ShantanuT01/DACTYL-Pretraining huggingface dataset:
The energy density is calculated in coordinate space for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb using a dispersive optical model constrained by all relevant data including the corresponding energy of the ground state. The energy density of $^{8}$Be is also calculated using the Green's function Monte-Carlo method employing the Argonne/Urbana two and three-body interactions. The nuclear interior minimally contributes to the total binding energy due to the 4$\pi r^2$ phase space factor. Thus, the volume contribution to the energy in the interior is not well constrained. The dispersive-optical-model energy densities are in good agreement with \textit{ab initio} self-consistent Green's function calculations of infinite nuclear matter restricted to treat only short-range and tensor correlations. These results call into question the degree to which the equation of state for nuclear matter is constrained by the empirical mass formula. In particular, the results in this paper indicate that saturated nuclear matter does not require the canonical value of 16 MeV binding per particle but only about 13-14 MeV when the interior of $^{208}$Pb is considered.
Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter $\theta$, a new hydrodynamics on non-commutative space is derived. It may be a step toward to find the hydrodynamics of granular materials whose minimum volume is given by $\theta$. To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined.
We report on the study of extremely high energy photons, pions and etas, produced in intermediate energy heavy-ion collisions. Possibility of imaging the final-state phase space in these collisions by the Bose-Einstein correlations for photons is critically examined.
In this note, we show that the canonical orientation data on the quiver hearts are compatible under the autoequivalence $\_\otimes\pi^*O(1)$, and hence glue to give an orientation data for the stack of coherent sheaves on local P2.
In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rate of convergence in the classical matching problem and in a generalized matching distribution.
We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of the Laplace transforms of the first passage densities for diffusions with piecewise linear drifts. The proposed method is applied to a reliability problem where the standard degradation model based on Wiener process is extended to diffusion processes with piecewise linear drifts.
Using data from large-scale surveys: 2MASS, GLIMPSE, MIPSGAL, VGPS, GRS, and IPHAS, we performed a multiwavelength study of the ISM in a region of about 20' x 20' towards the molecular cloud G35.2-0.74. Additionally, the Ap 2-1 nebula, that is seen in projection over the molecular cloud, was studied using optical data obtained with the 2.15 m telescope at CASLEO, Argentina. From the HI absorption study we estimate a distance of ~2 kpc for Ap 2-1 confirming that the nebula is embedded in the south portion of the molecular cloud G35.2-0.74. Performing a photometric study and analysing the spectral energy distributions of the sources likely embedded in the cloud, we confirm that this region is very active in star formation, mainly towards the north, where we discover a cluster of young stellar objects. From the H_alpha and [NII] lines we obtain a radial velocity of v_LSR ~ 31 km/s for the Ap 2-1 nebula, in coincidence with the velocity of the molecular cloud. Finally, we conclude that Ap 2-1 is an HII region probably excited by an early B-type star.
Recently, a combinatorial interpretation of Baldoni and Vergne's generalized Lidskii formula for the volume of a flow polytope was developed by Benedetti et al.. This converts the problem of computing Kostant partition functions into a problem of enumerating a set of objects called unified diagrams. We devise an enhanced version of this combinatorial model to compute the volumes of flow polytopes defined on a family of graphs called the k-caracol graphs, resulting in the first application of the model to non-planar graphs. At k=1 and k=n-1, we recover results for the classical caracol graph and the Pitman--Stanley graph. Furthermore, we introduce the notion of in-degree gravity diagrams for flow polytopes, which are equinumerous with (out-degree) gravity diagrams considered by Benedetti et al.. We show that for the k-caracol flow polytopes, these two kinds of gravity diagrams satisfy a natural combinatorial correspondence, which raises an intriguing question on the relationship in the geometry of two related polytopes.
The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impact-velocity dependencies of the restitution coefficient.
We study by molecular dynamics computer simulation a binary soft-sphere mixture that shows a pronounced decoupling of the species' long-time dynamics. Anomalous, power-law-like diffusion of small particles arises, that can be understood as a precursor of a double-transition scenario, combining a glass transition and a separate small-particle localization transition. Switching off small-particle excluded-volume constraints slows down, rather than enhances, small-particle transport. The data are contrasted with results from the mode-coupling theory of the glass transition.
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical spin systems} in the thermodynamic limit, including the occurrence of a phase transition, using topology arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is to show that, in the context of the studied classical models, the Euler characteristic $\chi(E)$ embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the studied models, such quantities are those that do not violate the laws of thermodynamics [with the proviso that Van der Waals loop states are mean field (MF) artifacts]. We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of $\chi(E)$ per site, and that using the {\it Boltzmann} microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the short-range $XY$ models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range ($T_c \neq 0$) and the short-range ($T_c = 0$) $XY$ models. Further studies are very desirable in order to clarify the extension of the validity of our proposal.
Feature reassembly, i.e. feature downsampling and upsampling, is a key operation in a number of modern convolutional network architectures, e.g., residual networks and feature pyramids. Its design is critical for dense prediction tasks such as object detection and semantic/instance segmentation. In this work, we propose unified Content-Aware ReAssembly of FEatures (CARAFE++), a universal, lightweight and highly effective operator to fulfill this goal. CARAFE++ has several appealing properties: (1) Unlike conventional methods such as pooling and interpolation that only exploit sub-pixel neighborhood, CARAFE++ aggregates contextual information within a large receptive field. (2) Instead of using a fixed kernel for all samples (e.g. convolution and deconvolution), CARAFE++ generates adaptive kernels on-the-fly to enable instance-specific content-aware handling. (3) CARAFE++ introduces little computational overhead and can be readily integrated into modern network architectures. We conduct comprehensive evaluations on standard benchmarks in object detection, instance/semantic segmentation and image inpainting. CARAFE++ shows consistent and substantial gains across all the tasks (2.5% APbox, 2.1% APmask, 1.94% mIoU, 1.35 dB respectively) with negligible computational overhead. It shows great potential to serve as a strong building block for modern deep networks.
We study the gauge invariance of the massive modes in the compactification of gauge theories from D=5 to D=4. We deal with Abelian gauge theories of rank one and two, and with non-Abelian ones of rank one. We show that St\"uckelberg fields naturally appear in the compactification mechanism, contrarily to what usually occurs in literature where they are introduced by hand, as a trick, to render gauge invariance for massive theories. We also show that in the non-Abelian case they appear in a very different way when compared with their usual implementation in the non-Abelian Proca model.
Shot noise measurements on atomic and molecular junctions provide rich information about the quantum transport properties of the junctions and on the inelastic scattering events taking place in the process. Dissipation at the nanoscale, a problem of central interest in nano-electronics, can be studied in its most explicit and simplified form. Here, we describe a measurement technique that permits extending previous noise measurements to a much higher frequency range, and to much higher bias voltage range, while maintaining a high accuracy in noise and conductance. We also demonstrate the advantages of having access to the spectral information for diagnostics.
We prove an analogue of a classical asymptotic stability result of standing waves of the Schr\"odinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition on the lattice Z of a result by Mizumachi and it involves a discrete Schr\"odinger operator H. The decay rates on the potential are less stringent than in Mizumachi, since we require for the potential $q\in \ell ^{1,1}$. We also prove $|e^{itH}(n,m)|\le C < t > ^{-1/3}$ for a fixed $C$ requiring, in analogy to Goldberg and Schlag only $q\in \ell ^{1,1}$ if $H$ has no resonances and $q\in \ell ^{1,2}$ if it has resonances. In this way we ease the hypotheses on H contained in Pelinovsky and Stefanov, which have a similar dispersion estimate.
In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian.
We present detections of 21-cm emission from neutral hydrogen (HI) in the circumgalactic medium (CGM) of the local edge-on galaxies NGC 891 and NGC 4565 using the Robert C. Byrd Green Bank Telescope (GBT). With our 5$\sigma$ sensitivity of $8.2 \times 10^{16}$ cm$^{-2}$ calculated over a 20 km s$^{-1}$ channel, we achieve $>5\sigma$ detections out to $90-120$ kpc along the minor axes. The velocity width of the CGM emission is as large as that of the disk $\approx 500$ km s$^{-1}$, indicating the existence of a diffuse component permeating the halo. We compare our GBT measurements with interferometric data from the Westerbork Synthesis Radio Telescope (WSRT). The WSRT maps the HI emission from the disk at high S/N but has limited surface brightness sensitivity at the angular scales probed with the GBT. After convolving the WSRT data to the spatial resolution of the GBT (FWHM = 9.1$'$), we find that the emission detected by the WSRT accounts for $48^{+15}_{-25}$% ($58^{+4}_{-18}$%) of the total flux recovered by the GBT from the CGM of NGC 891(NGC 4565). The existence of significant GBT-only flux suggests the presence of a large amount of diffuse, low column density HI emission in the CGM. For reasonable assumptions, the extended diffuse HI could account for $5.2\pm0.9$% and $2.0\pm0.8$% of the total HI emission of NGC 891 and NGC 4565.
As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables subject to possible change-points. Our formulation deals simultaneously with ordinary and with large deviations.
We provide the first systematic study of the viable parameter space for leptogenesis in the type-I seesaw model with three right-handed neutrinos whose Majorana masses lie below the electroweak scale. We highlight the very rich phenomenology of this scenario and discuss several mechanisms that can help to enhance the baryon asymmetry of the Universe. This allows for much larger heavy neutrino mixing angles than in the minimal scenario with two heavy neutrinos, resulting in solutions that can be probed with the LHC and other experiments. The light neutrino masses can be protected from radiative corrections by an approximate symmetry related to generalised lepton number.
In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes the flow depends on the space variable: $q=q(\mathbf{x})$. For the associated boundary-value problem we show that, in some situations, the log-H\"older continuity condition on $q$ can be dropped and the result of the existence of weak solutions still remain valid for any variable exponent $q\geq\alpha>\frac{2N}{N+2}$, where $\alpha=\mathrm{ess}\inf q$.
We study the gravitational collapse in ($n+2$)-D quasi-spherical Szekeres space-time (which possess no killing vectors) with dust as the matter distribution. Instead of choosing the radial coordinate `$r$' as the initial value for the scale factor $R$, we consider a power function of $r$ as the initial scale for the radius $R$. We examine the influence of initial data on the formation of singularity in gravitational collapse.
Reliable encoding of information in quantum systems is crucial to all approaches to quantum information processing or communication. This applies in particular to photons used in linear optics quantum computing (LOQC), which is scalable provided a deterministic single-photon emission and preparation is available. Here, we show that narrowband photons deterministically emitted from an atom-cavity system fulfill these requirements. Within their 500 ns coherence time, we demonstrate a subdivision into d time bins of various amplitudes and phases, which we use for encoding arbitrary qu-d-its. The latter is done deterministically with a fidelity >95% for qubits, verified using a newly developed time-resolved quantum-homodyne method.
We present mid-infrared spectra and photometry of thirteen redshift 0.4<z<1 dust-reddened quasars obtained with Spitzer IRS and MIPS. We compare properties derived from their infrared spectral energy distributions (intrinsic AGN luminosity and far-infrared luminosity from star formation) to the host luminosities and morphologies from HST imaging, and black hole masses estimated from optical and/or near-infrared spectroscopy. Our results are broadly consistent with models in which most dust reddened quasars are an intermediate phase between a merger-driven starburst triggering a completely obscured AGN, and a normal, unreddened quasar. We find that many of our objects have high accretion rates, close to the Eddington limit. These objects tend to fall below the black hole mass -- bulge luminosity relation as defined by local galaxies, whereas most of our low accretion rate objects are slightly above the local relation, as typical for normal quasars at these redshifts. Our observations are therefore most readily interpreted in a scenario in which galaxy stellar mass growth occurs first by about a factor of three in each merger/starburst event, followed sometime later by black hole growth by a similar amount. We do not, however, see any direct evidence for quasar feedback affecting star formation in our objects, for example in the form of a relationship between accretion rate and star formation. Five of our objects, however, do show evidence for outflows in the OIII 5007 Angstrom emission line profile, suggesting that the quasar activity is driving thermal winds in at least some members of our sample.
The overstability of the fundamental radial mode in M dwarf models was theoretically predicted by Rodr\'iguez-L\'opez et al. (2012). The periods were found to be in the ranges ~25-40 min and ~4-8 h, depending on stellar age and excitation mechanism. We have extended our initial M dwarf model grid in mass, metallicity, and mixing length parameter. We have also considered models with boundary conditions from PHOENIX NextGen atmospheres to test their influence on the pulsation spectra. We find instability of non-radial modes with radial orders up to k=3, degree l=0-3, including p and g modes, with the period range extending from 20 min up to 11 h. Furthermore, we find theoretical evidence of the potential of M dwarfs as solar-like oscillators.
The results from an investigation of the incoherent single pion electroweak production on the deuteron in the $\Delta$(1232) region are reported. The importance of including the nucleon-nucleon final state interactions in extracting the neutrino-nucleon cross sections from the data obtained from the experiments on the deuteron target is demonstrated.
We consider fast oscillating perturbations of dynamical systems in regions where one can introduce action-angle type coordinates. In an appropriate time scale, a diffusion approximation of the first-integrals evolution is described under the assumption that the set of resonance tori is small enough. If the action-angle coordinates can be introduced just piece-wise , the limiting diffusion process should be considered on an open book space. Such a process can be described by differential operators, one on each page, supplemented by some gluing conditions on the binding of the open book.
In these notes we present a detailed and complete scheme for the calculation of polarization phenomena in elastic electron-nucleon scattering. The longitudinal and transversal components of the polarization for the scattered nucleon, induced by the scattering of longitudinally polarized electrons and the asymmetries for the collision of polarized electrons with a polarized nucleon target are included. The calculations are done in the framework of the one-photon mechanism, in the Breit system, which is the most convenient for the analysis of polarization effects. We briefly discuss the region of applicability of such model and other mechanisms (radiative and electroweak corrections) which may come into this idealized picture.
Recently, the theory of Topologically massive gravity non-minimally coupled to a scalar field has been proposed which comes from Lorentz-Chern-Simons theory \cite{1}. That theory is a torsion free one. We extend that theory by adding an extra term which makes torsion to be non-zero. The extended theory can be regarded as an extension of Minimal massive gravity such that it is non-minimally coupled to a scalar field. We obtain equations of motion of extended theory such that they are expressed in terms of usual torsion free spin-connection. We show that BTZ spacetime is a solution of this theory when scalar field is constant. We define quasi-local conserved charge by the concept of generalized off-shell ADT current which both are conserved for any asymptotically Killing vector field as well as a Killing vector field which is admitted by spacetime everywhere. Also we find general formula for entropy of stationary black hole solution in the context of considered theory. We apply the obtained formulas on BTZ black hole solution, to calculate energy, angular momentum and entropy of this soultion. We obtain the central extension term, the central charges and the eigenvalues of the Virasoro algebra generators for the BTZ black hole solution. We calculate energy and angular momentum of BTZ black hole using the eigenvalues of the Virasoro algebra generators. Also we calculate the entropy of BTZ black hole by using the Cardy formula. We find that obtained results using two different ways are exactly matched as we expected.
In the setting of general initial data and whole space we perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma with capillarity tensor represented by the Navier Stokes Korteweg Poisson system. We shall provide a detailed mathematical description of the convergence process by analyzing the dispersion of the fast oscillating acoustic waves. However the standard acoustic wave analysis is not sufficient to control the high frequency oscillations in the electric field but it is necessary to estimates the dispersive properties induced by the capillarity terms. Therefore by using these additional estimates we will be able to control, via compensated compactness, the quadratic nonlinearity of the stiff electric force field. In conclusion, opposite to the zero capillarity case \cite{DM12} where persistent space localized time high frequency oscillations need to be taken into account, we show that as $\lambda \to 0$, the density fluctuation $\rho^{\lambda}-1$ converges strongly to zero and the fluids behaves according to an incompressible dynamics.
We present some remarkable properties of the symmetry group for gravitational plane waves. Our main observation is that metrics with plane wave symmetry satisfy every system of generally covariant vacuum field equations except the Einstein equations. The proof uses the homothety admitted by metrics with plane wave symmetry and the scaling behavior of generally covariant field equations. We also discuss a mini-superspace description of spacetimes with plane wave symmetry.