ShantanuT01/DACTYL-Pretraining huggingface dataset:
We establish global regularity for the logarithmically energy-supercritical wave equation $\Box u = u^5 \log(2+u^2)$ in three spatial dimensions for spherically symmetric initial data, by modifying an argument of Ginibre, Soffer and Velo \cite{gsv} for the energy-critical equation. This example demonstrates that critical regularity arguments can penetrate very slightly into the supercritical regime.
Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.
We present sets of equation of state (EOS) of nuclear matter including hyperons using an SU_f(3) extended relativistic mean field (RMF) model with a wide coverage of density, temperature, and charge fraction for numerical simulations of core collapse supernovae. Coupling constants of Sigma and Xi hyperons with the sigma meson are determined to fit the hyperon potential depths in nuclear matter, U_Sigma(rho_0) ~ +30 MeV and U_Xi(rho_0) ~ -15 MeV, which are suggested from recent analyses of hyperon production reactions. At low densities, the EOS of uniform matter is connected with the EOS by Shen et al., in which formation of finite nuclei is included in the Thomas-Fermi approximation. In the present EOS, the maximum mass of neutron stars decreases from 2.17 M_sun (Ne mu) to 1.63 M_sun (NYe mu) when hyperons are included. In a spherical, adiabatic collapse of a 15$M_\odot$ star by the hydrodynamics without neutrino transfer, hyperon effects are found to be small, since the temperature and density do not reach the region of hyperon mixture, where the hyperon fraction is above 1 % (T > 40 MeV or rho_B > 0.4 fm^{-3}).
We investigate the hypersurfaces which are the generation of the Fermat hypersufaces, and determine their projective isomorphism classes.
We present the results of an optical spectroscopic study of 12 GALEX-discovered star-forming Lyman alpha emitting galaxies (LAEs) at z ~ 0.3. We measure the emission line fluxes from these galaxies by fitting their observed spectra to stellar population models in order to correct for underlying stellar absorption. We revisit earlier stellar population model fitting results, finding that excluding now-known AGNs lowers the typical stellar population age and stellar mass of this sample to ~ 300 Myr and ~ 4 x 10^9 Msol, respectively. We calculate their dust extinction using the Balmer decrement, and find a typical visual attenuation of Av ~ 0.3 mag, similar to that seen in many high-redshift LAEs. Comparing the ratio of Lyalpha/Halpha and the Lyman alpha equivalent widths to the measured dust extinction, we find that the ISMs in these objects appear to be neither enhancing nor seriously attenuating the Lyman alpha equivalent widths, as would be the case in a quasi-clumpy ISM. Lastly, we perform a detailed analysis of the gas-phase metallicities of these galaxies, and we find that most galaxies in our sample have Z < 0.4 Zsol. We find that at a fixed stellar mass, these low-redshift LAE analogs are offset by ~ 0.6 dex lower in metallicity from the general galaxy population at similar redshifts based on the local mass-metallicity relationship. This implies that galaxies with Lyman alpha in emission may be systematically more metal poor than star-forming galaxies at the same stellar mass and redshift, similar to preliminary results at z ~ 2.
Recently it has been shown that the zero-energy eigenstate -- corresponding to the stationary state -- of a stochastic Hamiltonian with nearest-neighbour interaction in the bulk and single-site boundary terms, can always be written in the form of a so-called matrix-product state. We generalize this result to stochastic Hamiltonians with arbitrary, but finite, interaction range. As an application two different particle-hopping models with three-site bulk interaction are studied. For these models which can be interpreted as cellular automata for traffic flow, we present exact solutions for periodic boundary conditions and some suitably chosen boundary interactions.
We investigate the diffusive electron-transport properties of charge-doped graphene ribbons and nanoribbons with imperfect edges. We consider different regimes of edge scattering, ranging from wide graphene ribbons with (partially) diffusive edge scattering to ribbons with large width variations and nanoribbons with atomistic edge roughness. For the latter, we introduce an approach based on pseudopotentials, allowing for an atomistic treatment of the band structure and the scattering potential, on the self-consistent solution of the Boltzmann transport equation within the relaxation-time approximation and taking into account the edge-roughness properties and statistics. The resulting resistivity depends strongly on the ribbon orientation, with zigzag (armchair) ribbons showing the smallest (largest) resistivity and intermediate ribbon orientations exhibiting intermediate resistivity values. The results also show clear resistivity peaks, corresponding to peaks in the density of states due to the confinement-induced subband quantization, except for armchair-edge ribbons that show a very strong width dependence because of their claromatic behavior. Furthermore, we identify a strong interplay between the relative position of the two valleys of graphene along the transport direction, the correlation profile of the atomistic edge roughness, and the chiral valley modes, leading to a peculiar strongly suppressed resistivity regime, most pronounced for the zigzag orientation.
We report the detection of a massive neutral gas outflow in the z=2.09 gravitationally lensed Dusty Star-Forming Galaxy HATLASJ085358.9+015537 (G09v1.40), seen in absorption with the OH+(1_1-1_0) transition using spatially resolved (0.5"x0.4") Atacama Large Millimeter/submillimeter Array (ALMA) observations. The blueshifted OH+ line is observed simultaneously with the CO(9-8) emission line and underlying dust continuum. These data are complemented by high angular resolution (0.17"x0.13") ALMA observations of CH+(1-0) and underlying dust continuum, and Keck 2.2 micron imaging tracing the stellar emission. The neutral outflow, dust, dense molecular gas and stars all show spatial offsets from each other. The total atomic gas mass of the observed outflow is 6.7x10^9 M_sun, >25% as massive as the gas mass of the galaxy. We find that a conical outflow geometry best describes the OH+ kinematics and morphology and derive deprojected outflow properties as functions of possible inclination (0.38 deg-64 deg). The neutral gas mass outflow rate is between 83-25400 M_sun/yr, exceeding the star formation rate (788+/-300 M_sun/yr) if the inclination is >3.6 deg (mass-loading factor = 0.3-4.7). Kinetic energy and momentum fluxes span 4.4-290x10^9 L_sun and 0.1-3.7x10^37 dyne, respectively (energy-loading factor = 0.013-16), indicating that the feedback mechanisms required to drive the outflow depend on the inclination assumed. We derive a gas depletion time between 29 and 1 Myr, but find that the neutral outflow is likely to remain bound to the galaxy, unless the inclination is small, and may be re-accreted if additional feedback processes do not occur.
We show that any measure of entanglement that on pure bipartite states is given by a strictly concave function of the reduced density matrix is monogamous on pure tripartite states. This includes the important class of bipartite measures of entanglement that reduce to the (von Neumann) entropy of entanglement. Moreover, we show that the convex roof extension of such measures (e.g., entanglement of formation) are monogamous also on \emph{mixed} tripartite states. To prove our results, we use the definition of monogamy without inequalities, recently put forward[Gour and Guo, Quantum \textbf{2}, 81 (2018)]. Our results promote the theme that monogamy of entanglement is a property of quantum entanglement and not an attribute of some particular measures of entanglement.
A Ducci sequence is a sequence of integer $n$-tuples obtained by iterating the map \[ D : (a_1, a_2, \ldots, a_n) \mapsto \big(|a_1-a_2|,|a_2-a_3|,\ldots,|a_n-a_1|\big). \] Such a sequence is eventually periodic and we denote by $P(n)$ the maximal period of such sequences for given $n$. We prove lower bounds for $P(n)$ by counting certain partitions.
Aims: We aim to simulate radial profiles of molecular abundances and the gas temperature in cold and heavily shielded starless cores by combining chemical and radiative transfer models. Methods: A determination of the dust temperature in a modified Bonnor-Ebert sphere is used to calculate initial radial molecular abundance profiles. The abundances of selected cooling molecules corresponding to two different core ages are then extracted to determine the gas temperature at two time steps. The calculation is repeated in an iterative process yielding molecular abundances consistent with the gas temperature. Line emission profiles for selected substances are calculated using simulated abundance profiles. Results: The gas temperature is a function of time; the gas heats up as the core gets older because the cooling molecules are depleted onto grain surfaces. The contributions of the various cooling molecules to the total cooling power change with time. Radial chemical abundance profiles are non-trivial: different species present varying degrees of depletion and in some cases inward-increasing abundances profiles, even at t > 10^5 years. Line emission simulations indicate that cores of different ages can present significantly different line emission profiles, depending on the tracer species considered. Conclusions: Chemical abundances and the associated line cooling power change as a function of time. Most chemical species are depleted onto grain surfaces at densities exceeding ~10^5 cm^-3. Notable exceptions are NH_3 and N2H^+; the latter is largely undepleted even at n_H~10^6 cm-3. On the other hand, chemical abundances are not significantly developed in regions of low gas density even at t~10^5 years, revealed by inward-increasing abundance gradients. The gas temperature can be significantly different from the dust temperature; this may have implications on core stability.
The detected high-energy pulsars' population is growing in number, and thus, having agile and physically relevant codes to analyze it consistently is important. Here, we update our existing synchro-curvature radiation model by including a better treatment of the particle injection, particularly where the large pitch angle particles dominate the spectra, and by implementing a fast and accurate minimization technique. The latter allows a large improvement in computational cost, needed to test model enhancements and to apply the model to a larger pulsar population. We successfully fit the sample of pulsars with X-ray and $\gamma$-ray data. Our results indicate that, for every emitting particle, the spatial extent of their trajectory where the pitch angle is large and most of the detected X-ray radiation is produced is a small fraction of the light cylinder. We also confirm with this new approach that synchrotron radiation is not negligible for most of the gamma-ray pulsars detected. In addition, with the results obtained, we argue that J0357+3205 and J2055+2539 are MeV-pulsar candidates and are suggested for exhaustive observations in this energy band.
Measurements continuous in time were consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after the measurement when a certain trajectory of the measured observables is registered (the a posteriori states). In this paper a new derivation of filtering equations is presented, in the cases of counting processes and of measurement processes of diffusive type. It is also shown that the equation for the a posteriori dynamics in the diffusive case can be obtained, by a suitable limit, from that one in the counting case. Moreover, the paper is intended to clarify the meaning of the various concepts involved and to discuss the connections among them. As an illustration of the theory, simple models are worked out.
We present an analysis of the kinematic properties of stellar populations in the Galactic halo, making use of over 100,000 main sequence turnoff (MSTO) stars observed in the Sloan Digital Sky Survey. After dividing the Galactic halo into an inner-halo region (IHR) and outer-halo region (OHR), based on the spatial variation of carbon-to-iron ratios in the sample, we find that stars in the OHR exhibit a clear retrograde motion of $-$49 $\pm$ 4 km s$^{-1}$ and a more spherical distribution of stellar orbits, while stars in the IHR have zero net rotation ($-$3 $\pm$ 1 km s$^{-1}$) with a much more radially biased distribution of stellar orbits. Furthermore, we classify the carbon-enhanced metal-poor (CEMP) stars among the MSTO sample in each halo component into CEMP-no and CEMP-$s$ sub-classes, based on their absolute carbon abundances, $A$(C), and examine the spatial distributions and kinematics associated with each sub-class. The CEMP-no stars are the majority sub-class of CEMP stars in the OHR ($\sim$ 65%), and the minority sub-class in the IHR ($\sim$ 44%), similar to the results of several previous analyses. The CEMP-no stars in each halo region exhibit slightly higher counter-rotation than the CEMP-$s$ stars, but within statistical errors. The CEMP-no stars also show a more spherical distribution of orbits than the CEMP-$s$ stars in each halo region. These distinct characteristics provide strong evidence that numerous low-mass satellite galaxies (similar to the ultra-faint dwarf galaxies) have donated stars to the OHR, while more-massive dwarf galaxies provided the dominant contribution to the IHR.
Dynamics of the nuclear fragmentations and the charge exchange reactions in pion-nucleus collisions near the $\Delta$(1232) resonance energies has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport model. An isospin, momentum and density-dependent pion-nucleon potential is implemented in the model, which influences the pion dynamics, in particular the kinetic energy spectra, but weakly impacts the fragmentation mechanism. The absorption process in pion-nucleon collisions to form the $\Delta$(1232) resonance dominates the heating mechanism of target nucleus. The excitation energy transferred to the target nucleus increases with the pion kinetic energy and is similar for both $\pi^{-}$ and $\pi^{+}$ induced reactions. The magnitude of fragmentation of target nucleus weakly depends on the pion energy. The isospin ratio in the pion double charge exchange is influenced by the isospin ingredient of target nucleus.
A theoretical framework is presented for the estimation of nucleation times in systems with Brownian type dynamics. This framework is applied to a prototype system: the two-dimensional Ising model with spin-flip dynamics in an external magnetic field. Direct simulation results for the nucleation times, spanning more than four orders of magnitude, are compared with theoretical predictions. There are no free parameters; all system properties required by the theory are determined by simulations in equilibrium systems. Theoretical and simulation values are found to agree in most cases within 20%.
We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. The diameter of each inclusion is assumed to be proportional to a positive real parameter \epsilon. Under suitable assumptions, we show that the effective conductivity can be continued real analytically in the parameter \epsilon around the degenerate value \epsilon=0, in correspondence of which the inclusions collapse to points.
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in each patch at a rate proportional to the number of pairs of individuals in the patch (sexual reproduction) rather than simply the number of individuals as in the basic contact process. Offspring produced at a given patch either stay in their parents' patch or are sent to a nearby patch with some fixed probabilities. Specifically, we prove lower and upper bounds for the probability of long-term survival for the process starting with a single fully occupied patch. Our main finding is that, with probability close to one and for a certain set of parameters, the metapopulation survives in the presence of nearest neighbor interactions while it dies out in the presence of long range interactions, suggesting that the best strategy for the population to expand in space is to use intermediate dispersal ranges. This result is due to the presence of a so-called strong Allee effect induced by the birth mechanism and does not hold for the basic contact process.
Multiple parton interactions are typically implemented in Montecarlo codes by assuming a Poissonian distribution of collisions with average number depending on the impact parameter. A possible generalization, which links the process to hadronic diffraction, is shortly discussed.
This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations. In the second part, we focus on a specific minisuperspace universe, analyse it classically, and quantise it using the canonical quantisation method. The chosen model is a flat FLRW universe with a free massless scalar field and a perfect fluid. We extract the Wheeler--DeWitt equation, and calculate its solutions. There are three dynamical variables that may be used as clock parameters, namely a coordinate $t$ conjugated to the perfect fluid mass, the massless scalar field $\varphi$, and $v$, a positive power of the scale factor. We define three quantum theories, each one based on assuming one of the previous dynamical quantities as the clock. This quantisation method is then compared with the Dirac quantisation. We find that, in each quantisation procedure, covariance is broken, leading to inequivalent quantum theories. In the third part, the properties of each theory are analysed. Unitarity of each theory is implemented by adding a boundary condition on the allowed states. Requiring unitarity is what breaks general covariance in the quantum theory. In the fourth part, we study the numerical properties of the wave functions in the three theories, paying special attention to singularity resolution and other divergences from the classical theory. The $t$-clock theory is able to resolve the singularity, the $\varphi$-clock theory presents some non trivial dynamics that can be associated with a resolution of spatial infinity, and the $v$-clock theory does not show significant deviations from the classical theory. In the last part, we expand our analysis in order to include another quantisation method: path integral quantisation, and finally, we conclude.
Transport processes occurring in the radiative interior of solar-type stars are evidenced by the surface variation of light elements, in particular Li, and the evolution of their rotation rates. For the Sun, inversions of helioseismic data indicate that the radial profile of angular velocity in its radiative zone is nearly uniform, which implies the existence of angular momentum transport mechanisms. While there are many independent transport models for angular momentum and chemical species, there is a lack of self-consistent theories that permit stellar evolution models to simultaneously match the present-day observations of solar lithium abundances and radial rotation profiles. We explore how additional transport processes can improve the agreement between evolutionary models of rotating stars and observations. We constrain the resulting models by simultaneously using the evolution of the surface rotation rate and Li abundance in the solar-type stars of open clusters, and the solar surface and internal rotation profile as inverted from helioseismology. We show the relevance of penetrative convection for the depletion of Li. The rotational dependence of the depth of penetrative convection yields an anti-correlation between the initial rotation rate and Li depletion in our models of solar-type stars that is in agreement with the observed trend. Simultaneously, the addition of an ad hoc vertical viscosity leads to efficient transport of angular momentum between the core and the envelope. We also self-consistently compute for the first time the thickness of the tachocline and find that it is compatible with helioseismic estimations. However, the main sequence depletion of Li in solar-type stars is only reproduced when adding a parametric turbulent mixing below the convective envelope. The need for additional transport processes in stellar evolution models is confirmed.
For about twenty years, it has been the prevailing view that there can be no metallic state or metal-insulator transition in two dimensions in zero magnetic field. In the last several years, however, unusual behavior suggestive of such a transition has been reported in a variety of dilute two-dimensional electron and hole systems. The physics behind these observations is presently not understood. We review and discuss the main experimental findings and suggested theoretical models.
We report magnetic and inter-plane transport properties of Ca3Ru2O7 at high magnetic fields and low temperatures. Ca3Ru2O7 with a bilayered orthorhombic structure is a Mott-like system with a narrow charge gap of 0.1eV. Of a host of unusual physical phenomena revealed in this study, a few are particularly intriguing: (1) a collapse of the c-axis lattice parameter at a metal-nonmetal transition, TMI (=48 K), and a rapid increase of TMI with low uniaxial pressure applied along the c-axis; (2) quantum oscillations in the gapped, nonmetallic state for 20 mK<T<6.5 K; (3) tunneling colossal magnetoresistance, which yields a precipitate drop in resistivity by as much as three orders of magnitude; (4) different in-plane anisotropies of the colossal magnetoresistance and magnetization. All results appear to indicate a highly anisotropic ground state and a critical role of coupling between lattice and magnetism. The implication of these phenomena is discussed.
A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein field equations for any dependence of the matter action upon an independent connection.
We give an algebraic proof of properness of moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt. The proof combines a git construction of Schmitt, properness for twisted stable maps by Abramovich-Vistoli, a variation of a boundedness argument due to Ciocan-Fontanine-Kim-Maulik, and a removal of singularities for bundles on surfaces in Colliot-Th\'el\`ene-Sansuc.
We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite $U$ Hubbard model. We find that for one dimensional systems disorder has no influence, while for two dimensional systems disorder enhances the spin polarization of the system. The tendency of disorder to enhance magnetism in the ground state may be relevant to recent experimental observations of spin polarized ground states in quantum dots and small metallic grains.