ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using available data for C and M giants with Mbol<-3.6 in Magellanic Cloud clusters, we derive limits to the lifetimes of the corresponding evolutionary phases, as a function of stellar mass. The C-star phase is found to have a duration between 2 and 3 Myr for stars in the mass range from 1.5 to 2.8 Msun. There is also an indication that the peak of C-star lifetime shifts to lower masses (from slightly above to slightly below 2 Msun) as we move from LMC to SMC metallicities. The M-giant lifetimes also peak at 2 Msun in the LMC, with a maximum value of about 4 Myr, whereas in the SMC their lifetimes appear much shorter but, actually, they are poorly constrained by the data. These numbers constitute useful constraints to theoretical models of the TP-AGB phase. We show that several models in the literature underestimate the duration of the C-star phase at LMC metallicities.
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly non-ergodic statistical mechanical framework is constructed, which is based on L\'evy's generalized central limit theorem. As an example we calculate the distribution of $\bar{X}$: the time average of the position of the particle, for unbiased and uniformly biased particles, and show that $\bar{X}$ exhibits large fluctuations compared with the ensemble average $<X>$.
Let $\mathbf G$ be a graphing, that is a Borel graph defined by $d$ measure preserving involutions. We prove that if $\mathbf G$ is {\em treeable} then it arises as the local limit of some sequence $(G_n)_{n\in\mathbb{N}}$ of graphs with maximum degree at most $d$. This extends a result by Elek [G. Elek, Note on limits of finite graphs, Combinatorica 27 (2007)] (for $\mathbf G$ a treeing) and consequently extends the domain of the graphings for which Aldous-Lyons conjecture is known to be true.
We provide several asymptotic expansions of the prime counting function $\pi(x)$ and related functions. We define an {\it asymptotic continued fraction expansion} of a complex-valued function of a real or complex variable to be a possibly divergent continued fraction whose approximants provide an asymptotic expansion of the given function. We show that, for each positive integer $n$, two well-known continued fraction expansions of the exponential integral function $E_n(z)$ correspondingly yield two asymptotic continued fraction expansions of $\pi(x)/x$. We prove this by first establishing some general results about asymptotic continued fraction expansions. We show, for instance, that the "best"' rational function approximations of a function possessing an asymptotic Jacobi continued fraction expansion are precisely the approximants of the continued fraction, and as a corollary we determine all of the best rational function approximations of the function $\pi(e^x)/e^x$. Finally, we generalize our results on $\pi(x)$ to any arithmetic semigroup satisfying Axiom A, and thus to any number field.
We present a complete analysis of the dynamics of a Bose-Einstein condensate trapped in a symmetric triple-well potential. Our classical analogue treatment, based on a time-dependent variational method using SU(3) coherent states, includes the parameter dependence analysis of the equilibrium points and their local stability, which is closely related to the condensate collective behaviour. We also consider the effects of off-site interactions, and how these "cross-collisions" may become relevant for a large number of trapped bosons. Besides, we have shown analytically, by means of a simple basis transformation in the single-particle space, that an integrable sub-regime, known as twin-condensate dynamics, corresponds in the classical phase space to invariant surfaces isomorphic to the unit sphere. However, the quantum dynamics preserves the twin-condensate defining characteristics only partially, thus breaking the invariance of the associated quantum subspace. Moreover, the periodic geometry of the trapping potential allowed us to investigate the dynamics of finite angular momentum collective excitations, which can be suppressed by the emergence of chaos. Finally, using the generalized purity associated to the su(3) algebra, we were able to quantify the dynamical classicality of a quantum evolved system, as compared to the corresponding classical trajectory.
The Chapman-Enskog method is generalized for accounting the effect of kinetic modes on hydrodynamic evolution. Hydrodynamic states of phonon system of insulators have been studied in a small drift velocity approximation. For simplicity, the investigation was carried out for crystals of the cubic class symmetry. It has been found that in phonon hydrodynamics, local equilibrium is violated even in the approximation linear in velocity. This is due to the absence of phonon momentum conservation law that leads to a drift velocity relaxation. Phonon hydrodynamic equations which take dissipative processes into account have been obtained. The results were compared with the standard theory based on the local equilibrium validity. Integral equations have been obtained for calculating the objects of the theory (including viscosity and heat conductivity). It has been shown that in low temperature limit, these equations are solvable by iterations. Steady states of the system have been considered and an expression for steady state heat conductivity has been obtained. It coincides with the famous result by Akhiezer in the leading low temperature approximation. It has been established that temperature distribution in the steady state of insulator satisfies a condition of heat source absence.
We present spectroscopy and laser guide star adaptive optics (LGSAO) images of the doubly imaged lensed quasar SDSS J1206+4332. We revise the deflector redshift proposed previously to $z_{d}=0.745,$ and measure for the first time its velocity dispersion $\sigma=(290\pm30)$ km/s. The LGSAO data show the lensed quasar host galaxy stretching over the astroid caustic thus forming an extra pair of merging images, which was previously thought to be an unrelated galaxy in seeing limited data. Owing to the peculiar geometry, the lens acts as a natural coronagraph on the broad-line region of the quasar so that only narrow [O III] emission is found in the fold arc. We use the data to reconstruct the source structure and deflector potential, including nearby perturbers. We reconstruct the point-spread function (PSF) from the quasar images themselves, since no additional point source is present in the field of view. From gravitational lensing and stellar dynamics, we find the slope of the total mass density profile to be $\gamma^{\prime}=-\log\rho/\log r =1.93\pm0.09.$ We discuss the potential of SDSS J1206+4332 for measuring time delay distance (and thus H$_0$ and other cosmological parameters), or as a standard ruler, in combination with the time delay published by the COSMOGRAIL collaboration. We conclude that this system is very promising for cosmography. However, in order to achieve competitive precision and accuracy, an independent characterization of the PSF is needed. Spatially resolved kinematics of the deflector would reduce the uncertainties further. Both are within the reach of current observational facilities.
Many observed CEMP stars are found in binary systems and show enhanced abundances of $s$-elements. The origin of the chemical abundances of these CEMP-$s$ stars is believed to be accretion in the past of enriched material from a primary star in the AGB phase. We investigate the mechanism of mass transfer and the process of nucleosynthesis in low-metallicity AGB stars by modelling the binary systems in which the observed CEMP-$s$ stars were formed. For this purpose we compare a sample of $67$ CEMP-$s$ stars with a grid of binary stars generated by our binary evolution and nucleosynthesis model. We classify our sample CEMP-$s$ stars in three groups based on the observed abundance of europium. In CEMP$-s/r$ stars the europium-to-iron ratio is more than ten times higher than in the Sun, whereas it is lower than this threshold in CEMP$-s/nr$ stars. No measurement of europium is currently available for CEMP-$s/ur$ stars. On average our models reproduce well the abundances observed in CEMP-$s/nr$ stars, whereas in CEMP-$s/r$ stars and CEMP-$s/ur$ stars the abundances of the light-$s$ elements are systematically overpredicted by our models and in CEMP-$s/r$ stars the abundances of the heavy-$s$ elements are underestimated. In all stars our modelled abundances of sodium overestimate the observations. This discrepancy is reduced only in models that underestimate the abundances of most of the $s$-elements. Furthermore, the abundance of lead is underpredicted in most of our model stars. These results point to the limitations of our AGB nucleosynthesis model, particularly in the predictions of the element-to-element ratios. Finally, in our models CEMP-$s$ stars are typically formed in wide systems with periods above 10000 days, while most of the observed CEMP-$s$ stars are found in relatively close orbits with periods below 5000 days.
We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the \emph{Eisenstein cocycle} $\Psi $, a group cocycle for $GL_{n} (\Z )$; the special values are computed as periods of $\Psi $, and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for cubic and quartic fields of small discriminant.
By using first-principles tight-binding electronic structure calculation and Boltzmann transport equation, we investigate the size dependence of thermoelectric properties of silicon nanowires (SiNWs). With cross section area increasing, the electrical conductivity increases slowly, while the Seebeck coefficient reduces remarkably. This leads to a quick reduction of cooling power factor with diameter. Moreover, the figure of merit also decreases with transverse size. Our results demonstrate that in thermoelectric application, NW with small diameter is preferred. We also predict that isotopic doping can increase the value of ZT significantly. With 50% 29Si doping (28Si0.529Si0.5 NW), the ZT can be increased by 31%.
We investigate the origin of the resistance fluctuations of mesoscopic samples, near transitions between Quantum Hall plateaus. These fluctuations have been recently observed experimentally by E. Peled et al. [Phys. Rev. Lett. 90, 246802 (2003); ibid 90, 236802 (2003); Phys. Rev. B 69, R241305 (2004)]. We perform realistic first-principles simulations using a six-terminal geometry and sample sizes similar to those of real devices, to model the actual experiment. We present the theory and implementation of these simulations, which are based on the linear response theory for non-interacting electrons. The Hall and longitudinal resistances extracted from the Landauer formula exhibit all the observed experimental features. We give a unified explanation for the three regimes with distinct types of fluctuations observed experimentally, based on a simple generalization of the Landauer-Buttiker model. The transport is shown to be determined by the interplay between tunneling and chiral currents. We identify the central part of the transition, at intermediate filling factors, as the critical region where the localization length is larger than the sample size.
We study the equilibrium correlation function of the polaron-dressed tunnelling operator in the dissipative two-state system and compare the asymptoptic dynamics with that of the position correlations. For an Ohmic spectral density with the damping strength $K=1/2$, the correlation functions are obtained in analytic form for all times at any $T$ and any bias. For $K<1$, the asymptotic dynamics is found by using a diagrammatic approach within a Coulomb gas representation. At T=0, the tunnelling or coherence correlations drop as $t^{-2K}$, whereas the position correlations show universal decay $\propto t^{-2}$. The former decay law is a signature of unscreened attractive charge-charge interactions, while the latter is due to unscreened dipole-dipole interactions.
We consider positional numeration system with negative base, as introduced by Ito and Sadahiro. In particular, we focus on algebraic properties of negative bases $-\beta$ for which the corresponding dynamical system is sofic, which happens, according to Ito and Sadahiro, if and only if the $(-\beta)$-expansion of $-\frac{\beta}{\beta+1}$ is eventually periodic. We call such numbers $\beta$ Ito-Sadahiro numbers and we compare their properties with Parry numbers, occurring in the same context for R\'enyi positive base numeration system.
Based on the weakly-coupled two-Higgs-doublet model with spontaneous CP-violation (named Lee model) and the mechanism to generate the correlation between smallness of CP-violation and lightness of scalar mass, as we proposed earlier, we predicted a light CP-mixing scalar $\eta$ in which pseudoscalar component is dominant. It is a natural scenario in which $m_{\eta}\sim\mathcal{O}(10\textrm{GeV})\ll v$. Masses of all other scalars ($h$, $H$, $H^\pm$) should be around the electro-weak scale $v$. Among them, the 125 GeV Higgs ($h$) couplings are standard-model like, and the charged Higgs ($H^\pm$) mass should be around the heaviest neutral scalar ($H$) mass. We discussed all experimental constraints and showed that this scenario is still allowed by data. The strictest constraints come from the experiments of the flavor-changing processes and the EDM of lepton and neutron. We also discussed the future tests for this scenario. It is possible to discover the extra scalars or exclude this scenario at future colliders, especially at the LHC and $e^+e^-$ colliders with $\mathcal{O}(\textrm{ab}^{-1})$ luminosity. We also pointed out that the $Z$-mediated Higgs pair production via $e^+e^-\rightarrow h_ih_j$ ($h_i, h_j$ stand for two of the $\eta, h, H$) would be the key observable to confirm or exclude CP-violation in Higgs sector. The sensitivity to test this scenario is worth further studying in greater detail.
We investigate the symptoms of broken rotational invariance, caused by the use of light front dynamics, for deuterons obtained using one- and two-pion-exchange potentials. A large mass splitting between states with m=0 and m=1 is found for the deuteron obtained from the one-pion-exchange (OPE) potential. The size of the splitting is smaller when the chiral two-pion-exchange (TPE) potential is used. When the TPE potential constructed without chiral symmetry is used, the deuteron becomes unbound. These results arise from significant relativistic effects which are much larger than those of the Wick-Cutkosky model because of the presence of the tensor force.
We study the following problem, first introduced by Dekking. Consider an infinite word x over an alphabet {0,1,...,k-1} and a semigroup homomorphism S:{0,1,...,k-1}* -> N. Let L_x denote the set of factors of x. What conditions on S and the abelian complexity of x guarantee that S(L_x) contains all but finitely many elements of N? We examine this question for some specific infinite words x having different abelian complexity functions.
We report the phase-connected timing ephemeris, polarization pulse profiles, Faraday rotation measurements, and Rotating-Vector-Model (RVM) fitting results of twelve millisecond pulsars (MSPs) discovered with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) in the Commensal radio Astronomy FAST survey (CRAFTS). The timing campaigns were carried out with FAST and Arecibo over three years. Eleven of the twelve pulsars are in neutron star - white dwarf binary systems, with orbital periods between 2.4 and 100 d. Ten of them have spin periods, companion masses, and orbital eccentricities that are consistent with the theoretical expectations for MSP - Helium white dwarf (He WD) systems. The last binary pulsar (PSR J1912$-$0952) has a significantly smaller spin frequency and a smaller companion mass, the latter could be caused by a low orbital inclination for the system. Its orbital period of 29 days is well within the range of orbital periods where some MSP - He WD systems have shown anomalous eccentricities, however, the eccentricity of PSR J1912$-$0952 is typical of what one finds for the remaining MSP - He WD systems.
Let M be a moduli space of stable sheaves on a K3 or Abelian surface S. We express the class of the diagonal in the cartesian square of M in terms of the Chern classes of a universal sheaf. Consequently, we obtain generators of the cohomology ring of M. When S is a K3 and M is the Hilbert scheme of length n subschemes, this set of generators is sufficiently small in the sense that there aren't any relations among them in the stable cohomology ring.   When S is the cotangent bundle of a Riemann surface, we recover the result of T. Hausel and M. Thaddeus: The cohomology ring of the moduli spaces of Higgs bundles is generated by the universal classes.
We extend slightly the results of Evens-Mirkovi\'c, and "compute" the characteristic cycles of Intersection Cohomology sheaves on the transversal slices in the double affine Grassmannian and on the hypertoric varieties. We propose a conjecture relating the hyperbolic stalks and the microlocalization at a torus-fixed point in a Poisson variety.
We report muon-spin rotation, heat capacity, magnetization, and ac magnetic susceptibility measurements of the layered spin-1/2 antiferromagnet NaNiO2. These show the onset of long-range magnetic order below T_N = 19.5K. Rapid muon depolarization persisting to about 5K above T_N is consistent with the presence of short-range magnetic order. The temperature and frequency dependence of the ac susceptibility suggests that magnetic clusters persist above 25K in the paramagnetic state and that their volume fraction decreases with increasing temperature. A frequency dependent peak in the ac magnetic susceptibility at T_sf = 3K is observed, consistent with a slowing of spin fluctuations at this temperature. A partial magnetic phase diagram is deduced.
We present an idealised model of gravitational collapse, describing a collapsing rotating cylindrical shell of null dust in flat space, with the metric of a spinning cosmic string as the exterior. We find that the shell bounces before closed timelike curves can be formed. Our results also suggest slightly different definitions for the mass and angular momentum of the string.
We prove a theorem on additive Levy processes and give applications
We provide here a roadmap for modeling silicon nano-devices with one or two group V donors (D). We discuss systems containing one or two electrons, that is, D^0, D^-, D_2^+ and D_2^0 centers. The impact of different levels of approximation is discussed. The most accurate instances -- for which we provide quantitative results -- are within multivalley effective mass including the central cell correction and a configuration interaction account of the electron-electron correlations. We also derive insightful, yet less accurate, analytical approximations and discuss their validity and limitations -- in particular, for a donor pair, we discuss the single orbital LCAO method, the Huckel approximation and the Hubbard model. Finally we discuss the connection between these results and recent experiments on few dopant devices.
We analyze kinematic data of 41 nearby (z<0.1) relaxed galaxy clusters in terms of the projected phase-space density using a phenomenological, fully anisotropic model of the distribution function. We apply the Markov Chain Monte Carlo approach to place constraints on total mass distribution approximated by the universal NFW profile and the profile of the anisotropy of galaxy orbits. We find the normalization of the mean mass-concentration relation is c=6.9_{-0.7}^{+0.6} at the virial mass M_v=5x10^{14}M_sun. Assuming a one-to-one correspondence between sigma_8 and the normalization of the mass-concentration relation in the framework of the concordance model we estimate the normalization of the linear power spectrum to be sigma_8=0.91_{-0.08}^{+0.07}. Our constraints on the parameters of the mass profile are compared with estimates from other methods. We show that galaxy orbits are isotropic at the cluster centres (with the mean ratio of the radial-to-tangential velocity dispersions sigma_r/sigma_theta=0.97+/-0.04) and radially anisotropic at the virial sphere (with the mean ratio sigma_r/sigma_theta=1.75^{+0.23}_{-0.19}). Although the value of the central anisotropy appears to be universal, the anisotropy at the virial radius differs between clusters within the range 1<(sigma_r/sigma_theta)<2. Utilizing the Bautz-Morgan morphological classification and information on the prominence of a cool core we select two subsamples of galaxy clusters corresponding to less and more advanced evolutionary states. It is demonstrated that less evolved clusters have shallower mass profiles and their galaxy orbits are more radially biased at the virial sphere. This property is consistent with the expected evolution of the mass profiles as well as with the observed orbital segregation of late and early type galaxies.
The motion of picking up and placing an object in 3D space is full of subtle detail. Typically these motions are formed from the same constraints, optimizing for swiftness, energy efficiency, as well as physiological limits. Yet, even for identical goals, the motion realized is always subject to natural variation. To capture these aspects computationally, we suggest a deep generative model for human reach-and-place action, conditioned on a start and end position.We have captured a dataset of 600 such human 3D actions, to sample the 2x3-D space of 3D source and targets. While temporal variation is often modeled with complex learning machinery like recurrent neural networks or networks with memory or attention, we here demonstrate a much simpler approach that is convolutional in time and makes use of(periodic) temporal encoding. Provided a latent code and conditioned on start and end position, the model generates a complete 3D character motion in linear time as a sequence of convolutions. Our evaluation includes several ablations, analysis of generative diversity and applications.
We study the interplay of natural supersymmetry and a supersymmetric solution to the discrepancy observed in measurements of the muon magnetic moment. The strongest constraints on the parameter space currently come from chargino searches in the trilepton channel and slepton searches in the dilepton channel at the LHC, and vast regions are currently allowed, especially at large $\tan{\beta}$. With light top squarks in the spectrum, as required from naturalness arguments, the situation changes dramatically; stop-assisted chargino and neutralino production via $\tilde{t} \rightarrow b \tilde{\chi}_{1}^{\pm}$ and $\tilde{t} \rightarrow t \tilde{\chi}_{1}^0$ are already probing the entire parameter space compatible with the muon magnetic moment at $\tan{\beta} \sim \mathcal{O}(10)$, while upcoming stop searches will probe most of the parameter space at larger $\tan{\beta} \sim 40$. Direct Higgsino searches as well as compressed slepton and stop searches are crucial to close out corners of parameter space. We consider one such example: in the presence of light sleptons and charginos as required to obtain appreciable contributions to the muon magnetic moment, compressed stops can dominantly undergo the following decay $\tilde{t} \, \rightarrow \, b \tilde{\ell} \nu (\tilde{\nu} \ell) \, \rightarrow \, b \ell \nu \tilde{\chi}_{1}^0$, facilitated by off-shell charginos. We find that the enhanced branching to leptons leads to a $5 \sigma$ mass reach (with $3000$ fb$^{-1}$ of data at LHC14) of $m_{\tilde{t}} \, \sim \, 350$ GeV, with the mass difference between stops and the lightest neutralino being $\sim 80$ GeV. This will further close out a significant part of the parameter space compatible with naturalness and the muon magnetic moment.