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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

HI Absorption in Merger Remnants

It has been proposed that ultraluminous infrared galaxies (ULIRGs) pass through a luminous starburst phase, followed by a dust-enshrouded AGN phase, and finally evolve into optically bright "naked" quasars once they shed their gas/dust reservoirs through powerful wind events. We present the results of our recent 21- cm HI survey of 21 merger remnants with the Green Bank Telescope. These remnants were selected from the QUEST (Quasar/ULIRG Evolution Study) sample of ULIRGs and PG quasars; our targets are all bolometrically dominated by AGN and sample all phases of the proposed ULIRG -> IR-excess quasar -> optical quasar sequence. We explore whether there is an evolutionary connection between ULIRGs and quasars by looking for the occurrence of HI absorption tracing neutral gas outflows; our results will allow us to identify where along the sequence the majority of a merger's gas reservoir is expelled.

Teng, Stacy H.↗
NASA NTRS2015

System-Level Experimental Validations for Supersonic Commercial Transport Aircraft Entering Service in the 2018-2020 Time Period

This report describes the work conducted under NASA funding for the Boeing N+2 Supersonic Experimental Validation project to experimentally validate the conceptual design of a supersonic airliner feasible for entry into service in the 2018 -to 2020 timeframe (NASA N+2 generation). The primary goal of the project was to develop a low-boom configuration optimized for minimum sonic boom signature (65 to 70 PLdB). This was a very aggressive goal that could be achieved only through integrated multidisciplinary optimization tools validated in relevant ground and, later, flight environments. The project was split into two phases. Phase I of the project covered the detailed aerodynamic design of a low boom airliner as well as the wind tunnel tests to validate that design (ref. 1). This report covers Phase II of the project, which continued the design methodology development of Phase I with a focus on the propulsion integration aspects as well as the testing involved to validate those designs. One of the major airplane configuration features of the Boeing N+2 low boom design was the overwing nacelle. The location of the nacelle allowed for a minimal effect on the boom signature, however, it added a level of difficulty to designing an inlet with acceptable performance in the overwing flow field. Using the Phase I work as the starting point, the goals of the Phase 2 project were to design and verify inlet performance while maintaining a low-boom signature. The Phase II project was successful in meeting all contract objectives. New modular nacelles were built for the larger Performance Model along with a propulsion rig with an electrically-actuated mass flow plug. Two new mounting struts were built for the smaller Boom Model, along with new nacelles. Propulsion integration testing was performed using an instrumented fan face and a mass flow plug, while boom signatures were measured using a wall-mounted pressure rail. A side study of testing in different wind tunnels was completed as a precursor to the selection of the facilities used for validation testing. As facility schedules allowed, the propulsion testing was done at the NASA Glenn Research Center (GRC) 8 x 6-Foot wind tunnel, while boom and force testing was done at the NASA Ames Research Center (ARC) 9 x 7-Foot wind tunnel. During boom testing, a live balance was used for gathering force data. This report is broken down into nine sections. The first technical section (Section 2) covers the general scope of the Phase II activities, goals, a description of the design and testing efforts, and the project plan and schedule. Section 3 covers the details of the propulsion system concepts and design evolution. A series of short tests to evaluate the suitability of different wind tunnels for boom, propulsion, and force testing was also performed under the Phase 2 effort, with the results covered in Section 4. The propulsion integration testing is covered in Section 5 and the boom and force testing in Section 6. CFD comparisons and analyses are included in Section 7. Section 8 includes the conclusions and lessons learned.

Magee, Todd E.↗
NASA NTRS2016

MSL SAM-Like Evolved Gas Analyses of Si-rich Amorphous Materials

Chemical and mineralogical analyses of several samples from Murray Formation mudstones and Stimson Formation sandstones by the Mars Science Laboratory (MSL) revealed the presence of Si-rich amorphous or poorly ordered materials. It is possible to identify the presence of high-SiO2 vs. lower SiO2 amorphous materials (e.g., basaltic glasses), based on the position of the resulting wide diffraction features in XRD patterns from the Chemistry and Mineralogy (CheMin) instrument, but it is not possible to distinguish between several candidate high-SiO2 amorphous materials such as opal-A or rhyolitic glass. In the Buckskin (BS) sample from the upper Murray Formation, and the Big Sky (BY) and Greenhorn (GH) samples from the Stimson Formation, analyses by the Sample Analysis at Mars (SAM) instrument showed very broad H2O evolutions during sample heating at temperatures >450-500degC which had not been observed from previous samples. BS also had a significant broad evolution <450-500degC. We have undertaken a laboratory study targeted at understanding if the data from SAM can be used to place constraints on the nature of the amorphous phases. SAM-like evolved gas analyses have been performed on several opal and rhyolitic glass samples. Opal-A samples exhibited wide <500degC H2O evolutions, with lesser H2O evolved above ~500degC. H2O evolution traces from rhyolitic glasses varied, having either two broad H2O peaks, <300degC and >500degC, or a broad peak centered around 400degC. For samples that produced two evolutions, the lower temperature peak is more intense than the higher temperature peak, a trend also exhibited by opal-A. This trend is consistent with data from BS, but does not seem consistent with data from BY and GH which evolved most of their H2O >500degC. It may be that dehydration of opal-A and/or rhyolitic glass can result in some preferential loss of lower temperature H2O, to produce traces that more closely resemble BY and GH. This is currently under investigation and results will be reported.

McAdam, Amy↗
DOE OSTI2025

Dynamics of nanoscale phase decomposition in laser ablation

Abstract Laser ablation is a process that bears both fundamental physics interest and has wide industrial applications. For decades, the lack of probes on the relevant time and length scales has prevented access to the highly nonequilibrium phase decomposition processes triggered by laser excitation. In this study, a close integration of time-resolved probing by intense femtosecond X-ray pulses with large-scale atomistic modeling has yielded unique insights into the ablation dynamics of thin gold films irradiated by femtosecond laser pulses. The emergence and growth of nanoscale density heterogeneities in the expanding ablation plume, predicted in the simulations, are mapped to the rapid evolution of distinct small angle diffraction features. This mapping enables identification of the characteristic signatures of different phase decomposition processes occurring simultaneously in the plume, which are driven by photomechanical and thermodynamic driving forces. Beyond the specific insights into the ablation phenomenon, this study demonstrates the power of joint X-ray probing and atomistic modeling of material dynamics under extreme conditions of thermal and mechanical nonequilibrium.

Sun, Yanwen (ORCID:0000000159266565)↗
DOE OSTI2021

Adaptive machine learning for time-varying systems: low dimensional latent space tuning

Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map combinations of accelerator parameters and images which are 2D projections of the 6D phase space distributions of charged particle beams as they are transported between various particle accelerator locations. Despite their strengths, applying ML to time-varying systems, or systems with shifting distributions, is an open problem, especially for large systems for which collecting new data for re-training is impractical or interrupts operations. Particle accelerators are one example of large time-varying systems for which collecting detailed training data requires lengthy dedicated beam measurements which may no longer be available during regular operations. We present a novel method of adaptive ML for time-varying systems. Our approach is to map very high (N ≈ 100k) dimensional inputs (a combination of scalar parameters and images) into the low dimensional (N ≈ 2) latent space at the output of the encoder section of an encoder-decoder CNN. We then actively tune the low dimensional latent space-based representation of complex system dynamics by the addition of an adaptively tuned feedback vector directly before the decoder sections builds back up to our image-based high-dimensional phase space density representations. This method allows us to learn correlations within and to quickly tune the characteristics of incredibly large parameter space systems and to track their evolution in real time based on feedback without massive new data sets for re-training. We demonstrate that our method can accurately predict and track the phase space of charged particle beams at various locations in a particle accelerator by adaptively adjusting in real-time while the unknown input beam distribution of the accelerator is changing in shape, charge, and offset and while the RF system of the accelerator itself is also changing in an unpredictable way. For FACET-II we demonstrate that such an approach has the potential to use transverse deflecting cavity and energy spread spectrum beam measurements to accurately predict 2D projections of the 6D phase space of the electron beam at the plasma wakefield acceleration interaction point where such diagnostics are unavailable.

47 OTHER INSTRUMENTATION↗
NASA NTRS2006

NASA Laboratory Astrophysics Workshop 2006 Introductory Remarks

NASA Laboratory Astrophysics Workshop 2006, is the fourth in a series of workshops held at four year intervals, to assess the laboratory needs of NASA's astrophysics missions - past, current and future. Investigators who need laboratory data to interpret their observations from space missions, theorists and modelers, experimentalists who produce the data, and scientists who compile databases have an opportunity to exchange ideas and understand each other's needs and limitations. The multi-wavelength character of these workshops allows cross-fertilization of ideas, raises awareness in the scientific community of the rapid advances in other fields, and the challenges it faces in prioritizing its laboratory needs in a tight budget environment. Currently, we are in the golden age of Space Astronomy, with three of NASA s Great Observatories, Hubble Space Telescope (HST), Chandra X-Ray Observatory (CXO), and Spitzer Space Telescope (SST), in operation and providing astronomers and opportunity to perform synergistic observations. In addition, the Far Ultraviolet Spectroscopic Explorer (FUSE), XMM-Newton, HETE-2, Galaxy Evolution Explorer (GALEX), INTEGRAL and Wilkinson Microwave Anisotropy Probe (WMAP), are operating in an extended phase, while Swift and Suzaku are in their prime phase of operations. The wealth of data from these missions is stretching the Laboratory Astrophysics program to its limits. Missions in the future, which also need such data include the James Webb Space Telescope (JWST), Space Interferometry Mission (SIM), Constellation-X (Con-X), Herschel, and Planck. The interpretation of spectroscopic data from these missions requires knowledge of atomic and molecular parameters such as transition probabilities, f-values, oscillator strengths, excitation cross sections, collision strengths, which have either to be measured in the laboratory by simulating space plasma and interactions therein, or by theoretical calculations and modeling. Once the laboratory data are obtained, a key step to making them available to the observer is the creation and maintenance of critically compiled databases. Other areas of study, that are important for understanding planet formation, and for detection of molecules that are indicators of life, are also supported by the Laboratory Astrophysics program. Some examples are: studies of ices and dust grains in a space environment; nature and evolution of interstellar carbon-rich dust; and polycyclic aromatic hydrocarbons. In addition, the program provides an opportunity for the investigation of novel ideas, such as simulating radiative shock instabilities in plasmas, in order to understand jets observed in space. A snapshot of the currently funded program, mission needs, and relevance of laboratory data to interpreting observations, will be obtained at this workshop through invited and contributed talks and poster papers. These will form the basis for discussions in splinter groups. The Science Organization Committee will integrate the results of the discussions into a coherent White Paper, which will provide guidance to NASA in structuring the Laboratory Astrophysics program in subsequent years, and also to the scientific community in submitting research proposals to NASA for funding.

Hasan, Hashima↗
NASA NTRS1985

Was core formation violent enough to homogenize the early mantle?

The dynamics of iron, its thermal state and its phase in the accreting Earth probably played a major role in the Earth's early thermal evolution. Plausible impact thermal histories make it possible that pure iron was molten in the accreting Earth after it was about 10% grown. Hence, iron eutectic alloys (FeS, FeO) certainly were. Additionally, the initial temperature of the core is an important constraint on the secular cooling of the early Earth and on the strength of the early geodynamo. Whether iron is solid or molten would influence geochemical equilibria in the upper and lower mantle; the mode of core formation, by spherical or near-spherical blobs, stalk-like instabilities, or something more catastrophic would influence the partitioning of siderophiles between silicate and iron phases. Early descent of iron (during accretion) favors partitioning according to low-pressure phase equilibria, whereas late descent favors higher pressure. The later core formation occurs, the greater the heat pulse, due to the strong dependence of gravitational potential energy on planetary radius. The heat may homogenize the mantle if core formation is global; otherwise, heterogeneity of iron differentiation may leave some of the pre-archean mantle unaffected. The larger the chunks of proto-core (and hence smaller surface/volume ratios) the greater the heterogeneity.

Cooperman, S. A.↗
DOE OSTI2020

Automation and control of laser wakefield accelerators using Bayesian optimization

Laser wakefield accelerators promise to revolutionize many areas of accelerator science. However, one of the greatest challenges to their widespread adoption is the difficulty in control and optimization of the accelerator outputs due to coupling between input parameters and the dynamic evolution of the accelerating structure. Here, we use machine learning techniques to automate a 100 MeV-scale accelerator, which optimized its outputs by simultaneously varying up to six parameters including the spectral and spatial phase of the laser and the plasma density and length. Most notably, the model built by the algorithm enabled optimization of the laser evolution that might otherwise have been missed in single-variable scans. Subtle tuning of the laser pulse shape caused an 80% increase in electron beam charge, despite the pulse length changing by just 1%.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

In situ monitoring of microstructure evolution during thermal processing of uranium-zirconium alloys using laser-generated ultrasound

In this study, laser-generated ultrasound was used to monitor microstructure evolution during thermal processing of as-cast, polycrystalline binary uranium-zirconium metallic fuel alloys with compositions of U-20wt.%Zr (U-20Zr), U-50wt.%Zr (U-50Zr) and U-80wt.%Zr (U-80Zr). Ultrasonic waveforms were recorded during heating and cooling the samples from room temperature to >973 K and back. A phase transition temperature for all three compositions was estimated from the temperature at which an abrupt and rapid reduction in ultrasonic velocities was observed. Microstructural features on the length scale of tens of micrometers were inferred from the observation of scattering of ultrasonic waves by elastic heterogeneities above ~823 K in U-20Zr, while a hysteresis in the ultrasonic velocities of U-80Zr upon cooling was attributed to a partial retention of the high temperature phase following thermal annealing. The U-50Zr alloy exhibited a reversible viscoelastic response above 933 K, as evidenced by the observation of high frequency attenuation of the shear component of the waveforms at high temperature. Ultrasonic measurements were supplemented by in situ transmission electron microscopy (TEM). The TEM images revealed that the δ-U-Zr matrix in the three compositions underwent a spinodal decomposition above ~823 K into nanoscale regions. The ultrasonic measurements revealed larger, micron-scale structure evolution in the U-20Zr alloy at the same temperature. This large-scale structure is associated with heterogeneous regions having different Zr content. Our findings show the potential heating rate dependence of microstructural evolution in U-Zr alloys and highlight differences in the thermomechanical response and associated length scales during thermal annealing between single- and dual-phase compositions. These results demonstrate the utility of laser ultrasonics to rapidly and efficiently scan phase boundaries and monitor micrometer-scale structure evolution in metallic fuel alloys.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Multi-phase characterization of pitch-carbon coated nano-silicon anodes for lithium-ion batteries

Silicon (Si) is a leading next-generation Li-ion battery anode candidate that meets rigorous performance demands for portable power including enhanced power and energy density with robust cycling performance. However, a series of complex and interrelated reactions lead to reduced calendar life in Si-containing systems and therefore challenge practical adoption. In the present work, we probe the mechanisms underlying observed performance improvements by adding a pitch-carbon coating onto nano-Si material. We pair solid-phase (X-ray photoemission spectroscopy, Fourier-transform infrared), semi-volatile phase (solid-phase microextraction-gas chromatography-mass spectrometry), and gas-phase (gas chromatography-flame-ionization detector) characterization signals to comprehensively evaluate the impact of pitch-carbon coating on the evolution of the Si solid-electrolyte interphase (SEI) and the associated impacts on electrode/electrolyte reactivity. The pitch-carbon is found to serve as a physicochemical barrier, reducing the electro-active surface area for Si/electrolyte reactivity and preventing Si oxidation. Further, the pitch-carbon coating promotes the evolution of a more-favorable SEI by subsuming substantial functionality typically associated with the fluoroethylene carbonate (FEC) electrolyte additive - such as alkoxide scavenging and suppression of transesterification pathways - and by shifting the competitive electrolyte degradation pathways' favorability. The multi-phase characterization approach enables holistic end-products evaluation from complex (electro)chemical interfacial reactions, which informs a robust interpretation of the carbon coating's role in electrochemical performance improvements. The present mechanistic evaluation aids the rational design for improved nano-Si materials.

25 ENERGY STORAGE↗
DOE OSTI2023

Structures of elemental potassium at terapascal pressures

Here we investigate the pressure-temperature phase diagram of elemental potassium (K) up to multiterapascal (TPa) pressures using ab initio random structure searching (AIRSS), discovering eight structural phase transitions beyond the already known double hexagonal close-packed (dhcp) structure. Starting at 1.15 TPa, K transitions from the dhcp structure and passes through a variety of close-packed hexagonal and trigonal phases (dhcp → P6 3 /mmc → P3m1 → P$\bar{6}m2$), which differ only in their stacking sequence along the c axis. At 2.55 TPa, K adopts the hexagonal close-packed (hcp) structure, and at 7.21 TPa transitions into a complex orthorhombic phase of Fddd symmetry with 64 atoms in its (conventional) unit cell, before assuming an Ibam structure at 8.60 TPa, and, eventually, the face centered cubic (fcc) structure at 23.6 TPa, which persists well into the petapascal (PPa) regime. Further, we calculate the full pressure-temperature dependence of the melting line of K through extensive molecular dynamics simulations. We study the evolution of the bonding topology of K with pressure, finding that K passes through two quasi-molecular phases featuring diatomic pairs (the Fddd and Ibam structures), before ultimately becoming a high pressure electride (HPE) in the fcc phase. The electron-phonon and superconducting properties of K at these extreme pressures are also investigated, where we find the critical temperature T c rises to a maximum of between 7.65 K and 15.70 K in the hcp phase, before eventually decreasing to essentially zero in the fcc phase. Our results fully elucidate the structural and electronic behavior of K under the most extreme conditions, and provide new case studies for multi-TPa dynamic compression experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1991

The development of test beds to support the definition and evolution of the Space Station Freedom power system

Since the beginning of the Space Station Freedom Program (SSFP), the NASA Lewis Research Center (LeRC) and the Rocketdyne Division of Rockwell International have had extensive efforts underway to develop testbeds to support the definition of the detailed electrical power system design. Because of the extensive redirections that have taken place in the Space Station Freedom Program in the past several years, the test bed effort was forced to accommodate a large number of changes. A short history of these program changes and their impact on the LeRC test beds is presented to understand how the current test bed configuration has evolved. The current test objectives and the development approach for the current DC test bed are discussed. A description of the test bed configuration, along with its power and controller hardware and its software components, is presented. Next, the uses of the test bed during the mature design and verification phase of SSFP are examined. Finally, the uses of the test bed in the operation and evolution of the SSF are addressed.

Soeder, James F.↗
DOE OSTI2025

Kinetically Dormant Ni‐Rich Layered Cathode During High‐Voltage Operation

Abstract The degradation of Ni‐rich cathodes during long‐term operation at high voltage has garnered significant attention from both academia and industry. Despite many post‐mortem qualitative structural analyses, precise quantification of their individual and coupling contributions to the overall capacity degradation remains challenging. Here, by leveraging multiscale synchrotron X‐ray probes, electron microscopy, and post‐galvanostatic intermittent titration technique, the thermodynamically irreversible and kinetically reversible capacity loss is successfully deconvoluted in a polycrystalline LiNi 0.83 Mn 0.1 Co 0.07 O 2 cathode during long‐term charge/discharge cycling in full cell configuration. Contradicting the dramatic capacity loss, the layered structure remains highly alive even after 1000 cycles at 4.6 V while undergoing a three‐order of magnitude reduction in the mass transfer kinetics, leading to almost fully recoverable capacity under kinetic‐free conditions. Such kinetic dormant behavior after cycling is not simply ascribed to poor chemical diffusion by reconstructed cathode surface but highly synchronizes with the lattice strain evolution stemming from the structural heterogeneity between deeply delithiated layered and degraded rock‐salt phases at high voltage. These findings deepen the degradation mechanism of high‐voltage cathodes to achieve long‐cycling and fast‐charging performance.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Entanglement and topology in RG flows across dimensions: caps, bridges and corners

We quantitatively address the following question: for a QFT which is partially compactified, so as to realize an RG flow from a D-dimensional CFT in the UV to a d-dimensional CFT in the IR, how does the entanglement entropy of a small spherical region probing the UV physics evolve as the size of the region grows to increasingly probe IR physics? This entails a generalization of spherical regions to setups without full Lorentz symmetry, and we study the associated entanglement entropies holographically. We find a tight interplay between the topology and geometry of the compact space and the evolution of the entanglement entropy, with universal transitions from ‘cap’ through ‘bridge’ and ‘corner’ phases, whose features reflect the details of the compact space. As concrete examples we discuss twisted compactifications of 4d $\mathcal{N}$ = 4 SYM on T 2 , S 2 and hyperbolic Riemann surfaces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

An Integrated High-Speed Microstructural Characterization Method Using Simultaneous XRD, Stereo-DIC, and PCI

High-speed characterization of the deformation mechanisms in polycrystalline metals requires the quantification of full strain fields and local microstructural evolutions simultaneously. In this paper, we present a novel experimental method to integrate phase-contrast imaging (PCI), stereographic digital image correlation (stereo-DIC), and full-ring X-ray diffraction (XRD) to allow for the simultaneous characterization of polycrystalline metals at 1MHz or higher. A Kolsky bar was integrated into the synchrotron X-ray source in Sector 32 ID-B at the Advance Photon Source (APS) at Argonne National Laboratory. When the sample is dynamically loaded, the diagnostic methods of full-ring XRD, PCI, and stereo-DIC are properly synchronized to record the deformation behavior at both continuum and microstructural scales as a function of the loading history. An advanced high-strength steel (AHSS) is used as a model material to demonstrate the capabilities of this new experimental method.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microstructure Evolution of U–Zr System in A Thermal Cycling Neutron Diffraction Experiment: Extruded U–10Zr (wt. %)

Microstructure evolution of 1073 K extruded U–10Zr (wt. %) fuel during thermal cycling (303–1073 K with a ~9 hour hold at 873 K during cooling) was investigated using in situ neutron diffraction. Analysis was performed using Rietveld texture and crystal structure refinements from time–of–flight neutron diffraction data, with a focus on the evolution of textures and lattice parameters as a function of temperature. The α–U phase exhibits lattice contraction with increasing temperature along the b lattice direction and lattice expansion in the other directions while the other phases exhibit lattice expansion with temperature in all directions. Contrary to the established phase diagram, the β–U phase is absent at the temperatures of the thermal cycling. (001) α and (110) γ plane normals are observed with a strong preferred orientation along the extrusion direction. Finally, the variant selection of (001) α ||(110) γ is observed for the first time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Dislocation Loops in Proton Irradiated Uranium-Nitrogen-Oxygen System

Here in this study, we investigated the dislocation loop types formed in the proton-irradiated uranium-nitrogen-oxygen (U-N-O) system, which involves uranium mononitride (UN), uranium sesquinitride (a-U2N3), and uranium dioxide (UO2) phases. The dislocation loop formation is examined using specimens irradiated at 400°C and 710°C. Based on the detailed transmission-based electron microscopy characterization with i) the morphology-based on-zone and ii) the invisibility-criterion based two-beam condition imaging techniques, only a single type of dislocation loop in each phase is found: a/2?110?, a/2?111?, or a/3?111? dislocation loops in UN, a-U2N3, and UO2 phases, respectively. Molecular statics calculations for the formation energy of perfect and faulted dislocation loops in UN phases indicate a critical loop size of ~ 6 nm, above which perfect loops are energetically favorable. This could explain the absence of faulted loops in the experimental observation of the irradiated UN phase at two temperatures. This work will enhance the understanding of irradiation induced microstructural evolution for uranium nitrides as advanced nuclear fuels for the next-generation nuclear reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗