ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Ward identities of the Liouville gravity coupled to the minimal conformal matter are investigated. We introduce the pseudo-null fields and the generalized equations of motion, which are classified into series of the Liouville charges. These series have something to do with the W and Virasoro constraints. The pseudo-null fields have non-trivial contributions at the boundaries of the moduli space. We explicitly evaluate the several boundary contributions. Then the structures similar to the W and the Virasoro constraints appearing in the topological and the matrix methods are realized. Although our Ward identities have some different features from the other methods, the solutions of the identities are consistent to the matrix model results.
We propose a survey of Michel H\'enon works devoted to studying periodic solutions of the well-known celestial mechanics problem -- restricted three-body problem. The description of the main results obtained by H\'enon is given in comparison with results of russian mathematician Alexander Bruno. Finaly, a survey of H\'enon's works on Hill problem is given as well, and, more over, the authors propose some generalization of Hill problem that makes possible to provide the description of its families of periodic orbits in the form of common network.
Cesium Bromide films grown of glass substrates by thermal evaporation showed interesting optical properties. The UV-visible absorption spectra showed peaks which showed red shift with time. Structural and morphological studies suggested decrease in grain size with time which was unusual. Theoretical simulation shows the optical behaviour to be due to surface plasmon resonance resulting from Cesium clyindrical rods embedded in the films.
A unifying definition of trapped submanifold for arbitrary codimension by means of its mean curvature vector is presented. Then, the interplay between (generalized) symmetries and trapped submanifolds is studied, proving in particular that (i) stationary spacetimes cannot contain closed trapped nor marginally trapped submanifolds S of any codimension; (ii) S can be within the subset where there is a null Killing vector only if it is marginally trapped with mean curvature vector parallel to the null Killing; (iii) any submanifold orthogonal to a timelike or null Killing vector has a mean curvature vector orthogonal to it. All results are purely geometric, hold in arbitrary dimension, and can be appropriately generalized to many non-Killing vector fields, such as conformal Killing vectors and the like. A simple criterion to ascertain the trapping or not of a family of codimension-2 submanifolds is given. A path allowing to generalize the singularity theorems is conjectured as feasible and discussed.
We have used infrared polarimetric imaging with NICMOS to determine precisely the position of the star that illuminates (and presumably generated) the bipolar, pre-planetary reflection nebula RAFGL 2688 (the Egg Nebula). The polarimetric data pinpoint the illuminating star, which is not detected directly at wavelengths less than or equal to 2 microns, at a position well within the dark lane that bisects the nebula, 0.55" (about 550 AU) southwest of the infrared peak which was previously detected at the southern tip of the northern polar lobe. The inferred position of the central star corresponds to the geometric center of the tips of the four principle lobes of near-infrared H2 emission; identifying the central star at this position also reveals the strong point symmetric structure of the nebula, as seen both in the intensity and polarization structure of the polar lobes. The polarimetric and imaging data indicate that the infrared peak directly detected in the NICMOS images is a self-luminous source and, therefore, is most likely a distant binary companion to the illuminating star. Although present theory predicts that bipolar structure in pre-planetary and planetary nebulae is a consequence of binary star evolution, the separation between the components of the RAFGL 2688 binary system, as deduced from these observations, is much too large for the presence of the infrared companion to have influenced the structure of the RAFGL 2688 nebula.
We construct a large class of projective threefolds with one node (aka non-degenerate quadratic singularity) such that their small resolutions are not projective.
Using first-principles calculations based on density functional theory, we have studied the mechanical, electronic, and magnetic properties of Heusler alloys, namely, Ni$_{2}BC$ and Co$_{2}BC$ ($B$ = Sc, Ti, V, Cr and Mn as well as Y, Zr, Nb, Mo and Tc; $C$ = Ga and Sn). On the basis of electronic structure (density of states) and mechanical properties (tetragonal shear constant), as well as magnetic interactions (Heisenberg exchange coupling parameters), we probe the properties of these materials in detail. We calculate the formation energy of these alloys in the (face-centered) cubic austenite structure to probe the stability of all these materials. From the energetic point of view, we have studied the possibility of the electronically stable alloys having a tetragonal phase lower in energy compared to the respective cubic phase. A large number of the magnetic alloys is found to have the cubic phase as their ground state. On the other hand, for another class of alloys, the tetragonal phase has been found to have lower energy compared to the cubic phase. Further, we find that the values of tetragonal shear constant show a consistent trend : a high positive value for materials not prone to tetragonal transition and low or negative for others. In the literature, materials, which have been seen to undergo the martensite transition, are found to be metallic in nature. We probe here if there is any Heusler alloy which has a tendency to undergo a tetragonal transition and at the same time possesses a high spin polarization at the Fermi level. From our study, it is found that out of the four materials, which exhibit a martensite phase as their ground state, three of these, namely, Ni$_{2}$MnGa, Ni$_{2}$MoGa and Co$_{2}$NbSn have a metallic nature; on the contrary, Co$_{2}$MoGa exhibits a high spin polarization.
A permutation $\sigma\in S_n$ is said to be $k$-universal or a $k$-superpattern if for every $\pi\in S_k$, there is a subsequence of $\sigma$ that is order-isomorphic to $\pi$. A simple counting argument shows that $\sigma$ can be a $k$-superpattern only if $n\ge (1/e^2+o(1))k^2$, and Arratia conjectured that this lower bound is best-possible. Disproving Arratia's conjecture, we improve the trivial bound by a small constant factor. We accomplish this by designing an efficient encoding scheme for the patterns that appear in $\sigma$. This approach is quite flexible and is applicable to other universality-type problems; for example, we also improve a bound by Engen and Vatter on a problem concerning $(k+1)$-ary sequences which contain all $k$-permutations.
We study the interaction between two closely spaced but electrically isolated quasi-one-dimensional electrical wires by a drag experiment. In this work we experimentally demonstrate the generation of current in an unbiased (drag) wire, which results from the interactions with a neighboring biased (drive) wire. The direction of the drag current depends on the length of the one-dimensional wire with respect to the position of the barrier in the drag wire. When we additionally form a potential barrier in the drive wire, the direction of the drag current is determined by the relative position of the two barriers. We interpret this behavior in terms of electron excitations by phonon-mediated interactions between the two wires in presence of the electron scattering inside the drive wire.
In this work we consider the \emph{infinite color urn model} associated with a bounded increment random walk on $\Zbold^d$. This model was first introduced by Bandyopadhyay and Thacker (2013). We prove that the rate of convergence of the expected configuration of the urn at time $n$ with appropriate centering and scaling is of the order ${\mathcal O}\left(\frac{1}{\sqrt{\log n}}\right)$. Moreover we derive bounds similar to the classical Berry-Essen bound. Further we show that for the expected configuration a \emph{large deviation principle (LDP)} holds with a good rate function and speed $\log n$.
The structure of Nd$_{1-x}$Pb$_{x}$MnO$_{3}$ crystals is determined by single crystal X-ray diffraction. Substitution of Pb at the Nd site results in structural phase change from tetragonal (x = 0.25) to cubic (x = 0.37). These changes are attributed to the progressive removal of inter-octahedral tilting and minimization of the octahedral distortion leading to a higher symmetry as doping concentration increases. While the unit cell volume of tetragonal structure ($\it{P4/mmm}$) is comparable to that of parent NdMnO$_{3}$, the volume of cubic unit cell ($\it{Pm\bar{3}m}$) is doubled. Electron diffraction patterns support these results and rule out the possibility of twinning. Changes in transport properties as a function of temperature at different doping levels are in accordance with the observed structural changes. It is noticed that $\it{T_{c}}$ and $\it{T_{MI}}$ increase with x.
We advance the novel hypothesis that water in the presence of finite localized strain within fault gouges may lead to the phase transformation of stable minerals into metastable polymorphs of higher free energy density. Under increasing strain, the transformed minerals eventually become unstable, as shown from an application of Landau theory of structural phase transitions. We propose that this instability leads to an explosive transformation, creating a slightly supersonic shock wave propagating along the altered fault core leaving a wake of shaking fragments. As long as the resulting high-frequency acoustic waves remain of sufficient amplitude to lead to a fluidization of the fault core, the fault is unlocked and free to slip under the effect of the tectonic stress, thus releasing the elastic part of the stored energy. We briefly discuss observations that could be understood within this theory.
An excess of events with a rapidity gap between jets, over what would be expected from non-diffractive processes, has been observed at HERA. A process based on a perturbative QCD calculation of colour singlet exchange has been added to HERWIG. With this addition, HERWIG is able to describe the number of events with a gap between jets over the number without a gap. This gap fraction is predicted to rise at large rapidity intervals between jets which would only be visible if the detector coverage were increased.
To understand the world, we humans constantly need to relate the present to the past, and put events in context. In this paper, we enable existing video models to do the same. We propose a long-term feature bank---supportive information extracted over the entire span of a video---to augment state-of-the-art video models that otherwise would only view short clips of 2-5 seconds. Our experiments demonstrate that augmenting 3D convolutional networks with a long-term feature bank yields state-of-the-art results on three challenging video datasets: AVA, EPIC-Kitchens, and Charades.
We propose notions of "Noetherian" and "integral" for schemes over an abelian symmetric monoidal category $(\mathcal C,\otimes,1)$. For Noetherian integral schemes, we construct a "function field" that is a commutative monoid object of $(\mathcal C,\otimes,1)$. Under certain conditions, we show that a Noetherian scheme over $(\mathcal C,\otimes,1)$ is integral if and only if it is reduced and irreducible.
We show that, even in purely soft processes, the hadronic multiplicity in nucleus-nucleus interactions contains a term that scales with the number of binary collisions. In the absence of shadowing corrections, this term dominates at mid rapidities and high energies. Shadowing corrections are calculated as a function of impact parameter and the centrality dependence of mid-rapidity multiplicities is determined. The multiplicity per participant increases with centrality with a rate that increases between SPS and RHIC energies, in agreement with experiment.
In 1979 Goldfeld conjectured: 50\% of the quadratic twists of an elliptic curve defined over the rationals have analytic rank zero. In this expository article we present a few recent developments towards the conjecture, especially its first instance - the congruent number elliptic curves.
We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z-axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground state wavefunction with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a novel fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1) ``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing S^z = 0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as novel U(1) topological order. This state is stable to ALL zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wavefunction. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.
Recently, refinements have been made on both the theoretical and experimental determinations of the i.) mass of the lightest Higgs scalar, ii.) relic density of cold dark matter in the universe, iii.) branching fraction for radiative B decay BF(b \to s \gamma), iv.) muon anomalous magnetic moment, and v.) flavor violating decay B_s \to \mu^+\mu^-. In this work, we present constraints from each of these quantities on the minimal supergravity model as embedded in the updated version of the computer program ISAJET v7.64. Improvements and updates since our published work are especially emphasized. The combination of constraints points to certain favored regions of model parameter space where collider and non-accelerator SUSY searches may be more focused.
We study the surjectivity of suitable weighted Gaussian maps which provide a natural generalization of the standard Gaussian maps and encode the local geometry of the locus of curves endowed with a higher root of the canonical bundle having associated linear system of dimension at least r + 1. In particular, we get a bound on the dimension of its Zariski tangent space, which turns out to be sharp in the special case r = 0. Finally, we describe this locus in the case of complete intersection curves.
The discovery potential of the ATLAS experiment at the LHC for Higgs bosons of the MSSM is discussed. Several CP conserving and one CP violating benchmark scenario are investigated.
We investigate the [O II] emission line properties of 18,508 quasars at z<1.6 drawn from the Sloan Digital Sky Survey (SDSS) quasar sample. The quasar sample has been separated into 1,692 radio-loud and 16,816 radio-quiet quasars (RLQs and RQQs hereafter) matched in both redshift and i'-band absolute magnitude.   We use the [O II]\lambda3726+3729 line as an indicator of star formation. Based on these measurements we find evidence that star-formation activity is higher in the RLQ population. The mean equivalent widths (EW) for [O II] are EW([O II])_RL=7.80\pm0.30 \AA, and EW([O II])_RQ=4.77\pm0.06 \AA, for the RLQ and RQQ samples respectively. The mean [O II] luminosities are \log[L([O II])_RL/W]=34.31\pm0.01 and \log[L([O II])_RQ/W]=34.192\pm0.004 for the samples of RLQs and RQQs respectively. Finally, to overcome possible biases in the EW measurements due to the continuum emission below the [O II] line being contaminated by young stars in the host galaxy, we use the ratio of the [O II] luminosity to rest-frame i'-band luminosity, in this case, we find for the RLQs \log[L([O II])_RL/L_opt]=-3.89\pm0.01 and \log[L([O II])_RQ/L_opt]=-4.011\pm0.004 for RQQs. However the results depend upon the optical luminosity of the quasar. RLQs and RQQs with the same high optical luminosity \log(L_opt/W)>38.6, tend to have the same level of [O II] emission. On the other hand, at lower optical luminosities \log(L_opt/W)<38.6, there is a clear [O II] emission excess for the RLQs. As an additional check of our results we use the [O III] emission line as a tracer of the bolometric accretion luminosity, instead of the i'-band absolute magnitude, and we obtain similar results.   Radio jets appear to be the main reason for the [O II] emission excess in the case of RLQs. In contrast, we suggest AGN feedback ensures that the two populations acquire the same [O II] emission at higher optical luminosities.
The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are harder to identify. Recently, machine learning techniques have been shown to be capable of characterizing topological order in the presence of human supervision. Here, we propose an unsupervised approach based on diffusion maps that learns topological phase transitions from raw data without the need of manual feature engineering. Using bare spin configurations as input, the approach is shown to be capable of classifying samples of the two-dimensional XY model by winding number and capture the Berezinskii-Kosterlitz-Thouless transition. We also demonstrate the success of the approach on the Ising gauge theory, another paradigmatic model with topological order. In addition, a connection between the output of diffusion maps and the eigenstates of a quantum-well Hamiltonian is derived. Topological classification via diffusion maps can therefore enable fully unsupervised studies of exotic phases of matter.
We report on a first-principles investigation of the electronic structure and of the magnetic properties of the quasi-two-dimensional Mott insulator SrCu$_{2}$(BO$_{3}$)$_{2}$. Based on the hopping integrals and Coulomb interactions calculated with LDA and LSDA+U, we provide a microscopic explanation of the symmetric Heisenberg and antisymmetric Dzyaloshinskii-Moriya exchange integrals of SrCu$_{2}$(BO$_{3}$)$_{2}$. The intra-atomic exchange interaction of oxygen is shown to strongly contribute to the intra-dimer isotropic exchange. The results are in good agreement with those derived from experimental data, both regarding the orientation of the Dzyaloshinskii-Moriya vectors and the magnitude of all exchange integrals. The microscopic analysis is confirmed by the results of Green function's and total energies difference methods.
The isotropic majority-vote (MV) model which, apart from the one-dimensional case, is thought to be non-equilibrium and violating the detailed balance condition. We show that this is not true, when the model is defined on a complete graph. In the stationary regime, the MV model on a fully connected graph fulfills the detailed balance. We derive the exact expression for the probability distribution of finding the system in a given spin configuration. We show that it only depends on the absolute value of magnetization. Our theoretical predictions are validated by numerical simulations.
Oscillations in solar prominences are a frequent phenomenon, and they have been the subject of many studies. A full understanding of the mechanisms that drive them and their attenuation has not been reached yet. We numerically investigate the periodicity and damping of transverse and longitudinal oscillations in a 3D model of a curtain-shaped prominence. We carried out a set of numerical simulations of vertical, transverse and longitudinal oscillations with the high-order finite-difference Pencil Code. We solved the ideal magnetohydrodynamic (MHD) equations for a wide range of parameters, including the width and density of the prominence, and the magnetic field strength (B) of the solar corona. We studied the periodicity and attenuation of the induced oscillations. We found that longitudinal oscillations can be fit with the pendulum model, whose restoring force is the field aligned component of gravity, but other mechanisms such as pressure gradients may contribute to the movement. On the other hand, transverse oscillations are subject to magnetic forces. The analysis of the parametric survey shows, in agreement with observational studies, that the oscillation period (P) increases with the prominence width. For transverse oscillations we obtained that P increases with density and decreases with B. For longitudinal oscillations we also found that P increases with density, but there are no variations with B. The attenuation of transverse oscillations was investigated by analysing the velocity distribution and computing the Alfv\'en continuum modes. We conclude that resonant absorption is the mean cause. Damping of longitudinal oscillations is due to some kind of shear numerical viscosity.
We study within the perturbative many-body $GW$ and Bethe-Salpeter approach the low lying singlet charge-transfer excitations in molecular donor-acceptor complexes associating benzene, naphtalene and anthracene derivatives with the tetracyanoethylene acceptor. Our calculations demonstrate that such techniques can reproduce the experimental data with a mean average error of 0.1-0.15 eV for the present set of dimers, in excellent agreement with the best time-dependent density functional studies with optimized range-separated functionals. The present results pave the way to the study of photoinduced charge transfer processes in photovoltaic devices with a parameter-free \textit{ab initio} approach showing equivalent accuracy for finite and extended systems.
We consider a non relativistic charged particle in a 1-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex probability amplitude solution of a Schrodinger equation on a 1-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global approximate stabilization of the eigenstates by explicit feedback laws.
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for infinite graphs. We then apply these notions to critical percolation clusters, where the various dimensions have different values.
Let X be a complex analytic manifold and D \subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {\cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic differential operators {\cal D}_X(\log D). In this paper we study two related results: the relationship between the duals of any integrable logarithmic connection over the base rings {\cal D}_X and {\cal D}_X(\log D), and a differential criterion for the logarithmic comparison theorem. We also generalize a formula of Esnault-Viehweg in the normal crossing case for the Verdier dual of a logarithmic de Rham complex.