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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
DOE OSTI2014

The virial theorem for the polarizable continuum model

The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

The virial theorem and the ground state problem in polaron theory

The virial theorem for the translation-invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong-coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong-coupling polaron (the Pekar 1: 2: 3: 4 theorem).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Density functional, density matrix functional, and the virial theorem

On the basis of the virial theorem for finite motion of interacting electrons in a static external field, it is shown that ground-state energy is determined evidently by the one-particle density matrix. The exact expression for ground-state energy is found and can be applied to various problems, in particular, in studying the electronic structure of atoms, molecules, and other bound complexes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

STABILITY OF GAS CLOUDS IN GALACTIC NUCLEI: AN EXTENDED VIRIAL THEOREM

Cold gas entering the central 1–10{sup 2} pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to further include an external tidal field, which is equally crucial for the stability in the region of our interest—in dense star clusters, around SMBHs. We apply our extended Virial theorem to find new solutions to controversial problems, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The virial theorem and the dark matter problem in hybrid metric-Palatini gravity

Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed à la Palatini. The theory predicts the existence of a long-range scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics. Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter. In this work, we consider the generalized virial theorem in the scalar-tensor representation of the hybrid metric-Palatini gravity. More specifically, taking into account the relativistic collisionless Boltzmann equation, we show that the supplementary geometric terms in the gravitational field equations provide an effective contribution to the gravitational potential energy. We show that the total virial mass is proportional to the effective mass associated with the new terms generated by the effective scalar field, and the baryonic mass. In addition to this, we also consider astrophysical applications of the model and show that the model predicts that the mass associated to the scalar field and its effects extend beyond the virial radius of the clusters of galaxies. In the context of the galaxy cluster velocity dispersion profiles predicted by the hybrid metric-Palatini model, the generalized virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Virial theorem and Gibbs thermodynamic potential for Coulomb systems

Using the grand canonical ensemble and the virial theorem, we show that the Gibbs thermodynamic potential of the non-relativistic system of charged particles is uniquely defined by single-particle Green functions of electrons and nuclei. This result is valid beyond the perturbation theory with respect to the interparticle interaction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

The virial theorem in Eddington-Born-Infeld gravity

We consider the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides an alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations, finding an additional 'geometrical mass' term which provides an effective contribution to the gravitational binding energy. Using some approximations and assumptions for weak gravitational fields, and taking into account the collisionless relativistic Boltzmann equation, we derive a generalized version of the virial theorem in the framework of EBI gravity. We show that the 'geometrical mass' term may account for the well known virial mass discrepancy in clusters of galaxies. We also derive the velocity dispersion relation for galaxies in the clusters, which could provide an efficient method for testing EBI gravity from astrophysical observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Local Group timing argument and virial theorem mass estimators from cosmological simulations

ABSTRACT We identify Local Group (LG) analogues in the IllustrisTNG cosmological simulation, and use these to study two-mass estimators for the LG: One based on the timing argument (TA) and one based on the virial theorem (VT). Including updated measurements of the Milky Way-M31 tangential velocity and the cosmological constant, we show that the TA mass estimator slightly overestimates the true median LG-mass, though the ratio of the TA to the true mass is consistent at the approximate 90 per cent c.l.. These are in broad agreement with previous results using dark matter-only simulations. We show that the VT estimator better estimates the true LG-mass, though there is a larger scatter in the virial mass to true mass ratio relative to the corresponding ratio for the TA. We attribute the broader scatter in the VT estimator to several factors, including the predominantly radial orbits for LG satellite galaxies, which differs from the VT assumption of isotropic orbits. With the systematic uncertainties we derive, the updated measurements of the LG mass at 90 per cent c.l. are $4.75_{-2.41}^{+2.22} \times 10^{12}$ M⊙ from the TA and $2.0_{-1.5}^{+2.1} \times 10^{12}$ M⊙ from the VT. We consider the LMC’s effect on the TA and VT LG mass estimates, and do not find exact LMC–MW–M31 analogues in the Illustris simulations. However, in LG simulations with satellite companions as massive as the LMC, we find that the effect on the TA and VT estimators is small, though we need further studies on a larger sample of LMC–MW–M31 systems to confirm these results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Validity of virial theorem in all-electron mixed basis density functional, Hartree–Fock, and GW calculations

In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree–Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is in excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

The virial theorem for the smoothly and sharply, penetrably and impenetrably confined hydrogen atom

Confinement of atoms by finite or infinite boxes containing sharp (discontinuous) jumps has been studied since the fourth decade of the previous century, modelling the effect of external pressure. Smooth (continuous) counterparts of such confining potentials, that depend on a parameter such that in an appropriate limit they coincide with the sharp confining potentials, are investigated, with an emphasis on deriving the corresponding virial and Hellmann-Feynman theorems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Hellmann–Feynman connection for the relative Fisher information

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS link and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

VARIATIONAL PRINCIPLE FOR PLANETARY INTERIORS

In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have a simple analytical framework for describing planetary structures. The variational principle is a fundamental principle in physics, entailing that a physical system follows the trajectory, which minimizes its action. It is alternative to the differential equation formulation of a physical system. Applying the variational principle to the planetary interior can beautifully summarize the set of differential equations into one, which provides us some insight into the problem. From this principle, a universal mass–radius relation, an estimate of the error propagation from the equation of state to the mass–radius relation, and a form of the virial theorem applicable to planetary interiors are derived.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Coupled-cluster based basis sets for valence correlation calculations

Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via 〈r{sup n}〉 (−3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within “chemical accuracy” of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2012

MOLECULAR LINE OBSERVATIONS OF MCLD 123.5+24.9 IN THE POLARIS CIRRUS

In this paper, we present results of millimeter-wave observations with various molecular lines made toward MCLD 123.5+24.9 in the Polaris cirrus using the 45 m telescope at Nobeyama Radio Observatory. MCLD 123.5+24.9 is one of the rare dense cores forming in diffuse cirrus clouds where star formation may rarely take place. In order to investigate the structure, dynamics, the evolutionary stage of MCLD 123.5+24.9, we observed this core in 17 emission lines from 13 different molecular species. Emission lines of CS, CCS, and HC{sub 3}N are strongly detected all over the core, while those of SO and N{sub 2}H{sup +} are weak or remain undetected, indicating that MCLD 123.5+24.9 is in an early stage of core evolution in terms of chemical composition. Based on comparison of the fractional abundances of CCS and HC{sub 3}N, which are considered indicators of chemical age, with those of other cores with and without star formation as well as with model calculations in the literature, we suggest that MCLD 123.5+24.9 is in a phase prior to star formation. From the C{sup 18}O data obtained, we derived the total molecular mass of MCLD 123.5+24.9 to be {approx}3 M{sub Sun} at an assumed distance of 150 pc. There are three subcores in MCLD 123.5+24.9, called CS-A, CS-B, and CS-C. We derived their masses to be 0.2-0.6 M{sub Sun }. We also investigated the dynamical stability of MCLD 123.5+24.9 and the subcores by applying the virial theorem to find that MCLD 123.5+24.9 is not gravitationally bound as a whole, while the individual subcores are in the virial equilibrium and can collapse with a small increase of external pressure imposed on their surfaces.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Action principles for hydro- and thermo-dynamics

A Hamiltonian formulation of hydrodynamics is well known for the case of purely irrotational flows and it now exists in a more general case as well. The minimal extension of the action principle is obtained from two axioms: 1. That the number of independent degrees of freedom be 4, as in standard hydrodynamics. 2. That the equation of continuity must be one of the Euler-Lagrange equations, and that it allows for vorticity. Applications include: 1. Couette flow with a new criterion for the breakdown of laminar motion. 2. A rotating source for Einstein’s equation that respects the Bianchi identity. 3. A new approach to the electromagnetism of fluids. 4. A rigorous virial theorem for fluids. 5. A critique of the current state of the theory of atmospheres.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Isothermal-sweep theorems for ultracold quantum gases in a canonical ensemble

After deriving the isothermal Hellmann-Feynman theorem (IHFT) that is suitable for mixed states in a canonical ensemble, we use this theorem to obtain the isothermal magnetic-field sweep theorems for the free, average, and trapping energies and for the entropy, specific heat, pressure, and atomic compressibility of strongly correlated ultracold quantum gases. In particular, we apply the sweep theorems to two-component Fermi gases in the weakly interacting Bardeen-Cooper-Schrieffer and Bose-Einstein condensate limits, showing that the temperature dependence of the contact parameter can be determined by varying either the entropy or specific heat with respect to the scattering length. We also use the IHFT to obtain the virial theorem in a canonical ensemble and discuss its implications for quantum gases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

On the Origin of the Fundamental Plane and Faber–Jackson Relations: Implications for the Star Formation Problem

We provide an explanation of the properties of the fundamental plane (FP) relation and its observed projections for a sample of nearby early-type galaxies (ETGs) in terms of a fine-tuning between the time-averaged star formation rate 〈Ψ〉 and their structural and dynamical characteristics. Their total V luminosity is linked with 〈Ψ〉 and the central velocity dispersion σ through the relation log(L)=0.48(±0.06)log(〈Ψ〉)+1.00 (±0.13)log(σ)+7.81(±0.26), with an rms = 0.215 (R = 0.64 and P<1.2×10{sup −16}). This fine-tuning permits us to obtain the FP in terms of two distinct “virtual planes” in the log(R{sub e})--log(〈I{sub e}〉)--log(σ) space. The first one (the virial plane; VP) represents the total galaxy mass derived from the scalar virial theorem and the mass-to-light ratio M/L, while the second plane comes from the relation L=L{sub 0}{sup ′}σ{sup −2}, where L{sub 0}{sup ′} is a parameter connected with 〈Ψ〉. This is a mathematically convenient way for expressing the independence of the galaxy light from the virial equilibrium. Each galaxy in the log(R{sub e})--log(〈I{sub e}〉)--log(σ) space is identified by the intersection of these two planes. A posteriori, we show that the properties of the FP (tilt and scatter) and the zone of exclusion visible in the FP projections are consequences of this fine-tuning. The link between the FP properties and the SFR of galaxies provides a new view of the star formation phenomenon. The star formation history of an unperturbed galaxy seems to be driven by the initial conditions in the protogalaxies and is regulated across cosmic epochs by the variation of the main galaxy parameters (mass, luminosity, structural shape, and velocity dispersion).

79 ASTRONOMY AND ASTROPHYSICS↗