ShantanuT01/DACTYL-Pretraining huggingface dataset:
The magneto-optical (MO) effects not only are a powerful probe of magnetism and electronic structure of magnetic solids but also have valuable applications in high-density data-storage technology. Yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$) (YIG) and bismuth iron garnet (Bi$_3$Fe$_5$O$_{12}$) (BIG) are two widely used magnetic semiconductors with strong magneto-optical effects and have also attracted the attention for fundamental physics studies. In particular, YIG has been routinely used as a spin current injector. In this paper, we present a thorough theoretical investigation on magnetism, electronic, optical and MO properties of YIG and BIG, based on the density functional theory with the generalized gradient approximation plus onsite Coulomb repulsion. We find that both semiconductors exhibit large MO effects with their Kerr and Faraday rotation angles being comparable to that of best-known MO materials such as MnBi. Especially, the MO Kerr rotation angle for bulk BIG reaches -1.2$ ^{\circ}$ at photon energy $\sim2.4$ eV, and the MO Faraday rotation angle for BIG film reaches -74.6 $ ^{\circ}/\mu m$ at photon energy $\sim2.7$ eV. Furthermore, we also find that both valence and conduction bands across the MO band gap in BIG are purely spin-down states, i.e., BIG is a single spin semiconductor. These interesting findings suggest that the iron garnets will find valuable applications in semiconductor MO and spintronic nanodevices. The calculated optical conductivity spectra, MO Kerr and Faraday rotation angles agree well with the available experimental data. The main features in the optical and MO spectra of both systems are analyzed in terms of the calculated band structures especially by determining the band state symmetries and the main optical transitions at the $\Gamma$ point in the Brillouin zone.
In this paper, we first develop the projective truncation approximation (PTA) in the Green's function equation of motion (EOM) formalism for classical statistical models. To implement PTA for a given Hamiltonian, we choose a set of basis variables and projectively truncate the hierarchical EOM. We apply PTA to the one-dimensional $\phi^4$ lattice model. Phonon dispersion and static correlation functions are studied in detail. Using one- and two-dimensional bases, we obtain results identical to and beyond the quadratic variational approximation, respectively. In particular, we analyze the power-law temperature dependence of the static averages in the low- and high-temperature limits, and we give exact exponents.
We develop a classical kinetic theory of magnetotransport of 2D electrons in narrow channels with partly diffusive boundary scattering and apply it to description of magnetoresistance measured in the temperature interval 4.2-30 K in long mesoscopic bars fabricated from high-purity GaAs quantum well structures. Both experiment and theory demonstrate a number of characteristic features in the longitudinal and Hall resistances caused by the size effect in two dimensions owing to the high ballisticity of the transport. In addition to the features described previously, we also reveal a change in the slope of the first derivative of magnetoresistance when the cyclotron orbit diameter equals to half of the channel width. These features are suppressed with increasing temperature as a result of the electronic viscosity due to electron-electron interaction. By comparing theory and experiment, we determine the characteristic time of relaxation of angular distribution of electrons caused by electron-electron scattering.
Suppose a heavy neutral Higgs or scalar boson $H$ is discovered at the LHC, it is important to investigate its couplings to the standard model particles as much as possible. Here in this work we attempt to probe the CP-even and CP-odd couplings of the heavy Higgs boson to a pair of top quarks, through the decay $H \to t\bar t \to b W^+ \bar b W^-$. We use the helicity-amplitude method to write down the most general form for the angular distributions of the final-state $b$ quarks and $W$ bosons. We figure out that there are 6 types of angular observables and, under CP$\widetilde{\rm T}$ conservation, one-dimensional angular distributions can only reveal two of them. Nevertheless, the $H$ couplings to the   $t\bar t$ pair can be fully determined by exploiting the one-dimensional angular distributions. A Higgs-boson mass of 380 GeV not too far above the $t\bar t$ threshold is illustrated with full details. With a total of $10^4$ events of $H \to t\bar t \to bW^+ \bar b W^+$, one can determine the couplings up to 10-20 % uncertainties.
If $E$ is an elliptic curve defined over $\mathbb Q$ and $p$ is a prime of good reduction for $E$, let $E(\mathbb F_p)$ denote the set of points on the reduced curve modulo $p$. Define an arithmetic function $M_E(N)$ by setting $M_E(N):= \#\{p: \#E(\mathbb F_p)= N\}$. Recently, David and the third author studied the average of $M_E(N)$ over certain "boxes" of elliptic curves $E$. Assuming a plausible conjecture about primes in short intervals, they showed the following: for odd $N$, the average of $M_E(N)$ over a box with sufficiently large sides is $\sim \frac{K^{\ast}(N)}{\log{N}}$ for an explicitly-given function $K^{\ast}(N)$.   The function $K^{\ast}(N)$ is somewhat peculiar: defined as a product over the primes dividing $N$, it resembles a multiplicative function at first glance. But further inspection reveals that it is not, and so one cannot directly investigate its properties by the usual tools of multiplicative number theory. In this paper, we overcome these difficulties and prove a number of statistical results about $K^{\ast}(N)$. For example, we determine the mean value of $K^{\ast}(N)$ over all $N$, odd $N$ and prime $N$, and we show that $K^{\ast}(N)$ has a distribution function. We also explain how our results relate to existing theorems and conjectures on the multiplicative properties of $\# E(\mathbb F_p)$, such as Koblitz's conjecture.
The deposition of nano-crystalline ZnS/diamond composite protective coatings on silicon, sapphire, and ZnS substrates, as a preliminary step to coating infrared transparent ZnS substrates from powder mixtures by the aerosol deposition method is presented. Advantages of the aerosol deposition method include the ability to form dense, nanocrystalline films up to hundreds of microns thick at room temperature and at a high deposition rate on a variety of substrates. Deposition is achieved by creating a pressure gradient that accelerates micrometer-scale particles in an aerosol to high velocity.   Upon impact with the target substrate the particles fracture and embed. Continued deposition forms the thick compacted film. Deposition from an aerosolized mixture of ZnS and diamond powders onto all targets results in linear trend from apparent sputter erosion of the substrate at 100% diamond to formation of a film with increasing fractions of ZnS. The crossover from abrasion to film formation on sapphire occurs above about 50% ZnS and a mixture of 90% ZnS and 10% diamond forms a well-adhered film of about 0.7 \mu m thickness at a rate of 0.14 \mu m/min. Resulting films are characterized by scanning electron microscopy, profilometry, infrared transmission spectroscopy, and x-ray photoemission spectroscopy. These initial films mark progress toward the future goal of coating ZnS substrates for abrasion resistance.
We study scale-invariant Rayleigh Random Flights ("RRF") in random environments given by planar Scale-Invariant Random Spatial Networks ("SIRSN") based on speed-marked Poisson line processes. A natural one-parameter family of such RRF (with scale-invariant dynamics) can be viewed as producing "randomly-broken local geodesics" on the SIRSN; we aim to shed some light on a conjecture that a (non-broken) geodesic on such a SIRSN will never come to a complete stop en route. (If true, then all such geodesics can be represented as doubly-infinite sequences of sequentially connected line segments. This would justify a natural procedure for computing geodesics.) The family of these RRF ("SIRSNRRF"), is introduced via a novel axiomatic theory of abstract scattering representations for Markov chains (itself of independent interest). Palm conditioning (specifically the Mecke-Slivnyak theorem for Palm probabilities of Poisson point processes) and ideas from the ergodic theory of random walks in random environments are used to show that at a critical value of the parameter the speed of the scale-invariant SIRSNRRF neither diverges to infinity nor tends to zero, thus supporting the conjecture.
Supernova remnants (SNRs) are powerful particle accelerators. As a supernova (SN) blast wave propagates through the circumstellar medium (CSM), electrons and protons scatter across the shock and gain energy by entrapment in the magnetic field. The accelerated particles generate further magnetic field fluctuations and local amplification, leading to cosmic ray production. The wealth of data from Supernova 1987A is providing a template of the SN-CSM interaction, and an important guide to the radio detection and identification of core-collapse SNe based on their spectral properties. Thirty years after the explosion, radio observations of SNR 1987A span from 70 MHz to 700 GHz. We review extensive observing campaigns with the Australia Telescope Compact Array (ATCA) and the Atacama Large Millimeter/submillimeter Array (ALMA), and follow-ups with other radio telescopes. Observations across the radio spectrum indicate rapid changes in the remnant morphology, while current ATCA and ALMA observations show that the SNR has entered a new evolutionary phase.
The equilibrium state of a relativistic gas has been calculated based on the maximum entropy principle. Though the relativistic equilibrium state was long believed to be the Juttner distribution, a number of papers have been published in recent years proposing alternative equilibrium states. However, some of these papers do not pay enough attention to the covariance of distribution functions, resulting confusion in equilibrium states. Starting from a fully covariant expression to avoid this confusion, it has been shown in the present paper that the Juttner distribution is the maximum entropy state if we assume the Lorentz symmetry.
Let A be an abelian variety defined over a number field k and let F be a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we compute explicitly the algebraic part of the p-component of the equivariant Tamagawa number of the pair ( h^1(A/F)(1), Z[Gal(F/k)] ). By comparing the result of this computation with the theorem of Gross and Zagier we are able to give the first verification of the p-component of the equivariant Tamagawa number conjecture for an abelian variety in the technically most demanding case in which the relevant Mordell-Weil group has strictly positive rank and the relevant field extension is both non-abelian and of degree divisible by p. More generally, our approach leads us to the formulation of certain precise families of conjectural p-adic congruences between the values at s=1 of derivatives of the Hasse-Weil L-functions associated to twists of A, normalised by a product of explicit equivariant regulators and periods, and to explicit predictions concerning the Galois structure of Tate-Shafarevich groups. In several interesting cases we provide theoretical and numerical evidence in support of these more general predictions.
The discovery of GRB 170817A, the first unambiguous off-axis short gamma-ray burst arising from a neutron star merger, has challenged our understanding of the angular structure of relativistic jets. Studies of the jet propagation usually assume that the jet is ejected from the central engine with a top-hat structure and its final structure, which determines the observed light curve and spectra, is primarily regulated by the interaction with the nearby environment. However, jets are expected to be produced with a structure that is more complex than a simple top-hat, as shown by global accretion simulations. We present numerical simulations of short GRBs launched with a wide range of initial structures, durations and luminosities. We follow the jet interaction with the merger remnant wind and compute its final structure at distances $\gtrsim 10^{11}$~cm from the central engine. We show that the final jet structure, as well as the resulting afterglow emission, depend strongly on the initial structure of the jet, its luminosity and duration. While the initial structure at the jet is preserved for long-lasting SGRBs, it is strongly modified for jets barely making their way through the wind. This illustrates the importance of combining the results of global simulations with propagation studies in order to better predict the expected afterglow signatures from neutron star mergers. Structured jets provide a reasonable description of the GRB 170817A afterglow emission with an off-axis angle $\theta_{\rm obs} \approx 22.5^\circ$.
Recent observations of sunspot's umbra suggested that it may be finely structured at a sub-arcsecond scale representing a mix of hot and cool plasma elements. In this study we report the first detailed observations of the umbral spikes, which are cool jet-like structures seen in the chromosphere of an umbra. The spikes are cone-shaped features with a typical height of 0.5-1.0 Mm and a width of about 0.1 Mm. Their life time ranges from 2 to 3 min and they tend to re-appear at the same location. The spikes are not associated with photospheric umbral dots and they rather tend to occur above darkest parts of the umbra, where magnetic fields are strongest. The spikes exhibit up and down oscillatory motions and their spectral evolution suggests that they might be driven by upward propagating shocks generated by photospheric oscillations. It is worth noting that triggering of the running penumbral waves seems to occur during the interval when the spikes reach their maximum height.
Most star formation in our galaxy occurs within embedded clusters, and these background environments can affect the star and planet formation processes occurring within them. In turn, young stellar members can shape the background environment and thereby provide a feedback mechanism. This work explores one aspect of stellar feedback by quantifying the background X-ray radiation fields produced by young stellar objects. Specifically, the distributions of X-ray luminosities and X-ray fluxes produced by cluster environments are constructed as a function of cluster membership size $N$. Composite flux distributions, for given distributions of cluster sizes $N$, are also constructed. The resulting distributions are wide and the X-ray radiation fields are moderately intense, with the expected flux levels exceeding the cosmic and galactic X-ray backgrounds by factors of $\sim10-1000$ (for energies 0.2 -- 15 keV). For circumstellar disks that are geometrically thin and optically thick, the X-ray flux from the background cluster dominates that provided by a typical central star in the outer disk where $r \ga 9 - 14$ AU. In addition, the expectation value of the ionization rate provided by the cluster X-ray background is $\zeta_X\sim8\times10^{-17}$ s$^{-1}$, about 4 -- 8 times larger than the canonical value of the ionization rate from cosmic rays. These elevated flux levels in clusters indicate that X-rays can affect ionization, chemistry, and heating in circumstellar disks and in the material between young stellar objects.
Ingestible wireless capsule endoscopy is an emerging minimally invasive diagnostic technology for inspection of the GI tract and diagnosis of a wide range of diseases and pathologies. Medical device companies and many research groups have recently made substantial progresses in converting passive capsule endoscopes to active capsule robots, enabling more accurate, precise, and intuitive detection of the location and size of the diseased areas. Since a reliable real time pose estimation functionality is crucial for actively controlled endoscopic capsule robots, in this study, we propose a monocular visual odometry (VO) method for endoscopic capsule robot operations. Our method lies on the application of the deep Recurrent Convolutional Neural Networks (RCNNs) for the visual odometry task, where Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) are used for the feature extraction and inference of dynamics across the frames, respectively. Detailed analyses and evaluations made on a real pig stomach dataset proves that our system achieves high translational and rotational accuracies for different types of endoscopic capsule robot trajectories.
We present observations and analysis of an unusual [C II] emission line in the very luminous QSO SDSS J155426.16+193703.0 at z~4.6. The line is extremely broad (FWHM 735 km/s) and seems to have a flat-topped or double-peaked line profile. A velocity map of the line shows a gradient across the source that indicates large-scale rotation of star-forming gas. Together, the velocity map and line profile suggest the presence of a massive rotating disc with a dynamical mass M_dyn > 5x10^10 M_sun. Using the assumption of a rotating disc origin, we employ an empirical relation between galaxy disc circular velocity and bulge velocity dispersion (sigma) to estimate that sigma > 310 km/s, subject to a correction for the unknown disc inclination. This result implies that this source is consistent with the local M--sigma relation, or offset at most by an order of magnitude in black hole mass. In contrast, the assumption of a bulge origin for the [C II] emission line would lead to a conclusion that the black hole is nearly two orders of magnitude more massive than predicted by the M--sigma relation, similar to previous findings for other high-redshift QSOs. As disc rotation may be a common origin for [C II] emission at high redshifts, these results stress that careful consideration of dynamical origins is required when using observations of this line to derive properties of high-redshift galaxies.
In this paper we introduce the notion of hybrid trigonometric parametrization as a tuple of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in each block of functions are different. We analyze the main properties of the varieties defined by these parametrizations and we prove that they are exactly the class of real unirational varieties. In addition, we provide algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one, and viceversa.
The de Rham-Gabadadze-Tolley (dRGT) black string solution is a cylindrically symmetric and static solution of the Einstein field equation with graviton mass term. For the asymptotically de Sitter (dS) solution, it is possible to obtain the black string with two event horizons corresponding to two thermodynamic systems. The R\'enyi entropy is one of the entropic forms which is suitable to deal with nonextensive properties of the black string. In this work, we investigated the possibility to obtain a stable black string by using the R\'enyi entropy in both separated and effective approaches. We found that the nonextensivity provides the thermodynamically stable black string with moderate size in both approaches. The transition from the hot gas phase to the moderate-sized stable black string in the separated/effective description is a first-order/zeroth-order phase transition. The significant ways to distinguish the black string from both approaches are discussed.
We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e. a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power-law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.
The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family of classical trajectories, enveloped by a caustic. The energy eigenvalues and the values of the wave functions on the caustic are obtained by solving the 1-dim quantum Hamilton Jacobi equation of the caustic' arcs. Results are in good agreement with those obtained by usual methods.
(Abridged) We present deep Keck spectroscopy, using the DEIMOS and LRIS spectrographs, of a large and representative sample of 67 ``Extremely Red Objects'' (EROs) to H=20.5, with I-H>3.0, in three of the Las Campanas Infrared Survey fields. Spectroscopic redshifts are determined for 44 sources, of which only two are contaminating low mass stars. When allowance is made for incompleteness, the spectroscopic redshift distribution closely matches that predicted earlier on the basis of photometric data. Our spectra are of sufficient quality that we can address the important question of the nature and homogeneity of the z>0.8 ERO population. A dominant old stellar population is inferred for 75% of our spectroscopic sample; a higher fraction than that seen in smaller, less-complete samples with broader photometric selection criteria (e.g. R-K). However, only 28% have spectra with no evidence of recent star formation activity, such as would be expected for a strictly passively-evolving population. More than ~30% of our absorption line spectra are of the `E+A' type with prominent Balmer absorption consistent, on average, with mass growth of 5-15% in the past Gyr. We use our spectroscopic redshifts to improve earlier estimates of the spatial clustering of this population as well as to understand the significant field-to-field variation. Our spectroscopy enables us to pinpoint a filamentary structure at z=1.22 in the Chandra Deep Field South. Overall, our study suggests that the bulk of the ERO population is an established population of clustered massive galaxies undergoing intermittent activity consistent with continued growth over the redshift interval 0.8<z<1.6.
A class of projective actions of the orthogonal group on the projective space is being studied. It is shown that the Fock--Lorentz, and Magueijo--Smolin transformations known as Doubly Special Relativity are such transformations. The formalism easily lead to new type transformations.
Samples of the spectrum of the 36Ar nucleus are known in different energy windows. In addition to the ground state region (GS), the superdeformed (SD) state is observed, too, and there is a good candidate for the hyperdeformed (HD) one, as well. They are populated in different reactions. We intend to describe the gross features of the spectra of different energies, deformations and reactions in a unified way. We apply the multiconfigurational dynamical symmetry (MUSY). The SU(3) quantum numbers of the shape isomers from previous studies pave the way for this description. The MUSY reproduces the gross features of the spectra to a reasonable approximation. The energy spectrum of the three valleys (GS, SD, HD) indicates that the multiconfigurational symmetry is valid to a good approximation, and different cluster configurations coexist in the shape isomers.