ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have examined the success rates of 19 American, Canadian, Australian, and Dutch graduate programs in producing astronomers. A 20-year baseline was considered (1975-1994), incorporating 897 PhD recipients. The major conclusion from our study is that the fraction of PhD graduates still involved in astronomical research is surprisingly insensitive to the institutional source of one's PhD. With few exception, 55-75% of graduates, regardless of PhD source, remain active in the astronomical research community. While it remains true that graduates of so-called ``prestigious'' programs preferentially populate the same, it is also clear that an abundance of opportunities exist at smaller ``non-prestigious'' institutions, liberal arts colleges, government, and industry. The latter, of course, generally carry enhanced administrative and/or teaching duties, but, on the other hand, do not entirely preclude a role in the research community. A Kepler-Meier survival analysis of two disparate institutes demonstrates that ``success'' is a dynamical entity, and that blind consideration of a 20-year baseline sample can mask important recent trends. Within ten years of PhD receipt, an equilibrium is reached in which 45% of the graduates are in identifiably permanent positions, 20% remain in soft-money positions, and 35% have left research entirely. Graduates of American universities are 2-3 times more likely to find permanent employment in the USA than Canadian or Australian graduates are within their respective institute's country. While the number of American, Canadian, and Dutch PhDs have grown 20% during the past decade, the growth in Australia has been closer to 70%.
We study the roughening properties of the anharmonic elastic interface in the presence of temporally correlated noise. The model can be seen as a generalization of the anharmonic Larkin model, recently introduced by Purrello, Iguain, and Kolton [Phys. Rev. E {\bf 99}, 032105 (2019)], to investigate the effect of higher-order corrections to linear elasticity in the fate of interfaces. We find analytical expressions for the critical exponents as a function of the anharmonicity index $n$, the noise correlator range $\theta \in[0,1/2]$, and dimension $d$. In $d=1$ we find that the interface becomes faceted and exhibits anomalous scaling for $\theta > 1/4$ for any degree of anharmonicity $n > 1$. Analytical expressions for the anomalous exponents $\alpha_\mathrm{loc}$ and $\kappa$ are obtained and compared with a numerical integration of the model. Our theoretical results show that anomalous roughening cannot exist for this model in dimensions $d > 1$.
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
For an Euler system, with dynamics generated by a potential energy functional, we propose a functional format for the relative energy and derive a relative energy identity. The latter, when applied to specific energies, yields relative energy identities for the Euler-Korteweg, the Euler-Poisson, the Quantum Hydrodynamics system, and low order approximations of the Euler-Korteweg system. For the Euler-Korteweg system we prove a stability theorem between a weak and a strong solution and an associated weak-strong uniqueness theorem. In the second part we focus on the Navier-Stokes-Korteweg system (NSK) with non-monotone pressure laws: we prove stability for the NSK system via a modified relative energy approach. We prove continuous dependence of solutions on initial data and convergence of solutions of a low order model to solutions of the NSK system. The last two results provide physically meaningful examples of how higher order regularization terms enable the use of the relative energy framework for models with energies which are not poly- or quasi-convex, but compensating via higher-order gradients.
In this work, we study a family of non-Markovian trees modeling populations where individuals live and reproduce independently with possibly time-dependent birth-rate and lifetime distribution. To this end, we use the coding process introduced by Lambert. We show that, in our situation, this process is no longer a L{\'e}vy process but remains a Feller process and we give a complete characterization of its generator. This allows us to study the model through well-known Markov processes techniques. On one hand, introducing a scale function for such processes allows us to get necessary and sufficient conditions for extinction or non-extinction and to characterize the law of such trees conditioned on these events. On the other hand, using Lyapounov drift techniques , we get another set of, easily checkable, sufficient criteria for extinction or non-extinction and some tail estimates for the tree length. Finally, we also study scaling limits of such random trees and observe that the Bessel tree appears naturally.
The nearby Type Ia supernovae (SNe Ia) 2011fe and 2011by had nearly identical photospheric phase optical spectra, light-curve widths, and photometric colours, but at peak brightness SN 2011by reached a fainter absolute magnitude in all optical bands and exhibited lower flux in the near-ultraviolet (NUV). Based on those data, Foley & Kirshner (2013) argue that the progenitors of SNe 2011by and 2011fe were supersolar and subsolar, respectively, and that SN 2011fe generated 1.7 times the amount of 56Ni as SN 2011by. With this work, we extend the comparison of these SNe Ia to 10 days before and 300 days after maximum brightness with new spectra and photometry. We show that the nebular phase spectra of SNe 2011fe and 2011by are almost identical, and do not support a factor of 1.7 difference in 56Ni mass. Instead, we find it plausible that the Tully-Fisher distance for SN 2011by is an underestimate, in which case these SNe Ia may have reached similar peak luminosity, formed similar amounts of 56Ni, and had lower metallicity progenitors than previously estimated. Regardless of the true distance to SN 2011by, we find that the relative progenitor metallicity difference remains well supported by their disparity in NUV flux, which we show to be even stronger at pre-maximum epochs --- although contributions from differences in total ejecta mass, viewing angle, or progenitor density cannot be ruled out. We also demonstrate that, independent of distance modulus, SN 2011by exhibits a late-time luminosity excess that cannot be explained by a light echo, but is more likely to be the result of greater energy trapping by the nucleosynthetic products of SN 2011by.
Recent advances in quantum technology have led to the development and the manufacturing of programmable quantum annealers that promise to solve certain combinatorial optimization problems faster than their classical counterparts. Semi-supervised learning is a machine learning technique that makes use of both labeled and unlabeled data for training, which enables a good classifier with only a small amount of labeled data. In this paper, we propose and theoretically analyze a graph-based semi-supervised learning method with the aid of the quantum annealing technique, which efficiently utilize the quantum resources while maintaining a good accuracy. We illustrate two classification examples, suggesting the feasibility of this method even with a small portion (20%) of labeled data is involved.
We investigate when the product of two Hecke eigenforms for {\Gamma}_1(N) is again a Hecke eigenform. In this paper we prove that the product of two normalized eigenforms for {\Gamma}_1(N), of weight greater than 1, is an eigenform only 61 times, and give a complete list. Duke [Duk99] and Ghate [Gha00] independently proved that with eigenforms for SL_2(Z), there are only 16 such product identities. Ghate [Gha02] also proved related results for {\Gamma}_1(N), with N square free. Emmons [Emm05] proved results for eigenforms away from the level, for prime level. The methods we use are elementary and effective, and do not rely on the Rankin-Selberg convolution method used by both Duke and Ghate.
The ubiquitous diffuse soft (1/4 keV) X-ray background was one of the earliest discoveries of X-ray astronomy. At least some of the emission may arise from charge exchange between solar wind ions and neutral atoms in the heliosphere, but no detailed models have been fit to the available data. Here we report on a new model for charge exchange in the solar wind, which when combined with a diffuse hot plasma component filling the Local Cavity provides a good fit to the only available high-resolution soft X-ray and extreme ultraviolet (EUV) spectra using plausible parameters for the solar wind. The implied hot plasma component is in pressure equilibrium with the local cloud that surrounds the solar system, creating for the first time a self-consistent picture of the local interstellar medium.
Over the past twenty years, rectangle visibility graphs have generated considerable interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph $G$ is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a non-degenerate horizontal or vertical band of visibility joining the two rectangles. Our results include necessary and sufficient conditions for $K_n$, $K_{m,n}$, and trees to be URVGs, as well as a number of general edge bounds.
Classical Be stars are an enigmatic subclass of rapidly rotating hot stars characterized by dense equatorial disks of gas that have been inferred to orbit with Keplerian velocities. Although these disks seem to be ejected from the star and not accreted, there is substantial observational evidence to show that the stars rotate more slowly than required for centrifugally driven mass loss. This paper develops an idea (proposed originally by Hiroyasu Ando and colleagues) that nonradial stellar pulsations inject enough angular momentum into the upper atmosphere to spin up a Keplerian disk. The pulsations themselves are evanescent in the stellar photosphere, but they may be unstable to the generation of resonant oscillations at the acoustic cutoff frequency. A detailed theory of the conversion from pulsations to resonant waves does not yet exist for realistic hot-star atmospheres, so the current models depend on a parameterized approximation for the efficiency of wave excitation. Once resonant waves have been formed, however, they grow in amplitude with increasing height, steepen into shocks, and exert radial and azimuthal Reynolds stresses on the mean fluid. Using reasonable assumptions for the stellar parameters, these processes were found to naturally create the inner boundary conditions required for dense Keplerian disks, even when the underlying B-star photosphere is rotating as slowly as 60% of its critical rotation speed. Because there is evidence for long-term changes in Be-star pulsational properties, this model may also account for the long-term variability of Be stars, including transitions between normal, Be, and shell phases.
Magnetic tunnel junctions for spin-transfer torque switching were prepared to investigate the dielectric breakdown. The breakdown occurs typically at voltages not much higher than the switching voltages, a bottleneck for the implementation of spin-transfer torque Magnetic Random Access Memory. Intact and broken tunnel junctions are characterized by transport measurements and then prepared for transmission electron microscopy and energy dispersive x-ray spectrometry by focussed ion beam. The comparison to our previous model of the electric breakdown for thicker MgO tunnel barriers reveals significant differences arising from the high current densities.
We determine the fixed locus of the anticanonical complete linear system of a given anticanonical rational surface. The case of a geometrically ruled rational surface is fully studied, e.g., the monoid of numerically effective divisor classes of such surface is explicitly determined and is minimally generated by two elements. On the other hand, as a consequence in the particular case where $X$ is a smooth rational surface with $K_{X}^{2}>0$, the following expected result holds: every fixed prime divisor of the complete linear system $|-K_X|$ is a $(-n)$-curve, for some integer $n\geq 1$.
We calculate the spectral statistics of the Kramers-Weyl Hamiltonian $H=v\sum_{\alpha} \sigma_\alpha\sin p_\alpha+t \sigma_0\sum_\alpha\cos p_\alpha$ in a chaotic quantum dot. The Hamiltonian has symplectic time-reversal symmetry ($H$ is invariant when spin $\sigma_\alpha$ and momentum $p_\alpha$ both change sign), and yet for small $t$ the level spacing distribution $P(s)\propto s^\beta$ follows the $\beta=1$ orthogonal ensemble instead of the $\beta=4$ symplectic ensemble. We identify a supercell symmetry of $H$ that explains this finding. The supercell symmetry is broken by the spin-independent hopping energy $\propto t\cos p$, which induces a transition from $\beta=1$ to $\beta=4$ statistics that shows up in the conductance as a transition from weak localization to weak antilocalization.
We propose a simple method to evaluate $\alpha$-transition rates to low-lying excited states in even-even nuclei. For this a realistic $\alpha$-daughter double folding interaction is approximated by a parabola in the region where the decay process takes place. This allows us to evaluate the penetration probability analytically. The main experimental features of branching ratios to excited states are reproduced by this simple approach.
We report on work in progress by the Virgo consortium, a collaboration set up to carry out large simulations of the formation of galaxies and large-scale structure exploiting the latest generation of parallel supercomputers. We show results of $256^3$ particle N-body simulations of the clustering evolution of dark matter in four cold dark matter models with different cosmological parameters. The high resolution and large volume of these simulations allows us to determine reliably the mass autocorrelation function for pair separations in the range $40\hkpc$ to $20\hmpc$. Comparison of these with the observed galaxy correlation function shows that for any of these models to be viable, the distribution of galaxies must be biased relative to the distribution of mass in a non-trivial, scale-dependent fashion. In particular, low $\Omega_0$ models require the galaxies to be more ``weakly'' clustered than the mass at small and intermediate pair separations. Simulations which include the evolution of gas show that cold gas knots form with approximately the abundance expected on theoretical grounds, although a few excessively massive objects grow near the centres of rich clusters. The locations where these cold gas knots form are, in general, biased relative to the distribution of mass in a scale-dependent way. Some of these biases have the required sign but they are, for the most part, weaker than is necessary for agreement with observations. The antibias present in our low $\Omega_0$ N-body/SPH simulation appears to be related to the merging and disruption of galaxies in rich clusters.
We construct models of universe with a generalized equation of state $p=(\alpha \rho+k\rho^{1+1/n})c^2$ having a linear component and a polytropic component. In this paper, we consider negative indices $n<0$. In that case, the polytropic component dominates in the late universe where the density is low. For $\alpha=0$, $n=-1$ and $k=-\rho_{\Lambda}$, we obtain a model of late universe describing the transition from the matter era to the dark energy era. The universe exists eternally in the future and undergoes an inflationary expansion with the cosmological density $\rho_{\Lambda}=7.02 10^{-24} g/m^3$ on a timescale $t_{\Lambda}=1.46 10^{18} s$. For $\alpha=0$, $n=-1$ and $k=\rho_{\Lambda}$, we obtain a model of cyclic universe appearing and disappearing periodically. If we were living in this universe, it would disappear in about 2.38 billion years. We make the connection between the early and the late universe and propose a simple equation describing the whole evolution of the universe. This leads to a model of universe that is eternal in past and future without singularity (aioniotic universe). This model exhibits a nice "symmetry" between an early and late phase of inflation, the cosmological constant in the late universe playing the same role as the Planck constant in the early universe. The Planck density and the cosmological density represent fundamental upper and lower bounds differing by 122 orders of magnitude. The cosmological constant "problem" may be a false problem. We determine the potential of the scalar field (quintessence, tachyon field) corresponding to the generalized equation of state $p=(\alpha \rho+k\rho^{1+1/n})c^2$. We also propose a unification of pre-radiation, radiation and dark energy through the quadratic equation of state $p/c^2=-4\rho^2/3\rho_P+\rho/3-4\rho_{\Lambda}/3$.
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain parametrization. The mass asymmetry in binary cold fission of Th and U isotopes is explained as the result of adding a phenomenological shell correction to the liquid drop model deformation energy. Applications to binary, ternary, and quaternary fission are outlined.
Reliable calculations of the structure of heavy elements are crucial to address fundamental science questions such as the origin of the elements in the universe. Applications relevant for energy production, medicine, or national security also rely on theoretical predictions of basic properties of atomic nuclei. Heavy elements are best described within the nuclear density functional theory (DFT) and its various extensions. While relatively mature, DFT has never been implemented in its full power, as it relies on a very large number (~ 10^9-10^12) of expensive calculations (~ day). The advent of leadership-class computers, as well as dedicated large-scale collaborative efforts such as the SciDAC 2 UNEDF project, have dramatically changed the field. This article gives an overview of the various computational challenges related to the nuclear DFT, as well as some of the recent achievements.
The massive black hole (BH) population in dwarf galaxies ($M_{\rm BH} \lesssim 10^5~M_\odot$) can provide strong constraints on the origin of BH seeds. However, traditional optical searches for active galactic nuclei (AGNs) only reliably detect high-accretion, relatively high-mass BHs in dwarf galaxies with low amounts of star formation, leaving a large portion of the overall BH population in dwarf galaxies relatively unexplored. Here, we present a sample of 81 dwarf galaxies ($M_\star \le 3 \times 10^9~M_\odot$) with detectable [Fe X]$\lambda$6374 coronal line emission indicative of accretion onto massive BHs, only two of which were previously identified as optical AGNs. We analyze optical spectroscopy from the Sloan Digital Sky Survey and find [Fe X]$\lambda$6374 luminosities in the range $L_{\rm [Fe\,X]}\approx10^{36}$-$10^{39}$ erg s$^{-1}$, with a median value of $1.6 \times 10^{38}$ erg s$^{-1}$. The [Fe X]$\lambda$6374 luminosities are generally much too high to be produced by stellar sources, including luminous Type IIn supernovae (SNe). Moreover, based on known SNe rates, we expect at most 8 Type IIn SNe in our sample. On the other hand, the [Fe X]$\lambda$6374 luminosities are consistent with accretion onto massive BHs from AGNs or tidal disruption events (TDEs). We find additional indicators of BH accretion in some cases using other emission line diagnostics, optical variability, X-ray and radio emission (or some combination of these). However, many of the galaxies in our sample only have evidence for a massive BH based on their [Fe X]$\lambda$6374 luminosities. This work highlights the power of coronal line emission to find BHs in dwarf galaxies missed by other selection techniques and to probe the BH population in bluer, lower mass dwarf galaxies.
We establish that a viscosity solution to a multidimensional Hamilton-Jacobi equation with a convex non-degenerate hamiltonian and Bohr almost periodic initial data decays to its infimum as time $t\to+\infty$.
We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in stochastic geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total edge length of the $k$-nearest neighbors random graph, $(ii)$ the clique count in random geometric graphs, $(iii)$ the volume of the set approximation via the Poisson-Voronoi tessellation.
We present infrared photometry of the episodic dust-making Wolf-Rayet system WR19 (LS3), tracking its fading from a third observed dust-formation episode in 2007 and strengthening the view that these episodes are periodic (P = 10.1+/-0.1 y). Radial velocities of the O9 component observed between 2001 and 2008 show RV variations consistent with WC19 being a spectroscopic binary of high eccentricity (e=0.8), having periastron passage in 2007.14, shortly before the phase of dust formation. In this respect, WR19 resembles the archetypical episodic dust-making colliding-wind binary system WR140.
The issue concerning semi-classical methods recently developed in deriving the conditions for Hawking radiation as tunneling, is revisited and applied also to rotating black hole solutions as well as to the extremal cases. It is noticed how the tunneling method fixes the temperature of extremal black hole to be zero, unlike the Euclidean regularity method that allows an arbitrary compactification period. A comparison with other approaches is presented.