ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let G be a reductive group and X be a Luna stratum on the quotient space V//G of a rational G-module V. We consider torsors over X with both non-commutative and commutative structure groups. It allows us to compute the divisor class group and the Cox ring of a Luna stratum under mild assumptions. This techniques gives a simple cause why many Luna strata are singular along their boundary.
We calculate the orbital evolution of binary systems where the primary star is an evolved red giant branch (RGB) star, while the secondary star is a low-mass main sequence (MS) star or a brown dwarf. The evolution starts with a tidal interaction causes the secondary to spiral-in. Than either a common envelope (CE) is formed in a very short time, or alternatively the system reaches synchronization and the spiraling-in process substantially slows down. Some of the latter systems later enter a CE phase. We find that for a large range of system parameters, binary systems reach stable synchronized orbits before the onset of a CE phase. Such stable synchronized orbits allow the RGB star to lose mass prior to the onset of the CE phase. Even after the secondary enters the giant envelope, the rotational velocity is high enough to cause an enhanced mass-loss rate. Our results imply that it is crucial to include the pre-CE evolution when studying the outcome of the CE phase. We find that many more systems survive the CE phase than would be the case if these preceding spin-up and mass-loss phases had not been taken into account. Although we have made the calculations for RGB stars, the results have implications for other evolved stars that interact with close companions.
We prove that a one-parameter family of rationally connected varieties (over an algebraically closed field of characteristic 0) always has a section.
Using kinematic maps from the Sloan Digital Sky Survey (SDSS) Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, we reveal that the majority of low-mass quenched galaxies exhibit coherent rotation in their stellar kinematics. Our sample includes all 39 quenched low-mass galaxies observed in the first year of MaNGA. The galaxies are selected with $M_{r} > -19.1$, stellar masses $10^{9}$ M$_{\odot} < M_{\star} < 5\times10^{9}$ M$_{\odot}$, EW$_{H\alpha} <2$ \AA, and all have red colours $(u-r)>1.9$. They lie on the size-magnitude and $\sigma$-luminosity relations for previously studied dwarf galaxies. Just six ($15\pm5.7$ per cent) are found to have rotation speeds $v_{e,rot} < 15$ km s$^{-1}$ at $\sim1$ $R_{e}$, and may be dominated by pressure support at all radii. Two galaxies in our sample have kinematically distinct cores in their stellar component, likely the result of accretion. Six contain ionised gas despite not hosting ongoing star formation, and this gas is typically kinematically misaligned from their stellar component. This is the first large-scale Integral Field Unit (IFU) study of low mass galaxies selected without bias against low-density environments. Nevertheless, we find the majority of these galaxies are within $\sim1.5$ Mpc of a bright neighbour ($M_{K} < -23$; or M$_{\star} > 5\times10^{10}$ M$_{\odot}$), supporting the hypothesis that galaxy-galaxy or galaxy-group interactions quench star formation in low-mass galaxies. The local bright galaxy density for our sample is $\rho_{proj} = 8.2\pm2.0$ Mpc$^{-2}$, compared to $\rho_{proj} = 2.1\pm0.4$ Mpc$^{-2}$ for a star forming comparison sample, confirming that the quenched low mass galaxies are preferentially found in higher density environments.
We model the transport of cosmic ray nuclei in the Galaxy by means of a new numerical code. Differently from previous numerical models we account for a generic spatial distribution of the diffusion coefficient. We found that in the case of radially uniform diffusion, the main secondary/primary ratios (B/C, N/O and sub-Fe/Fe) and the modulated antiproton spectrum match consistently the available observations. Convection and re-acceleration do not seem to be required in the energy range we consider: $1 < E < 10^3$ GeV/nucleon. We generalize these results accounting for radial dependence of the diffusion coefficient, which is assumed to trace that of the cosmic ray sources. While this does not affect the prediction of secondary/primary ratios, the simulated longitude profile of the diffuse $\gamma$-ray emission is significantly different from the uniform case and may agree with EGRET measurements without invoking ad hoc assumptions on the galactic gas density distribution.
A new diagnostics to break the degeneracy between the total neutrino mass ($M_{\nu}$) and the primordial power spectrum amplitude ($\sigma_{8}$) by using the drifting coefficient of the field cluster mass function is presented. Analyzing the data from the Cosmological Massive Neutrino Simulations, we first determine the numerical mass functions of the field clusters at various redshifts. Then, we compare the numerical results with the analytical model characterized by a single parameter called the drifting coefficient which measures the drifts of the collapse density threshold, $\delta_{c}$, from the Einstein-de Sitter spherical value, $\delta_{sc}$, at a given mass scale. It is found that the analytic model for the field cluster mass function is found to work excellently even in the presence of massive neutrinos and that its drifting coefficient evolves differently in the cosmologies with different values of $M_{\nu}$. At low redshifts ($z\lesssim 0.3$) the more massive neutrinos drift $\delta_{c}$ further from $\delta_{sc}$, while the opposite trend is found at higher redshifts ($z\gtrsim0.3$). Speculating that this distinct redshift-dependent effect of massive neutrinos on the drifting coefficient of the field cluster mass function might help break the $\sigma_{8}$-$M_{\nu}$ degeneracy, we also show that the sensitivity of this new diagnostics to $M_{\nu}$ is high enough to discriminate the case of $M_{\nu}=0.1\,{\rm eV}$ from that of massless neutrinos.
We present the results of a ~ 3 year campaign to monitor the low luminosity active galactic nucleus (LLAGN) NGC 7213 in the radio (4.8 and 8.4 GHz) and X-ray bands (2-10 keV). With a reported X-ray Eddington ratio of 7 x 10^-4 L_Edd, NGC 7213 can be considered to be comparable to a hard state black hole X-ray binary. We show that a weak correlation exists between the X-ray and radio light curves. We use the cross-correlation function to calculate a global time lag between events in the X-ray and radio bands to be 24 +/- 12 days lag (8.4 GHz radio lagging X-ray), and 40 +/- 13 days lag (4.8 GHz radio lagging X-ray). The radio-radio light curves are extremely well correlated with a lag of 20.5 +/- 12.9 days (4.8 GHz lagging 8.4 GHz). We explore the previously established scaling relationship between core radio and X-ray luminosities and black hole mass L_{R} \propto M^{0.6-0.8} L_{X}^{0.6}, known as the `fundamental plane of black hole activity', and show that NGC 7213 lies very close to the best-fit `global' correlation for the plane as one of the most luminous LLAGN. With a large number of quasi-simultaneous radio and X-ray observations, we explore for the first time the variations of a single AGN with respect to the fundamental plane. Although the average radio and X-ray luminosities for NGC 7213 are in good agreement with the plane, we show that there is intrinsic scatter with respect to the plane for the individual data points.
The efficiency of energy transduction in a temporally asymmetric rocked ratchet is studied. Time asymmetry favours current in one direction and suppresses it in the opposite direction due to which large efficiency ~ 50% is readily obtained. The spatial asymmetry in the potential together with system inhomogeneity may help in further enhancing the efficiency. Fine tuning of system parameters considered leads to multiple current reversals even in the adiabatic regime.
We compute the dynamics and emission of dissipative shells that are subject to a strong Compton drag, under simplifying assumptions about the dissipation mechanism. We show that under conditions prevailing in blazars, substantial deceleration is anticipated on sub-parsec and parsec scales in cases of rapid dissipation. Such episodes may be the origin of some of the flaring activity occasionally observed in gamma ray blazars. The shape of the light curves thereby produced reflects the geometry of the emitting surface if the deceleration is very rapid, or the dynamics of the shell if the deceleration is delayed, or initially more gradual, owing, e.g., to continuous injection of energy and momentum.
The third and fourth cumulants of voltage in a current-biased diffusive metal contact of resistance $R$ are calculated for arbitrary temperatures and voltages using the semiclassical cascade approach. The third cumulant equals $e^2R^3I/3$ at high temperatures and $4e^2R^3I/15$ at low temperatures, whereas the fourth cumulant equals $2e^2R^3T/3$ at high temperatures and $(34/105)e^3R^4I$ at low temperatures.
When an atomic-size break junction is mechanically stretched, the total conductance of the contact remains approximately constant over a wide range of elongations, although at the same time the transmissions of the individual channels (valence orbitals of the junction atom) undergo strong variations. We propose a microscopic explanation of this phenomenon, based on Coulomb correlation effects between electrons in valence orbitals of the junction atom. The resulting approximate conductance quantization is closely related to the Friedel sum rule.
Three halo finder algorithms - hierarchical friends-of-friends, bound density maxima, and 6D minimum spanning tree - are discussed.
With the proposed Hund's rule correlation picture, i.e. the fluctuating Fe local moments with the As-bridged antiferromagnetic superexchange interactions, the exceptional collapsed tetragonal phase and related phase transitions observed in CaFe$_2$As$_2$ are well understood. With the same framework, a pressure-temperature phase diagram is predicted for BaFe$_2$As$_2$ as well, in which a paramagnetic tetragonal and a collinear antiferromagnetic orthorhombic structures to nonmagnetic tetragonal structure transitions take place around 4-8 GPa and 10-15 GPa respectively, and a nonmagnetic tetragonal to a nonmagnetic collapsed tetragonal structure transition takes place over 26 GPa. Our study helps better understand the complex correlation among crystal structure, magnetism, and electronic structure in pnictides, a precondition to understand the superconductivity in pnictides.
In this paper, we obtain an explicit formula for the discrepancy between the limit of the second inner variations of $p$-Laplace Allen-Cahn energies and the second inner variation of their $\Gamma$-limit which is the area functional. Our analysis explains the mysterious discrepancy term found in our previous paper \cite{Le} in the case $p=2$. The discrepancy term turns out to be related to the convergence of certain 4-tensors which are absent in the usual Allen-Cahn functional. These (hidden) 4-tensors suggest that, in the complex-valued Ginzburg-Landau setting, we should expect a different discrepancy term which we are able to identify. Along the way, we partially answer a question of Kohn and Sternberg \cite{KS} by giving a relation between the limit of second variations of the Allen-Cahn functional and the second inner variation of the area functional at local minimizers. Moreover, our analysis reveals an interesting identity connecting second inner variation and Poincar\'e inequality for area-minimizing surfaces with volume constraint in the work of Sternberg and Zumbrun \cite{SZ2}.
We show that, for a class of critical strings in ${\bf R}\times S^{1}$-target space, the description of string theory given by its field content (analog model) breaks down when the radius of $S^{1}$ decreases below $R_{0}=\sqrt{\alpha^{\prime}}$, the self-dual point of the partition function $Z(R)$. We find that $Z(R)$ has a soft singularity at $R_{0}$ (a finite jump in the first derivative of $Z$).
Image denoising algorithms are evaluated using images corrupted by artificial noise, which may lead to incorrect conclusions about their performances on real noise. In this paper we introduce a dataset of color images corrupted by natural noise due to low-light conditions, together with spatially and intensity-aligned low noise images of the same scenes. We also introduce a method for estimating the true noise level in our images, since even the low noise images contain small amounts of noise. We evaluate the accuracy of our noise estimation method on real and artificial noise, and investigate the Poisson-Gaussian noise model. Finally, we use our dataset to evaluate six denoising algorithms: Active Random Field, BM3D, Bilevel-MRF, Multi-Layer Perceptron, and two versions of NL-means. We show that while the Multi-Layer Perceptron, Bilevel-MRF, and NL-means with soft threshold outperform BM3D on gray images with synthetic noise, they lag behind on our dataset.
Using an energy density functional (EDF) based on the thermodynamic Gibbs-Duhem relation, found equivalent to the standard Skyrme EDF for infinite nuclear matter, it is demonstrated that the parameters of this EDF are not uniquely determined from the fit of the empirical and theoretical data related to nuclear matter. This prevents an unambiguous determination of the nucleon effective mass ($\frac{m_0^*}{m}$) and its isovector splitting ($\Delta m_0^*$). Complementary information from dipole polarizability of atomic nuclei helps in removing this ambiguity and plausible values of $\frac{m_0^*}{m}$ and $\Delta m_0^*$ can be arrived at. Presently considered fit data on infinite nuclear matter and dipole polarizability of finite nuclei yield $\frac{m_0^*}{m} =0.68 \pm 0.04 $ and $\Delta m_0^* =(-0.20 \pm 0.09)\delta $. This EDF is consistent with the constraint on the maximum mass of the neutron star.
We investigate the density of square-free values of polynomials with large coefficients over the rational function field $\mathbb{F}_q[t]$. Some interesting questions answered as special cases of our results include the density of square-free polynomials in short intervals, and an asymptotic for the number of representations of a large polynomial $N$ as a sum of a small $k$-th power and a square-free polynomial.
We consider a two-orbital impurity system with intra and inter-level Coulomb repulsion that is coupled to a single conduction channel. This situation can generically occur in multilevel quantum dots or in systems of coupled quantum dots. For finite energy-spacing between spin-degenerate orbitals, an in-plane magnetic field drives the system from a local singlet ground state to a "mixed-level" Kondo regime, where the Zeeman-split levels are degenerate for opposite spin states. We use the numerical renormalization group approach to fully characterize this mixed level Kondo state and discuss its properties in terms of the applied Zeeman field, temperature and system parameters. Under suitable conditions, the total spectral function is shown to develop a Fermi level resonance, so that the linear conductance of the system peaks at a finite Zeeman field while it decreases as function of temperature. These features, as well as the local moment and entropy contribution of the impurity system are commensurate with Kondo physics, which can be studied in suitably tuned quantum dot systems.
Moller's tetrad gravitational energy-momentum "tensor" is evaluated for a small vacuum region using an orthonormal frame adapted to Riemann normal coordinates. We find that it does satisfy the highly desired property of being a positive multiple of the Bel-Robinson tensor.
As an attempt to find a way to resolve the discrepancy between calculated by traditional methods PV effects and the available set of experimental data, we analyze the methods of calculations of symmetry violating effects in few-body nuclear systems. The overview of methods of calculations of PV and TRIV effects in few-body neutron induced reactions is presented with the analysis of values of calculated parameters and their accuracy.
We present a simple gluon production picture which is based on the McLerran-Venugopalan model and gluon BFKL evolution in relativistic heavy ion collision. Results for the multiplicity and transverse energy distribution in both the central and forward rapidity regions for gluon production in early stages of heavy ion collisions at the LHC are given. Finally, we provide a general qualitative discussion of the consequences of the forward rapidity behavior of produced gluons.
We consider the standard first passage percolation on $\mathbb{Z}^{d}$: with each edge of the lattice we associate a random capacity. We are interested in the maximal flow through a cylinder in this graph. Under some assumptions Kesten proved in 1987 a law of large numbers for the rescaled flow. Chayes and Chayes established that the large deviations far away below its typical value are of surface order, at least for the Bernoulli percolation and cylinders of certain height. Thanks to another approach we extend here their result to higher cylinders, and we transport this result to the model of first passage percolation.
We consider the relationship between fluid models of an interacting dark sector, and the field theoretical models that underlie such descriptions. This question is particularly important in light of suggestions that such interactions may help alleviate a number of current tensions between different cosmological datasets. We construct consistent field theory models for an interacting dark sector that behave exactly like the coupled fluid ones, even at the level of linear perturbations, and can be trusted deep in the nonlinear regime. As a specific example, we focus on the case of a Dirac, Born-Infeld (DBI) field conformally coupled to a quintessence field. We show that the fluid linear regime breaks before the field gradients become large; this means that the field theory is valid inside a large region of the fluid nonlinear regime.
We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y admitting a full exceptional sequence. Applications include the case in which X is Calabi-Yau and either X is a hypersurface in Y (this extends a previous result by the author and R.L. Karp, where Y was a weighted projective space) or Y is a hypersurface in X. The proof uses a resolution of the diagonal of Y constructed from the exceptional sequence.
The spectrum of the bosonic sector of the D=11 supermembrane with central charges is shown to be discrete and with finite multiplicities, hence containing a mass gap. The result extends to the exact theory our previous proof of the similar property for the SU(N) regularised model and strongly suggest discreteness of the spectrum for the complete Hamiltonian of the supermembrane with central charges. This theory is a quantum equivalent to a symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the space-like sector is a Riemann surface of positive genus. In this context, it is argued how the theory in 4D exhibits confinement in the N=1 supermembrane with central charges phase and how the theory enters in the quark-gluon plasma phase through the spontaneous breaking of the centre. This phase is interpreted in terms of the compactified supermembrane without central charges.
Present paper reports, the structural, microstructural, electrical, dielectric properties and ion dynamics of a sodium based solid polymer electrolyte films comprising of PEO8-NaPF6+ x wt. % SN. The structural and surface morphology properties have been investigated by XRD and FESEM. Different microscopic interaction among the polymer, salt and SN have been analyzed through FTIR. The dielectric permittivity and loss tangent enable us to estimate the dc conductivity, dielectric strength, double layer capacitance, and relaxation time. The loss tangent relaxation peak shifts towards high-frequency side which indicates the decrease of relaxation time and faster ion dynamics. Further, the relation among various relaxation times ...... has been developed systematically. The ionic conductivity has been estimated in whole frequency window including JPL and displays strong dependency on SN content. The sigma representation ........ has been introduced for exploring the ion dynamics by highlighting the dispersion region in Cole-Cole plot (........) at lower frequency window and increase in the radius of semicircle indicates a decrease of relaxation time. A well convincing/logical scheme has been proposed which justify the recorded experimental data.
We study the origin of the structure in the spin-polarized electron energy loss spectroscopy (SPEELS) spectra of ferromagnetic crystals. Our study is based on a 3d tight-binding Fe model, with constant onsite Coulomb repulsion U between electrons of opposite spin. We find it is not the total density of Stoner states as a function of energy loss which determines the response of the system in the Stoner region, as usually thought, but the densities of Stoner states for only a few interband transitions. Which transitions are important depends ultimately on how strongly umklapp processes couple the corresponding bands. This allows us to show, in particular, that the Stoner peak in SPEELS spectra does not necessarily indicate the value of the exchange splitting energy. Thus, the common assumption that this peak allows us to estimate the magnetic moment through its correlation with exchange splitting should be reconsidered, both in bulk and surface studies. Furthermore, we are able to show that the above mechanism is one of the main causes for the typical broadness of experimental spectra. Finally, our model predicts that optical spin waves should be excited in SPEELS experiments.
We present optical imaging and spectroscopy and HI imaging of the Virgo Cluster galaxy IC 3418, which is likely a "smoking gun" example of the transformation of a dwarf irregular into a dwarf elliptical galaxy by ram pressure stripping. IC 3418 has a spectacular 17 kpc length UV-bright tail comprised of knots, head-tail, and linear stellar features. The only H-alpha emission arises from a few HII regions in the tail, the brightest of which are at the heads of head-tail UV sources whose tails point toward the galaxy ("fireballs"). Several of the elongated tail sources have H-alpha peaks outwardly offset by 80-150 pc from the UV peaks, suggesting that gas clumps continue to accelerate through ram pressure, leaving behind streams of newly formed stars which have decoupled from the gas. Absorption line strengths, measured from Keck DEIMOS spectra, together with UV colors, show star formation stopped 300+/-100 Myr ago in the main body, and a strong starburst occurred prior to quenching. While neither H-alpha nor HI emission are detected in the main body of the galaxy, we have detected 4x10^7 M_sun of HI from the tail with the VLA. The gas consumption timescale in the tail is relatively long, implying that most of the stripped gas does not form stars but joins the ICM. The velocities of tail HII regions, measured from Keck LRIS spectra, extend only a small fraction of the way to the cluster velocity, suggesting that star formation does not happen in more distant parts of the tail. Stars in the outer tail have velocities exceeding the escape speed, but some in the inner tail should fall back into the galaxy, forming halo streams. One likely fallback stream is identified.