ShantanuT01/DACTYL-Pretraining huggingface dataset:
We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation using a novel compact notation and by implementing the constraints from polar, time and azimuthal motion. Four generic root structures with only simple roots give rise to eight non-generic root structures when either one root becomes coincident with the horizon, one root vanishes or two roots becomes coincident. We derive the explicit phase space of all such root systems in the basis of energy, angular momentum and Carter's constant and classify whether each corresponding radial geodesic motion is allowed or disallowed from existence of polar, time and azimuthal motion. The classification of radial motion within the ergoregion for both positive and negative energies leads to 6 distinguished values of the Kerr angular momentum. The classification of null radial motion and near-horizon extremal Kerr radial motion are obtained as limiting cases and compared with the literature. We explicitly parametrize the separatrix describing root systems with double roots as the union of the following three regions that are described by the same quartic respectively obtained when (1) the pericenter of bound motion becomes a double root; (2) the eccentricity of bound motion becomes zero; (3) the turning point of unbound motion becomes a double root.
In this paper we present theoretical investigation of optical conductivity for intermetallic TbNi_{5-x}Cu_x series. In the frame of LSDA+U calculations electronic structure for x=0,1,2 and on top of that optical conductivities were calculated. Disorder effects of Ni for Cu substitution on a level of LSDA+U densities of states (DOS) were taken into account via averaging over all possible Cu ion positions for given doping level x. Gradual suppression and loosing of structure of optical conductivity at 2 eV together with simultaneous intensity growth at 4 eV correspond to increase of Cu and decrease of Ni content. As reported before [Knyazev et al., Optics and Spectroscopy 104, 360 (2008)] plasma frequency has non monotonic doping behaviour with maximum at x=1. This behaviour is explained as competition between lowering of total density of states on the Fermi level N(E_F) and growing of number of carriers. Our theoretical results agree well with variety of recent experiments.
Ground and first radially excited scalar isoscalar meson states and a scalar glueball are described in a nonlocal U(3)xU(3) quark model. The glueball is introduced into the effective meson Lagrangian by means of the dilaton model on the base of the scale invariance of the meson Lagrangian. The scale invariance breaking by current quark masses and gluon anomalies is taken into account. The glueball anomalies turn out to be important for the description of the glueball-quarkonia mixing. The masses of five scalar isoscalar meson states and their strong decay widths are calculated. The state f_0(1500) is shown to be composed mostly of the scalar glueball.
Isolated Neutron Stars are some of the most exciting stellar objects known to astronomers: they have the most extreme magnetic fields, with values up to $10^{15}$ G, and, with the exception of stellar-mass black holes, they are the most dense stars, with densities of $\approx 10^{14}$ g cm$^{-3}$. As such, they are perfect laboratories to test theories of electromagnetism and nuclear physics under conditions of magnetic field and density unattainable on Earth. In particular, the interaction of radiation with strong magnetic fields is the cause of the {\em vacuum birefringence}, an effect predicted by quantum electrodynamics in 1936 but that lacked an observational evidence until now. Here, we show how the study of the polarisation of the optical radiation from the surface of an isolated neutron star yielded such an observational evidence, opening exciting perspectives for similar studies at other wavelengths.
We study the influence of initial conditions on the magnetic field amplification during the collapse of a magnetised gas cloud. We focus on the dependence of the growth and saturation level of the dynamo generated field on the turbulent properties of the collapsing cloud. In particular, we explore the effect of varying the initial strength and injection scale of turbulence and the initial uniform rotation of the collapsing magnetised cloud. In order to follow the evolution of the magnetic field in both the kinematic and the nonlinear regime, we choose an initial field strength of $\simeq 1\,\mkG$ with the magnetic to kinetic energy ratio, $E_{\rm m}/E_{\rm k} \sim 10^{-4}$. Both gravitational compression and the small-scale dynamo initially amplify the magnetic field. Further into the evolution, the dynamo-generated magnetic field saturates but the total magnetic field continues to grow because of compression. The saturation of the small-scale dynamo is marked by a change in the slope of $B/\rho^{2/3}$ and by a shift in the peak of the magnetic energy spectrum from small scales to larger scales. For the range of initial Mach numbers explored in this study, the dynamo growth rate increases as the Mach number increases from $v_{\rm rms}/c_{\rm s}\sim 0.2$ to 0.4 and then starts decreasing from $v_{\rm rms}/c_{\rm s}\sim 1.0$. We obtain saturation values of $E_{\rm m}/E_{\rm k} = 0.2 - 0.3$ for these runs. Simulations with different initial injection scales of turbulence also show saturation at similar levels. For runs with different initial rotation of the cloud, the magnetic energy saturates at $E_{\rm m}/E_{\rm k}\sim 0.2 - 0.4$ of the equipartition value. (Abridged)
Edges of an image are considered a crucial type of information. These can be extracted by applying edge detectors with different methodology. Edge detection is a vital step in computer vision tasks, because it is an essential issue for pattern recognition and visual interpretation. In this paper, we propose a new method for edge detection in images, based on the estimation by kernel of the probability density function. In our algorithm, pixels in the image with minimum value of density function are labeled as edges. The boundary between two homogeneous regions is defined in two domains: the spatial/lattice domain and the range/color domain. Extensive experimental evaluations proved that our edge detection method is significantly a competitive algorithm.
S. Montgomery-Smith provided a one dimensional model for the three dimensional, incompressible Navier-Stokes equations, for which he proved the blow up of solutions associated to a class of large initial data, while the same global existence results as for the Navier-Stokes equations hold for small data. In this note the model is adapted to the case of two and three space dimensions, with the additional feature that the divergence free condition is preserved. It is checked that the family of initial data constructed previously by J.-Y Chemin and I. Gallagher which is arbitrarily large but yet generates a global solution to the Navier-Stokes equations in three space dimensions, actually causes blow up for the toy model -- meaning that the precise structure of the nonlinear term is crucial to understand the dynamics of large solutions to the Navier-Stokes equations.
Heavy quarkonium decays can be used to search for New Physics beyond the Standard Model. In particular, a light Higgs boson could induce a slight (but observable) lepton universality breaking in Upsilon decays. In fact, current experimental data from CLEO presented in this Conference seem to point out to this direction within experimental accuracy. Moreover, LEP constraints on a light Higgs mass can be evaded by different models (like MSSM with a CPV Higgs sector) as shown in this Conference. We also consider spectroscopic consequences stemming from a possible mixing between Higgs and bottomonium states leading to discrepancies with the SM expectations (e.g. hyperfine splittings).
The thermal Sunyaev-Zel'dovich effect is an important probe of clusters of galaxies, and has the attractive property of being proportional to the thermal energy content of the intracluster medium. With the assistance of X-ray data, the effect can be used to measure the number of hot electrons in clusters, and thus measure cluster baryon contents. Cluster absolute distances and other structural parameters can also be measured by combining thermal Sunyaev-Zel'dovich, X-ray, and other data. This review presents an introduction to the effect, shows some representative results, and sketches imminent developments.
A L\'evy process is said to creep through a curve if, at its first passage time across this curve, the process reaches it with positive probability. We first study this property for bivariate subordinators. Given the graph $\{(t,f(t)):t\ge0\}$ of any continuous, non increasing function $f$ such that $f(0)>0$, we give an expression of the probability that a bivariate subordinator $(Y,Z)$ issued from 0 creeps through this graph in terms of its renewal function and the drifts of the components $Y$ and $Z$. We apply this result to the creeping probability of any real L\'evy process through the graph of any continuous, non increasing function at a time where the process also reaches its past supremum. This probability involves the density of the renewal function of the bivariate upward ladder process as well as its drift coefficients. We also investigate the case of L\'evy processes conditioned to stay positive creeping at their last passage time below the graph of a function. Then we provide some examples and we give an application to the probability of creeping through fixed levels by stable Ornstein-Uhlenbeck processes. We also raise a couple of open questions along the text.
This is an incomplete survey of some non-Abelian discrete symmetries which have been used recently in attempts to understand the flavor structure of leptons and quarks. To support such symmetries, new scalar particles are required. In some models, they are very massive, in which case there may not be much of a trace of their existence at the TeV scale. In other models, they are themselves at the TeV scale, in which case there is a reasonable chance for them to be revealed at the LHC (Large Hadron Collider) at CERN.
High-frequency ESR results on the S=1/2 Heisenberg hexagonal antiferromagnet InCu2/3V1/3O3 are reported. This compound appears to be a rare model substance for the honeycomb lattice antiferromagnet with very weak interlayer couplings. The high-temperature magnetic susceptibility can be interpreted by the S=1/2 honeycomb lattice antiferromagnet, and it shows a magnetic-order-like anomaly at TN=38 K. Although, the resonance field of our high-frequency ESR shows the typical behavior of the antiferromagnetic resonance, the linewidth of our high-frequency ESR continues to increase below TN, while it tends to decrease as the temperature in a conventional three-dimensional antiferromagnet decreases. In general, a honeycomb lattice antiferromagnet is expected to show a simple antiferromagnetic order similar to that of a square lattice antiferromagnet theoretically because both antiferromagnets are bipartite lattices. However, we suggest that the observed anomalous spin dynamics below TN is the peculiar feature of the honeycomb lattice antiferromagnet that is not observed in the square lattice antiferromagnet.
We study whether non-linear gravitational effects of relic neutrinos on the development of clustering and large-scale structure may be observable by weak gravitational lensing. We compute the density profile of relic massive neutrinos in a spherical model of a cluster of galaxies, for several neutrino mass schemes and cluster masses. Relic neutrinos add a small perturbation to the mass profile, making it more extended in the outer parts. In principle, this non-linear neutrino perturbation is detectable in an all-sky weak lensing survey such as EUCLID by averaging the shear profile of a large fraction of the visible massive clusters in the universe, or from its signature in the general weak lensing power spectrum or its cross-spectrum with galaxies. However, correctly modeling the distribution of mass in baryons and cold dark matter and suppressing any systematic errors to the accuracy required for detecting this neutrino perturbation is severely challenging.
We provide a new strategy to compute the exponential growth constant of enumeration sequences counting walks in lattice path models restricted to the quarter plane. The bounds arise by comparison with half-planes models. In many cases the bounds are provably tight, and provide a combinatorial interpretation of recent formulas of Fayolle and Raschel (2012) and Bostan, Raschel and Salvy (2013). We discuss how to generalize to higher dimensions.
We study the low-energy magnon spectrum of the skyrmion crystal (SkX) ground state, appearing in two-dimensional ferromagnet with Dzyaloshinskii-Moriya interaction and magnetic field. We approximate SkX hexagonal superlattice by a set of overlapping disks, and find the lattice period by minimizing the classical energy density. The determined spectrum of magnons on the disc of optimal radius is stable and only two lowest energy levels can be considered as localized. The subsequent hybridization of these levels in the SkX lattice leads to tight-binding spectrum. The localized character of the lowest magnon states is lost at small and at high fields, which is interpreted as melting of SkX. The classical energy of SkX is slightly above the energy of a single conical spiral, and a consideration of quantum corrections can favor the skyrmion ground state. Extending our analysis to three-dimensional case, we argue that these quantum corrections become more important at finite temperatures, when the average spin value is decreased.
In Randall-Sundrum models, by the use of general Noether theorem, the covariant angular momentum conservation law is obtained with the respect to the local Lorentz transformations. The angular momentum current has also superpotential and is therefore identically conserved. The space-like components $J_{ij}$ of the angular momentum for Randall-Sundrum models are zero. But the component $J_{04}$ is infinite.
The origin of ultra-high-energy cosmic rays (UHECRs) is one of the most intriguing problems of modern cosmic ray physics. We briefly review the main astrophysical models of their origin and the forthcoming orbital experiments TUS and JEM-EUSO, and discuss how the new data can help one solve the long-standing puzzle.
A permutiple is the product of a digit preserving multiplication, that is, a number which is an integer multiple of some permutation of its digits. Certain permutiple problems, particularly transposable, cyclic, and, more recently, palintiple numbers, have been well-studied. In this paper we study the problem of general digit preserving multiplication. We show how the digits and carries of a permutiple are related and utilize these relationships to develop methods for finding new permutiple examples from old. In particular, we shall focus on the problem of finding new permutiples from a known example having the same set of digits.
Let $d \ge 1$. We study a subspace of the space of automorphic forms of $\mathrm{GL}_d$ over a global field of positive characteristic (or, a function field of a curve over a finite field). We fix a place $\infty$ of $F$, and we consider the subspace $\mathcal{A}_{\mathrm{St}}$ consisting of automorphic forms such that the local component at $\infty$ of the associated automorphic representation is the Steinberg representation (to be made precise in the text).   We have two results.   One theorem (Theorem 16) describes the constituents of $\mathcal{A}_{\mathrm{St}}$ as automorphic representation and gives a multiplicity one type statement.   For the other theorem (Theorem 12), we construct, using the geometry of the Bruhat-Tits building, an analogue of modular symbols in $\mathcal{A}_{\mathrm{St}}$ integrally (that is, in the space of $\mathbb{Z}$-valued automorphic forms). We show that the quotient is finite and give a bound on the exponent of this quotient.
Set multipartite Ramsey numbers were introduced in 2004, ge-neralizing the celebrated Ramsey numbers. Let $C_4$ denote the four cycle and let $K_{1,n}$ denote the star on $n+1$ vertices. In this paper we investigate bounds on $C_4-K_{1,n}$ set multipartite Ramsey numbers. Relationships between these numbers and the classical $C_4-K_{1,n}$ Ramsey numbers are explored. Then several near-optimal or exact classes are derived as applications. As the main goal, polarity graphs from projective planes allow us to find suitable subgraphs which yield some optimal classes too.
We combine UV/Optical/near-IR/mid-IR data on a sample of ~240 S0 galaxies to examine various star formation related processes in them. We split the sample into bright and faint S0 galaxies based on their K band luminosity. Comparing the FUV-NUV versus NUV-K color-color diagram with a Simple Stellar Population (SSP) model shows that ellipticals and bright S0 galaxies are dominated by a stellar population of age > 10^9 years while faint S0 galaxies may contain stars as young as 10^8 years, providing evidence for relatively recent star formation activity. The strength of the 4000A break is also systematically higher in brighter S0 galaxies, again indicating the presence of an old stellar population. Their mid-IR colours indicate that bright S0 colours are like those of ellipticals while faint S0 colours are more like spirals. All these observations are consistent with a scenario in which low-luminosity S0 galaxies likely formed by the stripping of gas from the discs of late-type spiral galaxies, which in turn formed their pseudo bulges through secular evolution processes, possibly involving multiple episodes of star formation. On the other hand, more luminous S0 galaxies likely formed the bulk of their stars at early epochs, similar to the star formation in elliptical galaxies, and are characterised by an old coeval stellar population and classical bulge
The nature of various plausible causal links between sympathetic events is still a controversial issue. In this work, we present multi-wavelength observations of sympathetic eruptions, associated flares and coronal mass ejections (CMEs) occurring on 2013 November 17 in two close-by active regions. Two filaments i.e., F1 and F2 are observed in between the active regions. Successive magnetic reconnections, caused by different reasons (flux cancellation, shear and expansion) have been identified during the whole event. The first reconnection occurred during the first eruption via flux cancellation between the sheared arcades overlying filament F2, creating a flux rope and leading to the first double ribbon solar flare. During this phase we observed the eruption of overlaying arcades and coronal loops, which leads to the first CME. The second reconnection is believed to occur between the expanding flux rope of F2 and the overlying arcades of the filament F1. We suggest that this reconnection destabilized the equilibrium of filament F1, which further facilitated its eruption. The third stage of reconnection occurred in the wake of the erupting filament F1 between the legs of overlying arcades. This may create a flux rope and the second double ribbon flare and a second CME. The fourth reconnection was between the expanding arcades of the erupting filament F1 and the nearby ambient field, which produced the bi-directional plasma flows towards both upward and downward. Observations and a nonlinear force-free field extrapolation confirm the possibility of reconnection and the causal link between the magnetic systems.
We report resonant X-ray scattering measurements on the orbitally-degenerate triangular metallic antiferromagnet 2H-AgNiO2 to probe the spontaneous transition to a triple-cell superstructure at temperatures below 365 K. We observe a strong resonant enhancement of the supercell reflections through the Ni K-edge. The empirically extracted K-edge shift between the crystallographically-distinct Ni sites of 2.5(3) eV is much larger than the value expected from the shift in final states, and implies a core-level shift of ~1 eV, thus providing direct evidence for the onset of spontaneous honeycomb charge order in the triangular Ni layers. We also provide band-structure calculations that explain quantitatively the observed edge shifts in terms of changes in the Ni electronic energy levels due to charge order and hybridization with the surrounding oxygens.
Ubiquitous low frequency 1/f noise can be a limiting factor in the performance and application of nanoscale devices. Here, we quantitatively investigate low frequency electronic noise in single-layer transition metal dichalcogenide MoS2 field-effect transistors. The measured 1/f noise can be explained by an empirical formulation of mobility fluctuations with the Hooge parameter ranging between 0.005 and 2.0 in vacuum (< 10-5 Torr). The field-effect mobility decreased and the noise amplitude increased by an order of magnitude in ambient conditions, revealing the significant influence of atmospheric adsorbates on charge transport. In addition, single Lorentzian generation-recombination noise was observed to increase by an order of magnitude as the devices were cooled from 300 K to 6.5 K.
One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of such effects into a low-energy effective field theory is presented. An extension of the standard model that includes Lorentz- and CPT-breaking terms is developed. The restriction of the standard model extension to the QED sector is then discussed.
The sensitivity of the Rabi oscillations of a resonantly driven spin-1/2 system to a weak and slow modulation of the static longitudinal magnetic field, B_0, is studied theoretically. We establish the mapping of a weakly driven two-level system with modulation onto a strongly driven system without modulation. The mapping suggests that different regimes of spin dynamics, known for a strongly driven system, can be realized under common experimental conditions of weak driving (driving field B_ 1 << B_ 0) upon proper choice of the domains of modulation frequency, \omega_m, and amplitude, B_2. Fast modulation \omega_m >> \Omega_R, where \Omega_R is the Rabi frequency, emulates the regime of driving frequency much bigger than the resonant frequency. Strong modulation, B_2 >> B_1, emulates the regime B_1 >> B_0. Resonant modulation, \omega_m \approx \Omega_R, gives rise to an envelope of the Rabi oscillations. The shape of this envelope is highly sensitive to the detuning of the driving frequency from the resonance. Theoretical predictions for different domains of B_2 and \omega_m were tested experimentally using NMR of protons in water, where, without modulation, the pattern of Rabi oscillations could be observed over many periods. We present experimental results which reproduce the three predicted modulation regimes, and agree with theory quantitatively.