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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↗

NASA NTRS2018

Measurement of Atmospheric CO2 Column Concentrations to Cloud Tops With a Pulsed Multi-Wavelength Airborne Lidar

We have measured the column-averaged atmospheric CO2 mixing ratio to a variety of cloud tops by using an airborne pulsed multi-wavelength integrated-path differential absorption (IPDA) lidar. Airborne measurements were made at altitudes up to 13 km during the 2011, 2013 and 2014 NASA Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) science campaigns flown in the United States West and Midwest and were compared to those from an in situ sensor. Analysis of the lidar backscatter profiles shows the average cloud top reflectance was approx. 5% for the CO2 measurement at 1572.335 nm except to cirrus clouds, which had lower reflectance. The energies for 1 micro-s wide laser pulses reflected from cloud tops were sufficient to allow clear identification of CO2 absorption line shape and then to allow retrievals of atmospheric column CO2 from the aircraft to cloud tops more than 90% of the time. Retrievals from the CO2 measurements to cloud tops had minimal bias but larger standard deviations when compared to those made to the ground, depending on cloud top roughness and reflectance. The measurements show this new capability helps resolve CO2 horizontal and vertical gradients in the atmosphere. When used with nearby full-column measurements to ground, the CO2 measurements to cloud tops can be used to estimate the partial-column CO2 concentration below clouds, which should lead to better estimates of surface carbon sources and sinks. This additional capability of the range-resolved CO2 IPDA lidar technique provides a new benefit for studying the carbon cycle in future airborne and space-based CO2 missions.

atmospheric↗

NASA NTRS2014

A New Hybrid Spatio-temporal Model for Estimating Daily Multi-year PM2.5 Concentrations Across Northeastern USA Using High Resolution Aerosol Optical Depth Data

The use of satellite-based aerosol optical depth (AOD) to estimate fine particulate matter PM(sub 2.5) for epidemiology studies has increased substantially over the past few years. These recent studies often report moderate predictive power, which can generate downward bias in effect estimates. In addition, AOD measurements have only moderate spatial resolution, and have substantial missing data. We make use of recent advances in MODIS satellite data processing algorithms (Multi-Angle Implementation of Atmospheric Correction (MAIAC), which allow us to use 1 km (versus currently available 10 km) resolution AOD data.We developed and cross validated models to predict daily PM(sub 2.5) at a 1X 1 km resolution across the northeastern USA (New England, New York and New Jersey) for the years 2003-2011, allowing us to better differentiate daily and long term exposure between urban, suburban, and rural areas. Additionally, we developed an approach that allows us to generate daily high-resolution 200 m localized predictions representing deviations from the area 1 X 1 km grid predictions. We used mixed models regressing PM(sub 2.5) measurements against day-specific random intercepts, and fixed and random AOD and temperature slopes. We then use generalized additive mixed models with spatial smoothing to generate grid cell predictions when AOD was missing. Finally, to get 200 m localized predictions, we regressed the residuals from the final model for each monitor against the local spatial and temporal variables at each monitoring site. Our model performance was excellent (mean out-of-sample R(sup 2) = 0.88). The spatial and temporal components of the out-of-sample results also presented very good fits to the withheld data (R(sup 2) = 0.87, R(sup)2 = 0.87). In addition, our results revealed very little bias in the predicted concentrations (Slope of predictions versus withheld observations = 0.99). Our daily model results show high predictive accuracy at high spatial resolutions and will be useful in reconstructing exposure histories for epidemiological studies across this region.

Air pollution↗