ShantanuT01/DACTYL-Pretraining huggingface dataset:
Angular momentum in protostellar discs can be transported either radially, through turbulence induced by the magnetorotational instability (MRI), or vertically, through the torque exerted by a large-scale magnetic field. We present a model of steady-state discs where these two mechanisms operate at the same radius and derive approximate criteria for their occurrence in an ambipolar diffusion dominated disc. We obtain "weak field'' solutions - which we associate with the MRI channel modes in a stratified disc - and transform them into accretion solutions with predominantly radial angular-momentum transport by implementing a turbulent-stress prescription based on published results of numerical simulations. We also analyze "intermediate field strength'' solutions in which both radial and vertical transport operate at the same radial location. Our results suggest, however, that this overlap is unlikely to occur in real discs.
Encoded (or ciphered) manuscripts are a special type of historical documents that contain encrypted text. The automatic recognition of this kind of documents is challenging because: 1) the cipher alphabet changes from one document to another, 2) there is a lack of annotated corpus for training and 3) touching symbols make the symbol segmentation difficult and complex. To overcome these difficulties, we propose a novel method for handwritten ciphers recognition based on few-shot object detection. Our method first detects all symbols of a given alphabet in a line image, and then a decoding step maps the symbol similarity scores to the final sequence of transcribed symbols. By training on synthetic data, we show that the proposed architecture is able to recognize handwritten ciphers with unseen alphabets. In addition, if few labeled pages with the same alphabet are used for fine tuning, our method surpasses existing unsupervised and supervised HTR methods for ciphers recognition.
Singular degenerate differential operator equations are studied. The uniform separability of boundary value problems for degenerate elliptic equation and optimal regularity properties of Cauchy problem for degenerate parabolic equation are obtained. These problems have a numeros applications which occur in fluid mechanics, environmental engineering and atmospheric dispersion of pollutants.
A number of experiments on the hyperkagome iridate, Na$_4$Ir$_3$O$_8$, suggest existence of a gapless quantum spin liquid state at low temperature. Circumventing the slave particle approach commonly used in theoretical analyses of frustrated magnets, we provide a more intuitive, albeit more phenomenological, construction of a quantum spin liquid state for the hyperkagome Heisenberg model. An effective monomer-dimer model on the hyperkagome lattice is proposed a la Hao and Tchernyshyov's approach cultivated from the Husimi cactus model. Employing an arrow representation for the monomer-dimer model, we obtain a compact $U(1)$ gauge theory with a finite density of Fermionic spinons on the hyperoctagon lattice. The resulting theory and its mean field treatments lead to remarkable agreement with previous slave-particle construction of a quantum spin liquid state on the hyperkagome lattice. Our results offer novel insights on theoretical understanding of the emergence of spinon Fermi surfaces and useful predictions for future experiments.
A Robinson similarity matrix is a symmetric matrix where the entry values on all rows and columns increase toward the diagonal. Decompose the Robinson matrix into the sum of k {0, 1}-matrices, then these k {0, 1}-matrices are the adjacency matrices of a set of nested unit interval graphs. Previous studies show that unit interval graphs coincide with indifference graphs. An indifference graph has an embedding that maps each vertex to a real number, where two vertices are adjacent if their embedding is within a fixed threshold distance. In this thesis, consider k different threshold distances, we study the problem of finding an embedding that, simultaneously and with respect to each threshold distance, embeds the k indifference graphs corresponding to the k adjacency matrices. This is called a uniform embedding of a Robinson matrix with respect to the k threshold distances. We give a sufficient and necessary condition on Robinson matrices that have a uniform embedding, which is derived from paths in an associated graph. We also give an efficient combinatorial algorithm to find a uniform embedding or give proof that it does not exist, for the case where k = 2.
The electrical resistivity of the magnetically ordered CeCu_5Au has been investigated under pressure up to 8.5 GPa. In the magnetically ordered region (p<3.4 GPa) the residual resistivity rho_0 shows a pronounced maximum as a function of pressure. Even in the nonmagnetic region rho_0 decreases monotonically by more than a factor of three. These two effects can be qualitatively explained in terms of the interplay of pressure, magnetism and disorder in a strongly correlated electron system with weak disorder.
We have measured the thermal conductivity of the geometrically frustrated quasi-onedimensional spin system Cu$_3$Mo$_2$O$_9$ in magnetic fields. A contribution of the thermal conductivity due to spins has been observed in the thermal conductivity along the spin chains. The thermal conductivity due to phonons, $\kappa_{\rm phonon}$, has been found to decrease by the application of a magnetic field, which has been explained as being due to the reduction in the spin gap originating from the spin-singlet dimers. Moreover, it has been found that $\kappa_{\rm phonon}$ increases with increasing field in high fields above ~7 T at low temperatures. This suggests the existence of a novel field-induced spin state and is discussed in terms of the possible spin-chirality ordering in a frustrated Mott insulator.
We have analysed Chandra/High Energy Transmission Gratings spectra of the X-ray emission line gas in the Seyfert galaxy NGC 4151. The zeroth order spectral images show extended H- and He-like O and Ne, up to a distance $r \sim$ 200 pc from the nucleus. Using the 1st order spectra, we measure an average line velocity $\sim -230$ km s$^{-1}$, suggesting significant outflow of X-ray gas. We generated Cloudy photoionisation models to fit the 1st order spectra. We required three emission-line components, with column density, log$N_{H}$, and ionisation parameter, log$U$, of 22.5/1.0, 22.5/0.19, and 23.0/-0.50, respectively. To estimate the total mass of ionised gas and the mass outflow rates, we applied the model parameters to fit the zeroth order emission-line profiles of Ne~IX and Ne~X. We determined the total mass of $\approx 5.4 \times$ 10$^{5}$ M_sun. Assuming the same kinematic profile as that for the [O~III] gas, the peak X-ray mass outflow rate was $\approx 1.8$ M_sun yr$^{-1}$, at $r \sim 150$ pc. The total mass and mass outflow rates are similar to those determined using [O~III], implying that the X-ray gas is a major outflow component. However, unlike the optical outflows, the X-ray outflow rate does not drop off at $r >$ 100 pc, which suggests that it may have a greater impact on the host galaxy.
In this work, we present a non-linear difference equation for calculation of the zeros of the Riemann's zeta-function on the critical line. Our proposed non-linear map uses the Lambert W function and it can be easily implemented in a mathematical software. In order to check the quality of the zeros calculated, we show the factorization of an integer number by the calculation of the discrete cosine Riemann transform.
The effects of water wetting conditions on the transport properties of molecular nano-junctions are investigated theoretically by using a combination of classical molecular dynamics and first principles electronic transport calculations. These are at the level of the non-equilibrium Green's function method implemented for self-interaction corrected density functional theory. We find that water effectively produces electrostatic gating to the molecular junction, with a gating potential determined by the time-averaged water dipole field. Such a field is large for the polar benzene-dithiol molecule, resulting in a transmission spectrum shifted by about 0.6 eV with respect to that of the dry junction. The situation is drastically different for carbon nanotubes (CNTs). In fact, because of their hydro-phobic nature the gating is almost negligible, so that the average transmission spectrum of wet Au/CNT/Au junctions is essentially the same as that in dry conditions. This suggests that CNTs can be used as molecular interconnects also in water-wet situations, for instance as tips for scanning tunnel microscopy in solution or in biological sensors.
The Hamiltonian approach to the General Relativity and the Standard Model is studied in the context of its consistency with the Newton law, the Higgs effect, the Hubble cosmological evolution and the Cosmic Microwave Background radiation physics.   The version of the Higgs potential is proposed, where its constant parameter is replaced by the dynamic zeroth Fourier harmonic of the very Higgs field. In this model, the extremum of the Coleman--Weinberg effective potential obtained from the unit vacuum--vacuum transition amplitude immediately predicts mass of Higgs field and removes tremendous vacuum cosmological density.   We show that the relativity principles unambiguously treat the Planck epoch, in the General Relativity, as the present-day one. It was shown that there are initial data of the Electro-Weak epoch compatible with supposition that all particles in the Universe are final products of decays of primordial Higgs particles and W-, Z-vector bosons created from vacuum at the instant treated as the "Big-Bang".
We construct a discrete family of smooth non-supersymmetric three charge geometries carrying D1 brane, D5 brane and Kaluza-Klein monopole charges in Type IIB supergravity compactified on a six-torus, which can be interpreted as the geometric description of some special states of the brane system. These solutions are asymptotically flat in four dimensions, and generalise previous supersymmetric solutions. The solutions have a qualitatively similar structure to previous non-supersymmetric smooth solutions carrying D1 and D5 brane charges in five dimensions, and indeed can be viewed as the five-dimensional system placed at the core of a Kaluza-Klein monopole. The geometries are smooth, free of horizons and do not have closed timelike curves. One notable difference from the five-dimensional case is that the four-dimensional geometry has no ergoregion.
We introduce and study a new action of the symmetric group $\mathfrak{S}_n$ on the vector space spanned by noncrossing partitions of $\{1, 2, \dots, n\}$ in which the adjacent transpositions $(i, i+1) \in \mathfrak{S}_n$ act on noncrossing partitions by means of skein relations. We characterize the isomorphism type of the resulting module and use it to obtain new representation theoretic proofs of cyclic sieving results due to Reiner-Stanton-White and Pechenik for the action of rotation on various classes of noncrossing partitions and the action of K-promotion on two-row rectangular increasing tableaux. Our skein relations generalize the Kauffman bracket (or Ptolemy relation) and can be used to resolve any set partition as a linear combination of noncrossing partitions in a $\mathfrak{S}_n$-equivariant way.
Graphene has extraordinary electronic and optical properties and holds great promise for applications in photonics and optoelectronics. Demonstrations including high-speed photodetectors, optical modulators, plasmonic devices, and ultrafast lasers have now been reported. More advanced device concepts would involve photonic elements such as cavities to control light-matter interaction in graphene. Here we report the first monolithic integration of a graphene transistor and a planar, optical microcavity. We find that the microcavity-induced optical confinement controls the efficiency and spectral selection of photocurrent generation in the integrated graphene device. A twenty-fold enhancement of photocurrent is demonstrated. The optical cavity also determines the spectral properties of the electrically excited thermal radiation of graphene. Most interestingly, we find that the cavity confinement modifies the electrical transport characteristics of the integrated graphene transistor. Our experimental approach opens up a route towards cavity-quantum electrodynamics on the nanometre scale with graphene as a current-carrying intra-cavity medium of atomic thickness.
The dense, cold gas of Infrared Dark Clouds (IRDCs) is thought to be representative of the initial conditions of massive star and star cluster formation. We analyze 13CO(J=1-0) line emission data from the Galactic Ring Survey of Jackson et al. for two filamentary IRDCs, comparing the mass surface densities derived from 13CO, Sigma_13CO, with those derived from mid-infrared small median filter extinction mapping, Sigma_SMF, by Butler & Tan. After accounting for molecular envelopes around the filaments, we find approximately linear relations between Sigma_CO and Sigma_SMF, i.e. an approximately constant ratio Sigma_CO/Sigma_SMF in the clouds. There is a variation of about a factor of two between the two clouds. We find evidence for a modest decrease of Sigma_CO/Sigma_SMF with increasing mass surface density, which may be due to a systematic decrease in temperature, increase in importance of high 13CO opacity cores, increase in dust opacity, or decrease in 13CO abundance due to depletion in regions of higher column density. We perform ellipsoidal and filamentary virial analyses of the clouds, finding that the surface pressure terms are dynamically important and that globally the filaments may not yet have reached virial equilibrium. Some local regions along the filaments appear to be close to virial equilibrium, although still with dynamically important surface pressures, and these appear to be sites where star formation is most active.
We study the Hawking radiation emitted into the bulk by $(D+1)$-dimensional Schwarzschild black holes. It is well-known that the black-hole spectrum departs from exact blackbody form due to the frequency dependence of the `greybody' factors. For intermediate values of $D$ ($3\leq D\lesssim10$), these frequency-dependent factors may significantly modify the spectrum of the emitted radiation. However, we point out that for $D\gg1$, the typical wavelengths in the black-hole spectrum are much {\it shorter} than the size of the black hole. In this regime, the greybody factors are well described by the geometric-optics approximation according to which they are almost frequency-independent. Following this observation, we argue that for higher-dimensional black holes with $D\gg1$, the total power emitted into the bulk should be well approximated by the analytical formula for perfect blackbody radiation. We test the validity of this analytical prediction with numerical computations.
It has been noticed that confinement effects can be described by the addition of a $ \sqrt {- F_{\mu \nu}^a F^{a\mu \nu}} $ term in the Lagrangian density. We now study the combined effect of such "confinement term" and that of a mass term. The surprising result is that the interplay between these two terms gives rise to a Coulomb interaction. Our picture has a certain correspondence with the quasiconfinement picture described by Giles, Jaffe and de Rujula for QCD with symmetry breaking.
In this paper, we classify the 1-Weierstrass points of the Kuribayashi quartic curves with two parameters $a$ and $b$ defined by the equation \[C_{a,b}:x^{4}+y^{4}+z^{4}+ax^{2}y^{2}+b(x^{2}+y^{2})z^{2}=0,\] such that $(a^2-4)(b^2-4)(a^2-1)(b^{2}-a-2)\neq0.$ Furthermore, the geometry of these points is investigated.
In this paper we study static spherically symmetric Einstein-Vlasov shells, made up of equal mass particles, where the angular momentum L of particles takes values only on a discrete finite set. We consider first the case where there is only one value of L, and prove their existence by constructing explicit examples. Shells with either hollow or black hole interiors have finite thickness. Of particular interest is the thin shell limit of these systems and we study its properties using both numerical and analytic arguments to compare with known results. The general case of a set of values of L is also considered and the particular case where L takes only two values is analyzed, and compared with the corresponding thin shell limit already given in the literature, finding good agreement in all cases.
We investigate the scope of the LHC in probing the parameter space of a 4-site model supplemented by one composite Higgs state, assuming all past, current and future energy and luminosity stages of the CERN machine. We concentrate on the yield of charged di-boson production giving two opposite-charge different-flavour leptons and missing (transverse) energy, i.e., events induced via the subprocess $q\bar q\to e^+\nu_e \mu^-\bar\nu_\mu$ + ${\rm{c.c.}}$, which enables the production in the intermediate step of all additional neutral and charged gauge bosons belonging to the spectrum of this model, some of which in resonant topologies. We find this channel accessible over the background at all LHC configurations after a dedicated cut-based analysis. We finally compare the yield of the di-boson mode to that of Drell-Yan processes and establish that they have complementary strengths, one covering regions of parameter space precluded to the others and vice versa.
A simplified 1D (one-dimensional) model for a generalized 3N system is considered, as a testing ground for the explicit treatment of the meson dynamics in this system. We focus attention on the irreducible diagrams generated by the pion dynamics in the 3N system, and in particular to a new type of three-nucleon force discussed recently in the literature, and generated by the one-pion-exchange mechanism in presence of a nucleon-nucleon correlation. It is found that these new terms in the simplified model have an approximately 30% effect compared to the standard three-nucleon force terms in a `Triton' binding energy calculation. It is suggested that this effect should also not be ignored in realistic calculations.
We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that particle conservation law and the directed percolation-like local evolution of avalanches lead to the formation of a spatial structure in the steady state, with the density developing a power law tail away from the top. We determine the scaling exponents characterizing the avalanche distributions in terms of the critical exponents of directed percolation in all dimensions.
We report measurements of the x-ray scattering intensity as mesoporous glasses are filled with Neon. We outline a simple model to account for the non-linear increase in the intensity of the first peak in a liquid-like diffraction pattern as a monolayer is formed. This allows us to demonstrate an approach for surface area determination which does not rely on thermodynamic models, and is therefore complimentary to existing models.
We investigate the presence of discrete gauge symmetries in Grand Unification models based in $SO(10)$ and $E_6$. These models include {\it flipped} and {\it unflipped} $SU(5)$, $SU(4)\!\times\! SU(2)_L\!\times\! SU(2)_R$, $SU(3)_C\!\times\! SU(3)_L\!\times\! SU(3)_R$, and $SU(6)\!\times\! SU(2)$. Using the Dynkin formalism we find the $U(1)$ subalgebras contained in the unified groups, give an expression for the Higgs fields that preserve each discrete symmetry, and determine the low-energy matter content implied by chirality. We discuss two $Z_2$ and three $Z_3$ nonequivalent cases. Among the possibilities found, only the usual $Z_2$ matter parity (R-parity) of supersymmetric extensions is consistent with a minimal matter content with no right- handed neutrinos, extra Higgs doublets, or nonstandard {\it down}-type quarks.
We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or disconnect certain distinguished vertices when the size of the tree tends to infinity. New probabilistic explanations are given in terms of the so-called cut-tree and the tree of component sizes, which both encode different aspects of the destruction process. Finally, we establish the connection to Bernoulli bond percolation on large RRT's and present recent results on the cluster sizes in the supercritical regime.
Every compact symmetric space $M$ admits a dual noncompact symmetric space $\check{M}$. When $M$ is a generalized Grassmannian, we can view $\check{M}$ as a open submanifold of it consisting of space-like subspaces \cite{HL}. Motivated from this, we study the embeddings from noncompact symmetric spaces to their compact duals, including space-like embedding for generalized Grassmannians, Borel embedding for Hermitian symmetric spaces and the generalized embedding for symmetric R-spaces. We will compare these embeddings and describe their images using cut loci.
A heterostructure consisting of a magnetic Weyl semimetal and a conventional superconductor exhibits an equilibrium current parallel to the superconductor interface and perpendicular to the magnetization. Analyzing a minimal model, which as a function of parameters may be in a trivial magnetic insulator phase, a Weyl semimetal phase, or a three-dimensional weak Chern insulator phase, we find that the equilibrium current is sensitive to the presence of surface states, such as the topological Fermi-arc states of the Weyl semimetal or the chiral surface states of the weak Chern insulator. While there is a nonzero equilibrium current in all three phases, the appearance of the surface states in the topological regime leads to a reversal of the direction of the current, compared to the current direction for the trivial magnetic insulator phase. We discuss the interpretation of the surface-state contribution to the equilibrium current as a real-space realization of the superconductivity-enabled equilibrium chiral magnetic effect of a single chirality, predicted to occur in bulk Weyl superconductors.
The metal-rich Galactic globular cluster NGC 6366 is the fifth closest to the Sun. Despite its interest, it has received scarce attention, and little is known about its internal structure. Its kinematics suggests a link to the halo, but its metallicity indicates otherwise. We present a detailed chemical analysis of eight giant stars of NGC 6366, using high resolution and high quality spectra (R > 40000, S/N > 60) obtained at the VLT (8.2 m) and CFHT (3.6 m) telescopes. We attempted to characterize its chemistry and to search for evidence of multiple stellar populations. The atmospheric parameters were derived using the method of excitation and ionization equilibrium of FeI and FeII lines and from those atmospheric parameters we calculated the abundances for other elements and found that none of the elements measured presents star-to-star variation greater than the uncertainties. We compared the derived abundances with those of other globular clusters and field stars available in the literature. We determined a mean [Fe/H] = -0.60 +- 0.03 for NGC 6366 and found some similarity of this object with M 71, another inner halo globular cluster. The Na-O anticorrelation extension is short and no star-to-star variation in Al is found. The presence of second generation stars is not evident in NGC 6366.