ShantanuT01/DACTYL-Pretraining huggingface dataset:
Context. The use of ratios of small to large separations as a diagnostic of stellar interiors. Aims. To demonstrate that model fitting by comparing observed and model separation ratios at the same n values is in error, and to present a correct procedure. Methods. Theoretical analysis using phase shifts and numerical models. Results. We show that the separation ratios of stellar models with the same interior structure, but different outer layers, are not the same when compared at the same n values, but are the same when evaluated at the same frequencies by interpolation. The separation ratios trace the phase shift differences as a function of frequency not of n. We give examples from model fitting where the ratios at the same n values agree within the error estimates, but do not agree when evaluated at the same frequencies and the models do not have the same interior structure. The correct procedure is to compare observed ratios with those of models interpolated to the observed frequencies.
It has been recently shown that multiferroic logic - where logic bits are encoded in the magnetization orientation of a nanoscale magnetostrictive layer elastically coupled to a piezoelectric layer - can be Bennett clocked with small electrostatic potentials of few tens of mV applied to the piezoelectric layer. The potential generates stress in the magnetostrictive layer and rotates its magnetization by a large angle to carry out Bennett clocking. This method of clocking is far more energy-efficient than using spin transfer torque. In order to assess if such a clocking scheme can be also reasonably fast, we have studied the magnetization dynamics of a multiferroic logic array with nearest neighbor dipole coupling using the Landau-Lifshitz-Gilbert (LLG) equation. We find that switching delays of ~ 3 ns (clock rates of 0.33 GHz) can be achieved with proper design provided we clock non-adiabatically and dissipate ~48,000 kT (at room temperature) of energy per clock cycle per bit flip in the clocking circuit. This dissipation far exceeds the energy barrier separating the two logic states, which we assumed to be 32 kT to yield a bit error probability of . Had we used spin transfer torque to switch with the same ~ 3 ns delay, the energy dissipation would have been much larger (~ $6 \times 106$ kT). This shows that spin transfer torque, widely used in magnetic random access memory, is an inefficient way to switch a magnet, and multiferroic logic clocked with voltage-induced stress is a superior nanomagnetic logic scheme.
We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for this game, which we call the lazy cop number. Lazy Cops and Robbers was recently introduced by Offner and Ojakian, who provided asymptotic upper and lower bounds on the lazy cop number of the hypercube. By investigating expansion properties, we provide asymptotically almost sure bounds on the lazy cop number of binomial random graphs $\mathcal{G}(n,p)$ for a wide range of $p=p(n)$. By coupling the probabilistic method with a potential function argument, we also improve on the existing lower bounds for the lazy cop number of hypercubes. Finally, we provide an upper bound for the lazy cop number of graphs with genus $g$ by using the Gilbert-Hutchinson-Tarjan separator theorem.
Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-Mathis characterized them via representations in a real base $\beta$. However, the given condition turns to be not necessary. Hence, the goal of this paper is to provide a correction of Bertrand-Mathis' result. The main difference arises when $\beta$ is a Parry number, in which case are derived two associated Bertrand numeration systems. Along the way, we define a non-canonical $\beta$-shift and study its properties analogously to those of the usual canonical one.
The aim of this paper is to determine all algebraic relations among various special gamma values over function fields, and prove a Chowla-Selberg-type formula for quasi-periods of CM abelian $t$-modules. Our results are based on the intrinsic relations between gamma values in question and periods of CM dual $t$-motives, which are interpreted in terms of their "distributions". This also enables us to derive an analogue of the Deligne-Gross period conjecture for CM Hodge-Pink structures.
We consider ensembles of trajectories associated with large deviations of time-integrated quantities in stochastic models. Motivated by proposals that these ensembles are relevant for physical processes such as shearing and glassy relaxation, we show how they can be generated directly using auxiliary stochastic processes. We illustrate our results using the Glauber-Ising chain, for which biased ensembles of trajectories can exhibit ferromagnetic ordering. We discuss the relation between such biased ensembles and quantum phase transitions.
We have compared simultaneous Ryle Telescope radio and Rossi X-Ray Timing Explorer X-ray observations of the galactic microquasar GRS 1915+105, using the classification of the X-ray behaviour in terms of three states as previously established. We find a strong (one-to-one) relation between radio oscillation events and series of spectrally hard states in the X-ray light curves, if the hard states are longer than ~100s and are "well separated" from each other. In all other cases the source either shows a low-level or a high level radio emission, but no radio oscillation events. During intervals when the source stays in the hard spectral state for periods of days to months, the radio behaviour is quite different; during some of these intervals a quasi-continuous jet is formed with an almost flat synchrotron spectrum extending to at least the near-infrared. Based on the similarities between the oscillation profiles at different wavelengths, we suggest a scenario which can explain most of the complex X-ray : radio behaviour of GRS 1915+105. We compare this behaviour with that of other black hole sources and challenge previous reports of a relation between spectrally soft X-ray states and the radio emission.
We carry out fully 3-dimensional simulations of evolution from self-similar, spherically symmetric linear perturbations of a Cold Dark Matter dominated Einstein-de Sitter universe. As a result of the radial orbit instability, the haloes which grow from such initial conditions are triaxial with major-to-minor axis ratios of order 3:1. They nevertheless grow approximately self-similarly in time. In all cases they have power-law density profiles and near-constant velocity anisotropy in their inner regions. Both the power-law index and the value of the velocity anisotropy depend on the similarity index of the initial conditions, the former as expected from simple scaling arguments. Halo structure is thus not "universal" but remembers the initial conditions. On larger scales the density and anisotropy profiles show two characteristic scales, corresponding to particles at first pericentre and at first apocentre after infall. They are well approximated by the NFW model only for one value of the similarity index. In contrast, at all radii within the outer caustic the pseudo phase-space density can be fit by a single power law with an index which depends only very weakly on the similarity index of the initial conditions. This behaviour is very similar to that found for haloes formed from LCDM initial conditions and so can be considered approximately universal.
We study the nonequilibrium Casimir-Polder force on an atom prepared in an incoherent superposition of internal energy-eigenstates, which is placed in a magnetoelectric environment of nonuniform temperature. After solving the coupled atom--field dynamics within the framework of macroscopic quantum electrodynamics, we derive a general expression for the thermal Casimir-Polder force.
The first exact rotating charged black hole solution to the Einstein{nonlinear electrodynamics theory is reported. It is equipped with mass, rotation parameter, electric and magnetic charges, and three parameters due to the electrodynamics: beta is associated to the potential vectors A{mu} and starP{nu}, and two constants, F0 and G0, related to the presence of the invariants F and G in the Lagrangian L(F;G). This Petrov type D solution is characterized by the Weyl tensor eigenvalue Psi2, the Ricci tensor eigenvalue S = 2Phi(11), and the scalar curvature R; it allows for event horizons, exhibits a ring singularity and fulfills the energy conditions. Its Maxwell limit is the Kerr{Newman black hole.
The standard quantization formalism in spacetimes with event horizons implies a non-unitary evolution of quantum states, as initial pure states may evolve into thermal states. This phenomenon is behind the famous black hole information loss paradox which provoked long-standing debates on the compatibility of quantum mechanics and gravity. In this paper we demonstrate that within an alternative time-symmetric quantization formalism thermal radiation is absent and states evolve unitarily in spacetimes with event horizons. We also discuss the theoretical consistency of the proposed formalism. We explicitly demonstrate that the theory preserves the microcausality condition and suggest a "reinterpretation postulate" to resolve other apparent pathologies associated with negative energy states. Accordingly as there is a consistent alternative, we argue that choosing to use time-asymmetric quantization is a necessary condition for the black hole information loss paradox.
This note is devoted to the linear stability of the Couette flow for the non-isentropic compressible Euler equations in a domain $\mathbb{T}\times \mathbb{R}$. Exploiting the several conservation laws originated from the special structure of the linear system, we obtain a Lyapunov type instability for the density, the temperature, the compressible part of the velocity field, and also obtain an inviscid damping for the incompressible part of the velocity field.
We use deep learning to explore the nature of observed giant clumps in high-redshift disc galaxies, based on their identification and classification in cosmological simulations. Simulated clumps are detected using the 3D gas and stellar densities in the VELA zoom-in cosmological simulation suite, with $\sim \!\! 25\ \!\rm{pc}$ maximum resolution, targeting main sequence galaxies at $1\!<\!z\!<\!3$. The clumps are classified as long-lived clumps (LLCs) or short-lived clumps (SLCs) based on their longevity in the simulations. We then train neural networks to detect and classify the simulated clumps in mock, multi-color, dusty and noisy HST-like images. The clumps are detected using an encoder-decoder convolutional neural network (CNN), and are classified according to their longevity using a vanilla CNN. Tests using the simulations show our detector and classifier to be $\sim80\%$ complete and $\sim80\%$ pure for clumps more massive than $\sim10^{7.5}\rm{M_\odot}$. When applied to observed galaxies in the CANDELS/GOODS S+N fields, we find both types of clumps to appear in similar abundances in the simulations and the observations. LLCs are, on average, more massive than SLCs by $\sim 0.5\ \rm{dex}$, and they dominate the clump population above $M_{\rm c}\gtrsim 10^{7.6}\ \rm{M_\odot}$. LLCs tend to be found closer to the galactic centre, indicating clump migration to the centre or preferential formation at smaller radii. The LLCs are found to reside in high mass galaxies, indicating better clump survivability under supernova feedback there, due to clumps being more massive in these galaxies. We find the clump properties in the simulations and the observations to agree within a factor of $\sim\! 2$.
Building on the results of previous work, we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads naturally to canonical vierbein general relativity has the extrinsic curvature of the Cauchy surface represented by gravitational as well as non-gravitational degrees of freedom. Nevertheless the metric compatibility conditions are undisturbed, and this apparent derivative-coupling is seen to be an effect of working with (possibly orthonormal) linear frames. The formalism is adapted to consider a Dirac Fermion, where we find that a milder form of this apparent derivative-coupling appears.
Faces form the basis for a rich variety of judgments in humans, yet the underlying features remain poorly understood. Although fine-grained distinctions within a race might more strongly constrain possible facial features used by humans than in case of coarse categories such as race or gender, such fine grained distinctions are relatively less studied. Fine-grained race classification is also interesting because even humans may not be perfectly accurate on these tasks. This allows us to compare errors made by humans and machines, in contrast to standard object detection tasks where human performance is nearly perfect. We have developed a novel face database of close to 1650 diverse Indian faces labeled for fine-grained race (South vs North India) as well as for age, weight, height and gender. We then asked close to 130 human subjects who were instructed to categorize each face as belonging toa Northern or Southern state in India. We then compared human performance on this task with that of computational models trained on the ground-truth labels. Our main results are as follows: (1) Humans are highly consistent (average accuracy: 63.6%), with some faces being consistently classified with > 90% accuracy and others consistently misclassified with < 30% accuracy; (2) Models trained on ground-truth labels showed slightly worse performance (average accuracy: 62%) but showed higher accuracy (72.2%) on faces classified with > 80% accuracy by humans. This was true for models trained on simple spatial and intensity measurements extracted from faces as well as deep neural networks trained on race or gender classification; (3) Using overcomplete banks of features derived from each face part, we found that mouth shape was the single largest contributor towards fine-grained race classification, whereas distances between face parts was the strongest predictor of gender.
The critical dimension of the bosonic string in the harmonic and the deDonder gauge may be calculated from the time ordered product of two energy momentum tensors. We show that recently found ambiguities within that method in nonconformal gauges can be resolved by a treatment respecting background covariance.
For a primitive Dirichlet character $\chi$ modulo $q$, we define $M(\chi)=\max_{t } |\sum_{n \leq t} \chi(n)|$. In this paper, we study this quantity for characters of a fixed odd order $g\geq 3$. Our main result provides a further improvement of the classical P\'{o}lya-Vinogradov inequality in this case. More specifically, we show that for any such character $\chi$ we have $$M(\chi)\ll_{\varepsilon} \sqrt{q}(\log q)^{1-\delta_g}(\log\log q)^{-1/4+\varepsilon},$$ where $\delta_g := 1-\frac{g}{\pi}\sin(\pi/g)$. This improves upon the works of Granville and Soundararajan and of Goldmakher. Furthermore, assuming the Generalized Riemann hypothesis (GRH) we prove that $$ M(\chi) \ll \sqrt{q} \left(\log_2 q\right)^{1-\delta_g} \left(\log_3 q\right)^{-\frac{1}{4}}\left(\log_4 q\right)^{O(1)}, $$ where $\log_j$ is the $j$-th iterated logarithm. We also show unconditionally that this bound is best possible (up to a power of $\log_4 q$). One of the key ingredients in the proof of the upper bounds is a new Hal\'asz-type inequality for logarithmic mean values of completely multiplicative functions, which might be of independent interest.
The light curves of magnetic, chemically peculiar stars typically show periodic variability due to surface spots that in most cases can be modeled by low-order harmonic expansion. However, high-precision satellite photometry reveals tiny complex features in the light curves of some of these stars that are difficult to explain as caused by a surface phenomenon under reasonable assumptions. These features might originate from light extinction in corotating magnetospheric clouds supported by a complex magnetic field dominated by higher-order multipoles. We aim to understand the photometric signatures of corotating magnetospheres that are governed by higher-order multipoles. We determined the location of magnetospheric clouds from the minima of the effective potential along the magnetic field lines for different orders of multipoles and their combination. From the derived magnetospheric density distribution, we calculated light curves accounting for absorption and subsequent emission of light. For axisymmetric multipoles, the rigidly rotating magnetosphere model is able to explain the observed tiny features in the light curves only when the higher-order multipoles dominate the magnetic field not only at the stellar surface, but even at the Kepler radius. However, even a relatively weak nonaxisymmetric component leads to warping of equilibrium surfaces. This introduces structures that can explain the tiny features observed in the light curves of chemically peculiar stars. The light emission contributes to the light variability only if a significant fraction of light is absorbed in the magnetosphere.
In this paper, we discuss the constraints on the reheating temperature supposing an early post-reheating cosmological phase dominated by one or more simple scalar fields produced from inflaton decay and decoupled from matter and radiation. In addition, we explore the combined effects of the reheating and non-standard scalar field phases on the inflationary number of $e$-foldings.
The full low energy effective action of N=4 SYM is believed to be self-dual. Starting with the first two leading terms in a momentum expansion of this effective action, we perform a duality transformation and find the conditions for self-duality. These determine some of the higher order terms. We compare the effective action of N=4 SYM with the probe-source description of type II_B D3-branes in the AdS_5 \times S_5 background. We find agreement up to six derivative terms if we identify the separation of the 3-branes with a redefinition of the gauge scalar that involves the gauge field strength.
We report on the theoretical photoluminescence spectrum of the interacting two-dimensional electron gas at filling factor one (\nu=1). We considered a model similar to the one adopted to study the X-ray spectra of metals and solved it analytically using the bosonization method previously developed for the two-dimensional electron gas at \nu=1. We calculated the emission spectra of the right and the left circularly polarized radiations for the situations where the distance between the two-dimensional electron gas and the valence band hole are smaller and greater than the magnetic length. For the former, we showed that the polarized photoluminescence spectra can be understood as the recombination of the so-called excitonic state with the valence band hole whereas, for the latter, the observed emission spectra can be related to the recombination of a state formed by a spin down electron bound to n spin waves. This state seems to be a good description for the quantum Hall skyrmion.
Knowledge of magnetic symmetry is vital for exploiting nontrivial surface states of magnetic topological materials. EuIn$_{2}$As$_{2}$ is an excellent example, as it is predicted to have collinear antiferromagnetic order where the magnetic moment direction determines either a topological-crystalline-insulator phase supporting axion electrodynamics or a higher-order-topological-insulator phase with chiral hinge states. Here, we use neutron diffraction, symmetry analysis, and density functional theory results to demonstrate that EuIn$_{2}$As$_{2}$ actually exhibits low-symmetry helical antiferromagnetic order which makes it a stoichiometric magnetic topological-crystalline axion insulator protected by the combination of a 180$^{\circ}$ rotation and time-reversal symmetries: $C_{2}\times\mathcal{T}=2^{\prime}$. Surfaces protected by $2^{\prime}$ are expected to have an exotic gapless Dirac cone which is unpinned to specific crystal momenta. All other surfaces have gapped Dirac cones and exhibit half-integer quantum anomalous Hall conductivity. We predict that the direction of a modest applied magnetic field of $H\approx1$ to $2$ T can tune between gapless and gapped surface states.
Understanding the dynamics of the solar chromosphere is crucial to understanding energy transport across the solar atmosphere. The chromosphere is optically thick at many wavelengths and described by non-local thermodynamic equilibrium (NLTE), making it difficult to interpret observations. Furthermore, there is considerable evidence that the atmosphere is filamented, and that current instruments do not sufficiently resolve small scale features. In flares, it is likely that multithreaded models are required to describe the heating. The combination of NLTE effects and multithreaded modeling requires computationally demanding calculations, which has motivated the development of a model that can efficiently treat both. We describe the implementation of a solver in a hydrodynamic code for the hydrogen level populations that approximates the NLTE solutions. We derive an accurate electron density across the atmosphere, that includes the effects of non-equilibrium ionization for helium and metals. We show the effects on hydrodynamic simulations, which are used to synthesize light curves using a post-processing radiative transfer code. We demonstrate the utility of this model on IRIS observations of a small flare. We show that the Doppler shifts in Mg II, C II, and O I can be explained with a multithreaded model of loops subjected to electron beam heating, so long as NLTE effects are treated. The intensities, however, do not match observed values very well, which is due to assumptions about the initial atmosphere. We briefly show how altering the initial atmosphere can drastically alter line profiles, and therefore derived quantities, and suggest that it should be tuned to pre-flare observations.
The Borromean $^6$He nucleus is an exotic system characterized by two `halo' neutrons orbiting around a compact $^4$He (or $\alpha$) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for {\em ab initio} theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with $^4$He+$n$+$n$ cluster degrees of freedom largely solves this issue. We analyze the role played by the $\alpha$-clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.
Thermoelastic noise will be the most significant noise source in advanced-LIGO interferometers with sapphire test masses. The standard plan for advanced-LIGO has optimized the optics, within the framework of conventional mirrors, to reduce thermoelastic noise. Recently, we and our collaborators have proposed going beyond the bounds of traditional optics to increase the effective beam spot size and thus lower thermoelastic noise. One particular proposal for mirror shapes (``Mexican-hat mirrors'') yields the class of ``mesa'' beams.   In this paper, we outline a general procedure for analyzing light propagating in individual arm cavities, and the associated thermoelastic noise, in the presence of arbitrary optics. We apply these procedures to study the Mexican-hat proposal. Results obtained by the techniques of this paper were presented elsewhere, to demonstrate that the Mexican-hat proposal for advanced-LIGO both significantly lowers thermoelastic noise and does not significantly complicate the function of the interferometer.