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DOE OSTI2011

Suppression of the quantum-mechanical collapse by repulsive interactions in a quantum gas

The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -r{sup -2}) is a well-known issue in quantum theory. It is closely related to the quantum anomaly, i.e., breaking of the scaling invariance of the respective Hamiltonian by quantization. We demonstrate that the mean-field repulsive nonlinearity prevents the collapse and thus puts forward a solution to the quantum-anomaly problem that differs from that previously developed in the framework of the linear quantum-field theory. This solution may be realized in the 3D or 2D gas of dipolar bosons attracted by a central charge and in the 2D gas of magnetic dipoles attracted by a current filament. In the 3D setting, the dipole-dipole interactions are also taken into regard, in the mean-field approximation, resulting in a redefinition of the scattering length which accounts for the contact repulsion between the bosons. In lieu of the collapse, the cubic nonlinearity creates a 3D ground state (GS), which does not exist in the respective linear Schroedinger equation. The addition of the harmonic trap gives rise to a tristability, in the case when the Schroedinger equation still does not lead to the collapse. In the 2D setting, the cubic nonlinearity is not strong enough to prevent the collapse; however, the quintic term does it, creating the GS, as well as its counterparts carrying the angular momentum (vorticity). Counterintuitively, such self-trapped 2D modes exist even in the case of a weakly repulsive potential r{sup -2}. The 2D vortical modes avoid the phase singularity at the pivot (r=0) by having the amplitude diverging at r{yields}0 instead of the usual situation with the amplitude of the vortical mode vanishing at r{yields}0 (the norm of the mode converges despite of the singularity of the amplitude at r{yields}0). In the presence of the harmonic trap, the 2D quintic model with a weakly repulsive central potential r{sup -2} gives rise to three confined modes, the middle one being unstable, spontaneously developing into a breather. In both the 3D and 2D cases, the GS wave functions are found in a numerical form and in the form of an analytical approximation, which is asymptotically exact in the limit of the large norm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Pressure-induced half-collapsed-tetragonal phase in CaKFe 4 As 4

Here, we report the temperature-pressure phase diagram of CaKFe 4 As 4 established using high-pressure electrical resistivity, magnetization, and high-energy x-ray diffraction measurements up to 6 GPa. With increasing pressure, both resistivity and magnetization data show that the bulk superconducting transition of CaKFe 4 As 4 is suppressed and then disappears at p ≳ 4 GPa. High-pressure x-ray data clearly indicate a phase transition to a collapsed tetragonal phase in CaKFe 4 As 4 under pressure that coincides with the abrupt loss of bulk superconductivity near 4 GPa. The x-ray data, combined with resistivity data, indicate that the collapsed tetragonal transition line is essentially independent of pressure, occurring at 4.0(5) GPa for temperatures below 150 K. Density functional theory calculations also find a sudden transition to a collapsed tetragonal state near 4 GPa, as As-As bonding develops across the Ca layer. Bonding across the K layer only occurs for p ≥ 12 GPa. These findings demonstrate a different type of collapsed tetragonal phase in CaKFe 4 As 4 as compared to CaFe 2 As 2 : a half-collapsed tetragonal phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Collapse of neutrino wave functions under Penrose gravitational reduction

Models of spontaneous wave function collapse have been postulated to address the measurement problem in quantum mechanics. Their primary function is to convert coherent quantum superpositions into incoherent ones, with the result that macroscopic objects cannot be placed into widely separated superpositions for observably prolonged times. Many of these processes will also lead to loss of coherence in neutrino oscillations, producing observable signatures in the flavor profile of neutrinos at long travel distances. The majority of studies of neutrino oscillation coherence to date have focused on variants of the continuous state localization model, whereby an effective decoherence strength parameter is used to model the rate of coherence loss with an assumed energy dependence. Another class of collapse models that have been proposed posit connections to the configuration of gravitational field accompanying the mass distribution associated with each wave function that is in the superposition. A particularly interesting and prescriptive model is Penrose’s description of gravitational collapse which proposes a decoherence time τ determined through E g τ ∼ ℏ , where E g is a calculable function of the Newtonian gravitational potential. Here we explore application of the Penrose collapse model to neutrino oscillations, reinterpreting previous experimental limits on neutrino decoherence in terms of this model. We identify effects associated with both spatial collapse and momentum diffusion, finding that the latter is ruled out in data from the IceCube South Pole Neutrino Observatory so long as the neutrino wave packet width at production is σ ν , x ≤ 2 × 10 − 12 m . Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2015

Lung deformations and radiation-induced regional lung collapse in patients treated with stereotactic body radiation therapy

Purpose: To differentiate radiation-induced fibrosis from regional lung collapse outside of the high dose region in patients treated with stereotactic body radiation therapy (SBRT) for lung tumors. Methods: Lung deformation maps were computed from pre-treatment and post-treatment computed tomography (CT) scans using a point-to-point translation method. Fifty anatomical landmarks inside the lung (vessel or airway branches) were matched on planning and follow-up scans for the computation process. Two methods using the deformation maps were developed to differentiate regional lung collapse from fibrosis: vector field and Jacobian methods. A total of 40 planning and follow-ups CT scans were analyzed for 20 lung SBRT patients. Results: Regional lung collapse was detected in 15 patients (75%) using the vector field method, in ten patients (50%) using the Jacobian method, and in 12 patients (60%) by radiologists. In terms of sensitivity and specificity the Jacobian method performed better. Only weak correlations were observed between the dose to the proximal airways and the occurrence of regional lung collapse. Conclusions: The authors presented and evaluated two novel methods using anatomical lung deformations to investigate lung collapse and fibrosis caused by SBRT treatment. Differentiation of these distinct physiological mechanisms beyond what is usually labeled “fibrosis” is necessary for accurate modeling of lung SBRT-induced injuries. With the help of better models, it becomes possible to expand the therapeutic benefits of SBRT to a larger population of lung patients with large or centrally located tumors that were previously considered ineligible.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2011

Structural elements and collapse regimes in 3D flows on a slope

The mechanisms and structural elements of an instability whose development results in the collapse of flow fragments have been studied in the scope of the Hamilton version of the 'shallow water' 3D model on a slope. The study indicated that the 3D model differs from its 2D analog in a more varied set of collapsing solutions. In particular, the solutions describing anisotropic collapse, during which the area of a collapsing fragment in contact with the slope contracts into a segment rather than a point, exist together with the solutions describing radially symmetric (isotropic) collapse.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Structural elements of collapses in shallow water flows with horizontally nonuniform density

The mechanisms and structural elements of instability whose evolution results in the occurrence of the collapse are studied in the scope of the rotating shallow water model with a horizontally nonuniform density. The diagram stability based on the integral collapse criterion is suggested to explain system behavior in the space of constants of motion. Analysis of the instability shows that two collapse scenarios are possible. One scenario implies anisotropic collapse during which the contact area of a collapsing drop-like fragment with the bottom contracts into a rotating segment. The other implies isotropic contraction of the area into a point.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Spherical collapse for a viscous generalized Chaplygin GaS model

The nonlinear collapse for a viscous generalized Chaplygin gas model (VGCG) is analyzed in the framework of spherical top-hat collapse. Because the VGCG and baryons are essential to form the large-scale structure, we focus on their nonlinear collapse in this paper. We discuss the influence of model parameters α and ζ{sub 0} on the spherical collapse by varying their values and compare with the ΛCDM model. The results show that for the VGCG model, smaller ζ{sub 0} and larger α make the structure formation earlier and faster, and the collapse curves of the VGCG model are almost coincident with those of the ΛCDM model when the model parameter α is less than 10{sup −2}.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Diversity waves in collapse-driven population dynamics

Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt and severe collapses of the entire population of a single species freeing up resources for the remaining ones. This mechanism may be relevant e.g. for communities of bacteria, with strain-specific collapses caused e.g. by invading bacteriophages, or for other ecosystems where infectious diseases play an important role. The emergent dynamics of our system is cyclic ‘‘diversity waves’’ triggered by collapses of globally dominating populations. The population diversity peaks at the beginning of each wave and exponentially decreases afterwards. Species abundances are characterized by a bimodal time-aggregated distribution with the lower peak formed by populations of recently collapsed or newly introduced species while the upper peak - species that has not yet collapsed in the current wave. In most waves both upper and lower peaks are composed of several smaller peaks. This self-organized hierarchical peak structure has a long-term memory transmitted across several waves. It gives rise to a scale-free tail of the time-aggregated population distribution with a universal exponent of 1.7. We show that diversity wave dynamics is robust with respect to variations in the rules of our model such as diffusion between multiple environments, species-specific growth and extinction rates, and bet-hedging strategies.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2017

SPHERICALLY SYMMETRIC, COLD COLLAPSE: THE EXACT SOLUTIONS AND A COMPARISON WITH SELF-SIMILAR SOLUTIONS

We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

The Baryonic Collapse Efficiency of Galaxy Groups in the RESOLVE and ECO Surveys

We examine the z = 0 group-integrated stellar and cold baryonic (stars + cold atomic gas) mass functions (group SMF and CBMF) and the baryonic collapse efficiency (group cold baryonic to dark matter halo mass ratio) using the RESOLVE and ECO survey galaxy group catalogs and a galform semi-analytic model (SAM) mock catalog. The group SMF and CBMF fall off more steeply at high masses and rise with a shallower low-mass slope than the theoretical halo mass function (HMF). The transition occurs at the group-integrated cold baryonic mass M{sub bary}{sup cold} ∼ 10{sup 11} M{sub ⊙}. The SAM, however, has significantly fewer groups at the transition mass ∼10{sup 11} M{sub ⊙} and a steeper low-mass slope than the data, suggesting that feedback is too weak in low-mass halos and conversely too strong near the transition mass. Using literature prescriptions to include hot halo gas and potential unobservable galaxy gas produces a group BMF with a slope similar to the HMF even below the transition mass. Its normalization is lower by a factor of ∼2, in agreement with estimates of warm-hot gas making up the remaining difference. We compute baryonic collapse efficiency with the halo mass calculated two ways, via halo abundance matching (HAM) and via dynamics (extended all the way to three-galaxy groups using stacking). Using HAM, we find that baryonic collapse efficiencies reach a flat maximum for groups across the halo mass range of M{sub halo}∼10{sup 11.4−12} M{sub ⊙}, which we label “nascent groups.” Using dynamics, however, we find greater scatter in baryonic collapse efficiencies, likely indicating variation in group hot-to-cold baryon ratios. Similarly, we see higher scatter in baryonic collapse efficiencies in the SAM when using its true groups and their group halo masses as opposed to friends-of-friends groups and HAM masses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Strontium-84 Enrichments in Presolar Grains Provide First Evidence of p -process Nucleosynthesis in Core-collapse Supernovae

This study reports detection of rare p-process isotopes within presolar grains. Presolar grains are relic dust grains from dying stars. These microscopic dust particles are found in primitive solar system materials. Their distinct isotopic compositions record the nucleosynthetic processes in their parent stars and the Galactic chemical environment in which these stars formed. We studied presolar graphite grains of high-density type from the Murchison meteorite and found five grains with subgrains that show enrichments in 84 Sr compared to the solar abundance. 84 Sr is the neutron-deficient isotope of strontium that can be produced in the deep oxygen-rich interior of high-mass stars that end their lives as core-collapse supernovae. The observed 84 Sr excesses cannot be produced in low-mass asymptotic giant branch stars, the source of most high-density presolar graphites found in meteorites. High-density graphites with embedded 84 Sr excesses are, instead, compatible with a core-collapse supernovae origin. The graphite subgrains condensed from carbon-rich materials in the outer layers of core-collapse supernovae, where 84 Sr was destroyed by neutron captures during hydrostatic evolution of the stars and their final explosion. Based on current theoretical stellar models, a few percent of contribution from the inner regions of core-collapse supernovae, which are enriched in p-process nuclides, to the outer carbon-rich regions is the most likely explanation for the observed enrichment of 84 Sr in the subgrains of the high-density graphites. In this study, we present the first observational evidence that core-collapse supernovae produce and eject isotopes made by the p-process.

Astronomy and AstroPhysics↗

NASA NTRS1976

On a spherical star system with a collapsed core

Exact solutions of Einstein's equations for a perfect fluid that describe the gravitational collapse of matter around a collapsed core are presented. The collapsed region grows monotonically until an absolute Schwarzschild horizon is formed. It is found that the minimum redshift of light emitted radially from the boundary of the system and received at infinity is approximately 4.62. These systems are expected to describe the very last stages in the gravitational collapse of a globular star cluster with a central collapsed core.

Glass, E. N.↗

NASA NTRS1980

Semi-empirical estimates of gravitational wave generation by stellar collapse

The problems of the generation and detection of gravitational waves and the difficulty of detecting the burst of gravitational radiation produced by a stellar collapse in our Galaxy, or in neighbouring clusters of galaxies where such collapses are expected to occur frequently, have been reviewed elsewhere. As stellar collapses, explosions, or supernovae are poorly understood, the values of the strength of these sources depend on uncertain assumptions. However, it is possible to make some independent estimates on semi-empirical grounds, using observed facts concerning the remnants of stellar evolution. These estimates, reported here, have serious weaknesses. They must involve oversimplified models and very crude standard calculations of the collapse and radiation processes. Also, because they are based on observed properties of stellar remnants, they say nothing about collapses which do not produce observable remnants. Although this selection may introduce a strong bias, these estimates deserve consideration because they are tied to real data.

Katz, J. I.↗

NASA NTRS1980

Collapsing cloud models for Bok globules

The dynamic collapse of rotating gas clouds is calculated for a wide range of initial conditions. Properties of cloud models are compared with observed radio and optical properties of Bok globules, to test the hypothesis that globules undergo collapse and to determine parameters which are not easily observed. Five of the six globules studied are consistent with collapse models. It is inferred that these objects have masses of about 100 solar masses and ages smaller than their free-fall times. Inferred initial densities are much larger than minimum densities for gravitational collapse, suggesting that collapse is initiated by strong external compression or that globules are fragments of larger condensed clouds. Values inferred for the (C-13)O/H2 ratio are smaller than previous estimates and depend strongly on cloud density.

Villere, K. R.↗

NASA NTRS1980

Collapse, equilibrium, and fragmentation of rotating, adiabatic clouds

Numerical calculations of the collapse of adiabatic clouds from uniform density and rotation initial conditions show that when restricted to axisymmetry, the clouds form either near-equilibrium spheroids or rings. Rings form in the collapse of low thermal energy clouds and have a ratio of rotational kinetic energy to the absolute value of gravitational potential energy greater than approximately 0.43. When the axisymmetric constraint is removed and an initial m = 2 density variation is introduced, clouds either collapse to form near-equilibrium ellipsoids or else fragment into binary systems through a bar phase. Ellipsoids form in the collapse of high thermal energy clouds and have a rotational kinetic energy/absolute value of gravitational potential energy ratio less than approximately 0.27. The results are consistent with the critical values of the rotational kinetic energy/absolute value of gravitational potential energy ratio for instabilities in Maclaurin spheroids, and suggest that protostellar clouds may undergo a dynamic fragmentation in the nonisothermal collapse regime.

Boss, A. P.↗

NASA NTRS1981

Collapses of stellar protogalaxies from aspheric initial conditions

Numerical experimens are presented which were intended to verify the independence of bar formation in rotating galaxy models from special initial conditions. Three-dimensional n-body programs were run starting from aspherical initial conditions characterized by particle rotational and peculiar velocities and offsets from sphericity for a set of 100,000 particles. All the initial configurations examined are observed to collapse to a thin form, overshoot, collapse again and again overshoot, with diameters and central densities similar to those observed under spheric initial conditions. Every aspheric collapse is also found to result in bar formation within two rotation periods, which is even sooner than in initially spherical conditions. In the intermediate stages of collapse, transient sheet patterns are found to be destroyed at asymmetries of 2-3%, while transient rings survived asymmetries of 6-7% but not 15-18%. It is noted that the results may be applicable to galaxy formation in the early universe, and possible mechanisms for the arresting of protogalactic collapse are indicated.

Miller, R. H.↗

NASA NTRS1982

A numerical study of the effects of ambipolar diffusion on the collapse of magnetic gas clouds

The gravitational collapse of isothermal, nonrotating magnetic gas clouds have been calculated numerically, including the effects of ambipolar diffusion. The fractional ionization in the clouds is approximated by a power-law function of the gas density, f = K/n to the q-power, where K and q are adjustable parameters. Eleven numerical experiments were run, and the results indicate that the asymptotic character of collapse is determined mainly by the value of q and is largely independent of the other parameters characterizing a cloud (e.g., K, cloud mass). In particular, there is nearly a one-to-one correspondence between q and the slope, x, of the central magnetic field strength-gas density relationship. If q is no more than 0.8, a cloud collapses asymptotically, as though the magnetic field were 'frozen' to the neutral matter. The magnetic field strength at the center of a collapsing cloud is strongly amplified during collapse even for values of q of about 1, despite extremely low values of fractional ionization. A discussion of the theoretical basis for this unexpected behavior is given. Possible implications of our results for the problems of magnetic braking of rotating protostars and star formation in general are also presented.

Black, D. C.↗

NASA NTRS1985

Variation of the temperature coefficient of collapse field in bismuth-based bubble garnets

An approximation to the collapse-field formula is used to show its dependence on magnetization and wall energy and the effect of additions of Gd, Sm, and Eu on 1-micron Bi:YIG bubble materials. The collapse field, magnetization, and wall energy are fitted to quadratic functions of temperature from -50 to 150 C. It is shown that the addition of the various classes of rare earths reduces the temperature derivative of the collapse field in Bi:YIG. Gd influences the collapse field through the magnetization, Sm affects it through the domain wall energy, and Eu does both. The singular magnetic properties of Eu result in the most nearly constant temperature dependence of the collapse field and the best match to a barium-ferrite bias magnite.

Fratello, V. J.↗