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Results for “VIRIAL THEOREM”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions

The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.

Iwamoto, N.↗
NASA NTRS1990

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud.

Zweibel, Ellen G.↗
NASA NTRS1990

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud.

Zweibel, Ellen G.↗
NASA NTRS1992

On the virial theorem for turbulent molecular clouds

An Eulerian, rather than Lagrangian, form of the virial theorem is derived for a turbulent, magnetized cloud embedded in a steady, turbulent, low-density intercloud medium. The role of turbulent pressure in cloud confinement is clarified, and it is shown that, in the absence of a magnetic field, a cloud can be at a somewhat lower pressure than the intercloud medium. Simple forms for the magnetic term in the virial equation are obtained. Radiation pressure is considered; its effects are relatively small under average conditions in the interstellar medium. Under typical conditions, external pressure and magnetic fields are shown to have a relatively small effect on virial estimates of the mass of self-gravitating clouds.

Mckee, Christopher F.↗
NASA NTRS1986

Acoustic radiation stress in solids

It is shown that the radiation-induced static strains associated with acoustic waves propagating in solids are obtained directly from the virial theorem for an elastic continuum and that the radiation stresses result from combining the virial theorem with the Boltzmann-Ehrenfest principle of adiabatic invariance. The experimental confirmation of critical theoretical predictions in solids is reported. The implications of the results for the fundamental thermal properties of crystals are addressed.

Cantrell, John H.↗
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 NTRS1983

X-ray emission from clusters of galaxies

Some X-ray spectral observations of approximately 30 clusters of galaxies from HEAO-1 are summarized. There exists strong correlations between X-ray luminosity, L(x), and temperature kT in the form L(x)alphaT to the 2.3 power. This result combined with the L(x) central galaxy density relation and the virial theorem indicates that the core dadius of the gas should be roughly independent of L(x) or KT and that more luminous clusters have a greater fraction of their virial mass in gas. The poor correlation of KT and optical velocity dispersion seems to indicate that clusters have a variety of equations of state. There is poor agreement between X-ray imaging observations and optical and X-ray spectral measures of the polytropic index. Most clusters show Fe emission lines with a strong indication that they all have roughly 1/2 solar abundance. The evidence for cooling in the cores of several clusters is discussed based on spectral observations with the Einstein solid state spectrometer.

Mushotzky, R. F.↗
NASA NTRS1984

X-ray emission from clusters of galaxies

Some X-ray spectral observations of approximately 30 clusters of galaxies from HEAO-1 are summarized. There exists strong correlation betwen X-ray luminosity, L(x), and temperature kT in the form L(x)alphaT to the 2.3 power. This result combined with the L(x) central galaxy density relation and the virial theorem indicates that the core dadius of the gas should be roughly independent of L(x) or Kt and that more luminous clusters have a greater fraction of their virial mass in gas. The poor correlation of KT and optical velocity dispersion seems to indicate that clusters have a variety of equations of state. There is poor agreement between X-ray imaging observations and optical and X-ray spectral measures of the polytropic index. Most clusters show Fe emission lines with a strong indication that they all have roughly 1/2 solar abundance. The evidence for cooling in the cores several clusters is discussed based on spectral observations with the Einstein solid state spectrometer.

Mushotzky, R. F.↗
DOE OSTI2026

The Extended Baryonic Tully–Fisher Relation for SDSS MaNGA Galaxies

The baryonic Tully–Fisher relation (BTFR), a relationship between the rotational velocity and baryonic mass in spiral galaxies, probes the relative content of baryonic and total mass in galaxies and thus provides a good test of dark matter content in galaxies. Using Hα kinematics, we model the rotation curves of the Sloan Digital Sky Survey MaNGA DR17 spiral galaxies. To extend the BTFR to higher masses with elliptical galaxies, we estimate their total masses from their stellar velocity dispersions using the virial theorem and define the effective rotational velocity as the velocity a rotation-supported galaxy would exhibit given this mass. The baryonic mass of spiral galaxies is composed of stellar, H I , H 2 , and He mass, while only the stellar mass is used for the baryonic content of ellipticals. We construct joint BTFRs for 5743 MaNGA spiral and elliptical galaxies, TNG100 simulated galaxies with baryonic masses greater than 10 9 M ⊙ , and a cross-matched subsample between these two datasets (3149 spiral and 1423 elliptical galaxies). For the cross-matched subsample, we find agreement in the slopes between observed and simulated galaxies. We find a slope of $3.8{6}_{-0.62}^{+0.92}$ for the full MaNGA sample, which agrees well with the slope of 4.0 predicted by MOND and the fitted slope of $3.5{8}_{-0.38}^{+0.48}$ for the TNG100 galaxies. We find that a sample of lower-mass galaxies is necessary to differentiate between the two models.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1961

NEUTRINO EMISSION PROCESSES, STELLAR EVOLUTION AND SUPERNOVA. PART II.

When the internal temperature of a star exceeds 1 BK (109 °K) the evolution is very rapid. The time scale is around 3000 years. Energy dissipated by emission of neutrinos is several orders of magnitude higher than that by optical radiation. Neutrinos have exceedingly long mean free path (∼10(exp 20) gram/cm(exp 2)) and they will escape as soon as they are produced. The star will contract to release gravitational energy to make up the energy lost to neutrinos and the internal temperature will rise to comply with the virial theorem. It is possible in this fast evolutionary phase, to neglect optical radiations all together as compared with the neutrino radiation. A set of structural equations is thus obtained. The envelope is replaced by boundary conditions. A simple model is constructed to illustrate our approach.

Star↗