ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a detailed analysis of dark matter halo shapes, studying how the distributions of ellipticity, prolateness and axial ratios evolve as a function of time and mass. With this purpose in mind, we analysed the results of three cosmological simulations, running an ellipsoidal halo finder to measure triaxial halo shapes. The simulations have different scales, mass limits and cosmological parameters, which allows us to ensure a good resolution and statistics in a wide mass range, and to investigate the dependence of halo properties on the cosmological model. We confirm the tendency of haloes to be prolate at all times, even if they become more triaxial going to higher redshifts. Regarding the dependence on mass, more massive haloes are also less spherical at all redshifts, since they are the most recent forming systems and so still retain memory of their original shape at the moment of collapse. We then propose a rescaling of the shape-mass relations, using the variable $\nu = \delta_{c}/\sigma$ to represent the mass, which absorbs the dependence on both cosmology and time, allowing to find universal relations between halo masses and shape parameters (ellipticity, prolateness and the axial ratios) which hold at any redshift. This may be very useful to determine prior distributions of halo shapes for observational studies.
The thermoelectric properties of halide perovskites $\mathrm{CsMI_3}$ (M=Sn and Pb) are investigated from a combination of first-principles calculations and semiclassical Boltzmann transport theory by considering both the electron and phonon transport. The electronic part is performed using a modified Becke and Johnson (mBJ) exchange potential, including spin-orbit coupling (SOC), while the phonon part is computed using generalized gradient approximation (GGA). It is found that SOC has remarkable detrimental effect on n-type power factor, while has a negligible influence in p-type doping, which can be explained by considering SOC effect on conduction and valence bands. Calculated results show exceptionally low lattice thermal conductivities in $\mathrm{CsSnI_3}$ and $\mathrm{CsPbI_3}$, and the corresponding room-temperature lattice thermal conductivity is 0.54 $\mathrm{W m^{-1} K^{-1}}$ and 0.25 $\mathrm{W m^{-1} K^{-1}}$. At 1000 K, the maximal figure of merit $ZT$ is up to 0.63 and 0.64 for $\mathrm{CsSnI_3}$ and $\mathrm{CsPbI_3}$ with scattering time $\tau$=$10^{-14}$ s, and the peak $ZT$ is 0.49 and 0.41 with $\tau$=$10^{-15}$ s. These results make us believe that $\mathrm{CsMI_3}$ (M=Sn and Pb) in perovskite structures may be potential thermoelectric materials.
Lattice model with long-range interaction of power-law type that is connected with difference of non-integer order is suggested. The continuous limit maps the equations of motion of lattice particles into continuum equations with fractional Grunwald-Letnikov-Riesz derivatives. The suggested continuum equations describe fractional generalizations of the gradient and integral elasticity. The proposed type of long-range interaction allows us to have united approach to describe of lattice models for the fractional gradient and fractional integral elasticity. Additional important advantages of this approach are the following: (1) It is possible to use this model of long-range interaction in numerical simulations since this type of interactions and the Grunwald-Letnikov derivatives are defined by generalized finite difference; (2) The suggested model of long-range interaction leads to an equation containing the sum of the Grunwald-Letnikov derivatives, which is equal the Riesz's derivative. This fact allows us to get particular analytical solutions of fractional elasticity equations.
A particular initial state for the construction of a perturbative QCD expansion is investigated. It is formed as a coherent superposition of zero momentum gluon pairs and shows Lorentz as well as global $SU(3)$ symmetries. The general form of the Wick theorem is discussed, and it follows that the gluon and ghost propagators determined by the proposed vacuum state, coincides with the ones used in an alternative of the usual perturbation theory proposed in a previous work, and reviewed here. Therefore, the ability of such a procedure of producing a finite gluon condensation parameter already in the first orders of perturbation theory is naturally explained. It also follows that this state satisfies the physicality condition of the BRST procedure in its Kugo and Ojima formulation. A brief review of the canonical quantization for gauge fields, developed by Kugo and Ojima, is done and the value of the gauge parameter $\alpha$ is fixed to $\alpha=1$ where the procedure is greatly simplified. Therefore, after assuming that the adiabatic connection of the interaction does not take out the state from the interacting physical space, the predictions of the perturbation expansion for the physical quantities, at the value $\alpha=1$, should have meaning. The validity of this conclusion solves the gauge dependence indeterminacy remained in the proposed perturbation expansion.
1.02-1.16 micron spectra (R ~ 7,000) of the gravitationally lensed QSO APM 08279+5255 at z_em=3.911 were obtained during the commissioning run of IRCS, the 1-5 micron near-infrared camera and spectrograph for the Subaru 8.2 m Telescope. Strong MgII doublet at 2976,2800 angstrom and FeII (2600 angstrom), FeII (2587 angstrom) absorption lines at z_abs=2.974 were clearly detected in the rest-frame UV spectra, confirming the presence of a damped Lyman-alpha system at the redshift as suggested by Petitjean et al. Also MgI (2853 angstrom) absorption line is probably detected. An analysis of the absorption lines including velocity decomposition was performed. This is a first detailed study of MgII absorption system at high redshift (z > 2.5) where the MgII doublet shifts into the near-infrared in the observer's frame.   The spectra of the lensed QSO pair A and B with 0.38 arcsec separation were resolved in some exposure frames under excellent seeing condition. We extracted the MgII doublet spectra of A and B separately. Although three velocity components (v ~ -28, +5, +45 km/s) are known to exist in this MgII system (Petitjean et al.), the v ~ +45 km/s absorption line was not detected toward source B, showing that the +45 km/s MgII cloud lies only in the line of sight to the source A. Our results suggests that the size of the MgII absorbing clouds is as small as 200 pc, which corresponds to the separation of A and B at the redshift of the absorber. This is the first direct detection of the small-scale structure of MgII clouds at high-redshift, confirming the estimated cloud sizes from photoionization model by Churchill and Charlton.
We study the evolution of a system of free fermions in one dimension under the simultaneous effects of coherent tunneling and stochastic Markovian noise. We identify a class of noise terms where a hierarchy of decoupled equations for the correlation functions emerges. In the special case of incoherent, nearest-neighbour hopping the equation for the two-point functions is solved explicitly. The Green's function for the particle density is obtained analytically and a timescale is identified where a crossover from ballistic to diffusive behaviour takes place. The result can be interpreted as a competition between the two types of conduction channels where diffusion dominates on large timescales.
We present a spectroscopic catalogue of 40 luminous starburst galaxies at z=0.7--1.7 (median z=1.3). 19 of these are submillimetre galaxies (SMGs) and 21 are submillimetre-faint radio galaxies (SFRGs). This sample helps to fill in the redshift desert at z=1.2--1.7 in previous studies as well as probing a lower luminosity population of galaxies. Radio fluxes are used to determine star-formation rates for our sample which range from around 50 to 500 M$_\odot$ yr$^{-1}$ and are generally lower than those in z$\sim$2 SMGs. We identify nebular [OII] 3727 emission in the rest-UV spectra and use the linewidths to show that SMGs and SFRGs in our sample have larger linewidths and therefore dynamical masses than optically selected star-forming galaxies at similar redshifts. The linewidths are indistinguishable from those measured in the z$\sim$2 SMG populations suggesting little evolution in the dynamical masses of the galaxies between redshift 1--2. [NeV] and [NeIII] emission lines are identified in a subset of the spectra indicating the presence of an active galactic nucleus (AGN). In addition, a host of interstellar absorption lines corresponding to transitions of MgII and FeII ions are also detected. These features show up prominently in composite spectra and we use these composites to demonstrate that the absorption lines are present at an average blueshift of $-240\pm$50 kms$^{-1}$ relative to the systemic velocities of the galaxies derived from [OII]. This indicates the presence of large-scale outflowing interstellar gas in these systems (Abridged)
Given a $D$-module $M$ generated by a single element, and a polynomial $f$, one can construct several $D$-modules attached to $M$ and $f$ and can define the notion of the (generalized) $b$-function following M. Kashiwara. These modules are closely related to the localization and the local cohomology of $M$. We show that the $b$-function, if it exists, controls these modules and present general algorithms for computing these modules and the $b$-function (if it exists) without any further assumptions. For these algorithms, we reformulate the localization algorithm for $D$-modules.
Here, we present a set of time-dependent 3D RMHD simulations of a M-dwarf star representative of AD Leo, which extend from the upper convection zone into the chromosphere. The 3D model atmospheres are characterized by a very dynamic and intermittent structure on small spatial and temporal scales and a wealth of physical processes, which by nature cannot be described by means of 1D static model atmospheres. Artificial observations of these models imply that a combination of complementary diagnostics such as Ca II lines and the continuum intensity from UV to millimeter wavelengths, probe various properties of the dynamics, thermal and magnetic structure of the photosphere and the chromosphere and thus provide measures of stellar activity, which can be compared to observations. The complicated magnetic field structure and its imprint in synthetic diagnostics may have important implications for the understanding and characterization of stellar activity and with it possibly for the evaluation of planetary habitability around active M-dwarf stars.
The circular peak set of a permutation $\sigma$ is the set $\{\sigma(i)\mid \sigma(i-1)<\sigma(i)>\sigma(i+1)\}$. Let $\mathcal{P}_n$ be the set of all the subset $S\subseteq [n]$ such that there exists a permutation $\sigma$ which has the circular set $S$. We can make the set $\mathcal{P}_n$ into a poset $\mathscr{P}_n$ by defining $S\preceq T$ if $S\subseteq T$ as sets. In this paper, we prove that the poset $\mathscr{P}_n$ is a simplicial complex on the vertex set $[3,n]$. We study the $f$-vector, the $f$-polynomial, the reduced Euler characteristic, the M$\ddot{o}$bius function, the $h$-vector and the $h$-polynomial of $\mathscr{P}_n$. We also derive the zeta polynomial of $\mathscr{P}_n$ and give the formula for the number of the chains in $\mathscr{P}_n$. By the poset $\mathscr{P}_n$, we define two algebras $\mathcal{A}_{\mathscr{P}_n}$ and $\mathcal{B}_{\mathscr{P}_n}$. We consider the Hilbert polynomials and the Hilbert series of the algebra $\mathcal{A}_{\mathscr{P}_n}$ and $\mathcal{B}_{\mathscr{P}_n}$.
We extensively study the localization and the quantum Hall effect in the Hofstadter butterfly, which emerges in a two-dimensional electron system with a weak two-dimensional periodic potential. We numerically calculate the Hall conductivity and the localization length for finite systems with the disorder in general magnetic fields, and estimate the energies of the extended levels in an infinite system. We obtain the Hall plateau diagram on the whole region of the Hofstadter butterfly, and propose a theory for the evolution of the plateau structure with increasing disorder. There we show that a subband with the Hall conductivity $n e^2/h$ has $|n|$ separated bunches of extended levels, at least for an integer $n \leq 2$. We also find that the clusters of the subbands with identical Hall conductivity, which repeatedly appear in the Hofstadter butterfly, have a similar localization property.
By combining the data from surveys for HI 21-cm absorption at various impact parameters in near-by galaxies, we report an anti-correlation between the 21-cm absorption strength (velocity integrated optical depth) and the impact parameter. Also, by combining the 21-cm absorption strength with that of the emission, giving the neutral hydrogen column density, we find no evidence that the spin temperature of the gas (degenerate with the covering factor) varies significantly across the disk. This is consistent with the uniformity of spin temperature measured across the Galactic disk. Furthermore, comparison with the Galactic distribution suggests that intervening 21-cm absorption preferentially arises in disks of high inclinations (near face-on). We also investigate the hypothesis that 21-cm absorption is favourably detected towards compact radio sources. Although there is insufficient data to determine whether there is a higher detection rate towards quasar, rather than radio galaxy, sight-lines, the 21-cm detections intervene objects with a mean turnover frequency of 5 x 10^8 Hz, compared to 1 x 10^8 Hz for the non-detections. Since the turnover frequency is anti-correlated with radio source size, this does indicate a preferential bias for detection towards compact background radio sources.
We propose a universal manipulation to obtain Seiberg-like dualities of 3d $\mathcal{N}=2$ general quiver gauge theories with unitary, symplectic and orthogonal gauge groups coupled to fundamental and bifundamental matter fields. We illustrate this with several examples of linear, circular and star-shaped quiver gauge theories. We examine the local operators in the theories by computing supersymmetric indices and also find precise matching for the proposed dualities as strong evidence. We also generalize the dualities in the presence of a boundary on which the theories obey $\mathcal{N}=(0,2)$ chiral half-BPS boundary conditions.
We discuss multiplicative properties of the binary quadratic form $a x^2 + b x y + c y^2$ by considering a ring of matrices which is closed under a triple product. We prove that the ring forms a ternary algebra in the sense of Hestenes, and then derive both multiplicative formulas for a large class of binary quadratic forms and a type of multiplication for points on a conic section which generalizes the algebra of rational points on the unit circle.
The {\em independence ratio} of a graph $G$ is defined by \[ \iota(G) := \sup_{X \subset V(G)} \frac{|X|}{\alpha(X)},\] where $\alpha(X)$ is the independence number of the subgraph of $G$ induced by $X$. The independence ratio is a relaxation of the chromatic number $\chi(G)$ in the sense that $\chi(G) \geq \iota(G)$ for every graph $G$, while for many natural classes of graphs these quantities are almost equal. In this paper, we address two old conjectures of Erd\H{o}s on cycles in graphs with large chromatic number and a conjecture of Erd\H{o}s and Hajnal on graphs with infinite chromatic number.
The one-particle distribution function is of importance both in non-relativistic and relativistic statistical physics. In the relativistic framework, Lorentz invariance is possibly its most fundamental property. The present article on the subject is a contrastive one: we review, discuss critically, and, when necessary, complete, the treatments found in the standard literature.
A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved numerically to display the structure of split Landau subbands as functions of both wave number and magnetic flux. The effects of pseudo-spin coupling and Landau subbands mixing by a strong scattering potential have been demonstrated. Additionally, we investigated the square barrier tunneling problem when magnetic field is present, as well as demonstrate the crucial difference in the modulated band structure between graphene and the twodimensional electron gas. The low-magnetic field regime is particularly interesting for Dirac fermions and has been discussed. Tunneling of Dirac electrons through a magnetic potential barrier has been investigated to complement the reported results on electrostatic potential scattering in the presence of an ambient magnetic field.
We consider the statistics of volume fluctuations in a one-dimensional classical gas of non-interacting particles confined by a piston, and subjected to an arbitrary external potential. We show that despite the absence of interactions between particles, volume fluctuations of the gas are non-Gaussian, and are described by generalized extreme value distributions. The continuous shape parameter of these distributions is related to the ratio between the force acting on the piston, and the force acting on the particles. Gaussian fluctuations are recovered in the strong compression limit, when the effect of the external potential becomes negligible. Consequences for the thermodynamics are also discussed.
Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis. We propose two compact bilinear representations with the same discriminative power as the full bilinear representation but with only a few thousand dimensions. Our compact representations allow back-propagation of classification errors enabling an end-to-end optimization of the visual recognition system. The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further research in compact pooling methods. Experimentation illustrate the utility of the proposed representations for image classification and few-shot learning across several datasets.
We propose to study a new type of Backward stochastic differential equations driven by a family of It\^o's processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.
We present a spectroscopic analysis of nearly 8000 late-type dwarfs in the Sloan Digital Sky Survey. Using the Halpha emission line as an activity indicator, we investigate the fraction of active stars as a function of spectral type and find a peak near type M8, confirming previous results. In contrast to past findings, we find that not all M7-M8 stars are active. We show that this may be a selection effect of the distance distributions of previous samples, as the active stars appear to be concentrated near the Galactic Plane. We also examine the activity strength (ratio of the luminosity emitted in Halpha to the bolometric luminosity) for each star, and find that the mean activity strength is constant over the range M0-M5 and declines at later types. The decline begins at a slightly earlier spectral type than previously found. We explore the effect that activity has on the broadband photometric colors and find no significant differences between active and inactive stars. We also carry out a search for subdwarfs using spectroscopic metallicity indicators, and find 60 subdwarf candidates. Several of these candidates are near the extreme subdwarf boundary. The spectroscopic subdwarf candidates are redder by \~0.2 magnitudes in g-r compared to disk dwarfs at the same r-i color.
We consider a queue where the server is the Euclidean space, and the customers are random closed sets (RACS) of the Euclidean space. These RACS arrive according to a Poisson rain and each of them has a random service time (in the case of hail falling on the Euclidean plane, this is the height of the hailstone, whereas the RACS is its footprint). The Euclidean space serves customers at speed 1. The service discipline is a hard exclusion rule: no two intersecting RACS can be served simultaneously and service is in the First In First Out order: only the hailstones in contact with the ground melt at speed 1, whereas the other ones are queued; a tagged RACS waits until all RACS arrived before it and intersecting it have fully melted before starting its own melting. We give the evolution equations for this queue. We prove that it is stable for a sufficiently small arrival intensity, provided the typical diameter of the RACS and the typical service time have finite exponential moments. We also discuss the percolation properties of the stationary regime of the RACS in the queue.
Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called the degenerate polylogarithm function. Then we construct new type degenerate Bernoulli polynomials and numbers, called degenerate poly-Bernoulli polynomials and numbers,by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Bernoulli numbers
Light curves of young star systems show photometric variability due to different kinematic, and physical processes. One of the main contributors to the photometric variability is the changing mass accretion rate, which regulates the interplay between the forming young star and the protoplanetary disk. We collected high-resolution spectroscopy in eight different epochs, as well as ground-based and space-borne multi-epoch optical and infrared photometry of WX Cha, an M0 binary system, with an almost edge-on disk (i = 87degrees) in the Chamaeleon I star-forming region. Spectroscopic observations cover 72 days, the ground-based optical monitoring covers 42 days while space-borne TESS photometry extends for 56 days. The multi-wavelength light curves exhibit quasi-periodic variability of 0.35 - 0.53 mag in the near-infrared, and of 1.3 mag in g band. We studied the variability of selected emission lines that trace the accretion, computed the accretion luminosity and the mass accretion rate using empirical relations and obtained values of the accretion luminosity between 1.6 and 3.2 Lsun and mass accretion rate between 3.31x10{-7} Msun/yr and 7.76x10^{-7} Msun/yr. Our results show that WX Cha is accreting at a rate larger than what is typical for T Tauri stars in the same star-forming region with the same stellar parameters. We theorize that this is due to the higher disk mass of WX Cha than what is usual for stars with similar stellar mass, and to the binary nature of the system. Daily changes in the accretion luminosity and in the extinction can explain the photometric variability.
The paper concerns with positive solutions of problems of the type $-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^*-1}$ in $\Omega\subseteq\mathbb{R}^N$, $N\ge 3$, $2^*={2N\over N-2}$, $2<p<2^*$. Here $\Omega$ can be an exterior domain, i.e. $\mathbb{R}^N\setminus\Omega$ bounded, or the whole of $\mathbb{R}^N$. The potential $a\in L^{N/2}_{\rm loc}(\mathbb{R}^N)$ is assumed to be strictly positive and such that there exists $\lim_{|x|\to\infty}a(x):=a_\infty$, with $a_\infty>0$; in particular $a\equiv {\rm const}$ is allowed. First, some existence results of ground state solutions are proved. Then the case $a(x)\ge a_\infty$ is considered, with $a(x)\not\equiv a_\infty$ or $\Omega\neq\mathbb{R}^N$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small $\varepsilon$. No hypotheses are assumed on the size of $\mathbb{R}^N\setminus\Omega$ and on $\|a-a_\infty\|_{L^{N/2}}$.