ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a new sample of 25 fossil groups (FGs) at z < 0.1, along with a control sample of seventeen bright ellipticals located in non-fossil systems. Both the global properties of FGs (e.g. X-ray luminosity) as well as the photometric properties (i.e. isophotal shape parameter, a4) and spectroscopic parameters (e.g. the alpha-enhancement) of their first-ranked ellipticals are consistent with those of the control sample. This result favors a scenario where FGs are not a distinct class of systems, but rather a common phase in the life of galaxy groups. We also find no evidence for an evolutionary sequence explaining the formation of galaxies in fossil systems through the merging of galaxies in compact groups.
The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in $R^n$ akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978), Dodson, Dickinson (2000) and Beresnevich, Bernik, Kleinbock, Margulis (2002). In the case of planar curves, the complete Hausdorff dimension theory is developed
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational inequalities. Motivated by models for critical state problems and applications to free boundary problems in Mechanics and in Physics, in this work several known properties are collected and presented and a few novel results and examples are found.
Recent advance in understanding the supercritical state posits the existence of a new line above the critical point separating two physically distinct states of matter: rigid liquid and non-rigid gas-like fluid. The location of this line, the Frenkel line, remains unknown for important real systems. Here, we map the Frenkel line on the phase diagram of supercritical iron using molecular dynamics simulations. On the basis of our data, we propose a general recipe to locate the Frenkel line for any system, the recipe that importantly does not involve system-specific detailed calculations and relies on the knowledge of the melting line only. We further discuss the relationship between the Frenkel line and the metal-insulator transition in supercritical liquid metals. Our results enable predicting the state of supercritical iron in several conditions of interest. In particular, we predict that liquid iron in the Jupiter core is in the "rigid liquid" state and is highly conducting. We finally analyse the evolution of iron conductivity in the core of smaller planets such as Earth and Venus as well as exoplanets: as planets cool off, the supercritical core undergoes the transition to the rigid-liquid conducting state at the Frenkel line.
Recent observations of Type Ia supernova at high redshifts establish that the dark energy component of the universe has (a probably constant) ratio between pressure and energy density $w=p/\rho=-1.02(^{+0.13}_{-0.19})$. The conventional quintessence models for dark energy are restricted to the range $-1\le w < 0$, with the cosmological constant corresponding to $w=-1$. Conformally coupled quintessence models are the simplest ones compatible with the marginally allowed superaccelerated regime ($w<-1$). However, they are known to be plagued with anisotropic singularities.   We argue here that the extension of the classical approach to the semiclassical one, with the inclusion of quantum counterterms necessary to ensure the renormalization, can eliminate the anisotropic singularities preserving the isotropic behavior of conformally coupled superquintessence models. Hence, besides of having other interesting properties, they are consistent candidates to describe the superaccelerated phases of the universe compatible with the present experimental data.
Explicit path integration is carried out for the Green's functions of special relativistic harmonic oscillators in (1+1)- and (3+1)-dimensional Minkowski space-time modeled by a Klein-Gordon particle in the universal covering space-time of the anti-de Sitter static space-time. The energy spectrum together with the normalized wave functions are obtained. In the non-relativistic limit, the bound states of the one- and three-dimensional ordinary oscillators are regained.
The vertex for gluon emission during the splitting of a reggeized gluon into two is constructed in the framework of Lipatov effective action formalism. Its reduction to a pure transverse form for the diffractive amplitude gives the standard Bartels vertex plus an additional contribution corresponding to the emission from a pointlike splitting vertex. This additional contribution turns out to be given by a longitudinal integral divergent both in the ultraviolet and infrared. A certain specific recipe for this part, including the principal value prescription for the integration, allows to eliminate this unwanted contribution.
A model for two-dimensional colloids confined laterally by "structured boundaries" (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance D between the confining walls is reduced at constant particle number from an initial value D_0, for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from n to n-1 to n-2 etc.) and are accompanied by an almost periodic strain pattern, due to "soliton staircases" along the boundaries. Since standard simulation studies of such transitions are hampered by huge hysteresis effects, we apply the phase switch Monte Carlo method to estimate the free energy difference between the structures as a function of the misfit between D and D_0, thereby locating where the transitions occurs in equilibrium. For comparison, we also obtain this free energy difference from a thermodynamic integration method: the results agree, but the effort required to obtain the same accuracy as provided by phase switch Monte Carlo would be at least three orders of magnitude larger. We also show for a situation where several "candidate structures" exist for a phase, that phase switch Monte Carlo can clearly distinguish the metastable structures from the stable one. Finally, applying the method in the conjugate statistical ensemble (where the normal pressure conjugate to D is taken as an independent control variable) we show that the standard equivalence between the conjugate ensembles of statistical mechanics is violated.
We describe a phase-coherent multifrequency lock-in measurement technique that uses the inverse Fourier transform to reconstruct the nonlinear current-voltage characteristic (IVC) of a nanoscale junction. The method provides for a separation of the galvanic and displacement currents in the junction, and easy cancellation of the parasitic displacement current from the measurement leads. These two features allow us to overcome traditional limitations imposed by the low conductance of the junction and high capacitance of the leads, thus providing an increase in measurement speed of several orders of magnitude. We demonstrate the method in the context of conductive atomic force microscopy, acquiring IVCs at every pixel while scanning at standard imaging speed.
The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph. Moreover, we generalise the model to include a `temperature' parameter. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Finally, we also consider a discursive voter model, where voters discuss their opinions with their neighbours. Our proofs rely on the well-known duality to coalescing random walks and a detailed understanding of the structure of the random graphs.
We examined the variability of three ultra-luminous X-ray sources (ULXs) in the 2003, 110 ks XMM-Newton observation of NGC253. Remarkably, we discovered ULX1 to be three times more variable than ULX2 in the 0.3--10 keV band, even though ULX2 is brighter. Indeed, ULX1 exhibits a power density spectrum that is consistent with the canonical high state or very high/steep power law state, but not the canonical low state. The 0.3--10 keV emission of ULX1 is predominantly non-thermal, and may be related to the very high state. We also fitted the ULX spectra with disc blackbody, slim disc and convolution Comptonization (SIMPL x DISKBB) models. The brightest ULX spectra are usually described by a two emission components (disc blackbody + Comptonized component); however, the SIMPL model results in a single emission component, and may help determine whether the well known soft excess is a feature of ULX spectra or an artifact of the two-component model. The SIMPL models were rejected for ULX3 (and also for the black hole + Wolf-Rayet binary IC10 X-1); hence, we infer that the observed soft-excesses are genuine features of ULX emission spectra. We use an extended corona scenario to explain the soft excess seen in all the highest quality ULX spectra, and provide a mechanism for stellar mass black holes to exhibit super-Eddington luminosities while remaining locally sub-Eddington.
We present observations of background charge fluctuators near an Al-AlO_x-Al single-electron transistor on an oxidized Si substrate. The transistor design incorporates a heavily doped substrate and top gate, which allow for independent control of the substrate and transistor island potentials. Through controlled charging of the Si/SiO_2 interface we show that the fluctuators cannot reside in the Si layer or in the tunnel barriers. Combined with the large measured signal amplitude, this implies that the defects must be located very near the oxide surface.
$J/\Psi$ particles are abundantly produced at the Beijing Electron Positron Collider (BEPC). The $J/\Psi$ decays provide an excellent place for studying $N^*$ resonances. For $J/\Psi\to\bar NN\pi$ and $\bar NN\pi\pi$, the $\pi N$ and $\pi\pi N$ systems are limited to be pure isospin 1/2 due to isospin conservation. This is a big advantage in studying $N^*$ resonances from $J/\Psi$ decays, compared with $\pi N$ and $\gamma N$ experiments which suffer difficulty on the isospin decomposition of 1/2 and 3/2. All other $N^*$ decay channels which are presently under investigation at CEBAF(JLab, USA), ELSA(Bonn,Germany) and GRAAL(Grenoble, France) with real photon or space-like virtual photon can also be studied at BEPC complementally with the time-like virtual photon. The process $J/\Psi\to\bar NN^*$ or $N\bar N^*$ provides a new way to probe the internal structure of the $N^*$ resonances. The recent results and outlook of our new $N^*$ program at BEPC are presented.
We derive inequality [\int_{\r} |f^{'}(x)|^ph(f(x))dx \le (\sqrt{p-1})^p\int_{\r}(\sqrt{|f^{"}(x){\cal T}_h(f(x))|})^ph(f(x))dx,] where $f$ belongs locally to Sobolev space $W^{2,1}$ and $f^{'}$ has bounded support. Here $h(...)$ is a given function and ${\cal T}_h(...)$ is its given transform, it is independent of $p$. In case when $h\equiv 1$ we retrieve the well known inequality: (\int_{\r} |f^{'}(x)|^pdx \le (\sqrt{p-1})^p \int_{\r}(\sqrt{|f^{"}(x)f(x)|})^pdx.) Our inequalities have form similar to the classical second order Oppial inequalites. They also extend certain class of inequalities due to Mazya, used to obtain second order isoperimetric inequalities and capacitary estimates. We apply them to obtain new apriori estimates for nonlinear eigenvalue problems.
Relative abundances of the five stable isotopes of titanium (^46Ti to ^50Ti) are measured for 11 M dwarfs belonging to the thin disk (four stars), thick disk (three stars), the halo (one star), and either the thick or the thin disk (three stars). Over the metallicity range of the sample (-1<[Fe/H]<0), the isotopic ratios are approximately constant to the solar system ratios. There is no discernible difference between the isotopic ratios for thin and thick disk stars. Isotopic ratios are in fair accord with recent calculations of Galactic chemical evolution despite the fact that such calculations underpredict [Ti/Fe] by about 0.4 dex at all metallicities.
Given a sequence of real numbers $\{\psi(n)\}_{n\in\mathbb{N}}$ with $0\leq \psi(n)<1$, let $W(\psi)$ denote the set of $x\in[0,1]$ for which $|xn-m|<\psi(n)$ for infinitely many coprime pairs $(n,m)\in\mathbb{N}\times\mathbb{Z}$. The purpose of this note is to show that if there exists an $\epsilon>0$ such that $\sum_{n\in\mathbb{N}}\psi(n)^{1+\epsilon}\cdot\frac{\varphi(n)}{n}=\infty,$ then the Lebesgue measure of $W(\psi)$ equals 1.
We present results from high signal-to-noise optical spectropolarimetric observations of the Seyfert 1 galaxies NGC783 and Mrk509 in the 3500-7000 A range. We find complex structure in the polarized emission for both objects. In particular, Position Angle (PA) changes across the Balmer lines show a distinctive 'M'-shaped profile that had not been observed in this detail before, but could represent a common trait in Seyfert 1 galaxies. In fact, while this shape is observed in all Balmer lines in NGC3783, Mrk509 transitions into a 'M'-shaped PA profile for higher transitions lines. We have modeled the observed profiles using the STOKES radiative transfer code and assuming that the scattering region is co-spatial with the BLR and outflowing. The results give compelling new evidence for the presence of nuclear winds in these two Seyfert 1 galaxies.
We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.
The optimized $\delta$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $\lambda \phi^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $\delta$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
In this paper, we seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics, i.e. a characterization of curves in positive characteristics which are reduction of Shimura curve over the complex field. Specifically, we study the liftablity of a curve in moduli space of principally polarized abelian fourfolds over k, char k=p. We show that some conditions on the crystalline Hodge cycles over such a curve imply that this curve can be lifted to a Shimura curve.
We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{R}^N) \quad \text{with} \quad \|u\|^2_{L^2(\mathbb{R}^N)}=m. $$   Here $f\in C(\mathbb{R},\mathbb{R})$, $m>0$ is a given constant and $\mu\in\mathbb{R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\geq6$. In particular, all these solutions are sign-changing.
We have determined possible cluster members of the nearby open cluster Praesepe (M44) based on J and K photometry and proper motions from the PPMXL catalogue and z photometry from the Sloan Digital Sky Survey (SDSS). In total we identified 893 possible cluster members down to a magnitude of J = 15.5 mag, corresponding to a mass of about 0.15 Msun for an assumed cluster distance modulus of (m-M)_0 = 6.30 mag (d ~ 182 pc), within a radius of 3.5{\deg} around the cluster centre. We derive a new cluster centre for Praesepe ({\alpha}_centre = 8h 39m 37s, {\delta}_centre = 19{\deg} 35' 02"). We also derive a total cluster mass of about 630 Msun and a 2D half-number and half-mass radius of 4.25 pc and 3.90 pc respectively. The global mass function (MF) of the cluster members shows evidence for a turnover around m = 0.65 Msun. While more massive stars can be fit by a power-law {\xi}(m) ~ m^(-{\alpha}) with slope {\alpha} = 2.88 +/- 0.22, stars less massive than m = 0.65 Msun are best fitted with {\alpha} = 0.85 +/- 0.10. In agreement with its large dynamical age, we find that Praesepe is strongly mass segregated and that the mass function slope for high mass stars steepens from a value of {\alpha} = 2.32 +/- 0.24 inside the half-mass radius to {\alpha} = 4.90 +/- 0.51 outside the half-mass radius. We finally identify a significant population of binaries and triples in the colour-magnitude diagram of Praesepe. Assuming non-random pairing of the binary components, a binary fraction of about 35% for primaries in the mass range 0.6 < m/Msun < 2.20 is required to explain the observed number of binaries in the colour-magnitude diagram (CMD).
Gamma-Ray Bursts (GRBs) have been proposed as a leading candidate for acceleration of ultra high-energy cosmic rays, which would be accompanied by emission of TeV neutrinos produced in proton-photon interactions during acceleration in the GRB fireball. Two analyses using data from two years of the IceCube detector produced no evidence for this neutrino emission, placing strong constraints on models of neutrino and cosmic-ray production in these sources.
Deconfined quantum critical points govern continuous quantum phase transitions at which fractionalized (deconfined) degrees of freedom emerge. Here we study dynamical signatures of the fractionalized excitations in a quantum magnet (the easy-plane J-Q model) that realize a deconfined quantum critical point with emergent O(4) symmetry. By means of large-scale quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation functions, we obtain the dynamic spin structure factors in the $S^{x}$ and $S^{z}$ channels. In both channels, we observe broad continua that originate from the deconfined excitations. We further identify several distinct spectral features of the deconfined quantum critical point, including the lower edge of the continuum and its form factor on moving through the Brillouin Zone. We provide field-theoretical and lattice model calculations that explain the overall shapes of the computed spectra, which highlight the importance of interactions and gauge fluctuations to explaining the spectral-weight distribution. We make further comparisons with the conventional Landau O(2) transition in a different quantum magnet, at which no signatures of fractionalization are observed. The distinctive spectral signatures of the deconfined quantum critical point suggest the feasibility of its experimental detection in neutron scattering and nuclear magnetic resonance experiments.
We present a systematic, analytical study of geometrically thin, optically thick accretion disc solutions for magnetized turbulent flows, with an alpha-like viscosity prescription. Under the only assumptions that (1) Magneto-Rotational instability (MRI) generates the turbulence that produces the anomalous viscosity needed for accretion to proceed, and that (2) the magnetic field amplified by the instability saturates due to buoyant vertical escape, we are able to self-consistently solve the disc structure equations including the fraction of power, f, that is carried off by vertical Poynting flux (and likely dissipated outside the optically thick disc). For low-viscosity discs, we obtain stable high-f solutions at low accretion rates, when gas pressure dominates, and unstable, low-f, radiation pressure dominated solutions at high accretion rates. For high viscosity discs, instead, a new thermally and viscously stable, radiation pressure dominated solution is found, characterized by f~1 and appearing only above a critical accretion rate (of the order of few tenths of the Eddington one). We discuss the regimes of validity of our assumptions, and the astrophysical relevance of our solutions. We conclude that our newly discovered thin disc solutions, possibly accompanied by powerful, magnetically dominated coronae and outflows, should be seriously considered as models for black holes accreting at super-Eddington rates.
Motivated by the discovery of a handful of pulsating, extremely low mass white dwarfs (ELM WDs, mass $M \lesssim 0.17\, M_\odot$) which likely have WD companions, this paper discusses binary formation models for these systems. Formation of an ELM WD by unstable mass transfer (MT) or a common envelope (CE) event is unlikely. Stable Roche-lobe overflow with conservative MT produces only $M \gtrsim 0.2\, M_\odot$. This paper discusses the formation of ELM WD using angular momentum losses by magnetic braking. The initially more massive star becomes the companion WD through a CE event. The initially less massive star becomes the ELM WD as an evolved donor in a Cataclysmic Variable binary. Evolutionary models are constructed using the Modules for Experiments in Stellar Astrophysics (MESA), with ELM WD progenitors in the range $M_d=1.0-1.5\, M_\odot$ and WD companions in the range $M_{\rm a} \simeq 0.4-0.9\, M_\odot$. A prescription to reduce magnetic braking for thin surface convection zones is included. Upon the thinning of the evolved donor's envelope, the donor star shrinks out of contact and MT ceases, revealing the ELM WD. Systems with small masses have previously been suggested as possible AM CVN's. Systems with large masses, up to the limit $M \simeq 0.18\, M_\odot$ at which shell flashes occur on the WD cooling track, will tend to expand out to orbital periods $P_{\rm orb} \gtrsim 15\, {\rm hr}$. In between this range, ELM WD may become pulsators both as pre-WD and on the WD cooling track. Brickhill's criterion for convective mode driving is used to estimate the location of the blue edge of the g-mode instability strip.
We investigate the possibility of studying E$_6$ phenomenology at high energy hadron colliders. The production of heavy leptons pairs {\it via} a gluon-gluon fusion mechanism is discussed. An enhancement in the parton level cross-section is expected due to the heavy (s)fermion loops which couple to the gluons.
We explore a cyclic universe due to phantom and quintessence fields. We find that, in every cycle of the evolution of the universe, the phantom dominates the cosmic early history and quintessence dominates the cosmic far future. In this model of universe, there are infinite cycles of expansion and contraction. Different from the inflationary universe, the corresponding cosmic space-time is geodesically complete and quantum stable. But similar to the Cyclic Model, the flatness problem, the horizon problem and the large scale structure of the universe can be explained in this cyclic universe.