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At least 1,747 records · Page 97

Chemical vapor deposition modeling: An assessment of current status

The shortcomings of earlier approaches that assumed thermochemical equilibrium and used chemical vapor deposition (CVD) phase diagrams are pointed out. Significant advancements in predictive capabilities due to recent computational developments, especially those for deposition rates controlled by gas phase mass transport, are demonstrated. The importance of using the proper boundary conditions is stressed, and the availability and reliability of gas phase and surface chemical kinetic information are emphasized as the most limiting factors. Future directions for CVD are proposed on the basis of current needs for efficient and effective progress in CVD process design and optimization.

Gokoglu, Suleyman A.↗

Influence of nonequilibrium radiation and shape change on aerothermal environment of a Jovian entry body

The influence of nonequilibrium radiative energy transfer and the effect of probe configuration changes on the flow phenomena around a Jovian entry body are investigated. The radiating shock layer flow is assumed to be axisymmetric, viscous, laminar and in chemical equilibrium. The radiative transfer equations are derived under nonequilibrium conditions which include multilevel energy transitions. The equilibrium radiative transfer analysis is performed with an existing nongray radiation model which accounts for molecular band, atomic line, and continuum transitions. The nonequilibrium results are obtained with and without ablation injection in the shock layer. The nonequilibrium results are found to be greatly influenced by the temperature distribution in the shock layer. In the absence of ablative products, the convective and radiative heating to the entry body are reduced under nonequilibrium conditions. The influence of nonequilibrium is found to be greater at higher entry altitudes. With coupled ablation and carbon phenolic injection, 16 chemical species are used in the ablation layer for radiation absorption. Equilibrium and nonequilibrium results are compared under peak heating conditions.

Tiwari, S. N.↗

An Approach to Solving Enclosure Radiation Problems in A Multi-Physics Context

Thermal protection system analysis of complex features or damage sites can sometimes require modeling of high temperature enclosures. Implementing efficient and accurate view-factor algorithms required to model such problems is complex. The current work leverages the Non-equilibrium Radiation (NERO) software, which solves the radiation transport equation in a finite-volume scheme, to alleviating challenges often faced with view-factor calculations. By assuming heat transfer occurs only between grey bodies and that the medium is non-participating, computational cost of the method is significantly reduced. The enclosure physics are modeled through emitting and reflecting boundary conditions in NERO. The emitted radiative flux is dependent on the wall temperature which is a solution to the material response, obtained from Icarus, in this context. The Ares framework manages the time-advancement and exchange of the necessary data between the solvers. The surface energy balance is modified to account for the enclosure terms within the material response boundary condition. The methodology was verified against analytical solutions including radiating parallel plates, a hollow cylinder (shown in Fig. 1), and a hemisphere. Application of the methodology to inform the design of components of the Dragonfly system will be shown.

Ablation↗

Investigations of the dynamical evolution of protoplanetary nebulae

The spectral energy distributions (SED's) of all the known Class I (protostellar) sources in the Taurus molecular cloud were modelled. The Tereby, Shu, & Cassen (1984, TSC) density distribution for a rotating, infalling envelope was adopted. The radiative equilibrium temperature distribution from the spherical average of the TSC density distribution was calculated. The resulting spherically-symmetric temperature distribution then provides the source function to obtain the emergent spectrum at a given inclination angle i from the formal solution of the transfer equation, using the exact density (opacity) distribution. Results showed that the SED's of the protostar candidates in Taurus can be reproduced with TSC models having infall rates close to the values predicted by the theory of isothermal cloud collapse. Flat Spectrum T Tauri Stars were studied. The mid- to far-infrared fluxes of 'flat spectrum' T Tauri stars can be explained by radiative equilibrium emission from infalling dusty envelopes. This explanation indicated that models employing 'active' disks, in which the temperature distribution is a parameterized power law, should be invoked with caution. Infall also naturally explains the scattered light nebulae detected around many flat-spectrum sources. Results showed that the SED's of the protostar candidates in Taurus can be reproduced with TSC models having infall rates close to the values predicted by the theory of isothermal cloud collapse. Flattened infalling envelope models are also being studied.

Hartmann, Lee W.↗

Particle-in-cell simulations and passive bulk model of collisional capacitive discharge

Intermediate pressure (0.2–6.0 Torr), radio frequency capacitive discharges are of increasing importance in the thin film processing industry. However, existing low pressure (<0.1 Torr) discharge models are often used beyond their applicability in this pressure range. In this work, the authors performed one-dimensional particle-in-cell (PIC) simulations of a capacitive 2.5 cm gap argon discharge driven at 13.56 MHz with current density amplitude J 0 50 A/m 2 over a wide range of gas pressures p g = 0.04–20 Torr. For intermediate pressures, the PIC results showed that most of the ionization occurs near the plasma-sheath edges with very little occurring within the central bulk region. This led us to develop a “passive bulk” model of the discharge in which bulk electron heating does not contribute to ionization, and all the ionization is due solely to the sheath-heated electrons. The model assumes a constant ion-neutral mean free path λ i in the plasma bulk and either constant λ i or constant ion mobility μ i in the sheaths. The model is solved using an electron temperature iteration scheme. The PIC scalings of the discharge equilibrium parameters (e.g., electron density and temperature, sheath width, and voltage) with the input parameters p g and J 0 showed good agreement with those of the passive bulk model. A constant μ i sheath model showed the best agreement with the PIC results in the intermediate pressure regime of interest, but a constant λ i model is simpler to implement and showed reasonable agreement over a wide pressure range.

36 MATERIALS SCIENCE↗

HOST surface protection R and T overview

Most of the efforts in the HOST Surface Protection Subproject were focused on thermal barrier coating (TBC) life prediction. Also, a small effort, consisting primarily of wrapping up and reporting the work of previous years, remained on the airfoil deposition modeling. The work performed under the airfoil deposition modeling program element was concerned with modeling the deposition of corrodants onto turbine airfoils. Accomplishments included verification of the chemically frozen boundary (CFBL) theory. Encouraging results were also achieved with the recently developed local thermochemical equilibrium (LTCE) theory. The surface protection subprogram was devoted to thermal-barrier-coating life modeling. This modeling is an essential step in the development of TBC's.

Miller, Robert A.↗

Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo

The environments experienced by vehicles upon entry into planetary atmospheres generally result in severe aerothermodynamic loading. These flows are characterized by the formation of strong shock waves, behind which high temperatures and non-equilibrium environments are generated, and the accurate prediction of internal energy relaxation and chemical kinetics becomes important. This manuscript focuses on the internal relaxation of the rotational energy of polyatomic molecules. Previous work has described the implementation of a discrete rotational energy model for diatomic molecules (linear rotators). Later, Gimelshein et. al extended this model to include polyatomic molecular internal energies. However, they did not include details on how to generate the particles at equilibrium conditions and centrifugal distortion was not included in their model. The purpose of the present study is to extend the afore-mentioned models to the treatment of discrete rotational energy in polyatomic molecules with the addition of centrifugal distortion. An overview of the background theory needed for the implementation of the model will be given followed by the model itself and verification of the model. For example, sampled versus Boltzmann distributions are compared in Figure 1 for CH3 (oblate rotator – two quantum numbers) and examples of thermal relaxation behavior for linear and non-linear rotators are presented in Figure 2. In addition, comparisons of thermophysical properties will be presented, as well as examples of adiabatic relaxation and application to hypersonic flow.

Rarefied Gas Dynamics↗

Orbits of Saturn's Inner Moons and Other Observations Connected within the 1995-1996 Saturnian Ring Plane Crossing

We reduced and analyzed radio images of Saturn taken in 1990-1995 at 0.35, 2.0, 3.6 and 6.1 cm wavelength. The latitudinal brightness distribution varies substantially over time. Detailed modeling of these data shows that NH4SH condenses at the thermochemical equilibrium temperature of 235.5 K only at Northern mid-latitudes. Over most of the planet, condensation does not occur until the gas cools to 190 +/- 5 K. Supersaturation may also cause the dark equatorial region seen in 1995 at 6.1 cm. Observations of the rings show that the West (dusk) ansa is brighter than the East (dawn) ansa by factors up to 2. The magnitude of the asymmetry increases with increasing wavelength and with decreasing distance to the planet. This East-West asymmetry may be due to multiple scattering in gravitational wakes. We improved the Monte Carlo scattering code used to model the microwave emission from Saturn's rings at multiple wavelengths. The basic code outlined in Dunn, Molnar, and Fix describes the rings as a uniform, infinite layer of ice spheres with a finite vertical extent. The particle sizes follow a power law distribution and scatter light according to a linear combination of Mie and isotropic phase functions. These parameters may be adjusted to reflect the physical properties in the scattering properties of the ring particles. This is used to construct a model which can be directly compared to Very Large Array data. The code has been extended by including anisotropic particle distributions, primarily in the form of the wake structures that are likely to exist in the enhancements. The vertical extent of the wakes equals that of the ring layer. Between the wakes are regions of diminished density so that the optical depth integrated over many wakes matches that of the Voyager occultation experiments. This allows us to model the brightness temperature as a function of azimuth and look for asymmetric scattering behavior in the rings. By changing the width and relative density of the wakes, we can alter the nature of the gross scattering properties of the rings to match what is seen in our data.

Lissauer, Jack J.↗

Advancement of Entry System Modeling to Support Exploration of Giant Planets

This paper describes NASA’s efforts to advance entry system modeling and simulation capabilities to support future exploration of Giant planets. The Giant planets are key destinations of interest to the planetary science community for their potential to provide insight into the formation and evolution of our Solar System, as well as extrasolar planetary systems. To date, the Galileo atmospheric probe is the only purpose-built entry probe to a Giant planet. Post-flight analysis of Galileo’s performance showed that there was significant recession of the thermal protection system (TPS), well beyond what was anticipated on the flank, and this was due in part to insufficiently accurate capability for estimating the flight environment and TPS response. While Galileo ultimately survived its flight, the example serves to highlight the great challenge of designing successful missions for environments that are poorly understood or where models have not yet been validated. An important means to reduce mission risks is the incorporation of physics-based modeling with well-quantified uncertainties. The emphasis on physics-based modeling – in contrast to empirically-driven models – is motivated by the fact that it is impossible to completely replicate entry environments through ground tests and, therefore, extrapolation to the flight environment is required. Basing analysis in fundamental physics removes the bias of ground test limitations, though one must then be careful to properly characterize model inputs, simplifying assumptions, and the limits wherein the model is valid. NASA’s Entry Systems Modeling (ESM) Project is tasked with investigating such considerations for planetary science missions across the Solar System, and in recent years has begun to do so for Giant planets. The most distinctive features of the Giant planets, from an entry system perspective, are the atmospheres composed primarily of hydrogen and helium. The entry velocities of proposed missions are generally very large and can therefore be expected to result in significant convective and radiative heating generated by the vehicle’s shock layer. Yet thermochemical behavior of the hydrogen-helium system is not well understood under such conditions. The ESM project is leading efforts to develop accurate thermochemical databases based on state-of-the-art measurements in the Electric Arc Shock Tube and detailed computational chemistry. The large heat fluxes anticipated by missions has driven interest in new TPS materials, in particular woven materials, which may be enabling but have never been flown before. Consequently, multiscale models are in development to describe properties and performance of the materials from micro- to system-scale. The goal is to not only provide accurate thermal response but also to inform thermostructural reliability predictions for extreme entries. Additionally, new computational models have been developed to evaluate performance of non-destructive evaluation techniques which are vital to establishing acceptance of systems to be free of manufacturing faults like material cracking, voids, and debonding. Finally, in the area of guidance and control, aerocapture has been shown conceptually to provide a number of mission benefits, including reducing transit time and increasing payload fraction. The ESM project is building a launch-to-landing trajectory simulation capability to enable detailed studies of aerocapture maneuvers in the context of Giant planets missions. The final presentation and paper will describe each of these topics in detail, including discussion of specific gaps and the technical approach to solving them. In addition, the final paper will briefly discuss ongoing coordination between ESM project work and an ESA-funded technology development activity comprised of validation testing in the Oxford T6, IRS PWK and IST ESTHER tunnels, as well as state-to-state modeling of the shock layer to better represent non-Boltzmann energy distributions leading to non-equilibrium radiation.

Entry systems↗

Future Climate Impacts of Direct Radiative Forcing Anthropogenic Aerosols, Tropospheric Ozone, and Long-lived Greenhouse Gases

Long-lived greenhouse gases (GHGs) are the most important driver of climate change over the next century. Aerosols and tropospheric ozone (O3) are expected to induce significant perturbations to the GHG-forced climate. To distinguish the equilibrium climate responses to changes in direct radiative forcing of anthropogenic aerosols, tropospheric ozone, and GHG between present day and year 2100, four 80-year equilibrium climates are simulated using a unified tropospheric chemistry-aerosol model within the Goddard Institute for Space Studies (GISS) general circulation model (GCM) 110. Concentrations of sulfate, nitrate, primary organic (POA) carbon, secondary organic (SOA) carbon, black carbon (BC) aerosols, and tropospheric ozone for present day and year 2100 are obtained a priori by coupled chemistry-aerosol GCM simulations, with emissions of aerosols, ozone, and precursors based on the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emissions Scenario (SRES) A2. Changing anthropogenic aerosols, tropospheric ozone, and GHG from present day to year 2100 is predicted to perturb the global annual mean radiative forcing by +0.18 (considering aerosol direct effects only), +0.65, and +6.54 W m(sup -2) at the tropopause, and to induce an equilibrium global annual mean surface temperature change of +0.14, +0.32, and +5.31 K, respectively, with the largest temperature response occurring at northern high latitudes. Anthropogenic aerosols, through their direct effect, are predicted to alter the Hadley circulation owing to an increasing interhemispheric temperature gradient, leading to changes in tropical precipitation. When changes in both aerosols and tropospheric ozone are considered, the predicted patterns of change in global circulation and the hydrological cycle are similar to those induced by aerosols alone. GHG-induced climate changes, such as amplified warming over high latitudes, weakened Hadley circulation, and increasing precipitation over the Tropics and high latitudes, are consistent with predictions of a number of previous GCM studies. Finally, direct radiative forcing of anthropogenic aerosols is predicted to induce strong regional cooling over East and South Asia. Wintertime rainfall over southeastern China and the Indian subcontinent is predicted to decrease because of the increased atmospheric stability and decreased surface evaporation, while the geographic distribution of precipitation is also predicted to be altered as a result of aerosol-induced changes in wind flow.

Chen, Wei-Ting↗

The prediction and confirmation of critical epitaxial parameters

The coherency-incoherency transition in epitaxial crystals is said to take place at a critical misfit f(c) or, for a system in which a monolayer is subcritical, at a critical thickness h(c). In this paper, the physical principles and models used to predict critical parameters are analyzed and put into perspective. The dependence of the relevant principles on the equilibrium-nonequilibrium conditions under which the quantities are measured in practice is stressed. The advantages and disadvantages of the models used (essentially the Frenkel-Kontorowa and Volterra models) are highlighted.

Van Der Merwe, Jan↗

An alternative assessment of second-order closure models in turbulent shear flows

The performance of three recently proposed second-order closure models is tested in benchmark turbulent shear flows. Both homogeneous shear flow and the log-layer of an equilibrium turbulent boundary layer are considered for this purpose. An objective analysis of the results leads to an assessment of these models that stands in contrast to that recently published by other authors. A variety of pitfalls in the formulation and testing of second-order closure models are uncovered by this analysis.

Speziale, Charles G.↗

The VATMOS-SR Mission Concept: DSMC Studies of the Gas Sampling

VATMOS-SR (Venus ATMOSpheric - Sample Return) is a small spacecraft mission concept that would return a gas sample from the upper atmosphere of Venus to Earth for scientific analysis. This could be the first sample return mission for an extra-terrestrial atmosphere and potentially the first sample return from an Earth-sized planet. The VATMOS-SR mission concept consists of a SmallSat atmospheric sampling probe (45 deg. sphere/cone geometry, <1 m diameter) that is designed to skim through the Venus upper atmosphere and acquire gas samples below the homopause altitude (around ~110 km altitude), where the different atmospheric gases are mixed. The velocity of the spacecraft where sampling would occur is expected to be between ~10.5 km/s and ~13.1 km/s, depending on the trajectory chosen. This presentation will discuss hypervelocity sampling in the upper atmosphere of Venus with respect to the VATMOS-SR mission concept. VATMOS-SR would enable critical atmospheric measurements to form a complete picture of how, why, and when Venus evolved to be so different from Earth and Mars. The abundances and isotopic compositions of volatile elements (such as N, C, S, O, and the noble gases) in planetary atmospheres record volatile delivery during accretion, outgassing from planetary interiors, and atmospheric loss to space. Precise and accurate determinations of volatile atmospheric signatures are the key to understanding the origins and geodynamical evolution of Venus compared to the other terrestrial planets. Hypersonic sampling poses unique technical and scientific challenges. To ensure it is possible to relate the composition of the sampled gases to the free stream atmospheric composition, large-scale numerical simulations are employed to model the flow through the VATMOS-SR sampling system. In particular, an emphasis is placed on quantifying noble gas isotopic fractionation that occurs during the sample acquisition and transfer process to determine how measured isotopic ratios of noble gases in the sample compared to actual isotopic ratios in the Venusian atmosphere. The Direct Simulation Monte Carlo (DSMC) code SPARTA, an open-source software package developed by Sandia National Laboratories, is used in this work. SPARTA, based on Bird’s DSMC method, is a molecular-level gas-kinetic technique. As SPARTA is able to model hypervelocity reacting flows in strong chemical and thermal non-equilibrium, this software package is well suited to determine relevant flow properties for the VATMOS-SR mission concept and to numerically quantify the expected level of elemental and/or isotopic fractionation in the sample acquired by VATMOS-SR. This presentation will show results from 3D simulations correlating the noble gas isotopic fractionation in the gas acquired at hypervelocity speeds to its ambient atmosphere value. In particular, emphasis will be placed on Xenon isotopes of masses 128 and 130, as precise measurements of that ratio would yield comparison to Earth’s atmosphere. Additionally, sensitivity studies that quantify the uncertainties due to the freestream parameters, as well as the modeling parameters, will be performed.

direct simulation Monte Carlo↗

Direct Simulation Monte Carlo Studies of the Gas Sampling for the VATMOS-SR Mission Concept

VATMOS-SR (Venus ATMOSpheric - Sample Return) is a small spacecraft mission concept which would return a gas sample from the upper atmosphere of Venus to Earth for scientific analysis. This could be the first sample return mission for an extra-terrestrial atmosphere, and potentially the first sample return from an Earth-sized planet. The VATMOS-SR mission concept consists of a SmallSat atmospheric sampling probe (45 deg. sphere/cone geometry, <1 m diameter) that is designed to skim through the Venus upper atmosphere and acquire gas samples below the homopause altitude (around ~110 km altitude), where the different atmospheric gases are mixed. The velocity of the spacecraft where sampling would occur is expected to be between ~10.5 km/s and ~13.1 km/s, depending on the trajectory chosen. This presentation will discuss hypervelocity sampling in the upper atmosphere of Venus, with respect to the VATMOS-SR mission concept. VATMOS-SR would enable critical atmospheric measurements to form a full picture of how, why, and when Venus evolved to be so different from Earth and Mars. The abundances and isotopic compositions of volatile elements (such as N, C, S, O and the noble gases) in planetary atmospheres record volatile delivery during accretion, outgassing from planetary interiors, and atmospheric loss to space. Precise and accurate determinations of atmospheric volatile signatures are the key to understanding the origins and geodynamical evolution of Venus compared to the other terrestrial planets. Hypersonic sampling poses unique technical and scientific challenges. To ensure it is possible to relate the composition of the sampled gases to the free stream atmospheric composition, large-scale numerical simulations are employed to model the flow through the VATMOS-SR sampling system. In particular, an emphasis is placed on quantifying noble gas isotopic fractionation that occurs during the sample acquisition and transfer process in order to determine how measured isotopic ratios of noble gases in the sample compare to actual isotopic ratios in the Venusian atmosphere. The Direct Simulation Monte Carlo (DSMC) code SPARTA, an open source software package developed by Sandia National Laboratories, is used in this work. SPARTA, based on Bird’s DSMC method, is a molecular-level gas-kinetic technique. As SPARTA is able to model hypervelocity reacting flows in strong chemical and thermal non-equilibrium, this software package is well suited to determine relevant flow properties for the VATMOS-SR mission concept, and to numerically quantify the expected level of elemental and/or isotopic fractionation in the sample acquired by VATMOS-SR. This presentation will show results from 3D simulations correlating the noble gas isotopic fractionation in the gas acquired at hypervelocity speeds to its ambient atmosphere value. In particular, emphasis will be placed at Xenon isotopes of masses 128 and 130, as precise measurements of that ratio would yield a comparison to Earth’s atmosphere. Additionally, sensitivity studies that quantify the uncertainties due to the freestream parameters as well as the modeling parameters will be performed.

direct simulation Monte Carlo↗

A-B Transition in Superfluid $^3$He and Cosmological Phase Transitions

First-order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna. All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid $^3$He ideal for test of classical nucleation theory. As Leggett and others have noted, the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave production in the early universe. Here we discuss studies of the A-B phase transition dynamics in $^3$He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Towards Pareto optimal high entropy hydrides via data-driven materials discovery

The ability to rapidly screen material performance in the vast space of high entropy alloys is of critical importance to efficiently identify optimal hydride candidates for various use cases. Given the prohibitive complexity of first principles simulations and large-scale sampling required to rigorously predict hydrogen equilibrium in these systems, we turn to compositional machine learning models as the most feasible approach to screen on the order of tens of thousands of candidate equimolar high entropy alloys (HEAs). Critically, we show that machine learning models can predict hydride thermodynamics and capacities with reasonable accuracy (e.g. a mean absolute error in desorption enthalpy prediction of ~5 kJ mol H 2 –1 ) and that explainability analyses capture the competing trade-offs that arise from feature interdependence. We can therefore elucidate the multi-dimensional Pareto optimal set of materials, i.e., where two or more competing objective properties can't be simultaneously improved by another material. This provides rapid and efficient down-selection of the highest priority candidates for more time-consuming density functional theory investigations and experimental validation. Various targets were selected from the predicted Pareto front (with saturation capacities approaching two hydrogen per metal and desorption enthalpy less than 60 kJ mol H 2 –1 ) and were experimentally synthesized, characterized, and tested amongst an international collaboration group to validate the proposed novel hydrides. Finally, additional top-predicted candidates are suggested to the community for future synthesis efforts, and we conclude with an outlook on improving the current approach for the next generation of computational HEA hydride discovery efforts.

36 MATERIALS SCIENCE↗

Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems

The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the gap between the min- and the max-relative entropies to the thermal state is small, then the state can be approximately reversibly converted to and from the thermal state with thermal operations and a small source of coherence. Our proof provides a quantum version of the Shannon-McMillan-Breiman theorem for the relative entropy and a quantum Stein’s lemma for ergodic states and local Gibbs states. In this work, our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A-LEAF

A-LEAF is an electricity market simulation framework. It includes models for short-term market operations and long-term investment planning of generation, storage, and transmission. Model formulations include least cost and two-stage market equilibrium. Simulations can be flexibly structured over one or more years, including options for periodic samples or jumping to a single future year. Years can be simulated as 365 consecutive days at hourly or 5-minute sample rates, or they can be subsampled using a representative day group selection algorithm.

MANN, WILLIAM↗