ShantanuT01/DACTYL-Pretraining huggingface dataset:
In a previous paper we constructed a new class of Iwasawa modules as $\ell$--adic realizations of what we called abstract $\ell$--adic $1$--motives in the number field setting. We proved in loc. cit. that the new Iwasawa modules satisfy an equivariant main conjecture. In this paper we link the new modules to the $\ell$--adified Tate canonical class, defined by Tate in 1960 and give an explicit construction of (the minus part of) $\ell$--adic Tate sequences for any Galois CM extension $K/k$ of an arbitrary totally real number field $k$. These explicit constructions are significant and useful in their own right but also due to their applications (via our previous results on the Equivariant Main Conjecture in Iwasawa theory) to a proof of the minus part of the far reaching Equivariant Tamagawa Number Conjecture for the Artin motive associated to the Galois extension $K/k$.
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model. This dynamical model exhibits very interesting behavior. Our goal in thissurvey is to give an overview of the work in dynamical percolation that has been done (and some of which is in the process of being written up).
Observational studies of galaxy isophotal shapes have shown that galaxy orientations are anisotropic: a galaxy's long axis tends to be oriented toward the center of its host. This radial alignment is seen across a wide range of scales, from galaxies in massive clusters to small Milky Way type satellite systems. Recently, this effect has also been detected in dark matter simulations of cosmological structure, but the degree of alignment of dark matter substructures in these studies is significantly stronger than seen in observations. In this paper we attempt to reconcile these two results by performing high-resolution numerical experiments on N-body multi-component models of triaxial galaxies orbiting in an external analytical potential. The large number of particles employed allows us to probe deep into the inner structure of the galaxy: we show that the discrepancy between observed galaxies and simulated dark matter halos is a natural consequence of induced radial shape twisting in the galaxy by the external potential. The degree of twisting depends strongly on the orbital phase and eccentricity of the satellite, and it can, under certain conditions, be significant at radii smaller than the dark matter scale radius. Such internal misalignments will have important consequences, both for the dynamical evolution of the galaxy itself, and for mass modeling of galaxies in clustered environments.
Based on the analysis of a small sample of BATSE and Konus gamma-ray bursts (GRBs) with know redshift it has been reported that the width of the autocorrelation function (ACF) shows a remarkable bimodal distribution in the rest-frame of the source. However, the origin of these two well-separated ACF classes remains unexplained.We complement previous ACF analysis studying the corresponding power density spectra (PDS). With the addition of Beppo-SAX data and taken advantage of its broad-band capability, we not only increase the burst sample but we extend the analysis to X-ray energies. The rest-frame PDS analysis at gamma-ray energies shows that the two ACF classes are not simply characterised by a different low frequency cut-off, but they have a distinct variability as a whole in the studied frequency range. Both classes exhibit average PDS with power-law behaviour at high frequencies (f' > 0.1 Hz) but significantly different slopes, with index values close to those of Brownian (-2) and Kolmogorov (-5/3) spectra for the narrow and broad classes respectively. The latter spectrum presents an additional PDS component, a low-frequency noise excess with a sharp cut-off. At X-ray energies we find the power-law index unchanged for the broad class, but a significantly steeper slope in the narrow case (~ -3). We interpret this as an indication that the broad class bursts have weaker spectral evolution than the narrow ones, as suggested also by our analysis of the ACF energy dependence. The low and high frequency PDS components may then arise from two radiating regions involving different emission mechanisms.
We present a study of the structure and dynamics of the dense gas surrounding the HH 211-mm source, using VLA observations of the ammonia (1,1) and (2,2) inversion transitions. We find the envelope around this Class 0 source has an elongated geometry, extending about 104 AU in the direction perpendicular to the well-known HH 211 jet, and exhibits a velocity distribution consistent with rotation along the major axis. Our VLA observations indicate that the envelope is mostly in virial equilibrium. However, comparing our data with results from previous studies it appears that the gas within approximately 0.005 pc of the central protostar is undergoing dynamical collapse. The size of this collapsing radius may constrain the amount of mass that can eventually infall into the forming star. We also find that the envelope is mostly internally heated, most probably by radiation from the central protostar. In addition, we detect evidence of outflow-envelope interaction in the ammonia data. These include a velocity gradient in the dense gas along the outflow axis and significant line broadening that is spatially correlated with the jet and it might be the result of outflow-induced turbulence in the envelope.
We present surface resistance measurements of the archetypical heavy-fermion compound CeCu6 for frequencies between 3.7 and 18 GHz and temperatures from 1.2 to 6 K. The measurements were performed with superconducting stripline resonators that allow simultaneous measurements at multiple frequencies. The surface resistance of CeCu6 exhibits a pronounced decrease below 3 K, in consistence with dc resistivity. The low-temperature frequency dependence of the surface resistance follows a power law with exponent 2/3. While for conventional metals this would be consistent with the anomalous skin effect, we discuss the present situation of a heavy-fermion metal, where this frequency dependence might instead stem from the influence of electronic correlations.
We derive a new non-abelian Stokes theorem by rewriting the Wilson loop as a gauge-invariant area integral, at the price of integrating over an auxiliary field from the coset SU(N) / [U(1)]^{N-1} space. We then introduce the relativistic quark--monopole interaction as a Wess--Zumino-type action, and extend it to the non-abelian case. We show that condensation of monopoles and confinement can be investigated in terms of the behaviour of the monopole world lines. One can thus avoid hard problems of how to introduce monopole fields and dual Yang--Mills potentials.
Aims. J, H, and K' images obtained from the near-infrared imager CFHTIR on the Canada-France-Hawaii Telescope are used to derive the morphological parameters of the red giant branch (RGB) in the near-infrared color-magnitude diagrams for 12 metal-poor globular clusters in the Galactic bulge direction. Using the compiled data set of the RGB parameters for the observed 12 clusters, in addition to the previously studied 5 clusters, we discuss the properties of the RGB morphology for the clusters and compare them with the calibration relations for the metal-rich bulge clusters and the metal-poor halo clusters. Methods. The photometric RGB shape indices such as colors at fixed magnitudes of MK = MH = (-5.5, -5, -4, and -3), magnitudes at fixed colors of (J - K)o = (J - H)o = 0.7, and the RGB slope are measured from the fiducial normal points defined in the near- infrared color-magnitude diagrams for each cluster. The magnitudes of RGB bump and tip are also estimated from the differential and cumulative luminosity functions of the selected RGB stars. The derived RGB parameters have been used to examine the overall behaviors of the RGB morphology as a function of cluster metallicity. Results. The correlations between the near-infrared photometric RGB shape indices and the cluster metallicity for the programme clusters compare favorably with the previous observational calibration relations for metal-rich clusters in the Galactic bulge and the metal-poor halo clusters. The observed near-infrared magnitudes of the RGB bump and tip for the investigated clusters are also in accordance with the previous calibration relations for the Galactic bulge clusters.
Assuming that gas and dust separate in the interstellar medium (ISM) so that high-density regions, where stars can form, are almost devoid of dust, the amount of metals being removed from the ISM can be significantly reduced (minimized astration). Here, it is shown by simple analytical models that this may increase the total metal budget of a galaxy considerably. It is suggested that these extra metals may increase the mass of dust such that the "dust budget crisis", i.e., the fact that there seems to be more dust at high redshifts than can be accounted for, can be ameliorated. Reducing the amount of astration, the metal budget can be more than doubled, in particular for systems that evolve under continuous gas accretion.
Accreting black holes and neutron stars release an unknown fraction of the infalling particles and energy in the form of collimated jets. The jets themselves are radiatively inefficient, but their power can be constrained by observing their interaction with the surrounding environment. Here we present observations of X-ray binary jet-ISM interactions which produce optical line emission, using the ESO/MPI 2.2m and Isaac Newton Telescopes. We constrain the time-averaged power of the Cyg X-1 jet-powered nebula, and present a number of new candidate nebulae discovered. Comparisons are made to the large scale lobes of extragalactic AGN. We also speculate that some emission line emitters close to X-ray binaries in M31 are likely to be microquasar jet-powered nebulae.
There are either a near kinematic distance of 5.5 kpc or a far distance of 8.8 kpc for a Galactic supernova remnant (SNR) G32.8$-$0.1 derived by using the rotation curve of the Galaxy. Here we make sure that the remnant distance is the farther one 8.8 kpc through solving a group of equations for the shell-type remnants separately at the adiabatic-phase and the radiative-phase. For SNR G346.6$-$0.2 we determine its distance also the farther one 11 kpc rather than the nearer one 5.5 kpc.
A decomposition of a non-empty simple graph $G$ is a pair $[G,P]$, such that $P$ is a set of non-empty induced subgraphs of $G$, and every edge of $G$ belongs to exactly one subgraph in $P$. The chromatic index $\chi'([G,P])$ of a decomposition $[G,P]$ is the smallest number $k$ for which there exists a $k$-coloring of the elements of $P$ in such a way that: for every element of $P$ all of its edges have the same color, and if two members of $P$ share at least one vertex, then they have different colors. A long standing conjecture of Erd\H{o}s-Faber-Lov\'asz states that every decomposition $[K_n,P]$ of the complete graph $K_n$ satisfies $\chi'([K_n,P])\leq n$. In this paper we work with geometric graphs, and inspired by this formulation of the conjecture, we introduce the concept of chromatic index of a decomposition of the complete geometric graph. We present bounds for the chromatic index of several types of decompositions when the vertices of the graph are in general position. We also consider the particular case in which the vertices are in convex position and present bounds for the chromatic index of a few types of decompositions.
Recent observations have revealed that 8% of linear polarization patches in the internetwork quiet Sun are fully embedded in downflows. These are not easily explained with the typical scenarios for the source of internetwork fields which rely on flux emergence from below. We explore using radiative MHD simulations a scenario where magnetic flux is transported from the magnetic canopy overlying the internetwork into the photosphere by means of downward plumes associated with convective overshoot. We find that if a canopy-like magnetic field is present in the simulation, the transport of flux from the canopy is an important process for seeding the photospheric layers of the internetwork with magnetic field. We propose that this mechanism is relevant for the Sun as well, and it could naturally explain the observed internetwork linear polarization patches entirely embedded in downflows.
We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted Sobolev space with low regularity in the weight. The method used can be applied for other nonlinear dispersive models, for instance the multidimensional nonlinear Schrodinger equation.
Proves that if a curve has totally split reduction and the corresponding skeleton (as a metric graph) is a chain of loops with generic edge lengths, then every divisor on the graph with imposed ramification at the rightmost vertex $p$ of the skeleton lifts to a divisor class on the curve with the same ramification at some point $P$ that retracts to $p$, extending the work of Cartwright-Jensen-Payne. Gives a positive answer to lifting proper tropical intersections within a polytopal domain in an analytic torus.
The Square Kilometre Array will be a revolutionary instrument for the study of gas in the distant Universe. SKA1 will have sufficient sensitivity to detect and image atomic 21 cm HI in individual galaxies at significant cosmological distances, complementing ongoing ALMA imaging of redshifted high-J CO line emission and far-infrared interstellar medium lines such as [CII] 157.7 um. At frequencies below ~50 GHz, observations of redshifted emission from low-J transitions of CO, HCN, HCO+, HNC, H2O and CS provide insight into the kinematics and mass budget of the cold, dense star-forming gas in galaxies. In advance of ALMA band 1 deployment (35 to 52 GHz), the most sensitive facility for high-redshift studies of molecular gas operating below 50~GHz is the Karl G. Jansky Very Large Array (VLA). Here, we present an overview of the role that the SKA could play in molecular emission line studies during SKA1 and SKA2, with an emphasis on studies of the dense gas tracers directly probing regions of active star-formation.
The present work deals with irreversible Universal thermodynamics. The homogenous and isotropic flat model of the universe is chosen as open thermodynamical system and non-equilibrium thermodynamics comes into picture due to the mechanism of particle creation. For simplicity, entropy flow is considered only due to heat conduction. Further, due to Maxwell-Cattaneo modified Fourier law for non-equilibrium phenomenon, the temperature satisfies damped wave equation instead of heat conduction equation. Validity of generalized second law of thermodynamics (GSLT) has been investigated for Universe bounded by apparent or event horizon with cosmic substrutum as perfect fluid with constant or variable equation of state or interacting dark species. Finally, we have used three Planck data sets to constrain the thermal conductivity \lambda and the coupling parameter b^2. These constraints must be satisfied in order for GSLT to hold for Universe bounded by apparent or event horizons.
Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t)), t\in [0,S]$ be a Gaussian vector process and let $g(\boldsymbol{x}),\boldsymbol{x}\in\mathbb{R}^d$ be a continuous homogeneous function. In this paper we are concerned with the exact tail asymptotics of the chaos process $g(\boldsymbol{X}(t))+ h(t),t\in [0,S]$ with trend function $h$. Both scenarios $\boldsymbol{X}(t)$ is locally-stationary and $\boldsymbol{X}(t)$ is non-stationary are considered. Important examples include the product of Gaussian processes and chi-processes.
We prove three results on pure resolutions of vector bundles on projective spaces. First, we show that there are simple vector bundles of rank n on Pn with arbitrary homological dimension. We then analyze the pure resolutions given by the sheafification of the Koszul complex of a certain algebra and by the sheafification of the minimal free resolution of a compressed Gorenstein Artinian graded algebra, proving that their syzygies are simple vector bundles. Our main tool is a result originally established by Brambilla, for which we give an alternative proof using representations of quivers.
We present optical and millimetric data for 47 intermediate Hubble type spiral galaxies located either in dense environments or in the field. We compare correlations between global parameters, such as far-infrared luminosity, blue luminosity, and total molecular gas content, with other samples of galaxies, including normal galaxies, clusters and ultraluminous infrared galaxies. We find that overall our sample is a well defined subset of these other samples of galaxies.
Spin models that have been proposed to describe dimerized chains, ladders, two dimensional antiferromagnets, and other compounds are here studied when some spins are replaced by spinless vacancies, such as it occurs by $Zn$ doping. A small percentage of vacancies rapidly destroys the spin gap, and their presence induces enhanced antiferromagnetic correlations near those vacancies. The study is performed with computational techniques which includes Lanczos, world-line Monte Carlo, and the Density Matrix Renormalization Group methods. Since the phenomenon of enhanced antiferromagnetism is found to occur in several models and cluster geometries, a common simple explanation for its presence may exist. It is argued that the resonating-valence-bond character of the spin correlations at short distances of a large variety of models is responsible for the presence of robust staggered spin correlations near vacancies and lattice edges. The phenomenon takes place regardless of the long distance properties of the ground state, and it is caused by a ``pruning'' of the available spin singlets in the vicinity of the vacancies. The effect produces a broadening of the low temperature NMR signal for the compounds analyzed here. This broadening should be experimentally observable in the structurally dimerized chain systems   $Cu(NO_3)_2\cdot2.5H_2O$, $CuWO_4$, $(VO)_2P_2O_7$, and $Sr_{14}Cu_{24}O_{41}$, in ladder materials such as $Sr Cu_2 O_3$, in the spin-Peierls systems $CuGeO_3$ and $NaV_2 O_5$, and in several others since it is a universal effect common to a wide variety of models and compounds.
The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional spacetime and preserves gauge symmetry and Poincare symmetry in spite of the introduction of two mass scales, namely the ultraviolet (UV) cut-off $M_c$ and infrared (IR) cut-off $\mu_s$. It is shown that the dilation Ward identity which relates the three-point diagrams with the vacuum polarization diagrams gets the standard form of trace anomaly through quantum corrections in taking the consistent limit $M_c\to \infty$ and $\mu_s = 0$ which recovers the original integrals. This explicitly demonstrates that the loop regularization method is indeed a self-consistent regularization scheme which is applicable to the calculations not only for the chiral anomaly but also for the trace anomaly, at least at one-loop level. It is also seen that the consistency conditions which relates the tensor-type and scalar-type irreducible loop integrals (ILIs) are crucial for obtaining a consistent result. As a comparison, we also present the one-loop calculations by using the usual Pauli-Villars regularization and the dimensional regularization.
Semiconductor-metal hybrid structures can exhibit a very large geometrical magnetoresistance effect, the so-called extraordinary magnetoresistance (EMR) effect. In this paper, we analyze this effect by means of a model based on the finite element method and compare our results with experimental data. In particular, we investigate the important effect of the contact resistance $\rho_c$ between the semiconductor and the metal on the EMR effect. Introducing a realistic $\rho_c=3.5\times 10^{-7} \Omega{\rm cm}^2$ in our model we find that at room temperature this reduces the EMR by 30% if compared to an analysis where $\rho_c$ is not considered.
We study the regularity of solutions of elliptic fractional systems of order 2s, $s \in (0, 1)$, where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural conditions on the system we prove interior H\"older estimates in the spirit of [1]. Our results are stable in s allowing us to recover the classic results for elliptic systems due to S. Hildebrandt and K. Widman [6] and M. Wiegner [9].
Recently an intriguing transient AT 2018lqh, with only a day-scale duration and a high luminosity of $7\times 10^{42}\ {\rm erg\ s^{-1}}$, has been discovered. While several possibilities are raised on its origin, the nature of this transient is yet to be unveiled. We propose that a black hole (BH) with $\sim 30\, M_\odot$ forming from a rotating blue supergiant can generate a transient like AT 2018lqh. We find that this scenario can consistently explain the optical/UV emission and the tentative late-time X-ray detection, as well as the radio upper limits. If super-Eddington accretion onto the nascent BH powers the X-ray emission, continued X-ray observations may be able to test the presence of an accretion disk around the BH.
The recent discoveries of proximate quantum spin-liquid compounds and their potential application in quantum computing informs the search for new candidate materials for quantum spin-ice and spin-liquid physics. While the majority of such work has centered on members of the pyrochlore family due to their inherently frustrated linked tetrahedral structure, the rare-earth pyrogermanates also show promise for possible frustrated magnetic behavior. With the familiar stoichiometry $RE_2$Ge$_2$O$_7$, these compounds generally have tetragonal symmetry with a rare-earth sublattice built of a spiral of alternating edge and corner sharing rare-earth site triangles. Studies on Dy$_2$Ge$_2$O$_7$ and Ho$_2$Ge$_2$O$_7$ have shown tunable low temperature antiferromagnetic order, a high frustration index and spin-ice like dynamics. Here we use neutron diffraction to study magnetic order in Er$_2$Ge$_2$O$_7$ (space group $P4_{1}2_{1}2$ ) and find the lowest yet Ne\'el temperature in the pyrogermanates of 1.15 K. Using neutron powder diffraction we find the magnetic structure to order with $k = (0,0,0)$ ordering vector, magnetic space group symmetry $P4_{1}^{'}2_{1}2^{'}$ and a refined Er moment of $m = 8.1 \mu_B$ - near the expected value for the Er$^{3+}$ free ion. Provocatively, the magnetic structure exhibits similar 'local-Ising' behavior to that seen in the pyrocholres where the Er moment points up or down along the short Er-Er bond. Upon applying a magnetic field we find a first order metamagnetic transition at $\sim$ 0.35 T to a lower symmetry $P2_{1}^{'}2_{1}^{'}2$ structure. This magnetic transition involves an inversion of Er moments aligned antiparallel to the applied field describing a class I spin-flip type transition, indicating a strong local anisotropy at the Er site - reminiscent of that seen in the spin-ice pyrochlores.
We have observed a paramagnetic-to-ferromagnetic phase transition in short period InGaMnAs/InGaAs superlattices. The thicknesses of magnetic InGaMnAs layers in the structures studied was chosen to be 4 or 8 molecular layers (12 \AA or 24 \AA). The nonmagnetic InGaAs spacer layers are 12 \AA thick. The In content of InGaMnAs and InGaAs layers was chosen in such a way that magnetic layers were: deep potential wells, high potential barriers or shallow potential wells. For superlattices with 8 monolayer thick InGaMnAs magnetic layers and 4 monolayer thick InGaAs nonmagnetic spacers the temperatures of paramagnetic-to-ferromagnetic phase transition do not depend on the band offsets between InGaMnAs and InGaAs adjusted by the In content.