ShantanuT01/DACTYL-Pretraining huggingface dataset:
Quantum interference phenomena manifests itself in several ways in the polarized solar spectrum formed due to coherent scattering processes. One such effect arises due to interference between the fine structure (J) states giving rise to multiplets. Another effect is that which arises due to interference between the hyperfine structure (F) states. We extend the redistribution matrix derived for the J-state interference to the case of F-state interference. We then incorporate it into the polarized radiative transfer equation and solve it for isothermal constant property slab atmospheres. The relevant transfer equation is solved using a polarized approximate lambda iteration (PALI) technique based on operator perturbation. An alternative method derived from the Neumann series expansion is also proposed and is found to be relatively more efficient than the PALI method. The effects of PRD and the F-state interference on the shapes of the linearly polarized Stokes profiles are discussed. The emergent Stokes profiles are computed for hypothetical line transitions arising due to hyperfine structure splitting (HFS) of the upper J=3/2 and lower J=1/2 levels of a two-level atom model with nuclear spin I_s=3/2. We confine our attention to the non-magnetic scattering in the collisionless regime.
We construct the minimal regular model of the Fermat curve of odd squarefree composite exponent $N$ over the $N$-th cyclotomic integers. As an application, we compute upper and lower bounds for the arithmetic self-intersection of the dualizing sheaf of this model.
Gamma Ray Bursts (GRB) observed up to redshifts $z>8$ are fascinating objects to study due to their still unexplained relativistic outburst mechanisms and a possible use to test cosmological models. Our analysis of 77 GRB afterglows with known redshifts revealed a physical subsample of long GRBs with canonical {\it plateau breaking to power-law} light curves with a significant {\it luminosity $L^*_X$ - break time $T^*_a$} correlation in the GRB rest frame. This subsample forms approximately the {\it upper envelope} of the studied distribution. We have also found a similar relation for a small sample of GRB afterglows that belong to the intermediate class (IC) between the short and the long ones. It proves that within the full sample of afterglows there exist physical subclasses revealed here by tight correlations of their afterglow properties. The afterglows with regular (`canonical') light curves obey not only a mentioned tight physical scaling, but -- for a given $T^*_a$ -- the more regular progenitor explosions lead to preferentially brighter afterglows.
We analyze Mode Coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called "$A_3$" point. In these conditions structural relaxation and fluctuations appear to have universal form independent from the details of the system. The analysis of this limiting case suggests new ways for looking at the Mode Coupling equations in the general case.
Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the holonomies for multiple moving crossed cosmic strings and two plane topological defects-crossed by a cosmic string.
Quantum scattering in the presence of a potential valley followed by a barrier is examined for the case of a Morse potential, for which exact analytic solutions to the Schr\UNICODE{0xf6}dinger equation are known in terms of confluent hypergeometric functions. For our application the potential is characterized by three parameters: the height of the barrier, the distance of the barrier from the origin of the radial variable $r,$ and a diffuseness parameter. The wave function, defined in the interval $0\leq r<\infty ,$ is required to vanish at $r=0,$ and hence represents a radial partial wave for zero angular momentum. The vanishing at $r=0$ requires a special combination of hypergeometric functions, and can lead to resonances for incident energies which occur below the top of the barrier. Numerical values for the analytical phase shifts are presented in and outside the resonant regions, and the corresponding properties of the scattering S-matrix are examined in the complex momentum plane, mainly for pedagogical reasons. The validity of the Breit-Wigner approximation to the resonant phase shifts is tested, and the motion of a ''resonant'' wave packet slowly leaking out of the valley region is also displayed.
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application to ruin probability in a risk-theoretic model is also given.
We prove a version of Hilbert's Irreducibility Theorem in the quadratic case, giving a quantitative improvement to a result of Bilu-Gillibert in this restricted setting. As an application, we give improvements to several quantitative results counting quadratic fields with certain types of ideal class groups. The proof of the main theorem is based on a result of Stewart and Top on values of binary forms modulo squares.
We mapped two molecular cloud cores in the Orion A cloud with the ALMA ACA 7-m Array and with the Nobeyama 45-m radio telescope. These cores have bright N$_2$D$^+$ emission in single-pointing observations with the Nobeyama 45-m radio telescope, have relatively high deuterium fraction, and are thought to be close to the onset of star formation. One is a star-forming core, and the other is starless. These cores are located along filaments observed in N$_2$H$^+$, and show narrow linewidths of 0.41 km s$^{-1}$ and 0.45 km s$^{-1}$ in N$_2$D$^+$, respectively, with the Nobeyama 45-m telescope. Both cores were detected with the ALMA ACA 7m Array in the continuum and molecular lines at Band 6. The starless core G211 shows clumpy structure with several sub-cores, which in turn show chemical differences. Also, the sub-cores in G211 have internal motions that are almost purely thermal. The starless sub-core G211D, in particular, shows a hint of the inverse P Cygni profile, suggesting infall motion. The star-forming core G210 shows an interesting spatial feature of two N$_2$D$^+$ peaks of similar intensity and radial velocity located symmetrically with respect to the single dust continuum peak. One interpretation is that the two N$_2$D$^+$ peaks represent an edge-on pseudo-disk. The CO outflow lobes, however, are not directed perpendicular to the line connecting both N$_2$D$^+$ peaks.
We investigate the inverse spin Hall voltage of a 10nm thin Pt strip deposited on the magnetic insulators Y3Fe5O12 (YIG) and NiFe2O4 (NFO) with a temperature gradient in the film plane. We observe characteristics typical of the spin Seebeck effect, although we do not observe a change of sign of the voltage at the Pt strip when it is moved from hot to cold side, which is believed to be the most striking feature of the transverse spin Seebeck effect. Therefore, we relate the observed voltages to the longitudinal spin Seebeck effect generated by a parasitic out-of-plane temperature gradient, which can be simulated by contact tips of different material and heat conductivities and by tip heating. This work gives new insights into the interpretation of transverse spin Seebeck effect experiments, which are still under discussion.
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell connected to two macroscopic reservoirs of heat and particles is developed, based on fluctuating hydrodynamics. Within this approach, the fluctuating separation and thermodynamic efficiencies are defined. The conditions required to observe bimodal distributions of these efficiencies are determined, and the evolution of these distributions is investigated in the large-size and in the long-time limits. The results obtained are not restricted to thermodiffusion and can be generalized to systems where efficiency is defined as a ratio of stochastic state variables or dissipation rates.
Magnetic fields are usually observed in the quiet Sun as small-scale elements that cover the entire solar surface (the `salt and pepper' patterns in line-of-sight magnetograms). By using 3D radiative MHD numerical simulations we find that these fields result from a local dynamo action in the top layers of the convection zone, where extremely weak 'seed' magnetic fields (e.g., from a $10^{-6}$ G) can locally grow above the mean equipartition field, to a stronger than 2000~G field localized in magnetic structures. Our results reveal that the magnetic flux is predominantly generated in regions of small-scale helical downflows. We find that the local dynamo action takes place mostly in a shallow, about 500~km deep, subsurface layer, from which the generated field is transported into the deeper layers by convective downdrafts. We demonstrate that the observed dominance of vertical magnetic fields at the photosphere and horizontal fields above the photosphere can be explained by small-scale magnetic loops produced by the dynamo. Such small-scale loops play an important role in the structure and dynamics of the solar atmosphere and that their detection in observations is critical for understanding the local dynamo action on the Sun.
In this paper we analyse the evolutionary status of three open clusters: NGC 1817, NGC 2141, and Berkeley 81. They are all of intermediate age, two are located in the Galactic anti-centre direction while the third one is located in the Galactic centre direction. All of them were observed with LBC@LBT using the Bessel B, V, and I filters. The cluster parameters have been obtained using the synthetic colour-magnitude diagram (CMD) method, i.e. the direct comparison of the observational CMDs with a library of synthetic CMDs generated with different evolutionary sets (Padova, FRANEC, and FST). This analysis shows that NGC 1817 has subsolar metallicity, age between 0.8 and 1.2 Gyr, reddening E(B-V) in the range 0.21 and 0.34, and distance modulus (m-M)_0 of about 10.9; NGC 2141 is older, with age in the range 1.25 and 1.9 Gyr, E(B-V) between 0.36 and 0.45, (m-M)_0 between 11.95 and 12.21, and subsolar metallicity; Berkeley~81 has metallicity about solar, with age between 0.75 and 1.0 Gyr, has reddening E(B-V)~0.90 and distance modulus (m-M)_0~12.4. Exploiting the large field of view of the instrument we derive the structure parameters for NGC 2141 and Be 81 by fitting a King profile to the estimated density profile. Combining this information with the synthetic CMD technique we estimate a lower limit for the cluster total mass for these two systems.
Measuring time delays from strongly lensed supernovae (SNe) is emerging as a novel and independent tool for estimating the Hubble constant $(H_0)$. This is very important given the recent discord in the value of $H_0$ from two methods that probe different distance ranges. The success of this technique will rely of our ability to discover strongly lensed SNe with measurable time delays. Here, we present the magnifications and the time delays for the multiply-imaged galaxies behind the Hubble Frontier Fields (HFF) galaxy clusters, by using recently published lensing models. Continuing on our previous work done for Abell 1689 (A1689) and Abell 370, we also show the prospects of observing strongly lensed SNe behind the HFF clusters with the upcoming James Webb Space Telescope (JWST). With four 1-hour visits in one year, the summed expectations of all six HFF clusters are $\sim0.5$ core-collapse (CC) SNe and $\sim0.06$ Type Ia SNe (SNe Ia) in F115W band, while with F150W the expectations are higher, $\sim0.9$ CC SNe and $\sim0.06$ SNe Ia. These estimates match those expected by only surveying A1689, proving that the performance of A1689 as gravitational telescope is superior. In the five HFF clusters presented here, we find that F150W will be able to detect SNe Ia (SNe IIP) exploding in 93 (80) pairs multiply-imaged galaxies with time delays of less than 5 years.
Observations have revealed cold gas with large velocity dispersions (~300 km/s) within the hot outflows of ultra-luminous infrared galaxies (ULIRGs). This gas may trace its origin to the Rayleigh-Taylor (RT) fragmentation of a super-bubble or may arise on smaller scales. We model a ULIRG outflow at two scales to recreate this gas in three-dimensional hydrodynamic simulations using FLASH. Although resolution is limited, these models successfully produce cold gas in outflows with large velocity dispersions. Our small-scale models produce this cold gas through RT fragmentation of the super-bubble wall, but the large-scale models produce the cold gas after hot bubbles fragment the disc's gas into cold clouds which are then accelerated by thermal pressure, and supplemented by cooling within the outflow. We produce simple mock spectra to compare these simulations to observed absorption spectra and find line-widths of ~250 km/s, agreeing with the lower end of observations.
Let s be a special point on a Shimura variety, and x a pre-image of s in a fixed fundamental set of the associated Hermitian symmetric domain. We prove that the height of x is polynomially bounded with respect to the discriminant of the centre of the endomorphism ring of the corresponding Z-Hodge structure. Our bound is the final step needed to complete a proof of the Andre-Oort conjecture under the conjectural lower bounds for the sizes of Galois orbits of special points, using a strategy of Pila and Zannier.
We give examples of curves of arbitrarily high Clifford index such that the Prym map is not injective at any of their \'etale double covers.
This paper analytically investigates the Darcy-Poisson-Nernst-Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and two suspended oppositely charged chemical species with arbitrary valencies z_1 > 0 > z_2. We prove global existence and uniqueness of weak solutions in two space dimensions and three space dimensions. So far, most of the existence results have been proven for symmetric electrolyte solutions. These solutions consist of a neutral fluid and two suspended charged chemical species with symmetric valencies +/-z. As many electrolyte solutions in biological applications and hydrodynamical applications are not symmetric, the presented extension of the previous existence results is an important step.
Studies based on high-resolution spectroscopic data of rapidly oscillating Ap stars show a surprising diversity of pulsation behavior in the atmospheric layers, pointing, in particular, to the co-existence of running and standing waves. The correct interpretation of these data requires a careful modelling of pulsations in these magnetic stars. In light of this, in this work we present a theoretical analysis of pulsations in roAp stars, taking into account the direct influence of the magnetic field. We derive approximate analytical solutions for the displacement components parallel and perpendicular to the direction of the magnetic field, that are appropriate to the outermost layer. From these, we determine the expression for the theoretical radial velocity for an observer at a general position, and compute the corresponding pulsation amplitude and phase as function of height in the atmosphere. We show that the integral for the radial velocity has contributions from three different types of wave solutions, namely, running waves, evanescent waves, and standing waves of nearly constant amplitude. We then consider a number of case studies to illustrate the origin of the different pulsational behaviour that is found in the observations. Concerning pulsation amplitude, we find that it generally increases with atmospheric height. Pulsation phase, however, shows a diversity of behaviours, including phases that are constant, increasing, or decreasing with atmospheric height. Finally, we show that there are situations in which the pulsation amplitude goes through a zero, accompanied by a phase jumps of $\pi$, and argue that such behaviour does not correspond to a pulsation node in the outermost layers of the star, but rather to a visual effect, resulting from the observers inability to resolve the stellar surface.
We report angle-dependent magnetoresistance measurements on (TMTSF)2ClO4 that provide strong support for a new macroscopic quantum phenomenon, the interference commensurate (IC) effect, in quasi-one dimensional metals. In addition to observing rich magnetoresistance oscillations, and fitting them with one-electron calculations, we observe a clear demarcation of field-dependent behavior at local resistance minima and maxima (versus field angle). Anticipated by a theoretical treatment of the IC effect in terms of Bragg reflections in the extended Brillouin zone, this behavior results from 1D-2D topological crossovers of electron wave functions as a function of field orientation.
Let p > 2 be a prime, let n > m > 0. Let pi_n be the norm of zeta_{p^n} - 1 under C_{p-1}, so that Z_(p)[pi_n] | Z_(p) is a purely ramified extension of discrete valuation rings of degree p^{n-1}. The minimal polynomial of pi_n over Q(pi_m) is an Eisenstein polynomial; we give lower bounds for its coefficient valuations at pi_m. The function field analogue, as introduced by Carlitz and Hayes, is studied as well.
TThe glitch of anomalous X-ray pulsars \& soft gamma repeaters (AXP/SGRs) usually accompanied with detectable energy releases manifesting as X-ray bursts or outbursts, while the glitch of some pulsars like Vela release negligible energy. We find that these two types of glitches can naturally correspond to two types of starquake of solid strange stars. By applying the EoS of quark cluster star and some realistic pulsar parameters, we can reproduce consistent results compared with previous constraints and observations.
We consider a multivariate L\'evy process where the first coordinate is a L\'evy process with no negative jumps which is not a subordinator and the others are nondecreasing. We determine the Laplace-Stieltjes transform of the steady-state buffer content vector of an associated system of parallel queues. The special structure of this transform allows us to rewrite it as a product of joint Laplace-Stieltjes transforms. We are thus able to interpret the buffer content vector as a sum of independent random vectors.
Point cloud completion task aims to predict the missing part of incomplete point clouds and generate complete point clouds with details. In this paper, we propose a novel point cloud completion network, namely CompleteDT. Specifically, features are learned from point clouds with different resolutions, which is sampled from the incomplete input, and are converted to a series of \textit{spots} based on the geometrical structure. Then, the Dense Relation Augment Module (DRA) based on the transformer is proposed to learn features within \textit{spots} and consider the correlation among these \textit{spots}. The DRA consists of Point Local-Attention Module (PLA) and Point Dense Multi-Scale Attention Module (PDMA), where the PLA captures the local information within the local \textit{spots} by adaptively measuring weights of neighbors and the PDMA exploits the global relationship between these \textit{spots} in a multi-scale densely connected manner. Lastly, the complete shape is predicted from \textit{spots} by the Multi-resolution Point Fusion Module (MPF), which gradually generates complete point clouds from \textit{spots}, and updates \textit{spots} based on these generated point clouds. Experimental results show that, because the DRA based on the transformer can learn the expressive features from the incomplete input and the MPF can fully explore these feature to predict the complete input, our method largely outperforms the state-of-the-art methods.
Protostellar outflows and jets play a vital role in star formation as they carry away excess angular momentum from the inner disk surface, allowing the material to be transferred toward the central protostar. Theoretically, low velocity and poorly collimated outflows appear from the beginning of the collapse, at the first hydrostatic core (FHSC) stage. With growing protostellar core mass, high-density jets are launched which entrain an outflow from the infalling envelope. Until now, molecular jets have been observed at high velocity ($\gtrsim$ 100 km/s) in early Class\,0 protostars. We, for the first time, detect a dense molecular jet in SiO emission with small-velocity ($\sim$ 4.2 km\,s$^{-1}$, deprojected $\sim$ 24 km\,s$^{-1}$) from source G208.89-20.04Walma (hereafter, G208Walma) using ALMA Band\,6 observations. This object has some characteristics of FHSCs, such as a small outflow/jet velocity, extended 1.3\,mm continuum emission, and N$_2$D$^+$ line emission. Additional characteristics, however, are typical of early protostars: collimated outflow and SiO jet. The full extent of the outflow corresponds to a dynamical time scale of $\sim$ 930$^{+200}_{-100}$ years. The spectral energy distribution also suggests a very young source having an upper limit of T$_{bol}$ $\sim$ 31 K and L$_{bol}$ $\sim$ 0.8 L$_\sun$. We conclude that G208Walma is likely in the transition phase from FHSC to protostar, and the molecular jet has been launched within a few hundred years of initial collapse. Therefore, G208Walma may be the earliest object discovered in the protostellar phase with a molecular jet.
Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.
Transparent conducting or semiconducting oxides are important materials for (transparent) optoelectronics and power electronics applications. While most of these oxides can be doped n-type only with room-temperature electron mobilities on the order of 100cm^2/Vs p-type oxides are needed for the realization of pn-junction devices but typically suffer from exessively low (<<1cm^2/Vs) hole mobilities. Tin monoxide (SnO) is one of the few p-type oxides with a higher hole mobility, lacking a well-established understanding of its hole transport properties. Moreover, growth of SnO is complicated by its metastability with respect to SnO2 and Sn, requiring epitaxy for the realization of single crystalline material typically required for high-end applications. Here, we give a comprehensive account on the epitaxial growth of SnO, its (meta)stability, and its thermoelectric transport properties in the context of the present literature. Textured and single-crystalline, unintentionally-doped p-type SnO(001) films are grown by plasma-assisted molecular beam epitaxy. The metastability of this semiconducting oxide is addressed theoretically through an equilibrium phase diagram. Experimentally, the related SnO growth window is rapidly determined by an in-situ growth kinetics study as function of Sn-to-O-plasma flux ratio and growth temperature. The presence of secondary Sn and SnOx (1 < x <= 2) phases is comprehensively studied by different methods, indicating the presence of Sn3O4 or Sn as major secondary phases, as well as a fully oxidized SnO2 film surface. The hole transport properties, Seebeck coefficient, and density-of-states effective mass are determined and critically discussed in the context of the present literature on SnO, considering its anisotropic hole-effective mass.