ShantanuT01/DACTYL-Pretraining huggingface dataset:
Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the above example we then clarify the limitations of this approach: The diffeomorphism invariance of the action still leads to a nasty constraint algebra. Moreover, by simple changes of variables (e.g. in a path integral) one can reabsorb all the modifications of the original theory.
We use a set of AMR hydrodynamic simulations post-processed with the radiative-transfer code RADAMESH to study how inhomogeneous HeII reionization affects the intergalactic medium (IGM). We propagate radiation from active galactic nuclei (AGNs) considering two scenarios for the time evolution of the ionizing sources. We find that HeII reionization takes place in a very inhomogeneous fashion, through the production of well separated bubbles of the ionized phase that subsequently percolate. Overall, the reionization process is extended in time and lasts for a redshift interval Delta z>1. At fixed gas density, the temperature distribution is bimodal during the early phases of HeII reionization and cannot be described by a simple effective equation of state. When HeII reionization is complete, the IGM is characterized by a polytropic equation of state with index gamma~1.20. This relation is appreciably flatter than at the onset of the reionization process (gamma=1.56) and also presents a much wider dispersion around the mean. We extract HI and HeII Ly-alpha absorption spectra from the simulations and fit Voigt profiles to them. We find that the regions where helium is doubly ionized are characterized by different probability density functions of the curvature and of the Doppler b parameters of the HI Ly-alpha forest as a consequence of the bimodal temperature distribution during the early phases of HeII reionization. The column-density ratio in HeII and HI shows a strong spatial variability. Its probability density function rapidly evolves with time reflecting the increasing volume fraction in which ionizing radiation is harder due to the AGN contribution. Finally we show that the number density of the flux-transmission windows per unit redshift and the mean size of the dark gaps in the HeII spectra have the potential to distinguish between different reionization scenarios. (abridged)
We consider a one-dimensional continuum gas of pointlike positive and negative unit charges interacting via a logarithmic potential. The mapping onto a two-dimensional boundary sine-Gordon field theory with zero bulk mass provides the full thermodynamics (density-fugacity relationship, specific heat, etc.) of the log-gas in the whole stability range of inverse temperatures $\beta<1$. An exact formula for the excess chemical potential of a ``foreign'' particle of an arbitrary charge, put into the log-gas, is derived. The results are checked by a small-$\beta$ expansion and at the collapse $\beta=1$ point. The possibility to go beyond the collapse temperature is discussed.
The stability of the $\beta$-equilibrated dense nuclear matter is analyzed with respect to the thermodynamic stability conditions. Based on the density dependent M3Y effective nucleon-nucleon interaction, the effects of the nuclear incompressibility on the proton fraction in neutron stars and the location of the inner edge of their crusts and core-crust transition density and pressure are investigated. The high-density behavior of symmetric and asymmetric nuclear matter satisfies the constraints from the observed flow data of heavy-ion collisions. The neutron star properties studied using $\beta$-equilibrated neutron star matter obtained from this effective interaction for a pure hadronic model agree with the recent observations of the massive compact stars. The density, pressure and proton fraction at the inner edge separating the liquid core from the solid crust of neutron stars are determined to be $\rho_t=$ 0.0938 fm$^{-3}$, P$_t=$ 0.5006 MeV fm$^{-3}$ and x$_{p(t)}=$ 0.0308, respectively.
We have performed two kinds of non-linear fitting procedures to the single-particle energies in the $sdgh$ major shell to obtain better shell model results. The low-lying energy eigenvalues of the light Sn isotopes with $A=103-110$ in the $sdgh$-shell are calculated in the framework of the nuclear shell model by using CD-Bonn two-body effective nucleon-nucleon interaction. The obtained energy eigenvalues are fitted to the corresponding experimental values by using two different non-linear fitting procedures, i.e., downhill simplex method and clonal selection method. The unknown single-particle energies of the states $2s_{1/2}$, $1d_{3/2}$, and $0h_{11/2}$ are used in the fitting methods to obtain better spectra of the $^{104,106,108,110}$Sn isotopes. We compare the energy spectra of the $^{104,106,108,110}$Sn and $^{103,105,107,109}$Sn isotopes with/without a nonlinear fit to the experimental results.
The full quantum mechanical (QM) model of inclusive breakup of Ichimura-Austern-Vincent (IAV) is implemented in this paper to calculate breakup from heavy radioactive nuclei on a $^9$Be target at intermediate energies. So far it had been implemented and applied only to low energy reactions with light projectiles. The IAV model is successful in predicting absolute cross sections among other observables. In order to get insight on the content of the model in the case of the complicated heavy-ion reactions, results are compared with those of the semiclassical transfer to the continuum (TC) model. Because the TC is based on analytical formulae the dynamics of the breakup as it is contained in the rather involved IAV formalism will become more transparent. Heavy-ion reactions at high energies ($>$50A.MeV) are demanding from the computational point of view because of the high number of partial waves involved, typically around 100. The TC constitutes a useful alternative to the full QM calculations whenever predictions and/or estimates are necessary. It allows also for a systematic, fast evaluation of breakup observables. In the applications of both methods we use state-of-the art optical potentials and structure information. Excellent agreement is found between the calculated results of both methods and with available experimental data which shows that the qualitative and quantitative understanding of most aspects of one nucleon breakup is well under control.
In the low-redshift Universe, the most powerful radio sources are often associated with gas-rich galaxy mergers or interactions. We here present evidence for an advanced, gas-rich (`wet') merger associated with a powerful radio galaxy at a redshift of z~2. This radio galaxy, MRC 0152-209, is the most infrared-luminous high-redshift radio galaxy known in the southern hemisphere. Using the Australia Telescope Compact Array, we obtained high-resolution CO(1-0) data of cold molecular gas, which we complement with HST/WFPC2 imaging and WHT long-slit spectroscopy. We find that, while roughly M(H2) ~ 2 x 10$^{10}$ M$_{\odot}$ of molecular gas coincides with the central host galaxy, another M(H2) ~ 3 x 10$^{10}$ M$_{\odot}$ is spread across a total extent of ~60 kpc. Most of this widespread CO(1-0) appears to follow prominent tidal features visible in the rest-frame near-UV HST/WFPC2 imaging. Ly$\alpha$ emission shows an excess over HeII, but a deficiency over L(IR), which is likely the result of photo-ionisation by enhanced but very obscured star formation that was triggered by the merger. In terms of feedback, the radio source is aligned with widespread CO(1-0) emission, which suggests that there is a physical link between the propagating radio jets and the presence of cold molecular gas on scales of the galaxy's halo. Its optical appearance, combined with the transformational stage at which we witness the evolution of MRC 0152-209, leads us to adopt the name `Dragonfly Galaxy'.
Nested parentheses are forms in an algebra which define orders of evaluations. A class of well-formed sets of associated opening and closing parentheses is well studied in conjunction with Dyck paths and Catalan numbers. Nested parentheses also represent cuts through circles on a line. These become topologies of non-intersecting circles in the plane if the underlying algebra is commutative.   This paper generalizes the concept and answers quantitatively - as recurrences and generating functions of matching rooted forests - the questions: how many different topologies of nested circles exist in the plane if (i) pairs of circles may intersect, or (ii) even triples of circles may intersect. That analysis is driven by examining the symmetry properties of the inner regions of the fundamental type(s) of the intersecting pairs and triples.
In mechanical systems it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such models have recently been studied in the passage to the continuum by means of variational convergence ($\Gamma$-convergence). The $\Gamma$-limit results determine thresholds of the boundary condition, which mark a transition from purely elastic behaviour to the occurrence of a crack. In this article we provide a notion of fracture in the discrete setting and show that its continuum limit yields the same threshold as that obtained from the $\Gamma$-limit. Since the calculation of the fracture threshold is much easier with the new method, we see a good chance that this new approach will turn out useful in applications.
Extracting multi-scale information is key to semantic segmentation. However, the classic convolutional neural networks (CNNs) encounter difficulties in achieving multi-scale information extraction: expanding convolutional kernel incurs the high computational cost and using maximum pooling sacrifices image information. The recently developed dilated convolution solves these problems, but with the limitation that the dilation rates are fixed and therefore the receptive field cannot fit for all objects with different sizes in the image. We propose an adaptivescale convolutional neural network (ASCNet), which introduces a 3-layer convolution structure in the end-to-end training, to adaptively learn an appropriate dilation rate for each pixel in the image. Such pixel-level dilation rates produce optimal receptive fields so that the information of objects with different sizes can be extracted at the corresponding scale. We compare the segmentation results using the classic CNN, the dilated CNN and the proposed ASCNet on two types of medical images (The Herlev dataset and SCD RBC dataset). The experimental results show that ASCNet achieves the highest accuracy. Moreover, the automatically generated dilation rates are positively correlated to the sizes of the objects, confirming the effectiveness of the proposed method.
We study the transition between a Coulomb phase and a dimer crystal observed in numerical simulations of the three-dimensional classical dimer model, by mapping it to a quantum model of bosons in two dimensions. The quantum phase transition that results, from a superfluid to a Mott insulator at fractional filling, belongs to a class that cannot be described within the Landau-Ginzburg-Wilson paradigm. Using a second mapping, to a dual model of vortices, we show that the long-wavelength physics near the transition is described by a U(1) gauge theory with SU(2) matter fields.
In this note, boundary Type I blowups of suitable weak solutions to the Navier-Stokes equations are discussed. In particular, it has been shown that, under certain assumptions, the existence of non-trivial mild bounded ancient solutions in half space leads to the existence of suitable weak solutions with Type I blowup on the boundary.
We consider the evolution of the temperature $u$ in a material with thermal memory characterized by a time-dependent convolution kernel $h$. The material occupies a bounded region $\Omega$ with a feedback device controlling the external temperature located on the boundary $\Gamma$. Assuming both $u$ and $h$ unknown, we formulate an inverse control problem for an integrodifferential equation with a nonlinear and nonlocal boundary condition. Existence and uniqueness results of a solution to the inverse problem are proved.
We study the correlation-induced deformation of Fermi surfaces by means of a new diagrammatic method which allows for the analytical evaluation of Gutzwiller wave functions in finite dimensions. In agreement with renormalization-group results we find Pomeranchuk instabilities in two-dimensional Hubbard models for sufficiently large Coulomb interactions.
We confirm that the object DDO216-A1 is a substantial globular cluster at the center of Local Group galaxy DDO216 (the Pegasus dwarf irregular), using Hubble Space Telescope ACS imaging. By fitting isochrones, we find the cluster metallicity to be [M/H] = -1.6 +/-0.2, for reddening E(B-V) = 0.16 +/-0.02; the best-fit age is 12.3 +/-0.8 Gyr. There are ~30 RR Lyrae variables in the cluster; the magnitude of the fundamental mode pulsators gives a distance modulus of 24.77 +/-0.08 - identical to the host galaxy. The ratio of overtone to fundamental mode variables and their mean periods make DDO216-A1 an Oosterhoff Type I cluster. We find an I-band central surface brightness 20.85 +/-0.17 F814W mag per square arcsecond, a half-light radius of 3.1 arcsec (13.4 pc), and an absolute magnitude M814 = -7.90 +/-0.16 (approximately 10^5 solar masses). King models fit to the cluster give the core radius and concentration index, r_c = 2.1" +/-0.9" and c = 1.24 +/-0.39. The cluster is an "extended" cluster somewhat typical of some dwarf galaxies and the outer halo of the Milky Way. The cluster is projected <30 pc south of the center of DDO216, unusually central compared to most dwarf galaxy globular clusters. Analytical models of dynamical friction and tidal destruction suggest that it probably formed at a larger distance, up to ~1 kpc, and migrated inward. DDO216 has an unexceptional cluster specific frequency, S_N = 10. DDO216 is the lowest-luminosity Local Group galaxy to host a 10^5 solar mass globular cluster, and the only transition-type (dSph/dIrr) in the Local Group with a globular.
The modified scalar boson propagator due to the presence of a hyperplane semi-transparent mirror is computed. From this, the classical interaction between static charges and the mirror is investigated employing delta-like potentials and sources. Although the calculations for hyperplane mirrors are performed in arbitrary dimensions, and in a completely general way, it is shown that the results give rise to the usual image method as a particular case. The interaction between a point-like mirror and a point-like source is also considered in $3+1$ dimensions, where a central $1/R^{2}$ attractive potential is also obtained as a special case.
Total Ordinary Muon Capture (OMC) rates are calculated on the basis of the Quasiparticle Random Phase Approximation for several spherical nuclei from 90^Zr to 208^Pb. It is shown that total OMC rates calculated with the free value of the axial-vector coupling constant g_A agree well with the experimental data for medium-size nuclei and exceed considerably the experimental rates for heavy nuclei. The sensitivity of theoretical OMC rates to the nuclear residual interactions is discussed.
The renormalized energy density of a massless scalar field defined in a D-dimensional flat spacetime is computed in the presence of "soft" and "semihard" boundaries, modeled by some smoothly increasing potential functions. The sign of the renormalized energy densities for these different confining situations is investigated. The dependence of this energy on $D$ for the cases of "hard" and "soft/semihard" boundaries are compared.
We discuss how lensing by magnetic fields in galaxy clusters affects ultrahigh energy cosmic ray (UHECR) observations. As specific example, we use Virgo together with the cluster magnetic fields obtained earlier in a constrained simulation of structure formation including MHD processes. We find that, if M87 is the single source of UHECRs from Virgo, the emitted flux is strongly anisotropic in the most interesting energy range, (50-100)EeV, and differs from the average value by a factor five or more for a significant fraction of observers. Since magnetic lensing is energy dependent, the external energy spectrum as seen by different observers varies strongly too. These anisotropies are averaged out in the case that all active galactic nuclei in Virgo emit UHECRs. In both cases, the anisotropies of the emitted UHECR flux may introduce an important bias in the interpretation of UHECR data like, e.g., the determination of the source density n_s and the source energy spectrum of UHECRs.
We discuss the main features of the scalar sector of a class of BSM models with enlarged gauge symmetry, the so called 331 Models. The theoretical constraints on the scalar potential such as unitarity, perturbativity and boundedness-from-below, are presented, together with the analytical exact digitalization of the scalar sector. The phenomenology of exotic scenarios predicted by the 331 Models can be tested in light of these theoretical constraints.
We present statistics on the decompositions (with respect to a distinguished symmetric 2t-cycle) of vertices of the hypercube graph, whose negative parts are regarded as disjoint unions of two subsets of the ground set {1,...,t} of the corresponding oriented matroid.
Recently, the quantum counterpart of energy equipartition theorem has drawn considerable attention. Motivated by this, we formulate and investigate an analogous statement for the free energy of a quantum oscillator linearly coupled to a passive heat bath consisting of an infinite number of independent harmonic oscillators. We explicitly demonstrate that the free energy of the Brownian oscillator can be expressed in the form $F(T) = \langle f(\omega,T) \rangle $ where $f(\omega,T)$ is the free energy of an individual bath oscillator. The overall averaging process involves two distinct averages: the first one is over the canonical ensemble for the bath oscillators, whereas the second one signifies averaging over the entire bath spectrum of frequencies from zero to infinity. The latter is performed over a relevant probability distribution function $\mathcal{P}(\omega)$ which can be derived from the knowledge of the generalized susceptibility encountered in linear response theory. The effect of different dissipation mechanisms is also exhibited. We find two remarkable consequences of our results. First, the quantum counterpart of energy equipartition theorem follows naturally from our analysis. The second corollary we obtain is a natural derivation of the third law of thermodynamics for open quantum systems. Finally, we generalize the formalism to three spatial dimensions in the presence of an external magnetic field.
A cosmological description of the universe is proposed in the context of Hamiltonian formulation of a Bianchi IX cosmology minimally coupled to a massless scalar field. The classical and quantum results are studied with special attention to the case of closed Friedmann-Robertson-Walker model.
The correlations between global description of the ground state properties (binding energies, charge radii) and nuclear matter properties of the state-of-the-art covariant energy density functionals have been studied. It was concluded that the strict enforcement of the constraints on the nuclear matter properties (NMP) defined in Ref.\ \cite{RMF-nm} will not necessary lead to the functionals with good description of the binding energies and other ground and excited state properties. In addition, it will not substantially reduce the uncertainties in the predictions of the binding energies in neutron-rich systems. It turns out that the functionals, which come close to satisfying these NMP constraints, have some problems in the description of existing data. On the other hand, these problems are either absent or much smaller in the functionals which are carefully fitted to finite nuclei but which violate some NMP constraints. This is a consequence of the fact that the properties of finite nuclei are defined not only by nuclear matter properties but also by underlying shell effects. The mismatch of phenomenological content, existing in all modern functionals, related to nuclear matter physics and the physics of finite nuclei could also be responsible.
Hybridization between Ce $f$ and conduction $d$ states has been speculatively known to be one of the mechanisms responsible for magnetic instability of the ferromagnetic ground state of CeFe$_2$. Substituting Fe by small amounts of certain elements stabilizes it to an antiferromagnetic state below the Curie temperature via a first-order second phase transition. In the present work, we seek any direct relation between the $f-d$ hybridization and the second transition by measuring primarily dc magnetization and Ce M$_{4,5}$ edge x-ray absorption spectra of Ce(Fe$_{1-x}$M$_x$)$_2$ pseudobinaries, with M = Cr, Ag and Au. X-ray diffraction and x-ray photoelectron spectroscopy measurements are also performed essentially to monitor the quality of the samples. Whereas Cr impurity is found to cause the second transition, Ag and Au apparently do not induce any. In the former, the Curie and second transition temperatures vary systematically, but differently, with $x$. Our results imply that there is a definite proportionality between the $x$ dependences of the second transition temperature and the $f-d$ hybridization strength estimated qualitatively from the absorption spectra.
We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation of the other. The result is applied to estimate, with explicit error, expectations of functions of random vectors for some Ising models and exponential random graphs in "high temperature" regimes.
In the literature, the matchings between spacetimes have been most of the times implicitly assumed to preserve some of the symmetries of the problem involved. But no definition for this kind of matching was given until recently. Loosely speaking, the matching hypersurface is restricted to be tangent to the orbits of a desired local group of symmetries admitted at both sides of the matching and thus admitted by the whole matched spacetime. This general definition is shown to lead to conditions on the properties of the preserved groups. First, the algebraic type of the preserved group must be kept at both sides of the matching hypersurface. Secondly, the orthogonal transivity of two-dimensional conformal (in particular isometry) groups is shown to be preserved (in a way made precise below) on the matching hypersurface. This result has in particular direct implications on the studies of axially symmetric isolated bodies in equilibrium in General Relativity, by making up the first condition that determines the suitability of convective interiors to be matched to vacuum exteriors. The definition and most of the results presented in this paper do not depend on the dimension of the manifolds involved nor the signature of the metric, and their applicability to other situations and other higher dimensional theories is manifest.