert J.↗

NASA NTRS2002

Design Considerations for Lightweight Space Radiators Based on Fabrication and Test Experience With a Carbon-Carbon Composite Prototype Heat Pipe

This report discusses the design implications for spacecraft radiators made possible by the successful fabrication and proof-of-concept testing of a graphite-fiber-carbon-matrix composite (i.e., carbon-carbon (C-C)) heat pipe. The prototype heat pipe, or space radiator element, consists of a C-C composite shell with integrally woven fins. It has a thin-walled furnace-brazed metallic (Nb-1%Zr) liner with end caps for containment of the potassium working fluid. A short extension of this liner, at increased wall thickness beyond the C-C shell, forms the heat pipe evaporator section which is in thermal contact with the radiator fluid that needs to be cooled. From geometric and thermal transport properties of the C-C composite heat pipe tested, a specific radiator mass of 1.45 kg/sq m can be derived. This is less than one-fourth the specific mass of present day satellite radiators. The report also discusses the advantage of segmented space radiator designs utilizing heat pipe elements, or segments, in their survivability to micrometeoroid damage. This survivability is further raised by the use of condenser sections with attached fins, which also improve the radiation heat transfer rate. Since the problem of heat radiation from a fin does not lend itself to a closed analytical solution, a derivation of the governing differential equation and boundary conditions is given in appendix A, along with solutions for rectangular and parabolic fin profile geometries obtained by use of a finite difference computer code written by the author.

Juhasz, Albert J.↗

DOE OSTI2025

Develop Accurate Techniques for Passive SiC Temperature Monitoring of Miniature Samples for Cross-Cutting Applications

Passive thermometry is critically important because most fuels and materials irradiation experiments are not instrumented, and it is necessary to understand the irradiation temperature to properly interpret any post-irradiation examination data, including evolving properties and/or microstructures. The standard passive thermometry approach uses continuous dilatometry to evaluate changes in the instantaneous coefficient of thermal expansion during post-irradiation thermal annealing. This approach has limitations in terms of sample size (minimum length requirements) and the maximum irradiation temperature that can be accurately determined, which is limited by the reduced swelling (and therefore recovery) following higher temperature irradiation and limitations on the furnaces used with push-rod dilatometers. This work evaluates two new proposed techniques for post-irradiation evaluation of passive SiC temperature monitors: differential scanning calorimetry (DSC) and Raman spectroscopy. DSC is an extremely sensitive technique that can be used for any specimen geometry and is capable of higher temperature operation. Raman spectroscopy is similar in that it is a surface technique capable of examining extremely small samples (submillimeter), can be used with a heated stage up to 1,500°C (planned for future work), and is capable of mapping local irradiation temperatures throughout a sample. Existing SiC samples that were previously irradiated over a wide range of temperatures were cut into multiple pieces to allow for annealing studies using multiple different techniques: dilatometry, DSC, and Raman spectroscopy. This approach mitigates the concern that samples analyzed using one technique may have a slightly different irradiation history than those analyzed using a different technique. Recovery was clearly observed during annealing using both DSC and dilatometry. In some cases, a direct comparison could not be made due to some of the DSC runs accidentally including material from multiple specimens and issues with using an alternative DSC sample holder for the highest temperature annealing studies. Nevertheless, one trend was clear: the DSC runs resulted in higher irradiation temperatures compared to those of the dilatometry runs. Part of this could be attributed to the higher temperature ramp rates used during the DSC runs, which are often preferred to reduce noise in the measurements. By comparison, dilatometry has previously been shown to produce better data at lower ramp rates. Future work should further investigate the ideal ramp rate for both techniques to produce consistent results. Additional work should evaluate the best holder material to use for DSC runs exceeding 1,000°C to provide reliable data while preventing interactions between SiC and the holder.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

MO-AB-BRA-02: A Novel Scatter Imaging Modality for Real-Time Image Guidance During Lung SBRT

Purpose: A novel scatter imaging modality is developed and its feasibility for image-guided radiation therapy (IGRT) during stereotactic body radiation therapy (SBRT) for lung cancer patients is assessed using analytic and Monte Carlo models as well as experimental testing. Methods: During treatment, incident radiation interacts and scatters from within the patient. The presented methodology forms an image of patient anatomy from the scattered radiation for real-time localization of the treatment target. A radiographic flat panel-based pinhole camera provides spatial information regarding the origin of detected scattered radiation. An analytical model is developed, which provides a mathematical formalism for describing the scatter imaging system. Experimental scatter images are acquired by irradiating an object using a Varian TrueBeam accelerator. The differentiation between tissue types is investigated by imaging simple objects of known compositions (water, lung, and cortical bone equivalent). A lung tumor phantom, simulating materials and geometry encountered during lung SBRT treatments, is fabricated and imaged to investigate image quality for various quantities of delivered radiation. Monte Carlo N-Particle (MCNP) code is used for validation and testing by simulating scatter image formation using the experimental pinhole camera setup. Results: Analytical calculations, MCNP simulations, and experimental results when imaging the water, lung, and cortical bone equivalent objects show close agreement, thus validating the proposed models and demonstrating that scatter imaging differentiates these materials well. Lung tumor phantom images have sufficient contrast-to-noise ratio (CNR) to clearly distinguish tumor from surrounding lung tissue. CNR=4.1 and CNR=29.1 for 10MU and 5000MU images (equivalent to 0.5 and 250 second images), respectively. Conclusion: Lung SBRT provides favorable treatment outcomes, but depends on accurate target localization. A comprehensive approach, employing multiple simulation techniques and experiments, is taken to demonstrate the feasibility of a novel scatter imaging modality for the necessary real-time image guidance.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Derivation of an Analytical Solution to a Reaction-Diffusion Model for Autocatalytic Degradation and Erosion in Polymer Microspheres

A mathematical reaction-diffusion model is defined to describe the gradual decomposition of polymer microspheres composed of poly(D,L-lactic-co-glycolic acid) (PLGA) that are used for pharmaceutical drug delivery over extended periods of time. The partial differential equation (PDE) model treats simultaneous first-order generation due to chemical reaction and diffusion of reaction products in spherical geometry to capture the microsphere-size dependent effects of autocatalysis on PLGA erosion that occurs when the microspheres are exposed to aqueous media such as biological fluids. The model is solved analytically for the concentration of the autocatalytic carboxylic acid end groups of the polymer chains that comprise the microspheres as a function of radial position and time. The analytical solution for the reaction and transport of the autocatalytic chemical species is useful for predicting the conditions under which drug release from PLGA microspheres transitions from diffusion-controlled to erosion-controlled release, for understanding the dynamic coupling between the PLGA degradation and erosion mechanisms, and for designing drug release particles. The model is the first to provide an analytical prediction for the dynamics and spatial heterogeneities of PLGA degradation and erosion within a spherical particle. The analytical solution is applicable to other spherical systems with simultaneous diffusive transport and first-order generation by reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Reconstructing magnetic deflections from sets of proton images using differential evolution

Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields. When deflections are large, proton trajectories can overlap, and this nonlinearity creates regions of greatly increased proton fluence on the image, known as caustics. The formation of caustics has been a persistent barrier to reconstructing the underlying fields from proton images. We have developed a new method for reconstructing the path-integrated magnetic fields, which begins to address the problem posed by caustics. Our method uses multiple proton images of the same object, each image at a different energy, to fill in the information gaps and provide some uniqueness when reconstructing caustic features. We use a differential evolution algorithm to iteratively estimate the underlying deflection function, which accurately reproduces the observed proton fluence at multiple proton energies simultaneously. We test this reconstruction method using synthetic proton images generated for three different, cylindrically symmetric field geometries at various field amplitudes and levels of proton statistics and present reconstruction results from a set of experimental images. Here, the method we propose requires no assumption of deflection linearity and can reliably solve for fields underlying linear, nonlinear, and caustic proton image features for the selected geometries and is shown to be fairly robust to noise in the input proton intensity.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Develop Accurate Techniques for Passive SiC Temperature Monitoring of Miniature Samples for Cross-Cutting Applications

Passive thermometry is critically important because most fuels and materials irradiation experiments are not instrumented, and it is necessary to understand the irradiation temperature to properly interpret any post-irradiation examination data, including evolving properties and/or microstructures. The standard passive thermometry approach uses continuous dilatometry to evaluate changes in the instantaneous coefficient of thermal expansion during post-irradiation thermal annealing. This approach has limitations in terms of sample size (minimum length requirements) and the maximum irradiation temperature that can be accurately determined, which is limited by the reduced swelling (and therefore recovery) following higher temperature irradiation and limitations on the furnaces used with push-rod dilatometers. This work evaluates two new proposed techniques for post-irradiation evaluation of passive SiC temperature monitors: differential scanning calorimetry (DSC) and Raman spectroscopy. DSC is an extremely sensitive technique that can be used for any specimen geometry and is capable of higher temperature operation. Raman spectroscopy is similar in that it is a surface technique capable of examining extremely small samples (submillimeter), can be used with a heated stage up to 1,500°C (planned for future work), and is capable of mapping local irradiation temperatures throughout a sample. Existing SiC samples that were previously irradiated over a wide range of temperatures were cut into multiple pieces to allow for annealing studies using multiple different techniques: dilatometry, DSC, and Raman spectroscopy. This approach mitigates the concern that samples analyzed using one technique may have a slightly different irradiation history than those analyzed using a different technique. Recovery was clearly observed during annealing using both DSC and dilatometry. In some cases, a direct comparison could not be made due to some of the DSC runs accidentally including material from multiple specimens and issues with using an alternative DSC sample holder for the highest temperature annealing studies. Nevertheless, one trend was clear: the DSC runs resulted in higher irradiation temperatures compared to those of the dilatometry runs. Part of this could be attributed to the higher temperature ramp rates used during the DSC runs, which are often preferred to reduce noise in the measurements. By comparison, dilatometry has previously been shown to produce better data at lower ramp rates. Future work should further investigate the ideal ramp rate for both techniques to produce consistent results. Additional work should evaluate the best holder material to use for DSC runs exceeding 1,000°C to provide reliable data while preventing interactions between SiC and the holder.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗