ShantanuT01/DACTYL-Pretraining huggingface dataset:
A scaling argument is presented that leads to a shallow water theory of non-axisymmetric disturbances in annular sections of thin Keplerian disks. To develop a theoretical construction that will aid in physically understanding the relationship of known two-dimensional vortex dynamics to their three-dimensional counterparts in Keplerian disks. Using asymptotic scaling arguments varicose disturbances of a Keplerian disk are considered on radial and vertical scales consistent with the height of the disk while the azimuthal scales are the full $2\pi$ angular extent of the disk. The scalings lead to dynamics which are radially geostrophic and vertically hydrostatic. It follows that a potential vorticity quantity emerges and is shown to be conserved in a Lagrangian sense. Uniform potential vorticity linear solutions are explored and the theory is shown to contain an incarnation of the strato-rotational instability under channel flow conditions. Linearized solutions of a single defect on an infinite domain is developed and is shown to support a propagating Rossby edgewave. Linear non-uniform potential vorticity solutions are also developed and are shown to be similar in some respects to the dynamics of strictly two-dimensional inviscid flows. Based on the framework of this theory, arguments based on geophysical notions are presented to support the assertion that the strato-rotational instability is in a generic class of barotropic/baroclinic potential vorticity instabilities. Extensions of this formalism are also proposed. The shallow water formulation achieved by the asymptotic theory developed here opens a new approach to studying disk dynamics.
In this MSc. thesis, we have attempted to give an overview of the firewall paradox and various approaches towards its resolution. After an introductory chapter on some basic concepts in quantum field theory in curved spacetimes such as Hawking radiation, we introduce the paradox. It arises out of application of principles each of which is thought or assumed to be correct: 1) unitary black hole evaporation, 2) validity of quantum field theory in curved spacetime, 3) a measure of the number of black hole quantum states, 4) Einstein's equivalence principle. Then, we present various approaches that exist in the literature towards the resolution of the paradox.
(abridged) An object classified as a galaxy in on-line data bases and revealed on sky survey images as a distant ring galaxy is a rare case of polar ring galaxy where the ring is only slightly inclined to the equatorial plane of the central body. SDSS imaging indicates that the diameter of the ring is about 36 kpc. The SDSS data was combined with long-slit spectroscopic observations and with Fabry-Perot Interferometer H-beta mapping obtained at the Russian Academy of Sciences 6-m telescope. We derived the complex morphologies of this presumed ring galaxy from a combination of SDSS images and from the kinematical behaviour of the central body and of the ring, and determined the stellar population compositions of the two components from SDSS colours, spectroscopy, and evolutionary stellar synthesis models. The ring metallicity is slightly under-abundant. The total luminosity and the total mass of the system are not extreme, but the rather high M/L~20 indicates the presence of large amounts of dark matter. Two alternative explanations of this object are proposed (1) a ring formed by two semi-circular and tight spiral arms at the end of a central bar with a warp or precession of the ring material. The object could, therefore, be explained as an extreme SBa(R) galaxy, or (2) a Polar Ring Galaxy where the inner object is an S0 and the ring is significantly more luminous than the central object. The compound object would then be similar to the NGC 4650A galaxy, being a rare object with a polar component only modestly inclined to the equatorial plane of the central body. Arguments for (and against) both explanations are given and discussed, with the second alternative being more acceptable.
We study the far infrared (60-500 $\mu$m) colours of late-type galaxies in the $Herschel$ Reference Survey, a K-band selected, volume limited sample of nearby galaxies. The far infrared colours are correlated with each other, with tighter correlations for the indices that are closer in wavelength. We also compare the different colour indices to various tracers of the physical properties of the target galaxies, such as the surface brightness of the ionising and non-ionising stellar radiation, the dust attenuation and the metallicity. The emission properties of the cold dust dominating the far infrared spectral domain are regulated by the properties of the interstellar radiation field. Consistent with that observed in nearby, resolved galaxies, our analysis shows that the ionising and the non-ionising stellar radiation, including that emitted by the most evolved, cold stars, both contribute to the heating of the cold dust component. This work also shows that metallicity is another key parameter characterising the cold dust emission of normal, late-type galaxies. A single modified black body with a grain emissivity index $\beta$=1.5 better fits the observed SPIRE flux density ratios $S250/S350$ vs. $S350/S500$ than $\beta$=2, although values of $\beta$ $\simeq$ 2 are possible in metal rich, high surface brightness galaxies. Values of $\beta$ $\lesssim$ 1.5 better represent metal poor, low surface brightness objects. This observational evidence provides strong constraints for dust emission models of normal, late type galaxies.
With the increase in computation power and the development of new state-of-the-art deep learning algorithms, appearance-based gaze estimation is becoming more and more popular. It is believed to work well with curated laboratory data sets, however it faces several challenges when deployed in real world scenario. One such challenge is to estimate the gaze of a person about which the Deep Learning model trained for gaze estimation has no knowledge about. To analyse the performance in such scenarios we have tried to simulate a calibration mechanism. In this work we use the MPIIGaze data set. We trained a multi modal convolutional neural network and analysed its performance with and without calibration and this evaluation provides clear insights on how calibration improved the performance of the Deep Learning model in estimating gaze in the wild.
Accurate determination of the rotation rate in the radiative zone of the sun from helioseismic observations requires rotational frequency splittings of exceptional quality as well as reliable inversion techniques. We present here inferences based on mode parameters calculated from 2088-days long MDI, GONG and GOLF time series that were fitted to estimate very low frequency rotational splittings (nu < 1.7 mHz). These low frequency modes provide data of exceptional quality, since the width of the mode peaks is much smaller than the rotational splitting and hence it is much easier to separate the rotational splittings from the effects caused by the finite lifetime and the stochastic excitation of the modes. We also have implemented a new inversion methodology that allows us to infer the rotation rate of the radiative interior from mode sets that span l=1 to 25. Our results are compatible with the sun rotating like a rigid solid in most of the radiative zone and slowing down in the core (R_sun < 0.2). A resolution analysis of the inversion was carried out for the solar rotation inverse problem. This analysis effectively establishes a direct relationship between the mode set included in the inversion and the sensitivity and information content of the resulting inferences. We show that such an approach allows us to determine the effect of adding low frequency and low degree p-modes, high frequency and low degree p-modes, as well as some g-modes on the derived rotation rate in the solar radiative zone, and in particular the solar core. We conclude that the level of uncertainties that is needed to infer the dynamical conditions in the core when only p-modes are included is unlikely to be reached in the near future, and hence sustained efforts are needed towards the detection and characterization of g-modes.
Schottky Conjecture is analytically proved for multi-stage field emitters consisting on the superposition of rectangular or trapezoidal protrusions on a line under some specific limit. The case in which a triangular protrusion is present on the top of each emitter is also considered as an extension of the model. The results presented here are obtained via Schwarz-Christoffel conformal mapping and reinforce the validity of Schottky Conjecture when each protrusion is much larger than the ones above it, even when an arbitrary number of stages is considered. Moreover, it is showed that it is not necessary to require self-similarity between each of the stages in order to ensure the validity of the conjecture under the appropriate limits.
We present the first results of the estimation of gravity and effective temperature for some poorly studied chemically peculiar stars that were recently observed with the spectropolarimeter ESPaDOnS at CFHT. We have analyzed the spectra of HD71030, HD95608 and HD116235 to determine their radial velocity, Vsin(i) and the average abundance of several chemical species. We have also analyzed our results to verify for possible vertical abundance stratification of iron and chromium in these stars.
We apply the semi-classical limit of the generalized $SO(3)$ map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on $T^{\ast }\mathcal{S}_{2}$. Using the asymptotic form of the star-product, we manage to "quantize" one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.
Neutron diffraction and bulk measurements are used to determine the nature of the low-temperature ordered state in LiCu$_2$O$_2$, a $S=1/2$ spin-chain compound with competing interactions. The magnetic structure is found to be helimagnetic, with a propagation vector $(0.5,\zeta,0)$, $\zeta=0.174$. The nearest-neighbor exchange constant and frustration ratio are estimated to be $J=5.8$ meV and $J_2/J_1=0.29$, respectively. For idealized spin chains these parameter values would signify a gapped spin-liquid ground state. Long-range ordering is attributed to intrinsic non-stoichiometry.
Open string field theory is considered as a tool for deriving the effective action for the massless or tachyonic fields living on D-branes. Some simple calculations are performed in open bosonic string field theory which validate this approach. The level truncation method is used to calculate successive approximations to the quartic terms \phi^4, (A^\mu A_\mu)^2 and [A_\mu, A_\nu]^2 for the zero momentum tachyon and gauge field on one or many bosonic D-branes. We find that the level truncation method converges for these terms within 2-4% when all massive fields up to level 20 are integrated out, although the convergence is slower than exponential. We discuss the possibility of extending this work to determine the structure of the nonabelian Born-Infeld theory describing the gauge field on a system of many parallel bosonic or supersymmetric D-branes. We also describe a brane configuration in which tachyon condensation arises in both the gauge theory and string field theory pictures. This provides a natural connection between recent work of Sen and Zwiebach on tachyon condensation in string field theory and unstable vacua in super Yang-Mills and Born-Infeld field theory.
In the present article we shown a formula to compute the number of all matrices over the finite field $F$ whit prescribed eigenvalues. Using this formula we obtain one inequality for the number of $(k+1)$-potent elements over finite rings.
Sets of commuting charges constructed from the current of a U(1) Kac-Moody algebra are found. There exists a set S_n of such charges for each positive integer n > 1; the corresponding value of the central charge in the Feigin-Fuchs realization of the stress tensor is c = 13-6n-6/n. The charges in each series can be written in terms of the generators of an exceptional W-algebra.
We give a simple and short proof of the fact that the board game of Y cannot end in a draw. Our proof, based on the analogous result for the game of Hex (the so-called 'Hex Theorem'), is purely topological and does not depend on the shape of the board. We also include a simplified version of Gale's proof of Hex Theorem.
Graphene, consisting of an inert, thermally stable material with an atomically flat, dangling bond-free surface is by essence an ideal template layer for van der Waals heteroepitaxy of two-dimensional materials such as silicene. However, depending on the synthesis method and growth parameters, graphene (Gr) substrates could exhibit, on a single sample, various surface structures, thicknesses, defects, and step heights. These structures noticeably affect the growth mode of epitaxial layers, e.g. turning the layer-by-layer growth into the Volmer-Weber growth promoted by defect-assisted nucleation. In this work, the growth of silicon on chemical vapor deposited epitaxial Gr (1 ML Gr/1ML Gr buffer) on 6H-SiC(0001) substrate is investigated by a combination of atomic force microscopy (AFM), scanning tunneling microscopy (STM), x-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM) and Raman spectroscopy measurements. It is shown that the perfect control of full-scale almost defect-free 1 ML Gr with a single surface structure and the ultra-clean conditions for molecular beam epitaxy (MBE) deposition of silicon represent key prerequisites for ensuring the growth of extended silicene sheets on epitaxial graphene.
We compute the free energy of asymmetric nuclear matter in a Brueckner-Hartree-Fock approach at finite temperature, paying particular attention to the dependence on isospin asymmetry. The first- and second-order symmetry energies are determined as functions of density and temperature and useful parametrizations are provided. We find small deviations from the quadratic isospin dependence and very small corresponding effects on (proto)neutron star structure.
Large-scale bulk flows in the Universe distort the initial density field, broadening the baryon-acoustic-oscillation (BAO) feature that was imprinted when baryons were strongly coupled to photons. Additionally, there is a small shift inward in the peak of the conventional overdensity correlation function, a mass-weighted statistic. This shift occurs when high density peaks move toward each other. We explore whether this shift can be removed by applying to the density field a transform (such as a logarithm) that gives fairer statistical weight to fluctuations in underdense regions. Using configuration-space perturbation theory in the Zel'dovich approximation, we find that the log-density correlation function shows a much smaller inward shift in the position of the BAO peak at low redshift than is seen in the overdensity correlation function. We also show that if the initial, Lagrangian density of matter parcels could be estimated at their Eulerian positions, giving a displaced-initial-density field, its peak shift would be even smaller. In fact, a transformed field that accentuates underdensities, such as the reciprocal of the density, pushes the peak the other way, outward. In our model, these shifts in the peak position can be attributed to shift terms, involving the derivative of the linear correlation function, that entirely vanish in this displaced-initial-density field.
We have investigated the longitudinal thermal conductivity of $\alpha$-RuCl$_{3}$, the magnetic state of which is considered to be proximate to a Kitaev honeycomb model, along with the spin susceptibility and magnetic specific heat. We found that the temperature dependence of the thermal conductivity exhibits an additional peak around 100 K, which is well above the phonon peak temperature ($\sim$ 50 K). The higher-temperature peak position is comparable to the temperature scale of the Kitaev couplings rather than the N\'eel temperatures below 15 K. The additional heat conduction was observed for all five samples used in this study, and was found to be rather immune to a structural phase transition of $\alpha$-RuCl$_{3}$, which suggests its different origin from phonons. Combined with experimental results of the magnetic specific heat, our transport measurement suggests strongly that the higher-temperature peak in the thermal conductivity is attributed to itinerant spin excitations associated with the Kitaev couplings of $\alpha$-RuCl$_{3}$. A kinetic approximation of the magnetic thermal conductivity yields a mean free path of $\sim$ 20 nm at 100 K, which is well longer than the nearest Ru-Ru distance ($\sim$ 3 \AA), suggesting the long-distance coherent propagation of magnetic excitations driven by the Kitaev couplings.
One of the most fundamental questions in the field of relativistic heavy ion physics is how to reach and explore densities which are needed to cross the chiral and/or the deconfinement phase transition. In this analysis we investigate the information we can gather by analyzing baryonic and mesonic resonances on the hot and dense phase in such nuclear reactions. The decay products of these resonances carry information on the resonances properties at the space time point of their decay. We especially investigate the percentage of reconstructable resonances as a function of density for heavy ion collisions in the energy range between $E_{lab}$ = 30 AGeV and $\sqrt{s}$ = 200 AGeV, the energy domain between the future FAIR facility and the present RHIC collider.
We calculate properties like equilibrium lattice parameter, bulk modulus and monovacancy formation energy for nickel (Ni), iron (Fe) and chromium (Cr) using Kohn-Sham density functional theory (DFT). We compare relative performance of local density approximation (LDA) and generalized gradient approximation (GGA) for predicting such physical properties for these metals. We also make a relative study between two different flavors of GGA exchange correlation functional, namely, PW91 and PBE. These calculations show that there is a discrepancy between DFT calculations and experimental data. In order to understand this discrepancy in the calculation of vacancy formation energy, we introduce a correction for the surface intrinsic error corresponding to an exchange correlation functional using the scheme implemented by Mattsson et al. [Phys. Rev. B 73, 195123 (2006)] and compare the effectiveness of the correction scheme for Al and the 3d-transition metals.
We prove that the one dimensional Multi-Particle Diffusion Limited Aggregation model has linear growth whenever the particle density exceeds 1 answering a question of Kesten and Sidoravicius. As a corollary we prove linear growth in all dimensions d when the particle density is at least 1.
Results of a detailed abundance analysis of the solar twins 16 Cyg A and 16 Cyg B based on high-resolution, high signal-to-noise ratio echelle spectroscopy are presented. 16 Cyg B is known to host a giant planet while no planets have yet been detected around 16 Cyg A. Stellar parameters are derived directly from our high-quality spectra, and the stars are found to be physically similar, with Delta_T_eff = +43 K, Delta_logg = -0.02 dex, and Delta_xi = +0.10 km/s (in the sense of A - B), consistent with previous findings. Abundances of 15 elements are derived and are found to be indistinguishable between the two stars. The abundances of each element differ by <= 0.026 dex, and the mean difference is +0.003 +/- 0.015 (sigma) dex. Aside from Li, which has been previously shown to be depleted by a factor of at least 4.5 in 16 Cyg B relative to 16 Cyg A, the two stars appear to be chemically identical. The abundances of each star demonstrate a positive correlation with the condensation temperature of the elements (T_c); the slopes of the trends are also indistinguishable. In accordance with recent suggestions, the positive slopes of the [m/H]-T_c relations may imply that terrestrial planets have not formed around either 16 Cyg A or 16 Cyg B. The physical characteristics of the 16 Cyg system are discussed in terms of planet formation models, and plausible mechanisms that can account for the lack of detected planets around 16 Cyg A, the disparate Li abundances of 16 Cyg A and B, and the eccentricity of the planet 16 Cyg B b are suggested.
We perform Landau-Zener-Stuckelberg-Majorana (LZSM) spectroscopy on a system with strong spin-orbit interaction (SOI), realized as a single hole confined in a gated double quantum dot. In analogy to the electron systems, at magnetic field B=0 and high modulation frequencies we observe the photon-assisted tunneling (PAT) between dots, which smoothly evolves into the typical LZSM funnel-shaped interference pattern as the frequency is decreased. In contrast to electrons, the SOI enables an additional, efficient spin-flipping interdot tunneling channel, introducing a distinct interference pattern at finite B. Magneto-transport spectra at low-frequency LZSM driving show the two channels to be equally coherent. High-frequency LZSM driving reveals complex photon-assisted tunneling pathways, both spin-conserving and spin-flipping, which form closed loops at critical magnetic fields. In one such loop an arbitrary hole spin state is inverted, opening the way toward its all-electrical manipulation.
While current 3D object recognition research mostly focuses on the real-time, onboard scenario, there are many offboard use cases of perception that are largely under-explored, such as using machines to automatically generate high-quality 3D labels. Existing 3D object detectors fail to satisfy the high-quality requirement for offboard uses due to the limited input and speed constraints. In this paper, we propose a novel offboard 3D object detection pipeline using point cloud sequence data. Observing that different frames capture complementary views of objects, we design the offboard detector to make use of the temporal points through both multi-frame object detection and novel object-centric refinement models. Evaluated on the Waymo Open Dataset, our pipeline named 3D Auto Labeling shows significant gains compared to the state-of-the-art onboard detectors and our offboard baselines. Its performance is even on par with human labels verified through a human label study. Further experiments demonstrate the application of auto labels for semi-supervised learning and provide extensive analysis to validate various design choices.
We provide a simple proof of the fact that the ramification index of the compositum of two finite extensions of local fields is equal to the least common multiple of the ramification indices when at least one of the extensions is tamely ramified.