ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce the notion of log $p$-smoothness which weakens that of log-smoothness and that of having locally $p$-bases. We extend Berthelot's construction of arithmetic $D$-modules and some properties in this context.
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist large families of such waves that carry finite energy and exhibit an exponentially localized distribution of (nontrivial) vorticity. This is accomplished by combining ideas drawn from the theory of spike-layer solutions to singularly perturbed elliptic equations, with techniques from the study of steady solutions of the water wave problem.
Let K be an algebraically closed field of characteristic 2, and let X be a curve over K of genus g>1 and 2-rank r>0. For 2-subgroups S of the K-automorphism group Aut(X) of X, the Nakajima bound is |S| < 4g-3. For every g=2^h+1>8, we construct a curve X attaining the Nakajima bound and determine its relevant properties: X is a bielliptic curve with r=g, and its K-automorphism group has a dihedral K-automorphism group of order 4(g-1) which fixes no point in X. Moreover, we provide a classification of 2-groups S of K-automorphisms not fixing a point of X and such that |S|> 2g-1.
Black holes in dwarf/bulgeless galaxies play a crucial role in studying the co-evolution of galaxies and their central black holes. Identifying massive black holes in dwarf galaxies suggests that the growth of black holes could precede that of galaxies. However, some of the most intriguing candidate active galactic nuclei (AGN) in small galaxies have such low luminosities that the sample is vulnerable to contamination by other sources, such as supernova remnants. We re-analysed Chandra X-ray Observatory observations of candidate AGN in Henize 2-10 and NGC 4178, considering the potential signals of emission lines in the minimally-binned X-ray spectra. We find that hot plasma models, which are typical of supernova remnants, explain the observed spectra much better than simple power-law models, which are appropriate for AGN. We identify clear signals of X-ray lines in the faint X-ray source identified with the radio source in Henize 2-10 by Reines et al. 2016. Combining our work with the MUSE measurement of the ionization parameter in this region by Cresci et al. 2017 indicates that this radio and X-ray source is more likely a supernova remnant than an AGN. A similar analysis of the low-count X-ray spectrum of a candidate AGN in NGC 4178 shows that a hot plasma model is about seventeen times more probable than a simple power-law model. Our results indicate that investigation of X-ray spectra, even in a low-count regime, can be a crucial tool to identify thermally-dominated supernova remnants among AGN candidates.
We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like N^{theta}, being N the volume of the substrate and theta ranging from (1 - log 2/log3), for central target(s), to 1, for a single peripheral target.
An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number ($z$) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-$z$ limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the $2^N$-fold degeneracy of the local moments in the insulating phase. We show that the spinons are coupled to doublons/holons by a dissipative compact U(1) gauge field that is in the deconfined phase, stabilizing the spin-charge separated gapless spin liquid Mott insulator.
Most simulations of coronal mass ejections (CMEs) to date either focus on the interplanetary propagation of a giant plasma "blob" without paying too much attention to its origin and to the formation process or they focus on the complex evolution of the coronal magnetic field due to (sub-)photospheric motions which result in an eruption. Here, we present global simulations of CMEs where coronal motions are used to produce a realistic evolution of the coronal magnetic field and cause an eruption. We focus on active region 10069, which produced a number of eruptions in late August 2002, including the August 24, 2002 CME - a fast (~2000 km/s) eruption originating from W81-, as well as a slower eruption on August 22, 2002 (originating from W62). Using a three-dimensional magneto-hydrodynamic (MHD) simulation of these ejections with the Space Weather Modeling Framework (SWMF), we show how a realistic initiation mechanism enables us to study the deflection of the CME in the corona and in the heliosphere. Reconnection of the erupting magnetic field with that of neighboring streamers and active regions modify the solar connectivity of the field lines connecting to Earth and change the expected solar energetic particle fluxes. Comparing the results at 1 AU of our simulations with in situ observations by the ACE spacecraft, we propose an alternate solar origin for the shock wave observed at L1 on August 26.
We integrate numerically the nonlinear equation of motion for a collapsing spherical wavepacket in the context of theories that are expected to display behavior characteristic of classicalization. The classicalization radius sets the scale for the onset of significant deformations of the collapsing configuration, which result in the formation of shock fronts. A characteristic observable feature of the classicalization process is the creation of an outgoing field configuration that extends far beyond the classicalization radius. This feature develops before the deformed wavepacket reaches distances of the order of the fundamental scale. We find that in some models the scattering problem may not have real solutions over the whole space at late times. We determine the origin of this behavior and discuss the consistency of the underlying models.
Abell 1767 is a dynamically relaxed, cD cluster of galaxies with a redshift of 0.0703. Among 250 spectroscopically confirmed member galaxies within a projected radius of 2.5r_{200}, 243 galaxies (~ 97%) are spectroscopically covered by the Sloan Digital Sky Survey (SDSS). Based on this homogeneous spectral sample, the stellar evolutionary synthesis code, STARLIGHT, is applied to investigate the stellar populations and star formation histories (SFHs) of cluster galaxies. The star formation properties of galaxies, such as mean stellar ages, metallicities, stellar masses, and star formation rates (SFRs), are presented as the functions of local galaxy density. Strong environmental effect is found in the manner that massive galaxies in the high-density core region of cluster tend to have higher metallicities, longer mean stellar ages, and lower specific star formation rates (SSFRs), and their recent star formation activities have been remarkably suppressed. In addition, the correlations of the metallicity and SSFR with stellar mass are confirmed.
We consider the supersymmetric Calogero-Sutherland type N-particle problems in one dimension and show that the corresponding fermionic part can be identified with the generalized X-Y models in the presence of an inhomogeneous magnetic field. In particular we show that the generalized Haldane-Shastry models (with magnetic field) are themselves the fermionic partners of the Calogero-Sutherland type models. Several such models are discussed and a recipe is given for constructing spin models and finding their ground state energy from the corresponding N-particle problems.
The transverse momentum distribution of the diffractive final state provides an interesting test of models of diffractive deep-inelastic scattering at HERA. We present a comparison of several colour-singlet exchange models with thrust transverse momentum data from a recent H1 analysis. We also study the effect of constraints imposed on the kinematically-accessible phase space by data selection cuts and find that, as a result of the pseudo-rapidity cut which is used by H1 to select diffractive events, there is no dijet contribution at low transverse momenta. We are able to fit the large transverse momentum part of the data with a two-gluon dijet model. The results of this analysis are compared with a previous study of large pseudo-rapidity gap structure function data, and we discuss ways in which one might reconcile the results of the two analyses. We conclude that a significant small-$\beta$ 3-jet contribution is probably required to explain the data, and show that the combination of a two-gluon dijet model and an exponentially-decaying thrust transverse momentum distribution provides a good fit over the entire kinematic range of the thrust data.
A probabilistic construction for the solution of a general class of high order heat-type equations is constructed in terms of the scaling limit of random walks in the complex plane.
The quantity $T_0$, the cosmic microwave background (CMB) monopole, is an often neglected seventh parameter of the standard cosmological model. As well as its variation affecting the physics of the CMB, the measurement of $T_0$ is also used to calibrate the anisotropies, via the orbital dipole. We point out that it is easy to misestimate the effect of $T_0$ because the CMB anisotropies are conventionally provided in temperature units. In fact the anisotropies are most naturally described as dimensionless and we argue for restoring the convention of working with $\Delta T/T$ rather than $\Delta T$. As a free cosmological parameter, $T_0$ most naturally only impacts the CMB power spectra through late-time effects. Thus if we ignore the COBE-FIRAS measurement, current CMB data only weakly constrain $T_0$. Even ideal future CMB data can at best provide a percent-level constraint on $T_0$, although adding large-scale structure data will lead to further improvement. The FIRAS measurement is so precise that its uncertainty negligibly effects most, but not all, cosmological parameter inferences for current CMB experiments. However, if we eventually want to extract all available information from CMB power spectra measured to multipoles $\ell\simeq5000$, then we will need a better determination of $T_0$ than is currently available.
This paper reports the results of Suzaku observation of the spectral variation of the black hole binary LMCX-1 in the soft state. The observationwas carried out in 2009 from July 21 to 24. the obtained net count rate was $\sim$30 counts s$^{-1}$ in the 0.5--50 keV band with $\sim$10% peak-to-peak flux variation. The time-averaged X-ray spectrum cannot be described by a multi-color disk and single Compton component with its reflection, but requires additional Comptonized emissions. This double Compton component model allows a slightly larger inner radius of the multi-color disk, implying a lower spin parameter. Significant spectral evolution was observed above 8 keV along with a flux decrease on a timescale of $\sim$10$^4$--10$^5$ s. By spectral fitting, we show that this behavior is well explained by changes in the hard Comptonized emission component in contrast to the maintained disk and soft Comptonized emission.
We have studied magnetically frustrated Tb$_2$Sn$_2$O$_7$ by neutron diffraction and high resolution energy-resolved neutron scattering. At 0.1 K, we observe short range magnetic correlations with a typical scale of 4 \AA, close to the near neighbor distance between Tb$^{3+}$ ions. %(3.686 \AA), This short range order coexists with ferromagnetic correlations and long range spin ice order at the scales of 18 and 190 \AA, respectively. Spin dynamics was investigated at a time scale down to 10$^{-9}$s, by energy-resolved experiments on a backscattering spectrometer. We observe a freezing of the spin dynamics for all length-scales, with a strong slowing down of the spin fluctuations when long range order settles in. We discuss the spin fluctuations remaining in the ground state in comparison with previous data obtained by muon spectroscopy.
Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and provide a clear physical picture. Recent theoretical studies made a surprising discovery that in complex systems the symmetry of molecular forward/backward transition times with respect to local bias in the dynamics may be broken and it may take longer to go downhill than uphill. The physical origins of these phenomena remain not fully understood. Here we explore in more detail the microscopic features of the symmetry breaking in the forward/backward transition times by analyzing exactly solvable discrete-state stochastic models. In particular, we consider a specific case of two random walkers on four-sites periodic lattice as the way to represent the general systems with multiple pathways. It is found that the asymmetry in transition times depends on several factors that include the degree of deviation from equilibrium, the particle crowding and methods of measurements of dynamic properties. Our theoretical analysis suggests that the asymmetry in transition times can be explored experimentally for determining the important microscopic features of natural processes by quantitative measuring the local deviations from equilibrium and the degrees of crowding.
We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice experiments.
In the hierarchical scenario of structure formation, galaxy clusters are the ultimate virialised products in mass and time. Hot baryons in the intracluster medium (ICM) and cold baryons in galaxies inhabit a dark matter dominated halo. Internal processes, accretion, and mergers can perturb the equilibrium, which is established only at later times. However, the cosmic time when thermalisation is effective is still to be assessed. Here we show that massive clusters in the observed universe attained an advanced thermal equilibrium $\sim~1.8~\text{Gyr}$ ago, at redshift $z =0.14\pm0.06$, when the universe was $11.7\pm0.7~\text{Gyr}$ old. Hot gas is mostly thermalised after the time when cosmic densities of matter and dark energy match. We find in a statistically nearly complete and homogeneous sample of 120 clusters from the {\it Planck} Early Sunyaev-Zel'dovich (ESZ) sample that the kinetic energy traced by the galaxy velocity dispersion is a faithful probe of the gravitational energy since a look back time of at least $\sim5.4~\text{Gyr}$, whereas the efficiency of hot gas in converting kinetic to thermal energy, as measured through X-ray observations in the core-excised area within $r_{500}$, steadily increases with time. The evolution is detected at the $\sim 98$ per cent probability level. Our results demonstrate that halo mass accretion history plays a larger role for cluster thermal equilibrium than radiative physics. The evolution of hot gas is strictly connected to the cosmic structure formation.
We conduct a search for periodic emission in the very high-energy gamma-ray band (VHE; E > 100 GeV) from a total of 13 pulsars in an archival VERITAS data set with a total exposure of over 450 hours. The set of pulsars includes many of the brightest young gamma-ray pulsars visible in the Northern Hemisphere. The data analysis resulted in non-detections of pulsed VHE gamma rays from each pulsar. Upper limits on a potential VHE gamma-ray flux are derived at the 95% confidence level above three energy thresholds using two methods. These are the first such searches for pulsed VHE emission from each of the pulsars, and the obtained limits constrain a possible flux component manifesting at VHEs as is seen for the Crab pulsar.
Polar Crown Filaments (PCFs) form above the magnetic polarity inversion line, which separates the unipolar polar fields and the nearest dispersed fields from trailing part of active regions with opposite polarity. The statistical properties of PCFs are correlated with the solar cycle. Therefore, study of PCFs plays an important role in understanding the variation of solar cycle, especially the prolonged cycle 23 and the current "abnormal" solar cycle 24. In this study, we investigate PCFs using full disk H{\alpha} data from 1973 to early 2018, recorded by Kanzelhohe Solar Observatory (KSO) and Big Bear Solar Observatory (BBSO), in digital form from 1997 to 2018 and in 35 mm film (digitized) from 1973 to 1996. PCFs are identified manually because their segmented shape and close-to-limb location were not handled well by automatical detections in several previous studies. Our results show that the PCFs start to move poleward at the beginning of each solar cycle. When the PCFs approach to the maximum latitude, the polar field strength reduces to zero followed by a reversal. The migration rates are about 0.4 to 0.7 degree per Carrington rotation, with clear N-S asymmetric pattern. In cycles 21 and 23, the PCFs in the northern hemisphere migrate faster than those in the southern hemisphere. However, in the "abnormal" cycle 24, the southern PCFs migrate faster, which is consistent with other observations of magnetic fields and radio emission. In addition, there are more days in cycle 23 and 24 without PCFs than in the previous cycles.
We introduce \textsc{Gizmo-Simba}, a new suite of galaxy cluster simulations within \textsc{The Three Hundred} project. \textsc{The Three Hundred} consists of zoom re-simulations of 324 clusters with $M_{200}\gtrsim 10^{14.8}M_\odot$ drawn from the MultiDark-Planck $N$-body simulation, run using several hydrodynamic and semi-analytic codes. The \textsc{Gizmo-Simba} suite adds a state-of-the-art galaxy formation model based on the highly successful {\sc Simba} simulation, mildly re-calibrated to match $z=0$ cluster stellar properties. Comparing to \textsc{The Three Hundred} zooms run with \textsc{Gadget-X}, we find intrinsic differences in the evolution of the stellar and gas mass fractions, BCG ages, and galaxy colour-magnitude diagrams, with \textsc{Gizmo-Simba} generally providing a good match to available data at $z \approx 0$. \textsc{Gizmo-Simba}'s unique black hole growth and feedback model yields agreement with the observed BH scaling relations at the intermediate-mass range and predicts a slightly different slope at high masses where few observations currently lie. \textsc{Gizmo-Simba} provides a new and novel platform to elucidate the co-evolution of galaxies, gas, and black holes within the densest cosmic environments.
We consider critical points of the geometric obstacle problem on vectorial maps $u: \mathbb{B}^2 \subset \mathbb{R}^2 \to \mathbb{R}^N$ \[   \int_{\mathbb{B}^2} |\nabla u|^2 \quad \mbox{subject to $u \in \mathbb{R}^N \backslash \mathbb{B}^N(0)$}. \] Our main result is $C^{1,\alpha}$-regularity for any $\alpha < 1$.   Technically, we split the map $u=\lambda v$, where $v: \mathbb{B}^2 \to \mathbb{S}^{N-1}$ is the vectorial component and $\lambda = |u|$ the scalar component measuring the distance to the origin. While $v$ satisfies a weighted harmonic map equation with weight $\lambda^2$, $\lambda$ solves the obstacle problem for \[   \int_{\mathbb{B}^2} |\nabla \lambda|^2+\lambda^2 |\nabla v|^2, \quad \mbox{subject to $\lambda \geq 1$}. \] where $|\nabla v|^2 \in L^1(\mathbb{B}^2)$. We then play ping-pong between the increases in the regularity of $\lambda$ and $v$ to obtain finally the $C^{1,\alpha}$-result.
The effects of saturation and unitarization for hadron-hadron scattering at LHC energies are explored in several models. It is shown that different choices of saturation parameters lead to sizable differences in the energy dependence of total cross sections, and to dramatic changes in elastic differential cross sections.
We show any matrix of rank $r$ over $\mathbb{F}_q$ can have $\leq \binom{r}{k}(q-1)^k$ distinct columns of weight $k$ if $ k \leq O_q(\sqrt{\log r})$ (up to divisibility issues), and $\leq \binom{r}{k}(q-1)^{r-k}$ distinct columns of co-weight $k$ if $k \leq O_q(r^{2/3})$. This shows the natural examples consisting of only $r$ rows are optimal for both, and the proofs will recover some form of uniqueness of these examples in all cases.
Place recognition is one of the most fundamental topics in computer vision and robotics communities, where the task is to accurately and efficiently recognize the location of a given query image. Despite years of wisdom accumulated in this field, place recognition still remains an open problem due to the various ways in which the appearance of real-world places may differ. This paper presents an overview of the place recognition literature. Since condition invariant and viewpoint invariant features are essential factors to long-term robust visual place recognition system, We start with traditional image description methodology developed in the past, which exploit techniques from image retrieval field. Recently, the rapid advances of related fields such as object detection and image classification have inspired a new technique to improve visual place recognition system, i.e., convolutional neural networks (CNNs). Thus we then introduce recent progress of visual place recognition system based on CNNs to automatically learn better image representations for places. Eventually, we close with discussions and future work of place recognition.
In 1980, Albertson and Berman introduced partial coloring. In 2000, Albertson, Grossman, and Haas introduced partial list coloring. Here, we initiate the study of partial coloring for an insightful generalization of list coloring introduced in 2015 by Dvo\v{r}\'{a}k and Postle, DP-coloring (or correspondence coloring). We consider the DP-coloring analogue of the Partial List Coloring Conjecture, which generalizes a natural bound for partial coloring. We show that while this partial DP-coloring conjecture does not hold, several results on partial list coloring can be extended to partial DP-coloring. We also study partial DP-coloring of the join of a graph with a complete graph, and we present several interesting open questions.
Chiral molecules with broken parity symmetries can be modeled as quantum systems with cyclic-transition structures. By using these novel properties, we design two-step laser pulses to distinguish left- and right-handed molecules from the enantiomers. After the applied pulse drivings, one kind chiral molecules are trapped in coherent population trapping state, while the other ones are pumped to the highest states for ionizations. Then, different chiral molecules can be separated.