ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (DAC) experiments on the melting curve of xenon, a noble gas solid where van der Waals binding is challenging for traditional DFT methods. The calculations show excellent agreement with data below 20 GPa and that the high-pressure melt curve is well described by a Lindemann behavior up to at least 80 GPa, a finding in stark contrast to DAC data.
In a recent beautiful but technical article, William Y.C. Chen, Qing-Hu Hou, and Doron Zeilberger developed an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequences, namely those (like the Catalan and Motzkin sequences) that are expressible in terms of constant terms of powers of Laurent polynomials. We first give a leisurely exposition of their elementary but brilliant approach, and then extend it in two directions. The Laurent polynomials may be of several variables, and instead of single sums we have multiple sums. In fact we even combine these two generalizations! We conclude with some super-challenges.   In this version we report that Roberto Tauraso pointed out that all our conjectured super-congruences, at the end of our article are already known, except one, for which he supplied a beautiful proof that can be found here: arXiv:1606.05543.
Primordial black holes (PBHs) have been brought back into the spotlight by LIGO's first direct detection of a binary-black-hole merger. One of the poorly understood properties of PBHs is how clustered they are at formation. It has important implications on the efficacy of their merging in the early Universe, as well as on observational constraints. In this work we study the initial clustering of PBHs formed from the gravitational collapse of large density fluctuations in the early Universe. We give a simple and general argument showing that, in this scenario, we do not expect clustering on very small scales beyond what is expected from a random, Poisson distribution. We illustrate this result explicitly in the case where the underlying density field is Gaussian. We moreover derive a new analytic expression for the two-point correlation function of large-threshold fluctuations, generalizing previous results to arbitrary separation, and with broader implications than the clustering of PBHs.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
The growing ubiquity of drones has raised concerns over the ability of traditional air-space monitoring technologies to accurately characterise such vehicles. Here, we present a CNN using a decision tree and ensemble structure to fully characterise drones in flight. Our system determines the drone type, orientation (in terms of pitch, roll, and yaw), and performs segmentation to classify different body parts (engines, body, and camera). We also provide a computer model for the rapid generation of large quantities of accurately labelled photo-realistic training data and demonstrate that this data is of sufficient fidelity to allow the system to accurately characterise real drones in flight. Our network will provide a valuable tool in the image processing chain where it may build upon existing drone detection technologies to provide complete drone characterisation over wide areas.
The empirical finding with data from the Solar Dynamics Observatory (SDO) of positive (negative) horizontal Reynolds stress at the northern (southern) hemisphere for solar giant cells (Hathaway et al. 2013) is discussed for its consequences for the theory of the solar/stellar differential rotation. Solving the nonlinear Reynolds equation for the angular velocity under neglect of the meridional circulation we show that the horizontal Reynolds stress of the northern hemisphere is always negative at the surface but it is positive in the bulk of the solar convection zone by the action of the Lambda effect. The Lambda effect, which describes the angular momentum transport of rigidly rotating anisotropic turbulence and which avoids a rigid-body rotation of the convection zones, is in horizontal direction of cubic power in the rotation rate $\Omega$ and it is always equatorwards directed. Theories without Lambda effect which may also provide the observed solar rotation law only by the action of a meridional circulation lead to a horizontal Reynolds stress with the opposite sign as observed.
We shall show that 9, 165 are all of the odd unitary super perfect numbers.
Using a recently developed method for the inclusion of fluctuation in the BUU dynamics, we study the self-consistent propagation of inherent thermal noise of unstable nuclear matter. The large time behaviour of the evolving system exhibits synergism between fluctuation and non-linearities in a universal manner which manifest in the appearance of macroscopic structure in the average description.
Few layers Fe$_3$GeTe$_2$ is currently the only atomically thin ferromagnetic metal, and thus has drawn huge attention in the field of two-dimensional (2D) magnetism. In this paper, we perform a systematic first principle study on the electronic structure, magnetic anisotropy energy (MAE), and magneto-optical (MO) effects in monolayer (ML), bilayer (BL) and trilayer (TL) as well as bulk Fe$_3$GeTe$_2$. All the considered structures of Fe$_3$GeTe$_2$ are predicted to have large MAE of order $\sim$3.0 meV/f.u., being larger than reported 2D ferromagnetic semiconductors Cr$_2$Ge$_2$Te$_6$ and CrI$_3$ and also being comparable to that of FePt which has the largest MAE among the transition metal alloys. This large MAE thus stabilizes the long range ferromagnetic order down to atomically thin layers and also suggests promising applications of 2D Fe$_3$GeTe$_2$ in high density data storage. Furthermore, the calculated magneto-optical spectra show large magnetic circular dichroism, thus resulting in large MO Kerr rotation and Faraday rotation angles. In visible frequency range, Kerr rotation angles up to $\sim$1.0$^\circ$ for TL Fe$_3$GeTe$_2$ are found. Such values are larger than famous MO transition metal alloy MnBi. Also, large Faraday rotation angles are predicted for all considered Fe$_3$GeTe$_2$ structures. In particular, ML Fe$_3$GeTe$_2$ has a Faraday rotation angle of -156$^\circ$/$\mu m$, which is three times larger than famous MO oxide Bi$_3$Fe$_5$O$_{12}$. These important findings are analysed in terms of the calculated orbital-decomposed density of states and dipole selection rule derived from the group theory. Our findings thus suggest that few layers and bulk Fe$_3$GeTe$_2$ are promising MO materials and could be widely applied to nano MO devices in the future.
One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. Extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.
We present deep radio images of the inner 50 kpc of Centaurus A, taken with the Karl G. Jansky Very Large Array (VLA) at 90cm. We focus on the Transition Regions between the inner galaxy - including the active nucleus, inner radio lobes, and star-forming disk - and the outer radio lobes. We detect previously unknown extended emission around the Inner Lobes, including radio emission from the star-forming disk. We find that the radio-loud part of the North Transition Region, known as the North Middle Lobe, is significantly overpressured relative to the surrounding ISM. We see no evidence for a collimated flow from the Active Galactic Nucleus (AGN) through this region. Our images show that the structure identified by Morganti et al. (1999) as a possible large-scale jet appears to be part of a narrow ridge of emission within the broader, diffuse, radio-loud region. This knotty radio ridge is coincident with other striking phenomena: compact X-ray knots, ionized gas filaments, and streams of young stars. Several short-lived phenomena in the North Transition Region, as well as the frequent re-energization required by the Outer Lobes, suggest that energy must be flowing through both Transition Regioins at the present epoch. We suggest that the energy flow is in the form of a galactic wind.
We establish formulae for the Iwasawa invariants of Mazur--Tate elements of cuspidal eigenforms, generalizing known results in weight 2. Our first theorem deals with forms of "medium" weight, and our second deals with forms of small slope . We give examples illustrating the strange behavior which can occur in the high weight, high slope case.
Multiferroics, where two or more ferroic order parameters coexist, is one of the hottest fields in condensed matter physics and materials science[1-9]. However, the coexistence of magnetism and conventional ferroelectricity is physically unfavoured[10]. Recently several remedies have been proposed, e.g., improper ferroelectricity induced by specific magnetic[6] or charge orders[2]. Guiding by these theories, currently most research is focused on frustrated magnets, which usually have complicated magnetic structure and low magnetic ordering temperature, consequently far from the practical application. Simple collinear magnets, which can have high magnetic transition temperature, have never been considered seriously as the candidates for multiferroics. Here, we argue that actually simple interatomic magnetic exchange interaction already contains a driving force for ferroelectricity, thus providing a new microscopic mechanism for the coexistence and strong coupling between ferroelectricity and magnetism. We demonstrate this mechanism by showing that even the simplest antiferromagnetic (AFM) insulator MnO, can display a magnetically induced ferroelectricity under a biaxial strain.
Kaon production, in particular $K^+$ production in heavy ion collisions at intermediate energies is discussed. Main emphasis is put on the question if subthreshold $K^+$ production can serve as a suitable tool to test the high density phase of such reactions and to deliver information on the high density behavior of the nuclear equation of state. It is shown that the $K^+$ excitation function in heavy ($Au+Au$) over light ($C+C$) systems provides a robust observable which, by comparison to data, strongly favors a soft equation of state. A second question of interest is the existence of an in-medium kaon potential as predicted by effective chiral Lagrangiens. Here it is argued that transport calculations support this scenario with, in the meantime, a significant level of consistency.
Optical polarisation measurements are key tests for different models of the pulsar magnetosphere. Furthermore, comparing the relative orientation of the phase-averaged linear polarisation direction and the pulsar proper motion vector may unveil a peculiar alignment, clearly seen in the Crab pulsar. Our goal is to obtain the first measurement of the phase-averaged optical linear polarisation of the fifth brightest optical pulsar, PSR\, B0656+14, which has also a precisely measured proper motion, and verify a possible alignment between the polarisation direction and the proper motion vector. We carried out observations with the Very Large Telescope (VLT) to measure the phase-averaged optical polarisation degree (P.D.) and position angle (P.A.) of PSR B0656+14. We measured a P.D. of $11.9\%\pm5.5\%$ and a P.A. of $125.8\degr\pm13.2\degr$, measured East of North. Albeit of marginal significance, this is the first measurement of the phase-averaged optical P. D. for this pulsar. Moreover, we found that the P.A. of the phase-averaged polarisation vector is close to that of the pulsar proper motion ($93.12\degr\pm0.38\degr$).Deeper observations are needed to confirm our polarisation measurement of \psr, whereas polarisation measurements for more pulsars will better assess possible correlations of the polarisation degree with the pulsar parameters.
Gravity does not provide any scale for matter properties. We argue that this is also the implication of Mach's hypothesis of the relativity of inertia. The most general spacetime compatible with this property of gravity is that admitting three, independent spatial homothetic Killing vectors generating an arbitrary function of each one of the three spatial coordinates. The matter properties for such a spacetime are (spatially) arbitrary and the matter generating the spacetime admits {\it any} equation of state. This is also the most general spacetime containing the weak gravity physics in its entirety. This spacetime is machian in that it is {\em globally} degenerate for anti-machian situations such as vacuum, a single matter particle etc. and, hence, has no meaning in the absence of matter.
Numerical simulations of turbulent, magnetized, differentially rotating flows driven by the magnetorotational instability are often used to calculate the effective values of alpha viscosity that is invoked in analytical models of accretion discs. In this paper we use various dynamical models of turbulent magnetohydrodynamic stresses, as well as numerical simulations of shearing boxes, to show that angular momentum transport in MRI-driven accretion discs cannot be described by the standard model for shear viscosity. In particular, we demonstrate that turbulent magnetorotational stresses are not linearly proportional to the local shear and vanish identically for angular velocity profiles that increase outwards.
The following article deals with the critical value p_c of the three-dimensional bootstrap percolation. We will check the behavior of p_c for different lengths of the lattice and additionally we will scale p_c in the limit of an infinite lattice.
Based on a scenario of the inhomogeneous big-bang nucleosynthesis (IBBN), we investigate the detailed nucleosynthesis that includes the production of heavy elements beyond Li-7. From the observational constraints on light elements of He4 and D for the baryon-to-photon ratio given by WMAP, possible regions found on the plane of the volume fraction of the high density region against the ratio between high- and low-density regions.   In these allowed regions, we have confirmed that the heavy elements beyond Fe can be produced appreciably, where p- and/or r-process elements are produced well simultaneously compared to the solar system abundances. We suggest that recent observational signals such as He4 overabundance in globular clusters and high metallicity abundances in quasars could be partly due to the results of IBBN. Possible implications are given for the formation of the first generation stars
We have observed 8 faint cataclysmic variable stars photometrically. The nova-like Car2 was extensively sampled but showed little variability. V1040 Cen was observed near the end of a dwarf nova outburst and possessed dwarf nova and quasi-periodic oscillations. Ha 075648 has strong large amplitude flickering and a possible orbital modulation at 3.49 h. The correct identification for the nova remnant IL Nor (Nova Nor 1893) has been established. HS Pup (Nova Pup 1963) has a possible orbital period of 3.244 h. SDSS J2048-06 is a low mass transfer dwarf nova that in quiescence shows slow variations at 7.67 h (though poorly sampled with our observations) and an orbital modulation at 87.26 min. The dwarf nova CSS 081419-005022 has an orbital period of 1.796 h and the eclipsing dwarf nova CSS 112634-100210 has an orbital period of 1.8581 h.
A relativistic approach to describe nuclear and in general strongly interacting matter is introduced and discussed. Here, not only the nuclear forces but also the masses of the nucleons are generated through meson fields. Within this framework it is possible to calculate properties of finite nuclei at a level of accuracy similar to dedicated relativistic nuclear structure models. Due to the more general approach, a wider range of properties of hadronic states can be investigated. A number of results for heavy and neutron-rich nuclei toward the drip line are presented.
We use gravitational wave (GW) standard sirens, in addition to Type Ia supernovae (SNIa) and baryon acoustic oscillation (BAO) mock data, to forecast constraints on the electromagnetic and gravitational distance duality relations (DDR). We make use of a parameterised approach based on a specific DDR violation model, along with a machine learning reconstruction method based on the Genetic Algorithms. We find that GW provide an alternative to the use of BAO data to constrain violations of the DDR, reaching $3\%$ constraints on the violation parameter we consider when combined with SNIa, which is only improved by a factor of $\approx1.4$ if one instead considers the combination of BAO and SNIa. We also investigate the possibility that a neglected modification of gravity might lead to a false detection of DDR violations, even when screening mechanisms are active. We find that such a false detection can be extremely significant, up to $\approx10\sigma$ for very extreme modified gravity scenarios, while this reduces to $\approx4\sigma$ in a more realistic case. False detections can also provide a smoking gun for the modified gravity mechanism at play, as a result of the tension introduced between the SNIa+GW and SNIa+BAO combinations.
A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categories: schemes which extend the robustness to (i) spin or (ii) motional decoherence. We choose to focus on extensions of the $\sigma_x\otimes\sigma_x$ Molmer-Sorensen interaction using microwaves and a static magnetic field gradient. Nevertheless, some of the techniques discussed here can be relevant to other trapped ion architectures or physical qubit implementations. Finally, we experimentally realize a proof-of-concept interaction with simultaneous robustness to spin and motional decoherence by combining several quantum control methods presented in this manuscript.
We describe a conjectural stratification of the Brill-Noether variety for general curves of fixed genus and gonality. As evidence for this conjecture, we show that this Brill-Noether variety has at least as many irreducible components as predicted by the conjecture, and that each of these components has the expected dimension. Our proof uses combinatorial and tropical techniques. Specifically, we analyze containment relations between the various strata of tropical Brill-Noether loci identified by Pflueger in his classification of special divisors on chains of loops.
In this note we study the $L^p-L^q$ boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq q <\infty$. The underlying Fourier analysis is associated with the eigenfunctions of an anharmonic oscillator in some family of differential operators having derivatives of any order. Our analysis relies on a version of the classical Paley-type inequality, introduced by H\"ormander, that we extend in our nonharmonic setting.
Acoustic metafluids are defined as the class of fluids that allow one domain of fluid to acoustically mimic another, as exemplified by acoustic cloaks. It is shown that the most general class of acoustic metafluids are materials with anisotropic inertia and the elastic properties of what are known as pentamode materials. The derivation uses the notion of finite deformation to define the transformation of one region to another. The main result is found by considering energy density in the original and transformed regions. Properties of acoustic metafluids are discussed, and general conditions are found which ensure that the mapped fluid has isotropic inertia, which potentially opens up the possibility of achieving broadband cloaking.
Locally finite self-similar graphs with bounded geometry and without bounded geometry as well as non-locally finite self-similar graphs are characterized by the structure of their cell graphs. Geometric properties concerning the volume growth and distances in cell graphs are discussed. The length scaling factor $\nu$ and the volume scaling factor $\mu$ can be defined similarly to the corresponding parameters of continuous self-similar sets. There are different notions of growth dimensions of graphs. For a rather general class of self-similar graphs it is proved that all these dimensions coincide and that they can be calculated in the same way as the Hausdorff dimension of continuous self-similar fractals: \[\dim X=\frac{\log \mu}{\log \nu}.\]
This paper investigates the particle radiation from Gibbons-Maeda black hole. Taking into account the self-gravitation of the particle, we calculate the tunnelling rate of the massless particle across the horizon, then we promote the work to the radiation of the charged particle. The calculations prove that the rate of tunnelling equals precisely the exponent of the difference of the black hole entropy before and after emission and the radiation spectrum deviates from exact thermal. The conclusion supports the viewpoint of information conservation.
We report the discovery of two low redshift HI 21cm absorbers, one at z = 0.2212 towards the z_{em} = 0.630 quasar OI 363 (B0738+313), and the other at z = 0.3127 towards PKS B1127-145 (z_{em} = 1.187). Both were found during a survey of MgII selected systems at redshifts 0.2 < z < 1 using the new UHF-high system at the Westerbork Synthesis Radio Telescope (WSRT). New HST/FOS observations also identify both systems as damped Ly-alpha (DLa) absorbers. By comparing the column density from the DLa line with that from the HI 21cm line, we calculate the spin temperature, and find that T_s is approximately 1000 K for both of these low redshift absorbers. We briefly discuss some implications of this result.
We study generalized regular bent functions using a representation by bent rectangles, that is, special matrices with restrictions on rows and columns. We describe affine transformations of bent rectangles, propose new biaffine and bilinear constructions, study partitions of a vector space into affine planes of the same dimension and use such partitions to build bent rectangles. We illustrate the concept of bent rectangles by examples for the Boolean case.
We show that the shift in the transition temperature of the dilute homogeneous Bose gas is non-analytic in the scattering amplitude, $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This non-universal non-analytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a \to0$, since the linearity is apparent only for anomalously small $a$.