ShantanuT01/DACTYL-Pretraining huggingface dataset:
The most general coordinates transformations that allow for the exact separation of the kinetic energy operator of a quantum many-body system into total center of mass kinetic energy and internal kinetic energy are found and discussed. We find i) that the suitable transformations, depending on the number of particles, have a certain number of free parameters and this allows for the generalization of the Jacobi coordinates to a much larger class of coordinates with the same properties and ii) that there is a new, uncommon, additive group structure hidden in the transformation matrices that is connected to certain geometric properties of the set of coordinates.
Using the Hubble Space Telescope/Wide Field Camera 3 imaging data and multi-wavelength photometric catalog, we investigated the dust temperature of passively evolving and star-forming galaxies at 0.2<z<1.0 in the CANDELS fields. We estimated the stellar radiation field by low-mass stars from the stellar mass and surface brightness profile of these galaxies and then calculated their steady-state dust temperature. At first, we tested our method using nearby early-type galaxies with the deep FIR data by the Herschel Virgo cluster survey and confirmed that the estimated dust temperatures are consistent with the observed temperatures within the uncertainty. We then applied the method to galaxies at 0.2<z<1.0, and found that most of passively evolving galaxies with Mstar > 10^{10} Msun have a relatively high dust temperature of Tdust > 20 K, for which the formation efficiency of molecular hydrogen on the surface of dust grains in the diffuse ISM is expected to be very low from the laboratory experiments. The fraction of passively evolving galaxies strongly depends on the expected dust temperature at all redshifts and increases rapidly with increasing the temperature around Tdust ~ 20 K. These results suggest that the dust heating by low-mass stars in massive galaxies plays an important role for the continuation of their passive evolution, because the lack of the shielding effect of the molecular hydrogen on the UV radiation can prevent the gas cooling and formation of new stars.
We study finite $p$-subgroups of birational automorphism groups. By virtue of boundedness theorem of Fano varieties, we prove that there exists a constant $R(n)$ such that a rationally connected variety of dimension $n$ over an algebraically closed field is rational if its birational automorphism group contains a $p$-subgroups of maximal rank for $p > R(n)$. Some related applications on Jordan property are discussed.
We study the following nonlinear Schr\"odinger equation $$-\Delta u + V(x) u = g(x,u),$$ where V and g are periodic in x. We assume that 0 is a right boundary point of the essential spectrum of $-\Delta+V$. The superlinear and subcritical term g satisfies a Nehari type monotonicity condition. We employ a Nehari manifold type technique in a strongly indefitnite setting and obtain the existence of a ground state solution. Moreover we get infinitely many geometrically distinct solutions provided that g is odd.
We consider the chiral field model of the source of the Kerr-Newman (KN) solution and obtain that it represents a supersymmetric spinning soliton, bounded by the chiral domain wall (DW) of the ellipsoidal form. The known method for transformation of the planar DW to Bogomolnyi form we generalize to the curved DW-bubble adapted to the Kerr coordinate system and obtain the supersymmetric BPS-saturated source of the KN solution, having some remarkable features, in particular, the quantum angular momentum. The main new result is that the source forms a breather, i.e. the DW-antiDW combination. Taking into account that the KN solution describes the spinning particles with gyromagnetic ratio g = 2, as that of the Dirac electron, we touch the problem of the compatibility of the spinning particles with gravity.
We perform an unmodeled search for persistent, directional gravitational wave (GW) sources using data from the first and second observing runs of Advanced LIGO. We do not find evidence for any GW signals. We place limits on the broadband GW flux emitted at 25~Hz from point sources with a power law spectrum at $F_{\alpha,\Theta} <(0.05-25)\times 10^{-8} ~{\rm erg\,cm^{-2}\,s^{-1}\,Hz^{-1}}$ and the (normalized) energy density spectrum in GWs at 25 Hz from extended sources at $\Omega_{\alpha}(\Theta) <(0.19-2.89)\times 10^{-8} ~{\rm sr^{-1}}$ where $\alpha$ is the spectral index of the energy density spectrum. These represent improvements of $2.5-3\times$ over previous limits. We also consider point sources emitting GWs at a single frequency, targeting the directions of Sco X-1, SN 1987A, and the Galactic Center. The best upper limits on the strain amplitude of a potential source in these three directions range from $h_0 < (3.6-4.7)\times 10^{-25}$, 1.5$\times$ better than previous limits set with the same analysis method. We also report on a marginally significant outlier at 36.06~Hz. This outlier is not consistent with a persistent gravitational-wave source as its significance diminishes when combining all of the available data.
Perturbation techniques can be used as an alternative to supercomputer calculations in calculating gravitational radiation emitted by colliding black holes, provided the process starts with the black holes close to each other. We give a summary of the method and of the results obtained for various initial configurations, both axisymmetric and without symmetry: Initially static, boosted towards each other, counter-rotating, or boosted at an angle (pseudo-inspiral). Where applicable, we compare the perturbation results with supercomputer calculations.
The kinematics, structure, and stellar population properties in the centers of two early-type spiral galaxies of the Leo Triplet, NGC 3623 and NGC 3627, are studied by means of integral-field spectroscopy. Unlike our previous targets, NGC 3384/NGC 3368 in the Leo I group and NGC 5574/NGC 5576 in LGG379, NGC 3623 and NGC 3627 do not appear to experience a synchronous evolution. The mean ages of their circumnuclear stellar populations are quite different, and the magnesium overabundance of the nucleus in NGC 3627 is evidence for a very brief last star formation event 1 Gyr ago whereas the evolution of the central part of NGC 3623 looks more quiescent. In the center of NGC 3627 we observe noticeable gas radial motions, and the stars and the ionized gas in the center of NGC 3623 demonstrate more or less stable rotation. However, NGC 3623 has a chemically distinct core -- a relic of a past star formation burst -- which is shaped as a compact, dynamically cold stellar disk with a radius of about 250-350 pc which has been formed not later than 5 Gyr ago.
In this $\ll$ contribution we address the question to what extent surface charges affect contact-mode scanning force microscopy measurements. % We therefore designed samples where we could generate localized electric field distributions near the surface as and when required. % We performed a series of experiments where we varied the load of the tip, the stiffness of the cantilever and the hardness of the sample surface. % It turned out that only for soft cantilevers could an electrostatic interaction between tip and surface charges be detected, irrespective of the surface properties, i.\,e. basically regardless its hardness. % We explain these results through a model based on the alteration of the tip-sample potential by the additional electric field between charged tip and surface charges.
An association scheme is called skew-symmetric if it has no symmetric adjacency relations other than the diagonal one. In this paper, we study 4-class skew-symmetric association schemes. In J. Ma [On the nonexistence of skew-symmetric amorphous association schemes, submitted for publication], we discovered that their character tables fall into three types. We now determine their intersection matrices. We then determine the character tables and intersection numbers for 4-class skew-symmetric pseudocyclic association schemes, the only known examples of which are cyclotomic schemes. As a result, we answer a question raised by S. Y. Song [Commutative association schemes whose symmetrizations have two classes, J. Algebraic Combin. 5(1) 47-55, 1996]. We characterize and classify 4-class imprimitive skew-symmetric association schemes. We also prove that no 2-class Johnson scheme can admit a 4-class skew-symmetric fission scheme. Based on three types of character tables above, a short list of feasible parameters is generated.
We study the equilibrium of pressure truncated, filamentary molecular clouds that are threaded by rather general helical magnetic fields. We first derive a new virial equation appropriate for magnetized filamentary clouds, which includes the effects of non-thermal motions and the turbulent pressure of the surrounding ISM. When compared with the data, we find that many filamentary clouds have a mass per unit length that is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing such clouds.   We also develop exact numerical MHD models of filamentary molecular clouds with more general helical field configurations than have previously been considered. We also examine the effects of the equation of state by comparing ``isothermal'' filaments, with constant total (thermal plus turbulent) velocity dispersion, with equilibria constructed using a logatropic equation of state.   We perform a Monte Carlo exploration of our parameter space to determine which choices of parameters result in models that agree with the available observational constraints. We find that both equations of state result in equilibria that agree with the observational results. Moreover, we find that models with helical fields have more realistic density profiles than either unmagnetized models or those with purely poloidal fields; we find that most isothermal models have density distributions that fall off as r^{-1.8} to r^{-2}, while logatropes have density profiles that range from r^{-1} to r^{-1.8}. We find that purely poloidal fields produce filaments with steep density gradients that not allowed by the observations.
We study the total density distribution in the central regions ($<\, 1$ effective radius, $R_{\rm e}$) of early-type galaxies (ETGs), using data from the SPIDER survey. We model each galaxy with two components (dark matter halo + stars), exploring different assumptions for the dark matter (DM) halo profile, and leaving stellar mass-to-light ($M_{\rm \star}/L$) ratios as free fitting parameters to the data. For a Navarro et al. (1996) profile, the slope of the total mass profile is non-universal. For the most massive and largest ETGs, the profile is isothermal in the central regions ($\sim R_{\rm e}/2$), while for the low-mass and smallest systems, the profile is steeper than isothermal, with slopes similar to those for a constant-M/L profile. For a concentration-mass relation steeper than that expected from simulations, the correlation of density slope with mass tends to flatten. Our results clearly point to a "non-homology" in the total mass distribution of ETGs, which simulations of galaxy formation suggest may be related to a varying role of dissipation with galaxy mass.
We summarize the results of our ongoing investigation of the chemical abundances in the Sagittarius Dwarf Spheroidal Galaxy (Sgr dSph) and in the Canis Major Overdensity (CMa). 12 RGB stars were analyzed in the Sgr dSph, plus 5 in the associated globular Terzan 7, together with three CMa candidate members. Detailed abundances have been derived for up to 23 elements from Oxygen to Europium.
We have performed the largest ever particle simulation of a Milky Way-sized dark matter halo, and present the most comprehensive convergence study for an individual dark matter halo carried out thus far. We have also simulated a sample of 6 ultra-highly resolved Milky-way sized halos, allowing us to estimate the halo-to-halo scatter in substructure statistics. In our largest simulation, we resolve nearly 300,000 gravitationally bound subhalos within the virialized region of the halo. Simulations of the same object differing in mass resolution by factors up to 1800 accurately reproduce the largest subhalos with the same mass, maximum circular velocity and position, and yield good convergence for the abundance and internal properties of dark matter substructures. We detect up to four generations of subhalos within subhalos, but contrary to recent claims, we find less substructure in subhalos than in the main halo when regions of equal mean overdensity are compared. The overall substructure mass fraction is much lower in subhalos than in the main halo. Extrapolating the main halo's subhalo mass spectrum down to an Earth mass, we predict the mass fraction in substructure to be well below 3% within 100 kpc, and to be below 0.1% within the Solar Circle. The inner density profiles of subhalos show no sign of converging to a fixed asymptotic slope and are well fit by gently curving profiles of Einasto form. The mean concentrations of isolated halos are accurately described by the fitting formula of Neto et al. down to maximum circular velocities of 1.5 km/s, an extrapolation over some 5 orders of magnitude in mass. However, at equal maximum circular velocity, subhalos are more concentrated than field halos, with a characteristic density that is typically ~2.6 times larger and increases towards the halo centre.
In this paper, we study an anisotropic universe model with Bianchi-I metric using Joint Light-curve Analysis (JLA) sample of type Ia supernovae (SNe Ia). Because light-curve parameters of SNe Ia vary with different cosmological models and SNe Ia samples, we fit the SNe Ia light-curve parameters and cosmological parameters simultaneously employing Markov Chain Monte Carlo method. Therefore, the results on the amount of deviation from isotropy of the dark energy equation of state ($\delta$), and the level of anisotropy of the large-scale geometry ($\Sigma_0$) at present, are totally model-independent. The constraints on the skewness and cosmic shear are $-0.101<\delta<0.071$ and $-0.007<\Sigma_0<0.008$. This result is consistent with a standard isotropic universe ($\delta=\Sigma_0=0$). However, a moderate level of anisotropy in the geometry of the Universe and the equation of state of dark energy, is allowed. Besides, there is no obvious evidence for a preferred direction of anisotropic axis in this model.
We prove an equidistribution result for Hecke operators acting on the basic stratum of certain Shimura varieties. We relate the rate of convergence to the bounds from the Ramanujan conjecture of certain cuspidal automorphic representations on Gl_n for which this conjecture is known, and therefore we obtain optimal estimates on the rate of convergence.
We present spectroscopy of the host of GRB 051022 with GMOS nod and shuffle on Gemini South and NIRSPEC on Keck II. We determine a metallicity for the host of log(O/H)+12 = 8.77 using the R23 method (Kobulnicky & Kewley 2004 scale) making this the highest metallicity long burst host yet observed. The galaxy itself is unusually luminous for a LGRB host with a rest frame B band absolute magnitude -21.5 and has the spectrum of a rapidly star-forming galaxy. Our work raises the question of whether other dark burst hosts will show high metallicities.
This paper has a pedagogical introduction. We describe the correct method for performing Monte Carlo simulations of Ising model systems with spin greater than one half. Correct and incorrect procedures are clearly outlined and the consequences of using the incorrect procedure are shown. The difference between Kawasaki and Glauber dynamics is then outlined and both methods are applied to the antiferromagnetic square and triangular lattices for S =1.
We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E11. We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincar\'e group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle.
We studied the magnetic ordering of thin films and bulk crystals of rutile RuO$_2$ using resonant X-ray scattering across the Ru L$_2$ absorption edge. Combining polarization analysis and azimuthal-angle dependence of the magnetic Bragg signal, we have established the presence of G-type antiferromagnetism in RuO$_2$ with T$_N$ $>$ 300 K. In addition to revealing a spin-ordered ground state in the simplest ruthenium oxide compound, the persistence of magnetic order even in nanometer-thick films lays the ground for potential applications of RuO$_2$ in antiferromagnetic spintronics.
In this work, we study higher bottomonia up to the $nL=8S$, $6P$, $5D$, $4F$, $3G$ multiplets using the modified Godfrey-Isgur (GI) model, which takes account of color screening effects. The calculated mass spectra of bottomonium states are in reasonable agreement with the present experimental data. Based on spectroscopy, partial widths of all allowed radiative transitions, annihilation decays, hadronic transitions, and open-bottom strong decays of each state are also evaluated by applying our numerical wave functions. Comparing our results with the former results, we point out difference among various models and derive new conclusions obtained in this paper. Notably, we find a significant difference between our model and the GI model when we study $D, F$, and $G$ and $n\ge 4$ states. Our theoretical results are valuable to search for more bottomonia in experiments, such as LHCb, and forthcoming Belle II.
The applications of the recent results obtained in the theory of generalized Lambert functions, to the mean field theory of ferromagnetism are presented. As a consequence, all the predictions of the Weiss theory of ferromagnetism can be explicitly and exactly formulated. In several quantum mechanical problems involving delta function potentials, the solutions of the transcendental eigenvalue equations are expressed in terms of two parameters generalized Lambert functions. Some others, till unnoticed examples of eigenvalue equations whose solutions can be written using the Lambert W function, are also presented.
We classify potential cosmic strings according to the topological charge measurable outside the string core. We conjecture that in string theory it is this charge that governs the stability of long strings. This would imply that the SO(32) heterotic string can have endpoints, but not the E_8 x E_8 heterotic string. We give various arguments in support of this conclusion.
Ohmic currents induced prior to decoupling are investigated in a standard transport model accounting both for the expansion of the background geometry as well as of its relativistic inhomogeneities. The relative balance of the Ohmic electric fields in comparison with the Hall and thermoelectric contributions is specifically addressed. The impact of the Ohmic currents on the evolution of curvature perturbations is discussed numerically and it is shown to depend explicitly upon the evolution of the conductivity.
We observed the Rapid Burster with Chandra when it was in the 'banana' state that usually precedes the type-II X-ray bursting 'island' state for which the source is particularly known. We employed the High-Energy Transmission Grating Spectrometer in combination with the ACIS-S detector in continuous clocking mode. The observation yielded 20 thermonuclear type-I X-ray bursts emitted from the neutron star surface with recurrence times between 0.9 and 1.2 hr, and an e-folding decay time scale of 1 min. We searched for narrow spectral features in the burst emission that could constrain the composition of the ashes of the nuclear burning and the compactness of the neutron star, but found none. The upper limit on the equivalent width of narrow absorption lines between 2 and 6 keV is between 5 and 20 eV (single trial 3 sigma confidence level) and on those of absorption edges between 150 and 400 eV. The latter numbers are comparable to the levels predicted by Weinberg, Bildsten & Schatz (2006) for Eddington-limited thermonuclear bursts.
We study the evolution of galaxy rest-frame ultraviolet (UV) colors in the epoch 4 < z < 8. We use new wide-field near-infrared data in GOODS-S from the CANDELS, HUDF09 and ERS programs to select galaxies via photometric redshift measurements. Our sample consists of 2812 candidate galaxies at z > 3.5, including 113 at z = 7 to 8. We fit the observed spectral energy distribution to a suite of synthetic stellar population models, and measure the value of the UV spectral slope (beta) from the best-fit model spectrum. The median value of beta evolves significantly from -1.82 (+0.00,-0.04) at z = 4, to -2.37 (+0.26,-0.06) at z = 7. Additionally, we find that faint galaxies at z = 7 have beta = -2.68 (+0.39,-0.24) (~ -2.4 after correcting for observational bias); this is redder than previous claims in the literature, and does not require "exotic" stellar populations to explain their colors. This evolution can be explained by an increase in dust extinction, with the timescale consistent with low-mass AGB stars forming the bulk of the dust. We find no significant (< 2-sigma) correlation between beta and M_UV when measuring M_UV at a consistent rest-frame wavelength of 1500 A. This is particularly true at bright magnitudes, though our results do show evidence for a weak correlation at faint magnitudes when galaxies in the HUDF are considered separately, hinting that dynamic range in sample luminosities may play a role. We do find a strong correlation between beta and the stellar mass at all redshifts, in that more massive galaxies exhibit redder colors. The most massive galaxies in our sample have red colors at each redshift, implying that dust can build up quickly in massive galaxies, and that feedback is likely removing dust from low-mass galaxies at z > 7. Thus the stellar-mass - metallicity relation, previously observed up to z ~ 3, may extend out to z = 7 - 8.
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic oscillator is solved in two different types of canonical transformations. The quantum form of the classical Hamiton-Jacobi theory is also employed to solve time dependent Schr\"odinger wave equations, showing that when one uses the classical action as a generating function of the quantum canonical transformation of time evolutions of state vectors, the corresponding propagator can easily be obtained.