ShantanuT01/DACTYL-Pretraining huggingface dataset:
Supersymmetric grand unification based on $SO(10)$ is one of the most attractive paradigms in physics beyond the Standard Model. Inspired by the recent NANOGrav signal, we discuss the implications of detecting a stochastic gravitational wave background emitted by a network of cosmic strings for the $SO(10)$ grand unification. Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above $10^{14}\, \mathrm{GeV}$ that is favored by observable primordial gravitational waves. The observed spectrum can potentially narrow the possible range of the cosmic string scale and restricts the unified couplings and the unification scale by requiring gauge coupling unification. As an indirect consequence of the high cosmic string scale, the monopole abundance places non-trivial constraints on the theory. These are complementary to the proton decay constraints and probe different facets of supersymmetric $SO(10)$ unification theories.
We analyze the intrinsic polarization of two classical Be stars in the process of losing their circumstellar disks via a Be to normal B star transition originally reported by Wisniewski et al. During each of five polarimetric outbursts which interrupt these disk-loss events, we find that the ratio of the polarization across the Balmer jump (BJ+/BJ-) versus the V-band polarization traces a distinct loop structure as a function of time. Since the polarization change across the Balmer jump is a tracer of the innermost disk density whereas the V-band polarization is a tracer of the total scattering mass of the disk, we suggest such correlated loop structures in Balmer jump-V band polarization diagrams (BJV diagrams) provide a unique diagnostic of the radial distribution of mass within Be disks. We use the 3-D Monte Carlo radiation transfer code HDUST to reproduce the observed clockwise loops simply by turning "on/off" the mass decretion from the disk. We speculate that counter-clockwise loop structures we observe in BJV diagrams might be caused by the mass decretion rate changing between subsequent "on/off" sequences. Applying this new diagnostic to a larger sample of Be disk systems will provide insight into the time-dependent nature of each system's stellar decretion rate.
We present numerical simulations of misaligned discs around a spinning black hole covering a range of parameters. Previous simulations have shown that discs that are strongly warped by a forced precession -- in this case the Lense-Thirring effect from the spinning black hole -- can break apart into discrete discs or rings that can behave quasi-independently for short timescales. With the simulations we present here, we confirm that thin and highly inclined discs are more susceptible to disc tearing than thicker or low inclination discs, and we show that lower values of the disc viscosity parameter lead to instability at lower warp amplitudes. This is consistent with detailed stability analysis of the warped disc equations. We find that the growth rates of the instability seen in the numerical simulations are similar across a broad range of parameters, and are of the same order as the predicted growth rates. However, we did not find the expected trend of growth rates with viscosity parameter. This may indicate that the growth rates are affected by numerical resolution, or that the wavelength of the fastest growing mode is a function of local disc parameters. Finally, we also find that disc tearing can occur for discs with a viscosity parameter that is higher than predicted by a local stability analysis of the warped disc equations. In this case, the instability manifests differently producing large changes in the disc tilt locally in the disc, rather than the large changes in disc twist that typically occur in lower viscosity discs.
On the basis of the three-particle Bethe-Salpeter equation we formulated a relativistic quark model for baryons. Assuming the propagators to be given by their free form with constituent quark masses and the interaction kernel by an instantaneous potential, which contains a string-like parameterization of confinement and a flavor dependent interaction motivated by instanton effects we can account for the major features in the baryon spectrum, such as the low position of the Roper resonance and the occurrence of approximate parity doublets apparent in the Nucleon- and Lambda-spectra.
Estimating for the frequency drift rates of type III solar bursts is crucial for characterizing their source development in solar corona. According to Melnik et al. (Solar Phys. 269, 335, 2011), the analysis of powerful decameter type III solar bursts, observed in July-August 2002, found a linear approximation for the drift rate versus frequency. The conclusion contradicts to reliable results of many other well-known solar observations. In this paper we report on the reanalysis of the solar data, using a more advanced method. Our study has shown that decameter type III solar bursts of July-August 2002, as standard type III ones, follow a power law in frequency drift rates. We explain possible reasons for this discrepancy.
We consider clean Dirac metals where the linear band crossing is caused by a strong spin-orbit interaction, and study the quantum phase transitions from the paramagnetic phase to various magnetic phases, including homogeneous ferromagnets, ferrimagnets, canted ferromagnets, and magnetic nematics. We show that in all of these cases the coupling of fermionic soft modes to the order parameter generically renders the quantum phase transition first order, with certain gapless Dirac systems providing a possible exception. These results are surprising since a strong spin-orbit scattering suppresses the mechanism that causes the first order transition in ordinary metals. The important role of chirality in generating a new mechanism for a first-order transition is stressed.
In recent years several hypervelocity stars (HVSs) have been observed in the halo of our Galaxy. Such HVSs have possibly been ejected from the Galactic center and then propagated in the Galactic potential up to their current position. The recent survey for candidate HVSs show an asymmetry in the kinematics of candidate HVSs (position and velocity vectors), where more outgoing stars than ingoing stars (i.e. positive Galactocentric velocities vs. negative ones) are observed. We show that such kinematic asymmetry, which is likely due to the finite lifetime of the stars and Galactic potential structure, could be used in a novel method to probe and constrain the Galactic potential, identify the stellar type of the stars in the survey and estimate the number of HVSs. Kinematics-independent identification of the stellar types of the stars in such surveys (e.g. spectroscopic identification) could further improve these results. We find that the observed asymmetry between ingoing and outgoing stars favors specific Galactic potential models. It also implies a lower limit of ~54+-8 main sequence HVSs in the survey sample (>=648+-96 in the Galaxy), assuming that all of the main sequence stars in the survey originate from the Galactic center. The other stars in the survey are likely to be hot blue horizontal branch stars born in the halo rather than stars ejected from the Galactic center.
We present estimates of the signal to be expected in quiescent solar conditions, as would be obtained with the COronal Spectrographic Imager in the EUV in its coronagraphic mode (COSIE-C). COSIE-C has been proposed to routinely observe the relatively unexplored outer corona, where we know that many fundamental processes affecting both the lower corona and the solar wind are taking place. The COSIE-C spectral band, 186--205 A, is well-known as it has been observed with Hinode EIS. We present Hinode EIS observations that we obtained in 2007 out to 1.5 Rsun, to show that this spectral band in quiescent streamers is dominated by Fe XII and Fe XI and that the ionization temperature is nearly constant. To estimate the COSIE-C signal in the 1.5--3.1 Rsun region we use a model based on CHIANTI atomic data and SoHO UVCS observations in the Si XII and Mg X coronal lines of two quiescent 1996 streamers. We reproduce the observed EUV radiances with a simple density model, photospheric abundances, and a constant temperature of 1.4 MK. We show that other theoretical or semi-empirical models fail to reproduce the observations. We find that the coronal COSIE-C signal at 3 Rsun should be about 5 counts/s per 3.1" pixel in quiescent streamers. This is unprecedented and opens up a significant discovery space. We also briefly discuss stray light and the visibility of other solar features. In particular, we present UVCS observations of an active region streamer, indicating increased signal compared to the quiet Sun cases.
Carbon Nanotubes (CNs) are made of tubular graphite layers. These macromolecules have interesting features which are generally introduced in the first chapter of the thesis. In the rest of the thesis, the light conduction in metallic CNs is investigated. In chapter 2, by modeling metallic single-wall CNs as 2D free electron gas layers, we find the density of electrons on a 2D electron gas and solve the Maxwell's equations for these cylindrical waveguides. We assume the same time-dependency or frequency for the electrons oscillations on the 2D gas layers and the propagating electromagnetic waves along the CNs. This assumption is the necessary condition for the light conduction with surface plasmons, that is, the only mechanism to conduct laser beams on nanoscale and below the diffraction limit of light. In chapters 3 and 4, we apply boundary conditions to the solutions of Maxwell's equations, and find the dispersion relations of single-wall and double-wall CNs for the transverse electric (TE) and transverse magnetic (TM) modes. In chapter 5, we investigate the effect of applying relativistic electron beams on singlewall and double-wall CNs to create surface plasmons, and calculate the dispersion relation ghraphs of CNs in the presence of fast electron beams. This yield the frequencies, wavelengths and group velocities of surface plasmon waves created by relativistic beams along CN metallic waveguides.
A special class of solutions to the generalised WDVV equations related to a finite set of covectors is considered. We describe the geometric conditions ($\vee$-conditions) on such a set which are necessary and sufficient for the corresponding function to satisfy the generalised WDVV equations. These conditions are satisfied for all Coxeter systems but there are also other examples discovered in the theory of the generalised Calogero-Moser systems. As a result some new solutions for the generalized WDVV equations are found.
Quantum dynamics of anisotropic spin system with large spin moment in a swept magnetic field is theoretically investigated. Magnetic field of this type induces vortex static electrical field, that breaks down the axial symmetry and induces new coherent quantum phenomena: the occurrence of band energy spectrum with continuous spin states, Bloch-type oscillations and interband Zener tunnelling effect. These quantum phenomena display themselves, in particular, in magnetization jumps and susceptibility peaks in the investigated spin system.
Utilizing the Lorentz invariance of the correlation function we study the effects of anisotropic transverse flow on the HBT correlation function. In particular we show that directed flow would evidence itself by non zero ``side--long'' and ``side--out'' terms in the correlation function. We also show that the study of ratios of the correlation functions evaluated on different event subsamples and/or different Lorentz systems provides information on the source dimensions and velocity which could be less biased by corrections of different kinds. We present a fitting technique appropriate for HBT analysis which does not require binning and is especially useful for multidimensional fitting.
Pick's theorem is used to prove that if $P$ is a lattice polygon (that is, the convex hull of a finite set of lattice points in the plane), then every lattice point in the $h$-fold sumset $hP$ is the sum of $h$ lattice points in $P$.
We study the vertical and conical square functions defined via elliptic operators in divergence form. In general, vertical and conical square functions are equivalent operators just in $L^2$. But when this square functions are defined through the heat or Poisson semigroup that arise from an elliptic operator, we are able to find open intervals containing $2$ where the equivalence holds. The intervals in question depend ultimately on the range where the semigroup is uniformly bounded or has off-diagonal estimates. As a consequence we obtain new boundedness results for some square functions. Besides, we consider a non-tangential maximal function associated with the Poisson semigroup and extend the known range where that operator is bounded. Our methods are based on the use of extrapolation for Muckenhoupt weights and change of angle estimates. All our results are obtained in the general setting of a degenerate elliptic operator, where the degeneracy is given by an $A_2$ weight, in weighted Lebesgue spaces. Of course they are valid in the unweighted and/or non-degenerate situations, which can be seen as special cases, and provide new results even in those particular settings.   We also consider the square root of a degenerate elliptic operator in divergence form $L_w$ and improve the lower bound of the interval where this operator is known to be bounded on $L^p(vdw)$. To finish we give unweighted boundedness results for the degenerate operators under consideration.
We theoretically examine a cross effect of magnetic field and charge current on antiferromagnetic domain wall dynamics. Since antiferromagnetic materials are largely insensitive to external magnetic fields in general, charge current has been shown recently as an alternative and efficient way to manipulate antiferromagnets. We find a new role of the magnetic field in the antiferromagnetic dynamics that appears when it is combined with charge current, demonstrating a domain wall motion in the presence of both field and current. We show that a spatially-varying magnetic field can shift the current-driven domain-wall velocity, depending on the domain-wall structure and the direction of the field-gradient. Our result suggests a novel concept of field-control of current-driven antiferromagnetic dynamics.
We consider overdetermined problems of Serrin's type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence of a solution implies that the domain is a spherical sector.
Stationary states of Navier-Stokes fluids have been proposed to be described equivalently by several alternative equations, besides the NS equation itself. In particular equivalence between the NS evolution and a reversible. It is natural to test whether, assuming the Chaotic Hypothesis, the Fluctuation Theorem can be applied to the reversible flows. Here an example is provided which also leads to the possibility of testing the prediction of the fluctuation theorem even in systems evolving irreversibly.
In the present work, we prove the validity of two theorems on null-paths in a version of absolute parallelism geometry. A version of these theorems has been originally established and proved by Kermak, McCrea and Whittaker (KMW) in the context of Riemannian geometry. The importance of such theorems is their use, in applications, to derive a general formula for the red-shift of spectral lines coming from distant objects. The formula derived in the present work, can be applied for both cosmological and astrophysical red-shifts. It takes into account the shifts resulting from gravitation, different motions of the source of photons, spin of the moving particle (photons) and the direction of the line of sight. It is shown that this formula cannot be derived in the context of Riemannian geometry, but it can be reduced to a formula given by KMW under certain conditions.
We provide a homogeneous set of structural parameters of 83 star clusters located at the periphery of the Small Magellanic Cloud (SMC) and the Large Magellanic Cloud (LMC). The clusters' stellar density and surface brightness profiles were built from deep, AO assisted optical images, and uniform analysis techniques. The structural parameters were obtained from King and Elson et al. model fittings. Integrated magnitudes and masses (for a subsample) are also provided. The sample contains mostly low surface brightness clusters with distances between 4.5 and 6.5 kpc and between 1 and 6.5 kpc from the LMC and SMC centres, respectively. We analysed their spatial distribution and structural properties, comparing them with those of inner clusters. Half-light and Jacobi radii were estimated, allowing an evaluation of the Roche volume tidal filling. We found that: (i) for our sample of LMC clusters, the tidal radii are, on average, larger than those of inner clusters from previous studies; (ii) the core radii dispersion tends to be greater for LMC clusters located towards the southwest, with position angles of $\sim$200 degrees and about $\sim$5 degrees from the LMC centre, i.e., those LMC clusters nearer to the SMC; (iii) the core radius evolution for clusters with known age is similar to that of inner clusters; (iv) SMC clusters with galactocentric distances closer than 4 kpc are overfilling; (v) the recent Clouds collision did not leave marks on the LMC clusters' structure that our analysis could reveal.
The following long-standing problem in combinatorics was first posed in 1993 by Gessel and Reutenauer. For which multisubsets $B$ of the symmetric group $\fS_n$ is the quasisymmetric function $$Q(B) = \sum_{\pi \in B}F_{\Des(\pi), n}$$ a symmetric function? Here $\Des(\pi)$ is the descent set of $\pi$ and $F_{\Des(\pi), n}$ is Gessel's fundamental basis for the vector space of quasisymmetric functions. The purpose of this paper is to provide a useful characterization of these multisets. Using this characterization we prove a conjecture of Elizalde and Roichman. Two other corollaries are also given. The first is a short new proof that conjugacy classes are symmetric sets, a well known result first proved by Gessel and Reutenauer. Our second corollary is a unified explanation that both left and right multiplication of symmetric multisets, by inverse $J$-classes, is symmetric. The case of right multiplication was first proved by Elizalde and Roichman.
Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of the manifold and the underlying density. We prove the convergence of this microscopic distance, as the sample size goes to infinity, to a macroscopic one that we call Fermat distance as it minimizes a path functional, resembling Fermat principle in optics. The proof boils down to the study of geodesics in Euclidean first-passage percolation for nonhomogeneous Poisson point processes.
We have selected a group of 100 evolved planetary nebulae (PNe) and study their kinematics based upon spatially-resolved, long-slit, echelle spectroscopy. The data have been drawn from the San Pedro M\'artir Kinematic Catalogue of PNe (L\'opez et al. 2012). The aim is to characterize in detail the global kinematics of PNe at advanced stages of evolution with the largest sample of homogenous data used to date for this purpose. The results reveal two groups that share kinematics, morphology, and photo-ionization characteristics of the nebular shell and central star luminosities at the different late stages under study.The typical flow velocities we measure are usually larger than seen in earlier evolutionary stages, with the largest velocities occurring in objects with very weak or absent [N II] \lambda 6584 line emission, by all indications the least evolved objects in our sample. The most evolved objects expand more slowly. This apparent deceleration during the final stage of PNe evolution is predicted by hydrodynamical models, but other explanations are also possible. These results provide a template for comparison with the predictions of theoretical models.
A small fraction of the atomic-cooling halos assembling at z<15 may form out of minihalos that never experienced any prior star formation, and could in principle host small galaxies of chemically unenriched stars. Since the prospects of detecting isolated population III stars appear bleak even with the upcoming James Webb Space Telescope (JWST), these population III galaxies may offer one of the best probes of population III stars in the foreseeable future. By projecting the results from population III galaxy simulations through cluster magnification maps, we predict the fluxes and surface number densities of pop III galaxy galaxies as a function of their typical star formation efficiency. We argue that a small number of lensed population III galaxies in principle could turn up at z=7-10 in the ongoing Hubble Space Telescope survey CLASH, which covers a total of 25 low-redshift galaxy clusters.
After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket formalism, allows the choice of asymmetric boundary conditions analogous to the retarded solutions of the Maxwell equations for the radiation arrow of time. This led to irreversibility on the microphysical level as exemplified by decaying states or resonances. Resonances are mathematically represented by Gamow kets, functionals over a space of very well-behaved (Hardy class) vectors, which have been chosen by a boundary condition (outgoing for decaying states). Gamow states have all the properties that one heuristically needs for quasistable states. For them a Golden Rule can be derived from the fundamental probabilities that fulfills the time-asymmetry condition which could not be realized in the Hilbert space.
We calculate the leading and next-to-leading logarithmic resummed distribution for the jet broadening in deep inelastic scattering, as well as the power correction for both the distribution and mean value. A truncation of the answer at NLL accuracy, as is standard, leads to unphysical divergences. We discuss their origin and show how the problem can be resolved. We then examine DIS-specific procedures for matching to fixed-order calculations and compare our results to data. One of the tools developed for the comparison is an NLO parton distribution evolution code. When compared to PDF sets from MRST and CTEQ it reveals limited discrepancies in both.
When a gravitational wave is detected by Advanced LIGO/Virgo, sophisticated parameter estimation (PE) pipelines spring into action. These pipelines leverage approximants to generate large numbers of theoretical gravitational waveform predictions to characterize the detected signal. One of the most accurate and physically comprehensive classes of approximants in wide use is the "Spinning Effective One Body--Numerical Relativity" (SEOBNR) family. Waveform generation with these approximants can be computationally expensive, which has limited their usefulness in multiple data analysis contexts. In prior work we improved the performance of the aligned-spin approximant SEOBNR version 2 (v2) by nearly 300x. In this work we focus on optimizing the full eight-dimensional, precessing approximant SEOBNR version 3 (v3). While several v2 optimizations were implemented during its development, v3 is far too slow for use in state-of-the-art source characterization efforts for long-inspiral detections. Completion of a PE run after such a detection could take centuries to complete using v3. Here we develop and implement a host of optimizations for v3, calling the optimized approximant v3_Opt. Our optimized approximant is about 340x faster than v3, and generates waveforms that are numerically indistinguishable.