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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 667 records · Page 37

Study of x-ray fluorescence spectroscopy from high-energy-density plasmas (Final Report)

The primary objective of this subcontract was to support the development of x-ray fluorescence spectroscopy (XFS) as a diagnostic tool for high-energy-density (HED) plasmas. Several experimental campaigns were completed to develop and benchmark XFS at various plasmas conditions of interest for inertial confinement fusion and HED science. The experimental measurements at the Omega laser facility used x-ray absorption spectroscopy (XAS) to determine the plasma temperature from the shape of the K-edge to benchmark XFS data. During the course of these experiments, it was found that XAS can also constrain ionization from bound-bound absorption features, and it became a primary diagnostic in this study. Several experimental campaigns were conducted at the Omega laser facility to refine XAS and XFS measurements of warm dense copper.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Ecosystems and Networks Integrated with Genes and Molecular Assemblies (ENIGMA): Component 5: Imaging Protein Conformations, Shapes & Assemblies in Solution & Administration project (Final Scientific/Technical Report, Subcontract No. 6974584)

We set ambitious goals to examine microorganism communities and measure both their chemical input and output as a read out of specific biochemical activity. These scientific goals are driving the development of sophisticated algorithms to analyze large amounts of experimental measurements made using high throughput technologies to explain and predict how the environment influences biological function at multiple scales and how the microbial systems in tum modify the environment. By examining how bacteria communities rely on symbiotic metabolic relationships for survival and reproductive success, and how these relationships consequently affect their biochemical capabilities. This was accomplished using state-of-the-art mass spectrometry-based methods, and metabolic fingerprinting approaches with a high degree of chemical specificity and sensitivity. During this period the original effort transitioned and was consolidated into what is now ENIGMA, the efforts on technology development expanded to include more untargeted metabolomics and its application to organisms on a systems level.

59 BASIC BIOLOGICAL SCIENCES↗

Investigation of Flux Spreading in a Light-Trapping, Planar-Cavity Receiver for Enclosed Solar Particle Heating

Concentrating solar thermal power (CSP) technology development has recently focused on increasing the operating temperatures to accommodate high efficiency power cycles and thermochemical processes. Inert solid particles as heat transfer media enable solar receivers to operate above 700 degrees Celsius resulting in increased system thermal efficiency compared to the conventional molten salt based CSP system. An open-cavity falling-particle solar receiver that can efficiently heat particles by direct heating from concentrated solar radiation faces challenges with large particle losses from wind and unable to support thermochemical reactions. A light-trapping, planar cavity reiver (LTPCR) where particles are indirectly heated can significantly minimize the particle losses during the operation, support thermochemical reactions, and offer scalability potential. The LTPCR features an array of vertical planar receiver/absorber panels arranged within a cavity configuration. Concentrated solar radiation from heliostats is focused onto the receiver walls, where heat is indirectly transferred to solid particles flowing inside the receiver channels. Heat transfer occurs through direct contact between the receiver panel walls and particles, and can be enhanced by fluidizing particles with air. This fluidization increases particle-wall contact and extends particle residence time, maximizing heat transfer efficiency. The unique vertical planar receiver structure originated from a near-blackbody tubular light absorber, effectively distributing the incoming solar beam spread across the panel walls and trapping light. This flux spreading effect, driven by cosine projection, converts high incident solar flux into a lower, more uniform heat flux on the panel walls. This redistribution enhances heat transfer efficiency between particle-wall or reaction gases-wall, while preventing localized overheating of the receiver panel. Indirect planar cavity solar receivers completely separate solid particles from the ambient environment that can greatly reduce the thermal losses in heated particles resulting in high efficiency at high temperatures above 700 degrees Celsius. This design ensures no particle losses to the environment during the operation while open-cavity designs can experience significant particle losses from wind. An experimental investigation was conducted to observe flux spreading on the receiver panel wall. A lab-scale prototype planar receiver, fabricated using Haynes 230 alloy, was tested under direct concentrated solar radiation using the high-flux solar furnace (HFSF) facility at NREL. The experiment was performed under normal peak radiative heat fluxes ranging from 800 to 1900 kW/m2. A temperature distribution on the panel wall was measured using a thermal imaging camera (FLIR A 6600). To prevent overheating at the receiver front tip, prism-shaped heat shields (Zircar UNIFROM C1) were placed in front of the receiver, and their influence on flux spreading was also studied. Absorbed flux distribution on the panel wall was modeled using SolTrace. The total solar power and flux distributions delivered from HFSF were determined based on the heliostat mirror optical properties, direct normal irradiance (DNI) on the on-sun testing days, peak flux measurement during the on-sun testing, and shutter/attenuator settings Due to the large incident angles of the solar beam on the panel wall, the angular optical properties of Haynes 230 alloy and Zircar heat shields were incorporated into the model. This flux distribution model was then integrated into a computational fluid dynamics (CFD) simulation to predict the receiver panel wall temperature, which was compared with the experimental measurements. Both prediction and measurements identified a temperature hotspot at the backside of the panel, indicating that the incident solar beam can fully reach to the rear of the receiver. The heat shields positioned at the front of the receiver effectively reduced the excessive temperature rise at the receiver front tip. Overall, the temperature was well distributed over the panel wall, with a minor hotspot at the back of the receiver. The model slightly overpredicted the temperature, possibly due to discrepancies in optical properties of the panel and an underprediction of thermal loss in the receiver. The advancement of the particle LTPCR offers a viable alternative to open-cavity receivers by addressing particle loss issues. Additionally, it presents a pathway for enabling solar thermochemical processes, extending CSP technology beyond power generation to fuel and chemical production.

14 SOLAR ENERGY↗

Development of digital electronics for the search of SHE nuclei using GARIS-II/III at RIKEN

This work describes the implementation of a digital data acquisition system for the search and study of short-lived isotopes or superheavy elements at the GARIS-III separator at the RIKEN Nishina Center. Here a reduction to 26 ± 0.5 keV in the average value of the Full Width at Half Maximum of the alpha spectrum at 7.133 MeV was achieved, combined with a reduction of the dead time of the overall system to around a few tens of nanoseconds for the detection of very fast decay chains. Moreover, we measured a reduction of the background induced by particles crossing the implantation detector using pulse shape analysis techniques. The detail of the optimization and analysis will be presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A sui generis whipping-instability-based self-sequencing multi-monodisperse 2D spray from an anisotropic microfluidic liquid jet device

Well-defined aerosols pave the way for versatile basic and applied research. Here, we demonstrate a unique whipping instability that generates from a high-aspect-ratio microfluidic device resulting in a unique steady-state gas-focused whipping jet (WJ) without any need for electrification. This WJ device emanates a multi-monodisperse whipping spray jet with a two-dimensional (2D) profile. We demonstrate this phenomenon based on various fluidic parameters theoretically and experimentally. The 2D WJ’s unique behavior is derived using analytical fluid dynamics to explain jet diameter, whipping regime, and spreading angle. The phenomenon is further characterized experimentally by measuring the angle with respect to the flow rate, the distances between droplets, the droplet shapes, and the reproducibility of these parameters. We also explain the precise fabrication of such inexpensive devices. Lastly, we highlight these devices’ potential use as sample environments in versatile applications ranging from cryoelectron microscopy over mass spectrometry to drug formulation and structural studies at X-ray free-electron lasers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Yb Substitution and Ultralow Thermal Conductivity of the Ca 3– x Yb x AlSb 3 (0 ≤ x ≤ 0.81(1)) System

Here, a series of Yb-substituted Zintl phases in the Ca 3–x Yb x AlSb 3 (0 ≤ x ≤ 0.81(1)) system has been synthesized by initial arc melting and post-heat treatment, and their isotypic crystal structures were characterized by both powder and single crystal X-ray diffraction analysis. All four title compounds adopted the Ca 3 AlAs 3 -type structure (space group Pnma, Pearson code oP28, Z = 4). The overall structure can be described as a combination of the 1-dimensional (1D) infinite chain of ∞ 1 [Al(Sb 2 Sb 2/2 )] formed by two vertices sharing [AlSb 4 ] tetrahedral moieties and three Ca 2+ /Yb 2+ mixed sites located in between these 1D chains. The charge balance and the resultant independency of the 1D chains in the title system were explained by the Zintl-Klemm formalism [Ca 2+ /Yb 2+ ] 3 [(4b-Al 1– )(1b-Sb 2– ) 2 (2b-Sb 1– ) 2/2 ]. A series of DFT calculations proved that (1) the band overlap between the d-orbital states from two types of cations and the p-orbital states from Sb at the high symmetry Γ point implied a heavily doped degenerate semiconducting behavior of the quaternary Ca 2 YbAlSb 3 model and (2) the site preference of Yb for the M1 site was due to the electronic-factor criterion based on the Q values of each atomic site. The electron localization function calculations also proved that the two different shapes of lone pairs of the Sb atoms—the “umbrella-shape” and the “C-shape”—are determined by local geometry and the coordination environment on the anionic frameworks. Thermoelectric measurements of the quaternary title compound Ca 2.19(1) Yb 0.81 AlSb 3 showed an approximately two times larger ZT value than that of ternary Ca 3 AlSb 3 at 623 K due to increased electrical conductivity and ultralow thermal conductivity originated from Yb substitution for Ca.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamics of Polymer Nanocapsule Buckling and Collapse Revealed by In Situ Liquid-Phase TEM

Nanocapsules are hollow nanoscale shells that have applications in drug delivery, batteries, self-healing materials, and as model systems for naturally occurring shell geometries. In many applications, nanocapsules are designed to release their cargo as they buckle and collapse, but the details of this transient buckling process have not been directly observed. In this work, we use in situ liquid-phase transmission electron microscopy to record the electron-irradiation-induced buckling in spherical 60-187 nm polymer capsules with ~3.5 nm walls. We observe in real time the release of aqueous cargo from these nanocapsules and their buckling into morphologies with single or multiple indentations. The in situ buckling of nanoscale capsules is compared to ex situ measurements of collapsed and micrometer-sized capsules and to Monte Carlo (MC) simulations. The shape and dynamics of the collapsing nanocapsules are consistent with MC simulations, which reveal that the excessive wrinkling of nanocapsules with ultrathin walls results from their large Föppl-von Kármán numbers around 10 5 . Our experiments suggest design rules for nanocapsules with the desired buckling response based on parameters such as capsule radius, wall thickness, and collapse rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface Variability Mapping and Roughness Analysis of the Moon Using a Coarse–Graining Decomposition

The lunar surface contains a wide variety of topographic shapes and features, each with different distributions and scales, and any analysis technique to objectively measure roughness must respect these qualities. Coarse-graining is a naturally scale-dependent filtering technique that preserves scale-dependent symmetries and produces coarse elevation maps that gradually erase the smaller features from the original topography. In this study of the lunar surface, we present two surface variability metrics obtained from coarse-graining lunar topography: fine elevation and coarse curvature. Both metrics are isotropic, deterministic, slope-independent, and coordinate-agnostic. Fine (detrended) elevation is acquired by subtracting the coarse elevation from the original topography and contains features that are smaller than the coarse-graining length-scale. Coarse curvature is the Laplacian of coarsened topography, and naturally quantifies the curvature at any scale and indicates whether a location is elevated or depressed relative to its neighborhood at that scale. We find that highlands and maria have distinct roughness characteristics at all length-scales. Our topographic spectra reveal four scale-breaks that mark characteristic shifts in surface roughness: 100, 300, 1,000, and 4,000 km. Comparing fine elevation distributions between maria and highlands, we show that maria fine elevation is biased toward smaller-magnitude elevations and that the maria–highland discrepancies are more pronounced at larger length-scales. Here, we also provide local examples of selected regions to demonstrate that these metrics can successfully distinguish geological features of different length-scales.

58 GEOSCIENCES↗

The formation and structure of iron-dominated planetesimals

Metal-rich asteroids and iron meteorites are considered core remnants of differentiated planetesimals and/or products of oxygen-depleted accretion. Investigating the origins of iron-rich planetesimals could provide key insights into planet formation mechanisms. Using differentiation models, we evaluate the interior structure and composition of representative-sized planetesimals (~200 km diameter), while varying oxygen fugacity and initial bulk meteoritic composition. Under the oxygen-poor conditions that likely existed early in the inner regions of the Solar System and other protoplanetary disks, core fractions remain relatively consistent across a range of bulk compositions (CI, H, EH, and CBa). Some of these cores could incorporate significant amounts of silicon (10–30 weight%) and explain the metal fractions of Fe-rich bodies in the absence of mantle stripping. Conversely, planetesimals forming under more oxidizing conditions, such as beyond snow lines, could exhibit smaller cores, enriched in carbon, sulfur (>1 wt%), and oxides. Sulfur-rich cores, like those formed from EH and H bulk compositions, could remain partly molten, sustain dynamos, and even drive sulfur-rich volcanism. Additionally, bodies with high carbon contents, such as CI compositions, can form graphitic outer layers. These variations highlight the importance of initial formation conditions in shaping planetesimal structures. Future missions, such as NASA’s Psyche mission, offer an opportunity to measure the relative abundances of key elements (Fe, Ni, Si, and S) necessary to distinguish among formation scenarios and structure models for Fe-rich and reduced planetesimals.

meteorites↗

Response of a CMS HGCAL silicon-pad electromagnetic calorimeter prototype to 20–300 GeV positrons

The Compact Muon Solenoid collaboration is designing a new high-granularity endcap calorimeter, HGCAL, to be installed later this decade. As part of this development work, a prototype system was built, with an electromagnetic section consisting of 14 double-sided structures, providing 28 sampling layers. Each sampling layer has an hexagonal module, where a multipad large-area silicon sensor is glued between an electronics circuit board and a metal baseplate. The sensor pads of approximately 1.1 cm$^{2}$ are wire-bonded to the circuit board and are readout by custom integrated circuits. The prototype was extensively tested with beams at CERN's Super Proton Synchrotron in 2018. Based on the data collected with beams of positrons, with energies ranging from 20 to 300 GeV, measurements of the energy resolution and linearity, the position and angular resolutions, and the shower shapes are presented and compared to a detailed Geant4 simulation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Computational prediction of dielectric breakdown strength of a transformer paper in oil with uncertainty quantification

The determination of the dielectric breakdown strengths of microstructurally heterogeneous materials has been a primarily experimental endeavor. We report the development of a microstructure-level model for computationally predicting the breakdown strength and analyzing the interactions between electromagnetic pulses (EMP) and the constituents in a composite of cellulose-based paper and mineral oil found in electrical transformers. The model allows explicit simulation of the material breakdown process by tracking the transition of dielectric constituents from non-conductive to conductive states. The focus is on the electric fields induced in the materials and the overall conditions for dielectric breakdown (defined as the onset of avalanche) caused by the electric field induced in the composite. Responses to three distinct pulse shapes, i.e., Steep Front (SF), Lightning (L), and AC with spectra spanning 60–9 × 105 Hz are considered. It is found that the breakdown strength of the material is significantly affected by microstructure heterogeneities, the spatial variations of the constituent properties, and the pulse shapes. A probabilistic characterization of the breakdown strength is computationally obtained and compared with experimental measurements. Although one particular material is analyzed, the model and approach are applicable to other heterogeneous materials as well.

breakdowns↗

The impact of light polarization effects on weak lensing systematics

ABSTRACT A fraction of the light observed from edge-on disc galaxies is polarized due to two physical effects: selective extinction by dust grains aligned with the magnetic field and scattering of the anisotropic starlight field. Since the reflection and transmission coefficients of the reflecting and refracting surfaces in an optical system depend on the polarization of incoming rays, this optical polarization produces both (a) a selection bias in favour of galaxies with specific orientations and (b) a polarization-dependent point spread function (PSF). In this work, we build toy models to obtain for the first time an estimate for the impact of polarization on PSF shapes and the impact of the selection bias due to the polarization effect on the measurement of the ellipticity used in shear measurements. In particular, we are interested in determining if this effect will be significant for Wide-Field Infrared Survey Telescope (WFIRST). We show that the systematic uncertainties in the ellipticity components are 8 × 10−5 and 1.1 × 10−4 due to the selection bias and PSF errors respectively. Compared to the overall requirements on knowledge of the WFIRST PSF ellipticity (4.7 × 10−4 per component), both of these systematic uncertainties are sufficiently close to the WFIRST tolerance level that more detailed studies of the polarization effects or more stringent requirements on polarization-sensitive instrumentation for WFIRST are required.

79 ASTRONOMY AND ASTROPHYSICS↗

Modeling of transient interference phenomena in colinear laser spectroscopy

Colinear laser spectroscopy of fast atomic beams has been established as one of the main tools to perform precision experiments with atoms containing short-lived nuclei. Although highly sensitive, the spectral resolution of these techniques is typically limited to several MHz. Here, we study the use of transient interference phenomena to potentially improve the experimental resolution. Previous attempts to implement Ramsey-type measurements with fast beams were limited by the lack of understanding of the observed line shapes. Additionally, by using a simple model, we provide a satisfactory description of the previously observed line shapes and propose alternative experimental schemes to improve the resolution in fast ion-beam experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Superconducting pairing mechanism in CeCoIn 5 revisited

Spectroscopic-imaging scanning-tunneling microscopy (SI-STM) measurements have previously been applied to the study of the heavy-fermion system CeCoIn 5 to examine the superconducting gap structure and band dispersions via quasiparticle intereference. Here we directly measure the dispersing electron bands with angle-resolved-photoelectron spectroscopy (ARPES) and compare with first principles electronic structure calculations. By auto-correllating the ARPES-resolved bands with themselves we can measure the potential q-vectors and discern exactly which bands the STM is measuring. We find that the STM results are dominated by scattering associated with a cloverleaf shaped band centered at the zone corners. This same band is also a viable candidate to host the superconducting gap. Overall, the electronic structure calculations indicate that this region of the Fermi surface involves significant contributions from the Co d-electrons, an indication that the superconductivity in these materials is more 3-dimensional than that found in the related unconventional superconductors, the cuprates and the pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Correlations between flow and transverse momentum in Xe + Xe and Pb + Pb collisions at the LHC with the ATLAS detector: A probe of the heavy-ion initial state and nuclear deformation

The correlations between flow harmonics v n for n = 2, 3, and 4 and mean transverse momentum [p T ] in 129 Xe + 129 Xe and 208 Pb + 208 Pb collisions at $\sqrt{s}$ = 5.44 and 5.02 TeV, respectively, are measured using charged particles with the ATLAS detector. The correlations are potentially sensitive to the shape and size of the initial geometry, nuclear deformation, and initial momentum anisotropy. The effects from nonflow and centrality fluctuations are minimized, respectively, via a subevent cumulant method and an event-activity selection based on particle production at very forward rapidity. The v n -[p T ] correlations show strong dependencies on centrality, harmonic number n, p T , and pseudorapidity range. Current models qualitatively describe the overall centralityand system-dependent trends but fail to quantitatively reproduce all features of the data. In central collisions, where models generally show good agreement, the v 2 -[p T ] correlations are sensitive to the triaxiality of the quadruple deformation. Comparison of the model with the Pb + Pb and Xe + Xe data confirms that the 129 Xe nucleus is a highly deformed triaxial ellipsoid that has neither a prolate nor oblate shape. This provides strong evidence for a triaxial deformation of the 129 Xe nucleus from high-energy heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Effect of workpiece curvature on the tool influence function during hemispherical sub-aperture tool glass polishing

The influence of workpiece curvature on the tool influence function spot during polishing of fused silica glass with cerium oxide slurry, while using a rotating hemispherical pad-foam tool for a wide variety of process conditions (tool displacement, inclination angle, and rotation rate), has been investigated. (Workpiece curvature ranged from 500 mm radius concave to 43 mm radius convex.) The TIF spot decreases in diameter and increases in the peak removal rate on more convex workpieces. In contrast, the TIF spot increases both in diameter and peak removal rate on more concave workpieces. For the range of workpiece curvatures investigated, both the spot size and the peak removal rate changed significantly, as much as 2 times. An elastic sphere–sphere contact mechanics model, which utilizes both a modified displacement (that leads to a change in the applied load) as well as a mismatch factor (that influences the pressure distribution shape), has been developed. Furthermore, the model was validated using both offline load-displacement measurements and finite-element analysis simulations. The model quantitatively describes the measured change in the relative contact diameter and relative pressure distribution, as well as semiquantitively describes the change in the relative volumetric removal rate on a large variety of TIF spots. The change in the volumetric removal rate for convex workpieces is a result of the balance between a decreasing spot size (reducing removal) and an increasing peak pressure (increasing removal), which usually results in relatively small changes in volumetric removal. In the case of concave workpieces, the volumetric removal rate change is also governed by a similar balance, but the spot size increase contribution dominates, resulting in a significant increase in volumetric removal rate. Understanding these trends can enable methods to add greater determinism during the fabrication of freeform optics by adjusting polishing parameters (such as dwell time) while the tool translates along a workpiece surface with different local curvatures.

47 OTHER INSTRUMENTATION↗

Experimental Investigation of Low-Frequency Distributed Acoustic Strain-Rate Responses to Propagating Fractures

Summary Low-frequency distributed acoustic sensing (LF-DAS) responds to strain changes due to far-field fracture propagation. To better understand the LF-DAS response to fracture propagation, we performed laboratory-scale hydraulic fracture experiments with embedded optical strain sensors. The objectives of this research are to generate hydraulic fractures of known geometry, measure the strain response along the embedded fiber-optic cable comparable to LF-DAS measurements, and use the results to inform the interpretation of field-derived LF-DAS data. The experiments were conducted in unconfined transparent cubic blocks with a dimension of 8 in. on each side. The block was made of transparent epoxy to visualize the fracture propagation. Fiber-optic sensing cables were embedded in the block at different distances to the source of injection. We injected dyed water through an injection tubing to generate a transverse, radial fracture along an initial flaw. An optical interrogator recorded the response of offset fiber Bragg grating (FBG) strain sensors normal to the plane of the fracture. The strain data were visualized on a waterfall plot, akin to visualizations of field-derived LF-DAS data. Dimensional analysis was used to scale the laboratory results to field conditions. We compared the evolution of the strain response at the fiber-optic cable, injection pressure, and rate with known fracture geometry. The measured strains were compared with Sneddon’s (1946) linear elastic solution for a penny-shaped crack and found to follow this behavior. The generated radial fractures in transparent media can be modeled with Sneddon’s linear elastic radial fracture model and a Mode I critical stress intensity factor. The LF-DAS characteristic response of a narrowing region of extension surrounded by compression was exhibited as a fracture that approached and intersected the fiber-optic cable. The experimentally derived strain and strain-rate waterfall plots with known fracture geometry, injection rate, and pressure response provide insight in understanding LF-DAS responses in the field. Furthermore, we developed a method to estimate fracture geometry evolution from the fiber-optic strain data and validated the method against the experimental data.

Engineering↗

Cylinder Test

In 1941 G.I. Taylor proposed the cylinder test as an experiment to determine the properties of explosive products. The test consists of a hollow metal cylinder containing an unreacted cylindrical charge of explosives. The charge is detonated at one end of the cylinder and, as the detonation wave propagates, the product gas expands behind it. As the product gas is produced, the pressure acting on the metal increases and begins to push the walls outward. Consider the time at which the detonation wave has reached the halfway point between the two ends of the cylinder. In front of the wave nothing has changed and the metal tube has the same initial radius. Behind the wave, the radius of the tube has expanded. The farther behind the wave a section of tube is, the larger its radius has become. The longer the wall is exposed to the pressurized gas, the more it expands, so that the radius is largest where the detonation was initiated. The metal most commonly used for this experiment is soft copper. Its material properties are well known and soft copper is also easy to shape with precision machining. During the cylinder test the radial expansion of the cylinder is measured over time and this data is used to determine the amount of work applied to the cylinder wall by the product gas as a function of time. Since volume increases in this problem, the time dependence can be seen as a volume dependence. The volume dependent work yields a path in thermodynamic space. The cylinder test experiment can be modeled using simulation. The simulation gives you the answer, but it cannot tell you why. The goal of the proposed work is to use analytic analysis methods to give insight into the simulation solution.

36 MATERIALS SCIENCE↗