ShantanuT01/DACTYL-Pretraining huggingface dataset:
Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that each nonrigid trinomial variety has finite number of orbits. We investigate singular orbits and this gives us description of all orbits for some classes of flexible trinomial hypersurfaces. Also we obtain a description of orbits for a class of hypersurfaces having a unique variable with power one in the equation.
The FRI/FRII dichotomy is a much debated issue in the astrophysics of extragalactic radio sources. Study of the properties of HYbrid MOrphology Radio Sources (HYMORS) may bring crucial information and lead to a step forward in understanding the origin of FRI/FRII dichotomy. HYMORS are a rare class of double-lobed radio sources where each of the two lobes clearly exhibits a different FR morphology. This article describes follow-up high resolution VLBA observations of the five discovered by us HYMORS. The main aim of the observations was to answer the questions of whether the unusual radio morphology is connected to the orientation of objects towards the observer. We obtained the high resolution radio maps of five hybrid radio morphology objects with the VLBA at C-band and L-band. Two of them revealed milliarcsecond core-jet structures, the next two objects showed hints of parsec-scale jets, and the last one remained point-like at both frequencies. We compared properties of observed milliarcsecond structures of hybrid sources with the larger scale ones previously detected with the VLA. We find that on both scales the fluxes of their central components are similar, which may indicate the lack of additional emission in the proximity of the nucleus. This suggests that jets present on the 1-10 kpc scale in those objects are FRII-like. When possible, the detected core-jet structures were used for estimating the core's spatial orientation. The result is that neither the FRI-like nor the FRII-like side is preferred, which may suggest that no specific spatial orientation of HYMORS is required to explain their radio morphology. Their estimated viewing angles indicate they are unbeamed objects. The 178 MHz luminosity of observed HYMORS exceed the traditional FRI/FRII break luminosity, indicating they have radio powers similar to FRIIs.
We apply a principal component analysis (PCA) to the spectra of each of the 18 Seyfert 1-like objects observed more than 15 times by the international ultraviolet explorer (IUE) from 1978 until the end of 1991. PCA allows us to decompose the Lyman alpha and the C IV (1549 A) emission-lines of each object into two components with uncorrelated variations. We find that the principal component describes correlated continuum and line variations, whereas the rest component reveals the line-parts that do not vary in tune with the continuum. A cross-correlation analysis in NGC 5548 reveals that variable line features in the rest component follow the continuum by about 25 days. The symmetry usually observed in the component's line profiles excludes that the velocity field of the line-emitting region is dominated by radial motion. In some objects, the principal component reveals a clearly double-peaked line profile.   The results suggest that the variable line feature in the principal and the rest component is respectively emitted in the inner and outer parts of an extended broad-line region (BLR). The fraction of the line that varies together with the continuum seems to decrease significantly with increasing luminosity. We interpret this trend as a consequence of a larger BLR in more luminous objects. Finally, we propose a solution to the C IV/Ly_a ratio problem without referring to optically thin emission-line clouds.
Let F be a real quadratic field with ring of integers O and with class number 1. Let Gamma be a congruence subgroup of GL_2 (O). We describe a technique to compute the action of the Hecke operators on the cohomology H^3 (Gamma; C). For F real quadratic this cohomology group contains the cuspidal cohomology corresponding to cuspidal Hilbert modular forms of parallel weight 2. Hence this technique gives a way to compute the Hecke action on these Hilbert modular forms.
We sketch a method to compute mod $\ell$ Galois representations contained in the H2 \'etale of surfaces. We apply this method to the case of a representation with values in GL(3,9) attached to an eigenform over a congruence subgroup of SL(3). We obtain in particular a polynomial with Galois group isomorphic to the simple group PSU(3,9) and ramified at 2 and 3 only.
We investigate remote surface scattering (RSR) by the SiO$_2$/HfO$_2$ interface in Fully-Depleted Silicon-on-Insulator (FDSOI) devices using Non-Equilibrium Green's Functions. We show that the RSR mobility is controlled by cross-correlations between the surface roughness profiles at the Si/SiO$_2$ and SiO$_2$/HfO$_2$ interfaces. Therefore, surface roughness and remote surface roughness can not be modeled as two independent mechanisms. RSR tends to enhance the total mobility when the Si/SiO$_2$ interface and SiO$_2$ thickness profiles are correlated, and to decrease the total mobility when they are anti-correlated. We discuss the implications for the high-$\kappa$/Metal gate technologies.
We report the detection of linearly polarized emission at 53 and 89 $\mu$m, from the radio-loud active galactic nucleus (AGN) Cygnus A using HAWC+ onboard SOFIA. We measure a highly polarized core of $11\pm3$% and $9\pm2$% with a position angle (P.A.) of polarization of $43\pm8^{\circ}$ and $39\pm7^{\circ}$ at 53 and 89 $\mu$m, respectively. We find (1) a synchrotron dominated core with a flat spectrum ($+0.21\pm0.05$) and a turn-over at $543\pm120$ $\mu$m, which implies synchrotron emission is insignificant in the infrared (IR), and (2) a $2-500$ $\mu$m bump peaking at $\sim40$ $\mu$m described by a blackbody component with color temperature of $107\pm9$ K. The polarized SED has the same shape as the IR bump of the total flux SED. We observe a change in the P.A. of polarization of $\sim20^{\circ}$ from 2 to 89 $\mu$m, which suggests a change of polarization mechanisms. The ultraviolet, optical and near-IR polarization has been convincingly attributed to scattering by polar dust, consistent with the usual torus scenario, though this scattered component can only be directly observed from the core in the near-IR. By contrast, the gradual rotation by $\sim20^{\circ}$ towards the far-IR, and the near-perfect match between the total and polarized IR bumps, indicate that dust emission from aligned dust grains becomes dominant at $10-100$ $\mu$m, with a large polarization of 10% at a nearly constant P.A. This result suggests that a coherent dusty and magnetic field structure dominates the $10-100$ $\mu$m emission around the AGN.
According to the no-hair conjecture, equilibrium black holes are simple objects, completely determined by global charges which can be measured at infinity. This is the case in Einstein-Maxwell theory due to beautiful uniqueness theorems. However, the no-hair conjecture is not true in general, and there is now a plethora of matter models possessing hairy black hole solutions. In this note we focus on one such matter model: Einstein-Yang-Mills (EYM) theory, and restrict our attention to four-dimensional, static, non-rotating black holes for simplicity. We outline some of the menagerie of EYM solutions in both asymptotically flat and asymptotically anti-de Sitter space. We attempt to make sense of this black hole zoo in terms of Bizon's modified no-hair conjecture.
We study the coupled two-species non-equilibrium reaction-controlled diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by means of detailed Monte Carlo simulations in one and two dimensions. Particles of type A may independently hop to an adjacent lattice site provided it is occupied by at least one B particle. The B particle species undergoes diffusion-limited reactions. In an active state with nonzero, essentially homogeneous B particle saturation density, the A species displays normal diffusion. In an inactive, absorbing phase with exponentially decaying B density, the A particles become localized. In situations with algebraic decay rho_B(t) ~ t^{-alpha_B}, as occuring either at a non-equilibrium continuous phase transition separating active and absorbing states, or in a power-law inactive phase, the A particles propagate subdiffusively with mean-square displacement <x(t)^2_A> ~ t^{1-alpha_A}. We find that within the accuracy of our simulation data, \alpha_A = \alpha_B as predicted by a simple mean-field approach. This remains true even in the presence of strong spatio-temporal fluctuations of the B density. However, in contrast with the mean-field results, our data yield a distinctly non-Gaussian A particle displacement distribution n_A(x,t) that obeys dynamic scaling and looks remarkably similar for the different processes investigated here. Fluctuations of effective diffusion rates cause a marked enhancement of n_A(x,t) at low displacements |x|, indicating a considerable fraction of practically localized A particles, as well as at large traversed distances.
We introduce some (anti)M/D-branes through turning on the corresponding field strengths of the eleven- and ten-dimensional supergravity theories over AdS_4 x M^(7/6) spaces, where we use S^7/Z_k and CP^3 for the internal spaces. Indeed, when we add M2/D2-branes on the same directions with the near horizon branes of Aharony-Bergman-Jafferis-Maldacena model, all symmetries and supersymmetries are preserved trivially. In the case, we gain a localized object just in the horizon. This normalizable bulk massless scalar mode is a singlet of SO(8) and SU(4)x U(1), and agrees with a marginal boundary operator of the conformal dimension of {\Delta}_+=3. However, after performing a special conformal transformation, we see that the solution is localized in the Euclideanized AdS_4 space and is attributable to the included anti-M2/D2-branes, which are also necessary to ensure that there is no backreaction. The resultant theory now breaks all N=8,6 supersymmetries to N=0 while other symmetries are so preserved. The dual boundary operator then sets up from the skew-whiffing of the representations 8_s and 8_v for the supercharges and scalars respectively, while the fermions remain fixed in 8_c of the original theory. Besides, we also address another alternate bulk to boundary matching procedure through turning on one of the gauge fields of the full U(N)_k x U(N)_-k gauge group in the same lines with the similar situation faced in AdS_5/CFT_4 correspondence. The latter approach covers the difficulty already faced with of the bulk-boundary matching procedure for k=1,2 as well.
Particle production in p+p and central Pb+Pb collisions at LHC is discussed in the context of the statistical thermal model. For heavy-ion collisions, predictions of various particle ratios are presented. The sensitivity of several ratios on the temperature and the baryon chemical potential is studied in detail, and some of them, which are particularly appropriate to determine the chemical freeze-out point experimentally, are indicated. Considering elementary interactions on the other hand, we focus on strangeness production and its possible suppression. Extrapolating the thermal parameters to LHC energy, we present predictions of the statistical model for particle yields in p+p collisions. We quantify the strangeness suppression by the correlation volume parameter and discuss its influence on particle production. We propose observables that can provide deeper insight into the mechanism of strangeness production and suppression at LHC.
We use a dedicated 0.7-m telescope to image the halos of 119 galaxies in the Local Volume to $\mu_r \sim 28-30$ mag/arcsec$^2$. The sample is primarily from the 2MASS Large Galaxy Atlas and extended to include nearby dwarf galaxies and more distant giant ellipticals, and spans fully the galaxy colour-magnitude diagram including the blue cloud and red sequence. We present an initial overview, including deep images of our galaxies. Our observations reproduce previously reported low surface brightness structures, including extended plumes in M51, and a newly discovered tidally extended dwarf galaxy in NGC7331. Low surface brightness structures, or "envelopes", exceeding 50 kpc in diameter are found mostly in galaxies with $M_V<-20.5$, and classic interaction signatures are infrequent. Defining a halo diameter at the surface brightness 28 mag/arcsec$^2$, we find that halo diameter is correlated with total galaxy luminosity. Extended signatures of interaction are found throughout the galaxy colour-magnitude diagram without preference for the red or blue sequences, or the green valley. Large envelopes may be found throughout the colour-magnitude diagram with some preference for the bright end of the red sequence. Spiral and S0 galaxies have broadly similar sizes, but ellipticals extend to notably greater diameters, reaching 150 kpc. We propose that the extended envelopes of disk galaxies are dominated by an extension of the disk population rather than by a classical population II halo.
We consider the coadjoint action of a Loop group of a compact group on the dual of the corresponding centrally extended Loop algebra and prove that a Brownian motion in a Cartan subalgebra conditioned to remain in an affine Weyl chamber - which can be seen as a space time conditioned Brownian motion - is distributed as the radial part process of a Brownian sheet on the underlying Lie algebra.
Possible Kondo effect in Pr skutterudite is studied with attention to characteristic features of low-lying crystalline electric field (CEF) levels and the conduction band. A mechanism for the small CEF splitting between a singlet and a triplet is proposed as combination of the point-charge interaction and hybridization of 4f with ligand p states. Provided 4f^3 configurations dominate over 4f^1 as intermediate states, p-f hybridization favors the triplet, while point-charge interaction favors the singlet. For realistic parameters for hybridization as well as 4f^1 and 4f^3 levels, these singlet and triplet can form a nearly degenerate pseudo-quartet. It is found that one of two spin 1/2 objects composing the pseudo-quartet has a ferromagnetic exchange, while the other has an antiferromagnetic exchange with conduction electrons. The magnitude of each effective exchange depends strongly on a parameter characterizing the triplet wave function under the T_h symmetry. It is argued that differences of this parameter among Pr skutterdudites are responsible for the apparent diversity of their physical properties. Numerical renormalization group is used to derive the renormalization flows going toward singlet, doublet, triplet or quaret according to the CEF splitting and exchange interactions.
We study the cosmological power spectra (PS) of the differential and integral galaxy volume number densities $\gamma_i$ and $\gamma_i^{*}$, constructed with the cosmological distances $d_i$ $(i=A,G,L,Z)$, where $d_A$ is the angular diameter distance, $d_G$ is the galaxy area distance, $d_L$ is the luminosity distance and $d_z$ is the redshift distance. Theoretical and observational quantities were obtained in the FLRW spacetime with a non-vanishing $\Lambda$. The radial correlation $\Xi_i$, as defined in the context of these densities, is discussed in the wave number domain. All observational quantities were computed using luminosity function (LF) data obtained from the FORS Deep Field galaxy survey. The theoretical and observational PS of $\gamma_i$, $\gamma_i^{\ast}$, $\Xi_i$ and $\gamma_i / \gamma_i^\ast$ were calculated by performing Fourier transforms on these densities previously derived by Iribarrem et al. (2012) from the observed values $\gamma_{obs}$ and ${\gamma^\ast}_{obs}$ obtained using the galactic absolute magnitudes and galaxy LF Schechter's parameters presented in Gabasch et al. (2004, 2006) in the range $0.5 \le z \le5.0$. The results show similar behavior of the PS obtained from $\gamma$ and $\gamma^{\ast}$ using $d_L$, $d_z$ and $d_G$ as distance measures. The PS of the densities defined with $d_A$ have a different and inconclusive behavior, as this cosmological distance reaches a maximum at $z\approx 1.6$ in the adopted cosmology. For the other distances, our results suggest that the PS of ${\gamma_i}_{obs}$, ${\gamma^\ast_i}_{obs}$ and ${\gamma_i / \gamma^{\ast}_i}_{obs}$ have a general behavior approximately similar to the PS obtained with the galaxy two-point correlation function and, by being sample size independent, they may be considered as alternative analytical tools to study the galaxy distribution.
We consider a $U(1)$ Maxwell-Chern-Simons theory in $5$-dimensions, and analyze the vector perturbations around a classical charged black-brane background. We solve the equations of motion for these perturbations in a derivative expansion. By computing the boundary current, we find that time and spatial derivatives can be interpreted as the induced electric and magnetic field respectively, and the Chern-Simons term contributes to a nonzero divergence of the boundary current which indicates a quantum anomaly. Using holography, we construct a two-derivative effective action for the vector perturbations. By complexifying the radial coordinate, and using appropriate transformation, we construct the full solution on the complexified bulk contour. By computing the on-shell action for the full Schwinger-Keldysh geometry, we obtain the Keldysh functional. We find that the single boundary on-shell action mixes parity, whereas the Keldysh functional does not depend on the Chern-Simons term up to the quadratic orders in derivative expansion.
It is now possible for hydrodynamical simulations to reproduce a representative galaxy population. Accordingly, it is timely to assess critically some of the assumptions of traditional semi-analytic galaxy formation models. We use the Eagle simulations to assess assumptions built into the Galform semi-analytic model, focussing on those relating to baryon cycling, angular momentum and feedback. We show that the assumption in Galform that newly formed stars have the same specific angular momentum as the total disc leads to a significant overestimate of the total stellar specific angular momentum of disc galaxies. In Eagle, stars form preferentially out of low specific angular momentum gas in the interstellar medium (ISM) due to the assumed gas density threshold for stars to form, leading to more realistic galaxy sizes. We find that stellar mass assembly is similar between Galform and Eagle but that the evolution of gas properties is different, with various indications that the rate of baryon cycling in Eagle is slower than is assumed in Galform. Finally, by matching individual galaxies between Eagle and Galform, we find that an artificial dependence of AGN feedback and gas infall rates on halo mass doubling events in Galform drives most of the scatter in stellar mass between individual objects. Put together our results suggest that the Galform semi-analytic model can be significantly improved in light of recent advances.
The NuMoon project uses the Westerbork Synthesis Radio Telescope to search for short radio pulses from the Moon. These pulses are created when an ultra high energy cosmic ray or neutrino initiates a particle cascade inside the Moon's regolith. The cascade has a negative charge excess and moves faster than the local speed of light, which causes coherent Cherenkov radiation to be emitted. With 100 hours of data, a limit on the neutrino flux can be set that is an order of magnitude better than the current one (based on FORTE). We present an analysis of the first 10 hours of data.
Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence. Moreover, on scales less than injection scale of turbulence, CRs' transport becomes super-diffusive. Quantitative predictions for both the normal diffusion on large scale and super diffusion are confronted with recent numerical simulations. Implication for shock acceleration is briefly discussed.
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A.Traulsen, J.C. Claussen, and C.Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e. whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate $u_c$ is obtained separating two scenarios: above $u_c$ the population predominantly consists of a mixture of strategies whereas below $u_c$ the population tends to be in homogenous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics.
The light curves of the first overtone Pop. I Cepheids (s-Cepheids) show a discontinuity in their phi_21 vs. P diagram, near P=3.2 day. This feature, commonly attributed to the 2:1 resonance between the first and the fourth overtones (omega_4=2 omega_1), is not reproduced by the hydrodynamical models. With the goal of reexamining the resonance hypothesis, we have obtained new CORAVEL radial velocity curves for 14 overtone Cepheids. Together with 10 objects of Krzyt et al. (1999), the combined sample covers the whole range of overtone Cepheid periods. The velocity Fourier parameters display a strong characteristic resonant behavior. In striking contrast to photometric ones, they vary smoothly with the pulsation period and show no jump at 3.2 day. The existing radiative hydrodynamical models match the velocity parameters very well. The center of the omega_4 = 2 omega_1 resonance is estimated to occur at P_r = 4.58+-0.04 day, i.e. at a period considerably longer than previously assumed (3.2 day). We identify two new members of the s-Cepheid group: MY Pup and V440 Per.