ShantanuT01/DACTYL-Pretraining huggingface dataset:
Hickson Compact Group (HCG) 16 is a prototypical compact group of galaxies, apparently in an intermediate stage of evolution, where its galaxies are losing gas to the intra-group medium (IGrM). The wide variety of ongoing process in HCG 16 make it an ideal case study for exploring which processes are likely to dominate the late stages of evolution in compact groups. In order to build a coherent picture of the evolution of this group we make use of the multi-wavelength data available, but focus particularly on HI as a tracer of interactions and evolutionary phase. We reprocess archival VLA L-band data of HCG 16 using the multi-scale CLEAN algorithm to accurately recover diffuse features. Despite the clear disruption of the HI component of HCG 16 we find that it is not globally HI deficient, even though HCG 16a and b have lost the majority of their HI and almost 50% of the group's HI is in the IGrM, including a 160 kpc long tail extending towards the SE. This study indicates that in the recent past (~1 Gyr) galaxies HCG 16a and b likely underwent major interactions that unbound gas without triggering significant star formation. This gas was then swept away by a high speed, close encounter with NGC 848. The starburst events HCG 16c and d have triggered galactic winds which, in the case of HCG 16d, appears to have disrupted its HI reservoir. The tidal features still connected to these galaxies indicate that more HI will soon be lost to the IGrM, while that which remains in the discs will likely be consumed by star formation episodes. This is expected to result in a collection of gas-poor galaxies embedded in a diffuse HI structure, which will gradually be evaporated by the UV background, resembling the final stage of the evolutionary model of compact groups. This work is accompanied by a complete workflow to reproduce the final data products, intended to improve reproducibility. (Abridged)
This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the $d$-dimensional Wiener process. We first obtain some verification theorems for diffusions, based on the Green kernel representation of the value function associated with the problem. Specializing to the multidimensional Wiener process, we apply the Martin boundary theory to obtain a set of tractable integral equations involving only harmonic functions that characterize the stopping region of the problem. These equations allow to formulate a discretization scheme to obtain an approximate solution. The approach is illustrated through the optimal stopping problem of a $d$-dimensional Wiener process with a positive definite quadratic form reward function.
In this paper we analyze a class of phase field models for the dynamics of phase transitions which extend the well-known Caginalp and Penrose-Fife models. Existence and uniqueness of the solution to the related initial boundary value problem are shown. Further regularity of the solution is deduced by exploiting the so-called regularizing effect. Then, the large time behavior of such a solution is studied and several convergence properties of the trajectory as time tends to infinity are discussed.
We present a method to find the decompositions of tripartite entangled pure states which are smaller than two successive Schmidt decompositions. The method becomes very simple when one of the subsystems is a qubit. In this particular case, we get a classification of states according to their decompositions. Furthermore, we also use this method to classify the entangled states that can be inter-converted through stochastic local operations and classical communication (SLOCC). More general tripartite systems are briefly discussed.
Lack of a consistent metric for generating rotating wormholes motivates us to present a new one endowed with interesting physical and geometrical properties. When combined with the generalized method of superposition of fields, which consists in attaching a form of matter to each moving frame, it generates massive and charged (charge without charge) two-fluid-sourced, massive and two-charged three-fluid-sourced, rotating as well as new static wormholes which, otherwise, can hardly be derived by integration. If the lapse function of the static wormhole is bounded from above, no closed timelike curves occur in the rotating counterpart. For positive energy densities dying out faster than $1/r$, the angular velocity includes in its expansion a correction term, to the leading one that corresponds to ordinary stars, proportional to $\ln r/r^4$. Such a term is not present in the corresponding expansion for the Kerr-Newman black hole. Based on this observation and our previous work, the dragging effects of falling neutral objects may constitute a substitute for other known techniques used for testing the nature of the rotating black hole candidates that are harbored in the center of galaxies. We discuss the possibility of generating ($n+1$)-fluid-sourced, $n$-charged, rotating as well as static wormholes.
Hot subdwarf stars with F-K main sequence binary companions have been known for decades, but the first orbital periods for such systems were published just recently. Current observations suggest that most have long periods, on the order of years, and that some are or once were hierarchical triple systems. As part of a survey with the Hobby-Eberly Telescope, we have been monitoring the radial velocities of several composite-spectra binaries since 2005 in order to determine their periods, velocities, and eccentricities. Here we present observations and orbital solutions for two of these systems, PG 1449+653 and PG 1701+359. Similar to the other sdB+F/G/K binaries with solved orbits, their periods are long, 909 d and 734 d, respectively, and pose a challenge to current binary population synthesis models of hot subdwarf stars. Intrigued by their relatively large systemic velocities, we also present a kinematical analysis of both targets and find that neither is likely a member of the Galactic thin disk.
We investigate the applicability of a random-matrix model to the description of non-collective excitations in heavy-ion reactions around the Coulomb barrier. To this end, we study fusion in the reaction $^{16}$O + $^{208}$Pb, taking account of the known non-collective excitations in the $^{208}$Pb nucleus. We show that the random-matrix model for the corresponding couplings reproduces reasonably well the exact calculations, obtained using empirical deformation parameters. This implies that the model may provide a powerful method for systems in which the non-collective couplings are not so well known.
We show the impact of the electroweak, and in one instance the QCD, one-loop corrections on the relic density of dark matter in the MSSM which is provided by the lightest neutralino. We cover here some of the most important scenarii: annihilation into fermions for a bino-like neutralino, annihilation involving gauge bosons in the case of a mixed neutralino, the neutralino-stau co-annihilation region and annihilation into a bottom quark pair. The corrections can be large and should be taken into account in view of the present and forthcoming increasing precision on the relic density measurements. Our calculations are made possible thanks to a newly developed automatic tool for the calculation at one-loop of any process in the MSSM. We have implemented a complete on-shell gauge invariant renormalisation scheme, with the possibility of switching to other schemes. In particular we will report on the impact of different renormalisation schemes for tan beta.
A series of Yb2Ti2O7 doped samples demonstrates the effects of off-stoichiometry on Yb2Ti2O7's structure, properties, and magnetic ground state via x-ray diffraction, specific heat, and magnetization measurements. A stoichiometric single crystal of Yb2Ti2O7 grown by the traveling solvent floating zone technique (solvent = 30 wt% rutile TiO2 and 70 wt% Yb2Ti2O7) is characterized and evaluated in light of this series. Our data shows that upon positive x doping, the cubic lattice parameter a increases and the Curie-Weiss temperature decreases. Heat capacity measurements of stoichiometric Yb2Ti2O7 samples exhibit a sharp, first-order peak at T = 268(4) mK that is suppressed in magnitude and temperature in samples doped off ideal stoichiometry. The full entropy recovered per Yb ion is 5.7 J/K ~ Rln2. Our work establishes the effects of doping on Yb2Ti2O7's physical properties, which provides further evidence indicating that previous crystals grown by the traditional floating zone method are doped off ideal stoichiometry. Additionally, we present how to grow high-quality colorless single crystals of Yb2Ti2O7 by the traveling solvent floating zone growth method.
We construct an effective topological Landau-Ginzburg theory that describes general SU(2) incompressible quantum liquids of strongly correlated particles in two spatial dimensions. This theory characterizes the fractionalization of quasiparticle quantum numbers and statistics in relation to the topological ground-state symmetries, and generalizes the Chern-Simons, BF and hierarchical effective gauge theories to an arbitrary representation of the SU(2) symmetry group. Our main focus are fractional topological insulators with time-reversal symmetry, which are treated as generalizations of the SU(2) quantum Hall effect.
Let $\mathbb{F}_q[t]$ denote the ring of polynomials over $\mathbb{F}_q$, the finite field of $q$ elements. We prove an estimate for fractional parts of polynomials over $\mathbb{F}_q[t]$ satisfying a certain divisibility condition analogous to that of intersective polynomials in the case of integers. We then extend our result to consider linear combinations of such polynomials as well.
High spatial resolution magnetic imaging has driven important developments in fields ranging from materials science to biology. However, to uncover finer details approaching the nanoscale with greater sensitivity requires the development of a radically new sensor technology. The nitrogen-vacancy (NV) defect in diamond has emerged as a promising candidate for such a sensor based on its atomic size and quantum-limited sensing capabilities afforded by long spin coherence times. Although the NV center has been successfully implemented as a nanoscale scanning magnetic probe at room temperature, it has remained an outstanding challenge to extend this capability to cryogenic temperatures, where many solid-state systems exhibit non-trivial magnetic order. Here we present NV magnetic imaging down to 6 K with 6 nm spatial resolution and 3 {\mu}T/$\sqrt{\mbox{Hz}}$ field sensitivity, first benchmarking the technique with a magnetic hard disk sample, then utilizing the technique to image vortices in the iron pnictide superconductor BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$ with $T_c$ = 30 K. The expansion of NV-based magnetic imaging to cryogenic temperatures represents an important advance in state-of-the-art magnetometry, which will enable future studies of heretofore inaccessible nanoscale magnetism in condensed matter systems.
We propose a proof for conjectures of Langlands, Shelstad and Waldspurger known as the fundamental lemma for Lie algebras and the non-standard fundamental lemma. The proof is based on a study of the decomposition of the l-adic cohomology of the Hitchin fibration into direct sum of simple perverse sheaves.
The second law of thermodynamics is asymmetric with respect to time as it says that the entropy of the universe must have been lower in the past and will be higher in the future. How this time-asymmetric law arises from the time-symmetric equations of motion has been the subject of extensive discussion in the scientific literature. The currently accepted resolution of the problem is to assume that the universe began in a low entropy state for an unknown reason. But the probability of this happening by chance is exceedingly small, if all microstates are assigned equal a-priori probabilities. In this paper, I explore another possible explanation, which is that our observations of the time-asymmetric increase of entropy could simply be the result of the way we assign a-priori probabilities differently to past and future events.
Vassiliev (finite type) invariants of knots can be described in terms of weight systems. These are functions on chord diagrams satisfying so-called 4-term relations. In the study of the sl2 weight system, it was shown that its value on a chord diagram depends on the intersection graph of the diagram rather than on the diagram itself. Moreover, it was shown that the value of this weight system on an intersection graph depends on the cy- cle matroid of the graph rather than on the graph itself. This result arose the question whether there is a natural way to introduce a 4-term relation on the space spanned by matroids, similar to the one for graphs. It happened however that the answer is negative: there are graphs having isomorphic cycle matroids such that applying the "second Vassiliev move" to a pair of corresponding vertices a;b of the graphs we obtain two graphs with nonisomorphic matroids.   The goal of the present paper is to show that the situation is different for binary delta-matroids: one can define both the first and the second Vassiliev moves for binary delta-matroids and introduce a 4-term relation for them in such a way that the mapping taking a chord diagram to its delta-matroid respects the corresponding 4-term relations. Moreover, this mapping admits a natural extension to chord diagrams on several circles, which correspond to singular links. Delta-matroids were introduced by A. Bouchet for the purpose of studying embedded graphs, whence their relationship with (multiloop) chord diagrams is by no means unexpected. Some evidence for the existence of such a relationship can be found, for example, the Tutte polynomial for embedded graphs has been introduced. It was shown that this polynomial depends on the delta-matroid of the embedded graph rather than the graph itself and satises the Vassilev 4-term relation.
Within the framework of Skyrme energy-density functional theory, the nucleus-nucleus potential is calculated and potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM$^{\ast}$, SkP, SIII, Ska and SLy4, which correspond to the different equation of state for the isospin symmetry nuclear matter. It is found that the nucleus-nucleus potential is associated with the collision orientation and Skyrme parameters. More repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter. The available data in the fusion-evaporation reaction of $^{48}$Ca+$^{238}$U are nicely reproduced with the SkM$^{\ast}$ parameter by implementing into the dinuclear system model.
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance is studied in a model with separable quadrupole-quadrupole residual interactions. The method of Wigner function moments is applied to derive the dynamical equations for angular momentum and quadrupole moment. Analytical expressions for energies, B(M1)- and B(E2)-values, sum rules and flow-patterns of both modes are found for arbitrary values of the deformation parameter. Some predictions for the case of superdeformation are given. The subtle nature of the phenomenon and its peculiarities are clarified.
Quarkonium production is a sensitive probe of the dynamics of hard scattering, which can `measure' the environment of the heavy quark pair after it is created in a hard process. Quarkonium hadroproduction data indicates that the produced pair experiences a secondary, hard interaction and then ceases to interact at a stage when the pair is still compact (compared to the size of the quarkonium wave function). These features differ from scenarios mostly discussed so far. An approach which relies on an early, perturbative rescattering of the pair with a comoving color field can explain many observed features, including the polarization, the $\chi_1/\chi_2$ ratio and the nuclear target $A$-dependence, which are difficult to understand otherwise.
This is an expository article on the averaged version of Colmez's conjecture, relating Faltings heights of CM abelian varieties to Artin L-functions. It is based on the author's lectures at the Current Developments in Mathematics conference held at Harvard in 2018.
While studying a characteristic number of manifolds we noticed that the calculation was simply computing a multiple of a multinomial coefficient. We were, at the time, interested in computing the greatest common divisor of these characteristic numbers, and from that came this fun and interesting number theory problem. In this short paper, I will give the answer to this problem, which gives the greatest common divisor of certain multinomial coefficients.
These notes are based on a lecture given at the 2016 Euclid Summer School in Narbonne. I will first give a quick overview of the concept of nuisance parameters in the context of large galaxy surveys. The second part will examine the case study of intrinsic alignments, a potential important contamination of weak lensing observables.
The finite momentum optical response $\sigma({\boldsymbol{q}},\omega)$ of graphene can be probed with the innovative technique of infrared nanoscopy where mid-infrared radiation is confined by an atomic force microscope cantilever tip. In contrast to conventional $q\sim 0$ optical absorption which primarily involves Dirac fermions with momentum near the Fermi momentum, $k\sim k_F$, for finite $q$, $\sigma({\boldsymbol{q}},\omega)$ has the potential to provide information on many body renormalizations and collective phenomena which have been found at small $k< k_F$ near the Dirac point in electron-doped graphene. For electron-electron interactions, the low energy excitation spectrum characterizing the incoherent part of the quasiparticle spectral function of Dirac electrons with $k\sim k_F$ consists of a flat, small amplitude background which scales with chemical potential and Fermi momentum. However, probing of the states with $k$ near $k=0$ will reveal plasmarons, a collective state of a charge carrier and a plasmon. These collective modes in graphene have recently been seen in angle-resolved photoemission spectroscopy and here we describe how they manifest in near field optics.
We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov's system of axioms. We show that this new measure verifies the usual properties of a probability; in particular, we treat the conditional hyperbolic probability and we prove the hyperbolic analogues of the multiplication theorem, of the law of total probability and of Bayes' theorem. Our probability may take values which are zero--divisors and we discuss carefully this peculiarity.
We report the serendipitous discovery of a collision ring galaxy, identified as 2MASX J06470249+4554022, which we have dubbed 'Auriga's Wheel', found in a SUPRIME-CAM frame as part of a larger Milky Way survey. This peculiar class of galaxies is the result of a near head-on collision between typically, a late type and an early type galaxy. Subsequent GMOS-N long-slit spectroscopy has confirmed both the relative proximity of the components of this interacting pair and shown it to have a redshift of 0.111. Analysis of the spectroscopy reveals that the late type galaxy is a LINER class Active Galactic Nuclei while the early type galaxy is also potentially an AGN candidate, this is very uncommon amongst known collision ring galaxies. Preliminary modeling of the ring finds an expansion velocity of ~200 kms^-1 consistent with our observations, making the collision about 50 Myr old. The ring currently has a radius of about 10 kpc and a bridge of stars and gas is also visible connecting the two galaxies.
The relativistic approach to electroweak properties of two-particle composite systems developed previously is generalized here to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. A special mathematical technique is used for the parametrization of matrix elements of electroweak current operators in terms of form factors. The parametrization is a realization of the generalized Wigner--Eckart theorem on the Poincar\'e group, form factors are corresponding reduced matrix elements and they have the sense of distributions (generalized functions). The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of electromagnetic current it also automatically satisfies the conservation law.
In this paper, we find an identity which connects the overpartition function and the function of Rogers--Ramanujan--Gordon type overpartitions by considering the weights and gaps. This identity can be seen as an analogue of the weighted identity of Alladi.
We performed timing and spectral analysis of multi-epoch Suzaku, XMM-Newton and NuSTAR observations of the ultraluminous X-ray source (ULX) Circinus ULX5, to put constraints on the mass of the central object and the accretion mode operating in this source. We aim to answer whether the source contains a stellar mass black hole with a super-Eddington accretion flow or an intermediate mass black hole accreting matter in a sub-Eddington mode. Moreover, we search for major observed changes in spectra and timing occur, and determine if they are associated with major structural changes in the disk, similar to those in black hole X-ray binaries. We performed timing and spectral analysis to study the relation between luminosity and inner disk temperature. We constructed the hardness ratio versus intensity diagram to reveal spectral state transitions in Circinus ULX5. Our spectral analysis revealed at least three distinctive spectral states of Circinus ULX5, in analogy to state transitions in Galactic black hole X-ray binaries. Disk-dominated spectra are found in high flux states and the power-law dominated spectra are found in lower flux states. The source was also observed in an intermediate state, where the flux was low, but spectrum is dominated by a disk component. Over eighteen years of collected data, ULX5 appeared two times in the high, three times in the low, and two times in the intermediate state. The fastest observed transition was $\sim$7 months. Our analysis suggests that the central object in Circinus ULX5 is a stellar mass BH ($<10\ \rm M_{\odot}$), or possibly a NS even though we do not detect pulsations in the lightcurves. Fractional variability amplitudes are consistent with state transitions in Circinus ULX5 wherein higher variability from the power law-like Comptonized emission gets suppressed in the thermal disk-dominated state.
In an earlier paper, Tatong and Suvarnamani explores the Diophantine equation $p^x + p^y = z^2$ for a prime number $p$. In that paper they find some solutions to the equation for $p=2, 3$. In this paper, we look at a general version of this equation and solve it completely.