ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic-hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli's function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system introduced in \cite{WengXin19} to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates.
We prove a strong form of the quantitative Sobolev inequality in $\mathbb{R}^n$ for $p\geq 2$, where the deficit of a function $u\in \dot W^{1,p} $ controls $\| \nabla u -\nabla v\|_{L^p}$ for an extremal function $v$ in the Sobolev inequality.
The copper-oxide based high temperature superconductors have complex phase diagrams with multiple ordered phases. It even appears that the highest superconducting transition temperatures for certain cuprates are found in samples which display simultaneous onset of magnetism and superconductivity. We show here how the thermodynamics of fluid mixtures - a touchstone for chemists as well as hard and soft condensed matter physics - accounts for this startling observation, as well as many other properties of the cuprates in the vicinity of the instability towards ``striped'' magnetism.
We present a class of permutations for which the number of distinctly ordered subsequences of each permutation approaches an almost optimal value as the length of the permutation grows to infinity.
We have derived elemental abundances of three field red horizontal branch stars using high-resolution (R$\simeq$ 45,000), high signal-to-noise ratio (S/N $\gtrsim$ 200) $H$ and $K$ band spectra obtained with the Immersion Grating Infrared Spectrograph (IGRINS). We have determined the abundances of 21 elements including $\alpha$ (Mg, Si, Ca, S), odd-Z (Na, Al, P, K), Fe-group (Sc, Ti, Cr, Co, Ni), neutron-capture (Ce, Nd, Yb), and CNO group elements. S, P and K are determined for the first time in these stars. $H$ and $K$ band spectra provide a substantial number of S I lines, which potentially can lead to a more robust exploration of the role of sulfur in the cosmochemical evolution of the Galaxy. We have also derived $^{12}$C/$^{13}$C ratios from synthetic spectra of the first overtone (2$-$0) and (3$-$1) $^{12}$CO and (2$-$0) $^{13}$CO lines near 23440 \AA\ and $^{13}$CO (3$-$1) lines at about 23730 \AA. Comparison of our results with the ones obtained from the optical region suggests that the IGRINS high-resolution $H$ and $K$ band spectra offer more internally self-consistent atomic lines of the same species for several elements, especially the $\alpha$ elements. This in turn provides more reliable abundances for the elements with analytical difficulties in the optical spectral range.
Let $\mathcal{DZ}_k$ be the $\mathbb{Q}$-vector space spanned by double zeta values with weight $k$, and $\mathcal{DM}_k$ be its quotient space divided by the space $\mathcal{PZ}_k$ spanned by the zeta value $\zeta(k)$ and products of two zeta values with total weight $k$. When $k$ is even, an upper bound for the dimension of $\mathcal{DM}_k$ is known. By adding the dimensions of $\mathcal{DM}_k$ and $\mathcal{PZ}_k$, an upper bound of $\mathcal{DZ}_k$ which equals $k/2$ minus the dimension of the space of modular forms of weight $k$ on the modular group is given. In this note, we obtain some specific sets of generators for $\mathcal{DM}_k$ which represent the upper bound. These yield the corresponding sets and the upper bound for $\mathcal{DZ}_k$.
Quiescent emission from the neutron star low-mass X-ray binary Cen X-4 is seen to be variable on timescales from hundreds of seconds to years, suggesting that at least in this object, low-level accretion is important during quiescence. Here we present results from recent XMM-Newton and Swift observations of Cen X-4, where the X-ray flux (0.5 - 10 keV) varies by a factor of 6.5 between the brightest and faintest states. We find a positive correlation between the X-ray flux and the simultaneous near-UV flux, where as there is no significant correlation between the X-ray and simultaneous optical (V, B) fluxes. This suggests that while the X-ray and UV emitting regions are somehow linked, the optical region originates elsewhere. Comparing the luminosities, it is plausible that the UV emission originates due to reprocessing of the X-ray flux by the accretion disk, with the hot inner region of the disk being a possible location for the UV emitting region. The optical emission, however, could be dominated by the donor star. The X-ray/UV correlation does not favour the accretion stream-impact point as the source of the UV emission.
O-C diagram is a useful technique to analyse the period changes of a pulsator by using the maximum (or minimum) value points which have been obtained from the historical data. But if an object is a double-mode or multi-mode pulsator, the extreme value points are the results of all the modes other than just the fundamental mode. We discussed these situations and give out some criteria to judge whether the O-C diagram can be used in these situations.
Industrial Control Systems depend heavily on security and monitoring protocols. Several tools are available for this purpose, which scout vulnerabilities and take screenshots from various control panels for later analysis. However, they do not adequately classify images into specific control groups, which can difficult operations performed by manual operators. In order to solve this problem, we use transfer learning with five CNN architectures, pre-trained on Imagenet, to determine which one best classifies screenshots obtained from Industrial Controls Systems. Using 337 manually labeled images, we train these architectures and study their performance both in accuracy and CPU and GPU time. We find out that MobilenetV1 is the best architecture based on its 97,95% of F1-Score, and its speed on CPU with 0.47 seconds per image. In systems where time is critical and GPU is available, VGG16 is preferable because it takes 0.04 seconds to process images, but dropping performance to 87,67%.
The Kondo lattice model with substitutional disorder is studied with attention to the size of the Fermi surface and the associated Dingle temperature. The model serves for understanding heavy-fermion Ce compounds alloyed with La according to substitution Ce{x}La{1-x}. The Fermi surface is identified from the steepest change of the momentum distribution of conduction electrons, and is derived at low enough temperature by the dynamical mean-field theory (DMFT) combined with the coherent potential approximation (CPA). The Fermi surface without magnetic field increases in size with decreasing x from x=1 (Ce end), and disappears at such x that gives the same number of localized spins as that of conduction electrons. From the opposite limit of x=0 (La end), the Fermi surface broadens quickly as x increases, but stays at the same position as that of the La end. With increasing magnetic field, a metamagnetic transition occurs, and the Fermi surface above the critical field changes continuously across the whole range of x. The Dingle temperature takes a maximum around x=0.5. Implication of the results to experimental observation is discussed.
While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local collective rearrangements of various scales, is not determined by the smallest scale but by a length $l^*$ that grows at low energies. In real space we find a hierarchy of fast and slow regions: each slow region is geometrically insulated from all faster degrees of freedom, which are localized in fast pockets below percolation thresholds. A tentative analogy with structural glasses is given, which attributes the slowing down of the dynamics to the growing size of mobile elementary excitations, rather than to the size of some domains.
The radio-quiet quasar Q2059-360 at redshift $z=3.08$ is known to be close to a small Lyman $\alpha$ blob (LAB) and to be absorbed by a proximate damped Ly$\alpha$ (PDLA) system.   Here, we present the Multi Unit Spectroscopic Explorer (MUSE) integral field spectroscopy follow-up of this quasi-stellar object (QSO). Our primary goal is to characterize this LAB in detail by mapping it both spatially and spectrally using the Ly$\alpha$ line, and by looking for high-ionization lines to constrain the emission mechanism.   Combining the high sensitivity of the MUSE integral field spectrograph mounted on the Yepun telescope at ESO-VLT with the natural coronagraph provided by the PDLA, we map the LAB down to the QSO position, after robust subtraction of QSO light in the spectral domain.   In addition to confirming earlier results for the small bright component of the LAB, we unveil a faint filamentary emission protruding to the south over about 80 pkpc (physical kpc); this results in a total size of about 120 pkpc. We derive the velocity field of the LAB (assuming no transfer effects) and map the Ly$\alpha$ line width. Upper limits are set to the flux of the N V $\lambda 1238-1242$, C IV $\lambda 1548-1551$, He II $\lambda 1640$, and C III] $\lambda 1548-1551$ lines. We have discovered two probable Ly$\alpha$ emitters at the same redshift as the LAB and at projected distances of 265 kpc and 207 kpc from the QSO; their Ly$\alpha$ luminosities might well be enhanced by the QSO radiation. We also find an emission line galaxy at $z=0.33$ near the line of sight to the QSO.   This LAB shares the same general characteristics as the 17 others surrounding radio-quiet QSOs presented previously. However, there are indications that it may be centered on the PDLA galaxy rather than on the QSO.
The calculation of the optical properties of doped semiconductor quantum wells is an intricate many-body problem because of the dynamical response of the excess carriers to the photogenerated valence band hole. At low densities, however, where the main effect of the dynamical response is the formation of trions, a simple cluster meanfield approximation can be effectively employed to calculate the optical susceptibility.
Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the joint light-curve analysis (JLA) data set. In contrast to the $\chi^2$ approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with $\chi^2$ analysis results, we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6 $\sigma$ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4 $\sigma$. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the $\chi^2$ analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end, we implement a fully consistent compression method of the JLA data set that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia data sets.
We consider variational integrals of the form $\int F(D^2u)$ where $F$ is convex and smooth on the Hessian space. We show that a critical point $u\in W^{2,\infty}$ of such a functional under compactly supported variations is smooth if the Hessian of $u$ has a small oscillation.
The Marcus-Lushnikov process is a finite stochastic particle system, in which each particle is entirely characterized by its mass. Each pair of particles with masses $x$ and $y$ merges into a single particle at a given rate $K(x,y)$. Under certain assumptions, this process converges to the solution to Smoluchowski equation, as the number of particles increases to infinity. The Marcus-Lushnikov process gives at each time the distribution of masses of the particles present in the system, but does not retain the history of formation of the particles. In this paper, we set up a historical analogue of the Marcus-Lushnikov process (built according the rules of construction of the usual Markov-Lushnikov process) each time giving what we call the historical tree of a particle. The historical tree of a particle present in the Marcus-Lushnikov process at a given time $t$ encodes information about the times and masses of the coagulation events that have formed that particle. We prove a law of large numbers for the empirical distribution of such historical trees. The limit is a natural measure on trees which is constructed from a solution to Smoluchowski coagulation equation.
Here I describe recent studies of objects with molecular hydrogen emission that is strong relative to other spectral lines. Large telescopes and fast spectrometers have made the 2 {\mu}m window accessible even for relatively faint objects. I summarize several environments where strong molecular hydrogen 2.121 micron emission is observed. The line is hard to excite due to its large excitation potential, and is most emissive in regions that have temperatures that are nearly high enough to dissociate molecular hydrogen. I outline several case studies. In the Helix planetary nebula strong emission is produced by rapidly flowing molecular gas that is exposed to an intense ionizing radiation field. This advective production of molecular hydrogen is a fundamentally non-equilibrium process. In the filaments surrounding brightest cluster galaxies in cool core clusters ionizing particles penetrate into magnetically confined molecular cores and excite the gas. Finally, I outline ongoing work on the Crab Nebula, where the first complete maps of molecular emission have only recently been completed. Both ionizing particles and high-energy photons may be important. Finally I speculate on the origin of the correlation between H2 / H I intensity ratios and other properties found in Active Galaxies. This is suggestive of a hardening of the radiation field along the Eigenvector 1 sequence. In all of this work I take the approach of understanding H2 emission along with emission from low and moderate ionization species, a necessary step if we are to really understand the context in which molecular hydrogen emission forms.
We study the response of star clusters to individual tidal perturbations using controlled $N$-body simulations. We consider perturbations by a moving point mass and by a disc, and vary the duration of the perturbation as well as the cluster density profile. For fast perturbations (i.e. `shocks'), the cluster gains energy in agreement with theoretical predictions in the impulsive limit. For slow disc perturbations, the energy gain is lower, and this has previously been attributed to adiabatic damping. However, the energy gain due to slow perturbations by a point-mass is similar to, or larger than that due to fast shocks, which is not expected because adiabatic damping should be almost independent of the nature of the tides. We show that the geometric distortion of the cluster during slow perturbations is of comparable importance for the energy gain as adiabatic damping, and that the combined effect can qualitatively explain the results. The half-mass radius of the bound stars after a shock increases up to $\sim$7\% for low-concentration clusters, and decreases $\sim$3\% for the most concentrated ones. The fractional mass loss is a non-linear function of the energy gain, and depends on the nature of the tides and most strongly on the cluster density profile, making semi-analytic model predictions for cluster lifetimes extremely sensitive to the adopted density profile.
We present analyses of substantially extended series for both interacting self-avoiding walks (ISAW) and polygons (ISAP) on the square lattice. We argue that these provide good evidence that the free energies of both linear and ring polymers are equal above the theta-temperature, extending the application of a theorem of Tesi et. al. to two dimensions. Below the $\theta$-temperature the conditions of this theorem break down, in contradistinction to three dimensions, but an analysis of the ratio of the partition functions for ISAP and ISAW indicates that the free energies are in fact equal at all temperatures to at least within 1%. Any perceived difference can be interpreted as the difference in the size of corrections-to-scaling in both problems. This may be used to explain the vastly different values of the cross-over exponent previously estimated for ISAP to that predicted theoretically, and numerically confirmed, for ISAW. An analysis of newly extended neighbour-avoiding SAW series is also given.
We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of integration and addition rule in momentum space the model may be completed so as to merely deform Lorentz invariance, or so as to introduce a preferred frame. Models which violate Lorentz invariance have a negative UV asymptotic dimension and a very red spectrum of quantum vacuum fluctuations. Instead, models which preserve frame independence can exhibit running to a UV dimension of 2, and a scale-invariant spectrum of fluctuations. The bispectrum of the fluctuations is another point of divergence between the two casings proposed here for the original model.
In this study, we define a new type of Fibonacci and Lucas num- bers which are called bicomplex Fibonacci and bicomplex Lucas numbers. We obtain the well-known properties e.g. Docagnes, Cassini, Catalan for these new types. We also give the identities of negabicomplex Fibonacci and negabi- complex Lucas numbers, Binet formulas and relations of them.
The spatial structure of the emission lines and continuum over the 50 arcsecond extent of the nearby, O-rich, planetary nebula NGC 7009 (Saturn Nebula) have been observed with the MUSE integral field spectrograph on the ESO Very Large Telescope. Science Verification data, in <0.6 arcsecond seeing, have been reduced and analysed as images over the wavelength range 4750-9350A. Emission line maps over the bright shells are presented, from neutral to the highest ionization available (He II and [Mn V]). For collisionally excited lines (CELs), maps of electron temperature (T_e from [N II] and [S III]) and electron density (N_e from [S II] and [Cl III]) are available and for optical recombination lines (ORLs) temperature (from the Paschen jump and ratio of He I lines) and density (from high Paschen lines). These estimates are compared: for the first time, maps of the differences in CEL and ORL T_e's have been derived, and correspondingly a map of t^2 between a CEL and ORL temperature, showing considerable detail. Total abundances of He and O were formed, the latter using three ionization correction factors. However the map of He/H is not flat, departing by ~2% from a constant value, with remnants corresponding to ionization structures. Ionization correction factor methods are compared for O abundance, but none delivers a flat map. An integrated spectrum over an area of 2340 square arcseconds was also formed and compared to 1D photoionization models. The spatial variation of a range of nebular parameters illustrates the complexity of the ionized media in NGC 7009. These MUSE data are very rich with detections of many lines over areas of hundreds of square arcseconds and follow-on studies are indicated. (Abridged)
The plenty information from multiple views data as well as the complementary information among different views are usually beneficial to various tasks, e.g., clustering, classification, de-noising. Multi-view subspace clustering is based on the fact that the multi-view data are generated from a latent subspace. To recover the underlying subspace structure, the success of the sparse and/or low-rank subspace clustering has been witnessed recently. Despite some state-of-the-art subspace clustering approaches can numerically handle multi-view data, by simultaneously exploring all possible pairwise correlation within views, the high order statistics is often disregarded which can only be captured by simultaneously utilizing all views. As a consequence, the clustering performance for multi-view data is compromised. To address this issue, in this paper, a novel multi-view clustering method is proposed by using \textit{t-product} in third-order tensor space. Based on the circular convolution operation, multi-view data can be effectively represented by a \textit{t-linear} combination with sparse and low-rank penalty using "self-expressiveness". Our extensive experimental results on facial, object, digits image and text data demonstrate that the proposed method outperforms the state-of-the-art methods in terms of many criteria.
Current semi-analytic models (SAMs) of galaxy formation over-predict the fraction of passive small late-type satellite galaxies in dense environments by a factor of two to three. We hypothesize that this is due to inaccurate prescriptions on cold gas evolution. In the hope of solving this problem we apply detailed prescriptions on the evolution of diffuse hot gases in satellites and on stellar mass loss, both of which are critical to model cold gas evolution. We replace the conventional shock-heating motivated instant stripping with a realistic gradual prescription based on ram pressure and tidal stripping. We also carefully consider stellar mass loss in our model. When both mechanisms are included, the fraction of passive late types matches the data much more closely. The satellite over-quenching problem is still present in small galaxies in massive haloes, however. In terms of the detectable residual star formation rates, gradual diffuse gas stripping appears to be much more important than stellar mass loss in our model. The implications of these results and other possibilities, such as redshift-dependent merging geometry and tidal disruption, are also discussed.