ShantanuT01/DACTYL-Pretraining huggingface dataset:
Until recently, determining the rotational properties of galaxies in the early universe (z>4, Universe age <1.5Gyr) was impractical, with the exception of a few strongly lensed systems. Combining the high resolution and sensitivity of ALMA at (sub-) millimeter wavelengths with the typically high strength of the [CII] 158um emission line from galaxies and long-developed dynamical modeling tools raises the possibility of characterizing the gas dynamics in both extreme starburst galaxies and normal star forming disk galaxies at z~4-7. Using a procedure centered around GIPSY's ROTCUR task, we have fit tilted ring models to some of the best available ALMA [CII] data of a small set of galaxies: the MS galaxies HZ9 & HZ10, the Damped Lyman-alpha Absorber (DLA) host galaxy ALMA J0817+1351, the submm galaxies AzTEC/C159 and COSMOS J1000+0234, and the quasar host galaxy ULAS J1319+0950. This procedure directly derives rotation curves and dynamical masses as functions of radius for each object. In one case, we present evidence for a dark matter halo of O(10^11) solar masses. We present an analysis of the possible velocity dispersions of AzTEC/C159 and ULAS J1319+0950 based on matching simulated observations to the integrated [CII] line profiles. Finally, we test the effects of observation resolution and sensitivity on our results. While the conclusions remain limited at the resolution and signal-to-noise ratios of these observations, the results demonstrate the viability of the modeling tools at high redshift, and the exciting potential for detailed dynamical analysis of the earliest galaxies, as ALMA achieves full observational capabilities.
We report 1.7 GHz Very Long Baseline Interferometry (VLBI) observations of IRAS F10214+4724, a lensed z=2.3 obscured quasar with prodigious star formation. We detect what we argue to be the obscured active nucleus with an effective angular resolution of < 50 pc at z = 2.3 . The S_{1.7} = 210 micro-Jy (9-\sigma) detection of this unresolved source is located within the HST rest-frame ultraviolet/optical arc, however, >~100 mas northward of the arc centre of curvature. This leads to a source plane inversion that places the European VLBI Network detection to within milli-arcseconds of the modelled cusp caustic, resulting in a very large magnification (\mu ~70), over an order of magnitude larger than the CO (1-0) derived magnification of a spatially resolved JVLA map, using the same lens model. We estimate the quasar bolometric luminosity from a number of independent techniques and with our X-ray modelling find evidence that the AGN may be close to Compton-thick, with an intrinsic bolometric luminosity log(L_{bol,QSO} / L_sun) = 11.34 +- 0.27 dex. We make the first black hole mass estimate of IRAS F10214+4724 and find log(M_{BH}/M_sun) = 8.36 +- 0.56 which suggests a low black hole accretion rate (\lambda = \dot{M} / \dot{M}_{Edd} ~ 3\pm^7_2 percent). We find evidence for a M_{BH}/M_{spheroid} ratio that is 1-2 orders of magnitude larger than that of submillimetre galaxies (SMGs) at z~2. At face value, this suggests IRAS F10214+4724 has undergone a different evolutionary path compared to SMGs at the same epoch. A primary result of this work is the demonstration that emission regions of differing size and position can undergo significantly different magnification boosts (> 1 dex) and therefore distort our view of high-redshift, gravitationally lensed galaxies.
The theory of impurities in excitonic insulator is investigated in the light of the recent experiments on hexaborides. First, we study the bound state around the impurity and find that the bound state emerges when ${Re}\Delta$ is positive. Second, we study the continuum state using Abrikosov-Gor'kov's approach. We find that the energy gap is reduced strongly when ${Im}\Delta=0$. Finally, we solve Bogoliubov-de Gennes equations for excitonic insulator numerically. We get the results consistent with the analytic ones.   We also find that incomplete ferromagnetism appears in doped triplet excitonic insulator with impurity. We make a short qualitative discussion on the ferromagnetism of doped hexaborides using our result.
In this Chapter we examine the role of the ngVLA to further our understanding of the different manifestations of convective or turbulence-driven stellar activity on red giant and supergiant stars. The combination of high spatial resolution and high sensitivity will enable the ngVLA to significantly improve our understanding of the processes that dissipate energy in the extended atmospheres of cool evolved stars, and drive ubiquitous stellar outflows. The high spatial resolution will enable us to image the surfaces of nearby red supergiants, and to measure the atmospheric extent of red giants. Multi-frequency observations will permit thermal continuum tomography on the largest angular diameter stars, providing key empirical data to test theoretical models. The complementary frequencies and similar spatial resolutions of the ngVLA and ALMA will be a powerful synergy.
The generalized Fibonacci sequences are sequences $\{f_n\}$ which satisfy the recurrence $f_n(s, t) = sf_{n - 1}(s, t) + tf_{n - 2}(s, t)$ ($s, t \in \mathbb{Z}$) with initial conditions $f_0(s, t) = 0$ and $f_1(s, t) = 1$. In a recent paper, Amdeberhan, Chen, Moll, and Sagan considered some arithmetic properites of the generalized Fibonacci sequence. Specifically, they considered the behavior of analogues of the $p$-adic valuation and the Riemann zeta function. In this paper, we resolve some conjectures which they raised relating to these topics. We also consider the rank modulo $n$ in more depth and find an interpretation of the rank in terms of the order of an element in the multiplicative group of a finite field when $n$ is an odd prime. Finally, we study the distribution of the rank over different values of $s$ when $t = -1$ and suggest directions for further study involving the rank modulo prime powers of generalized Fibonacci sequences.
We show that the average number of integral points on elliptic curves, counted modulo the natural involution on a punctured elliptic curve, is bounded from above by $2.1 \times 10^8$. To prove it, we design a descent map, whose prototype goes at least back to Mordell, which associates a pair of binary forms to an integral point on an elliptic curve. Other ingredients of the proof include the upper bounds for the number of solutions of a Thue equation by Evertse and Akhtari-Okazaki, and the estimation of the number of binary quartic forms by Bhargava-Shankar. Our method applies to $S$-integral points to some extent, although our present knowledge is insufficient to deduce an upper bound for the average number of them. We work out the numerical example with $S=\{2\}$.
Recently, several people study finite multiple zeta values (FMZVs) and finite polylogarithms (FPs). In this paper, we introduce finite multiple polylogarithms (FMPs), which are natural generalizations of FMZVs and FPs, and we establish functional equations of FMPs. As applications of these functional equations, we calculate special values of FMPs containing generalizations of congruences obtained by Me\v{s}trovi\'c, Z. W. Sun, Z. W. Sun-L. L. Zhao, and Tauraso-J. Zhao. We show supercongruences for certain generalized Bernoulli numbers and the Bernoulli numbers as an appendix.
Dynamical effects under geometrical frustration are considered in a model for artificial spin ice on a square lattice in two dimensions. Each island of the spin ice has a three-component Heisenberg-like dipole moment subject to shape anisotropies that influence its direction. The model has real dynamics, including rotation of the magnetic degrees of freedom, going beyond the Ising-type models of spin ice. The dynamics is studied using a Langevin equation solved via a second order Heun algorithm. Thermodynamic properties such as the specific heat are presented for different couplings. A peak in specific heat is related to a type of melting-like phase transition present in the model. Hysteresis in an applied magnetic field is calculated for model parameters where the system is able to reach thermodynamic equilibrium.
Complex contact manifolds have recently received considerable attention. Many of the newer publications approach contact manifolds via the covering family of minimal rational curves. This short note furthers the study of these curves.   It is known that for any point x in X, the subvariety, which is covered by those curves which contain x, is Legendrian. We will now study the deformations of these subvarieties which are generated by moving the base point.   As a main application, we give a positive answer to a question of J.M. Hwang in the case of contact manifolds: a sufficiently general tangent vector is contained in at most a single minimal rational curve. The author believes that this is a necessary step towards a full classification of contact manifolds.   We give a second application by showing that the normalization of the subvariety of minimal curves through x is isomorphic to a projective cone.
The plane-wave limit of ${\rm AdS}_3 \times {\rm S}^3 \times {\rm S}^3 \times {\rm S}^1$ is analysed for generic null-geodesics that are not necessarily BPS. For the case of pure NS-NS flux it is shown how the resulting spectrum can be reproduced as a suitable limit of the world-sheet description in terms of WZW models. Since supersymmetry is broken, most of the degeneracies are lifted, and thus the identification of states is quite unambiguous.
Using the Pan-STARRS1 survey, we derive limiting magnitude, spatial completeness and density maps that we use to probe the three dimensional structure and estimate the stellar mass of the so-called Monoceros Ring. The Monoceros Ring is an enormous and complex stellar sub-structure in the outer Milky Way disk. It is most visible across the large Galactic Anticenter region, 120 < l < 240 degrees, -30 < b < +40 degrees. We estimate its stellar mass density profile along every line of sight in 2 X 2 degree pixels over the entire 30,000 square degree Pan-STARRS1 survey using the previously developed MATCH software. By parsing this distribution into a radially smooth component and the Monoceros Ring, we obtain its mass and distance from the Sun along each relevant line of sight. The Monoceros Ring is significantly closer to us in the South (6 kpc) than in the North (9 kpc). We also create 2D cross sections parallel to the Galactic plane that show 135 degrees of the Monoceros Ring in the South and 170 degrees of the Monoceros Ring in the North. We show that the Northern and Southern structures are also roughly concentric circles, suggesting that they may be a wave rippling from a common origin. Excluding the Galactic plane, we observe an excess stellar mass of 4 million solar masses across 120 < l < 240 degrees. If we interpolate across the Galactic plane, we estimate that this region contains 8 million solar masses. If we assume (somewhat boldly) that the Monoceros Ring is a set of two Galactocentric rings, its total stellar mass is 60 million solar masses. Finally, if we assume that it is a set of two circles centered at a point 4 kpc from the Galactic center in the anti-central direction, as our data suggests, we estimate its stellar mass to be 40 million solar masses.
Let $\Omega$ be a domain in $\mathbb R^3$ with $\partial\Omega = \partial\left(\mathbb R^3\setminus \overline{\Omega}\right)$, where $\partial\Omega$ is unbounded and connected, and let $u$ be the solution of the Cauchy problem for the heat equation $\partial_t u= \Delta u$ over $\mathbb R^3,$ where the initial data is the characteristic function of the set $\Omega^c = \mathbb R^3\setminus \Omega$. We show that, if there exists a stationary isothermic surface $\Gamma$ of $u$ with $\Gamma \cap \partial\Omega = \varnothing$, then both $\partial\Omega$ and $\Gamma$ must be either parallel planes or co-axial circular cylinders . This theorem completes the classification of stationary isothermic surfaces in the case that $\Gamma\cap\partial\Omega=\varnothing$ and $\partial\Omega$ is unbounded. To prove this result, we establish a similar theorem for {\it uniformly dense domains } in $\mathbb R^3$, a notion that was introduced by Magnanini, Prajapat \& Sakaguchi in \cite{MPS2006tams}. In the proof, we use methods from the theory of surfaces with constant mean curvature, combined with a careful analysis of certain asymptotic expansions and a surprising connection with the theory of transnormal functions.
We study magnetohydrodynamic stability of neutron star core matter composed of neutrons, protons and leptons threaded by a magnetar-strength magnetic field $10^{14}$--$10^{17}$ G, where quantum electrodynamical effects and Landau quantization of fermions are important. Stability is determined using the Friedman--Schutz formalism for the canonical energy of fluid perturbations, which we calculate for a magnetizable fluid with $H\neq B$. Using this and the Euler--Heisenberg--Fermi--Dirac Lagrangian for a strongly magnetized fluid of Landau-quantized charged fermions, we calculate the local stability criteria for a fluid slab as a stand-in for a segment of a neutron star core, accounting for magnetic and composition gradient buoyancy. The slab is threaded by a field orthogonal to the gravitational field, the Cartesian analogy to a toroidal field. We find that, for sufficiently strong fields $B\gtrsim10^{15}$ G, the magnetized fluid is unstable to a magnetosonic-type instability with growth times of order $10^{-3}$ s. The instability is triggered by sharp changes in the second-order field derivative of the Euler--Heisenberg--Fermi--Dirac Lagrangian which occur where additional Landau levels start being populated. These sharp changes are divergent at zero temperature, but are finite for nonzero temperature, so realistic neutron star core temperatures $5\times10^7$ K$<T<5\times10^8$ K are used. We conjecture that this mechanism could promote the formation of magnetic domains as predicted by Blandford and Hernquist (1982) and Suh and Mathews (2010).
We calculate the one-loop anomalous dimension matrix for the dimension-six baryon number violating operators of the Standard Model effective field theory, including right-handed neutrino fields. We discuss the flavor structure of the renormalization group evolution in the contexts of minimal flavor violation and unification.
A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials phi and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.
The ``social brain hypothesis'' for the evolution of large brains in primates has led to evidence for the coevolution of neocortical size and social group sizes. Extrapolation of these findings to modern humans indicated that the equivalent group size for our species should be approximately 150 (essentially the number of people known personally as individuals). Here, we combine data on human grouping in a comprehensive and systematic study. Using fractal analysis, we identify with high statistical confidence a discrete hierarchy of group sizes with a preferred scaling ratio close to 3: rather than a single or a continuous spectrum of group sizes, humans spontaneously form groups of preferred sizes organized in a geometrical series approximating 3, 9, 27,... Such discrete scale invariance (DSI) could be related to that identified in signatures of herding behavior in financial markets and might reflect a hierarchical processing of social nearness by human brains.
We study the early-time behavior of isotropic and homogeneous solutions in vacuum as well as radiation-filled cosmological models in the full, effective, four dimensional gravity theory with higher derivatives. We use asymptotic methods to analyze all possible ways of approach to the initial singularity of such universes. In order to do so, we construct autonomous dynamical systems that describe the evolution of these models, and decompose the associated vector fields. We prove that, at early times, all flat vacua as well as general curved ones are globally attracted by the "universal" square root scaling solution. Open vacua, on the other hand show in both, future and past directions a dominant asymptotic approach to horizon-free, Milne states that emerge from initial data sets of smaller dimension. Closed universes exhibit more complex logarithmic singularities. Our results on asymptotic stability show a possible relation to cyclic and ekpyrotic cosmologies at the passage through the singularity. In the case of radiation-filled universes of the same class we show the essential uniqueness and stability of the resulting asymptotic scheme, once more dominated by $t^{1/2}$, in all cases except perhaps that of the conformally invariant Bach-Weyl gravity. In all cases, we construct a formal series representation valid near the initial singularity of the general solution of these models and prove that curvature as well as radiation play a subdominant role in the dominating form. A discussion is also made on the implications of these results for the generic initial state of the theory.
Resolving a conjecture of Zhi-Wei Sun, we prove that every rational number can be represented as a sum of distinct unit fractions whose denominators are practical numbers. The same method applies to allowed denominators that are closed under multiplication by two and include a multiple of every positive integer, including the odious numbers, evil numbers, Hardy-Ramanujan numbers, Jordan-Polya numbers, and fibbinary numbers.
We show how transitions between different Lifshitz phases in bilayer Dirac materials with and without spin-orbit coupling can be studied by driving the system. The periodic driving is induced by a laser and the resultant phase diagram is studied in the high frequency limit using the Brillouin-Wigner perturbation approach to leading order. The examples of such materials include bilayer graphene and spin-orbit coupled materials such as bilayer silicene. The phase diagrams of the effective static models are analyzed to understand the interplay of topological phase transitions, with changes in the Chern number and topological Lifshitz transitions, with the ensuing changes in the Fermi surface. Both the topological transitions and the Lifshitz transitions are tuned by the amplitude of the drive.
In the quest for quantum spin liquids, thin films are expected to open the way for the control of intricate magnetic interactions in actual materials by exploiting epitaxial strain and two-dimensionality. However, materials compatible with conventional thin-film growth methods have largely remained undeveloped. As a promising candidate towards the materialization of quantum spin liquids in thin films, we here present a robust ilmenite-type oxide with a honeycomb lattice of edge-sharing IrO$_6$ octahedra artificially stabilized by superlattice formation with an ilmenite-type antiferromagnetic oxide MnTiO$_3$. The stabilized sub-unit-cell-thick Mn-Ir-O layer is isostructural to MnTiO$_3$, having the atomic arrangement corresponding to ilmenite-type MnTiO$_3$ not discovered yet. By spin Hall magnetoresistance measurements, we found that antiferromagnetic ordering in the ilmenite Mn sublattice is suppressed by modified magnetic interactions in the MnO$_6$ planes via the IrO$_6$ planes. These findings lay the foundation for the creation of two-dimensional Kitaev candidate materials, accelerating the discovery of exotic physics and applications specific to quantum spin liquids.
Employing diagrammatic perturbation theory, we calculate the (charge) Coulomb drag resistivity $\rho_D$ and spin Coulomb drag resistivity $\rho_{\uparrow\downarrow}$ in the presence of Rashba spin-orbit coupling. Analytical expressions for $\rho_D$ and $\rho_{\uparrow\downarrow}$ are derived, and it is found that spin-orbit interaction produces a small enhancement to $\rho_D$ and $\rho_{\uparrow\downarrow}$ in the ballistic regime while $\rho_D$ is unchanged in the diffusive regime. This enhancement in the ballistic regime is attributed to the enhancement of the nonlinear susceptibility (i.e. current produced through the rectification of the thermal electric potential fluctuations in the passive layer) while the lack of enhancement in the diffusive regime is due to the suppression by disorder.
Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this review, we highlight some connections between superconformal four dimensional Yang-Mills theory and various integrable systems. In particular, we focus on the role of Yangian symmetries in studying the gauge theory dual of closed string excitations. We also briefly review how the gauge theory connects to Calogero models and open quantum spin chains through the study of the gauge theory duals of D3 branes and open strings ending on them. This invited review, written for Modern Physics Letters-A, is based on a seminar given at the Institute of Advanced Study, Princeton.
Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of $1/\sqrt{S}$. This term is acquired using the Holstein-Primakoff approximation of the spin operator and valid for small $\delta S$ fluctuations of the ordered moment. We propose an algorithm that allows magnetic ground states with general moment directions and single-Q incommensurate ordering wave vector using a local coordinate transformation for every spin and a rotating coordinate transformation for the incommensurability. Finally we show, how our model can determine the spin wave spectrum of the magnetic C-site langasites with incommensurate order.
It has been widely accepted that planar boron structures, composed of triangular and hexagonal motifs are the most stable two dimensional (2D) phases and likely precursors for boron nanostructures. Here we predict, based on ab initio evolutionary structure search, novel 2D boron structure with non-zero thickness, which is considerably, by 50 meV/atom lower in energy than the recently proposed alpha-sheet structure and its analogues. In particular, this phase is identified for the first time to have a distorted Dirac cone, after graphene and silicene the third elemental material with massless Dirac fermions. The buckling and coupling between the two sublattices not only enhance the energetic stability, but also are the key factors for the emergence of the distorted Dirac cone.
We establish an analytic Hasse principle for linear spaces of affine dimension m on a complete intersection over an algebraic field extension K of Q. The number of variables required to do this is no larger than what is known for the analogous problem over Q. As an application we show that any smooth hypersurface over K whose dimension is large enough in terms of the degree is K-unirational, provided that either the degree is odd or K is totally imaginary.