ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Cauchy problem of the compressible Oldroyd-B model without damping mechanism in R^n$ with $n\ge2$ is considered. The lack of dissipation in density and stress tensor in the model is compensated by exploiting an intrinsic structure and introducing new quantities between density, velocity and stress tensor. Therefore, global solutions to the system with small initial data in critical Besov spaces are obtained. As a byproduct, optimal time decay rates of the solutions are derived by using an energy estimation argument. The results remain valid for the compressible viscoelastic system without the `div-curl structure assumption and thus improve those given by Hu and Wang [ J. Differential Equations, {\bf 250}, 1200--1231, 2011] and Qian and Zhang [Arch. Ration. Mech. Anal., {\bf 198}, 835--868, 2010].
Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical temperature of the infinite system the mean value and the most probable value of the magnetization scale differently with N, and the probability distribution of the magnetization is not a Gaussian, even for large N. Similar results inconsistent with the usual understanding of mean-field theory are found at the spinodal. We relate these results to the breakdown of hyperscaling and show how hyperscaling can be restored by increasing N while holding the Ginzburg parameter rather than the temperature fixed.
We consider the central spin model in the box approximation taking into account external magnetic field and anisotropy of the hyperfine interaction. From the exact Hamiltonian diagonalization we obtain analytical expressions for the nuclear spin dynamics in the limit of many nuclear spins. We predict the nuclear spin precession in zero magnetic field for the case of anisotropic interaction between electron and nuclear spins. We calculate and describe the nuclear spin noise spectra in the thermodynamic equilibrium. The obtained results can be used for the analysis of the nuclear spin induced current fluctuations in organic semiconductors.
Symmetric multiple zeta values (SMZVs) are elements in the ring of all multiple zeta values modulo the ideal generated by $\zeta(2)$ introduced by Kaneko-Zagier as counterparts of finite multiple zeta values. It is known that symmetric multiple zeta values satisfy double shuffle relations and duality relations. In this paper, we construct certain lifts of SMZVs which live in the ring generated by all multiple zeta values and $2\pi i$ as certain iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty\}$ along a certain closed path. We call this lifted values as refined symmetric multiple zeta values (RSMZVs). We show double shuffle relations and duality relations for RSMZVs. These relations are refinements of the double shuffle relations and the duality relations of SMZVs. Furthermore we compare RSMZVs to other variants of lifts of SMZVs. Especially, we prove that RSMZVs coincide with Bachmann-Takeyama-Tasaka's $\xi$-values.
The well-established Type Ia remnant of Tycho's supernova (SN 1572) reveals discrepant ambient medium density estimates based on either the measured dynamics or on the X-ray emission properties. This discrepancy can potentially be solved by assuming that the supernova remnant (SNR) shock initially moved through a stellar wind bubble, but is currently evolving in the uniform interstellar medium with a relatively low density.   We investigate this scenario by combining hydrodynamical simulations of the wind-loss phase and the supernova remnant evolution with a coupled X-ray emission model, which includes non-equilibrium ionization. For the explosion models we use the well-known W7 deflagration model and the delayed detonation model that was previously shown to provide good fits to the X-ray emission of Tycho's SNR.   Our simulations confirm that a uniform ambient density cannot simultaneously reproduce the dynamical and X-ray emission properties of Tycho. In contrast, models that considered that the remnant was evolving in a dense, but small, wind bubble reproduce reasonably well both the measured X-ray emission spectrum and the expansion parameter of Tycho's SNR. Finally, we discuss possible mass loss scenarios in the context of single- and double-degenerate models which possible could form such a small dense wind bubble.
In this work, we reported uniform layer-by-layer sublimation of black phosphorus under heating below 600 K. The uniformity and crystallinity of BP samples after thermal thinning were confirmed by Raman spectra and 2D Raman imaging. A uniform and crystalline bilayer black phosphorus flake with an area of 180 um^2 was prepared with this method. No micron scale defects were observed. The sublimation rate of BP was around 0.18 nm / min at 500 K and 1.5 nm / min at 550 K. Both room and high temperature Raman peak intensity ratio Si/A2g vs. BP thickness relations were established for in-situ thickness determination. The sublimation thinning method was shown to be a controllable and scalable approach to prepare few-layer black phosphorus.
Collective monopole vibrations are studied in the framework of an antisymmetrized version of molecular dynamics as a function of the vibration amplitude. The giant monopole resonance energy in ${}^{40}Ca$ is sensitive to the incompressibility of the effective interaction, in good agreement with complete time-dependent Hartree-Fock calculations. The collective response of ${}^{12}C$, ${}^{16}O$ and ${}^{24}Mg$ is also studied. For these lighter nuclei that have an important contribution of an $\alpha$-clustered component, different frequencies are observed, corresponding to two different types of vibrations associated with breathing and moving of the underlying clusters. Possible connections with direct breakup into $\alpha$ clusters at high excitation energy are discussed.
We obtain an asymptotic for the regularized fourth moment of the Eisenstein series for the full modular group, in agreement with the Random Wave Conjecture.
In this paper we study varieties covered by rational or elliptic curves. First, we show that images of Calabi-Yau or irreducible symplectic varieties under rational maps are almost always rationally connected. Second, we investigate elliptically connected and elliptically chain connected varieties, and varieties swept out by a family of elliptic curves. Among other things, we show that Calabi-Yau or hyperk\"ahler manifolds which are covered by a family of elliptic curves contain uniruled divisors and that elliptically chain connected varieties of dimension at least two contain a rational curve, and so do K-trivial varieties with finite fundamental group which are covered by elliptic curves.
The hydrogen-deficient star DY Cen has been reported as an R CrB-type variable, an extreme helium star (with some hydrogen), and as a single-lined spectroscopic binary. It has been associated with a dramatic change in visual brightness and colour corresponding to a change in effective temperature ($T_{\mathrm eff}$) of some 20,000 K in the last century. To characterize the binary orbit and $T_{\mathrm eff}$ changes more precisely, new high-resolution spectroscopy has been obtained with SALT. The previous orbital period is not confirmed; previous measurements may have been confused by the presence of pulsations. Including data from earlier epochs (1987, 2002, and 2010), self-consistent spectral analyses from all four epochs demonstrate an increase in $T_{\mathrm eff}$ from 18,800 to 24,400 K between 1987 and 2015. Line profiles demonstrate that the surface rotation has increased by a factor two over the same interval. This is commensurate with the change in $T_{\mathrm eff}$ and an overall contraction. Rotation will exceed critical if contraction continues. The 1987 spectrum shows evidence of a very high abundance of the s-process element strontium. The very rapid evolution, non-negligible surface hydrogen and high surface strontium point to a history involving a very late thermal pulse. Observations over the next thirty years should look for a decreasing pulsation period, reactivation of R CrB-type activity as the star seeks to shed angular momentum and increasing illumination by emission lines from nebular material ejected in the past.
Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with the selection of proper scale factors, a matrix formed by stacking fundamental matrices between pairs of images has rank 6. Moreover, this matrix forms the symmetric part of a rank 3 matrix whose factors relate directly to the corresponding camera matrices. We use this new characterization to produce better estimations of fundamental matrices by optimizing an L1-cost function using Iterative Re-weighted Least Squares and Alternate Direction Method of Multiplier. We further show that this procedure can improve the recovery of camera locations, particularly in multi-view settings in which fewer images are available.
The application of renormalization group methods to microscopic nuclear many-body calculations is discussed. We present the solution of the renormalization group equations in the particle-hole channels for neutron matter and the application to S-wave pairing. Furthermore, we point out that the inclusion of tensor and spin-orbit forces leads to spin non-conserving effective interactions in nuclear matter.
HESS J1857+026 is an extended TeV gamma-ray source that was discovered by H.E.S.S. as part of its Galactic plane survey. Given its broadband spectral energy distribution and its spatial coincidence with the young energetic pulsar PSR J1856+0245, the source has been put forward as a pulsar wind nebula (PWN) candidate. MAGIC has performed follow-up observations aimed at mapping the source down to energies approaching 100 GeV in order to better understand its complex morphology. HESS J1857+026 was observed by MAGIC in 2010, yielding 29 hours of good quality stereoscopic data that allowed us to map the source region in two separate ranges of energy. We detected very-high-energy gamma-ray emission from HESS J1857+026 with a significance of $12 \sigma$ above $150$ GeV. The differential energy spectrum between $100$ GeV and $13$ TeV is well described by a power law function $dN/dE = N_0(E/1\textrm{TeV})^{-\Gamma}$ with $N_0 = (5.37 \pm0.44_{stat} \pm1.5_{sys}) \times 10^{-12} (\textrm{TeV}^{-1} \textrm{cm}^{-2}$ $\textrm{ s}^{-1})$ and $\Gamma = 2.16\pm0.07_{stat} \pm0.15_{sys}$, which bridges the gap between the GeV emission measured by Fermi-LAT and the multi-TeV emission measured by H.E.S.S.. In addition, we present a detailed analysis of the energy-dependent morphology of this region. We couple these results with archival multi-wavelength data and outline evidence in favor of a two-source scenario, whereby one source is associated with a PWN, while the other could be linked with a molecular cloud complex containing an HII region and a possible gas cavity.
We introduce Synscapes -- a synthetic dataset for street scene parsing created using photorealistic rendering techniques, and show state-of-the-art results for training and validation as well as new types of analysis. We study the behavior of networks trained on real data when performing inference on synthetic data: a key factor in determining the equivalence of simulation environments. We also compare the behavior of networks trained on synthetic data and evaluated on real-world data. Additionally, by analyzing pre-trained, existing segmentation and detection models, we illustrate how uncorrelated images along with a detailed set of annotations open up new avenues for analysis of computer vision systems, providing fine-grain information about how a model's performance changes according to factors such as distance, occlusion and relative object orientation.
V4332 Sgr is a red transient (red nova) whose eruption was observed in 1994. The remnant of the eruption shows a unique optical spectrum: strong emission lines of atoms and molecules superimposed on an M-type stellar spectrum. The stellar-like remnant is presumably embedded in a disc-like dusty envelope seen almost face-on. The observed optical spectrum is assumed to result from interactions of the central-star radiation with dust and gas in the disc and outflows initiated in 1994. We reduced and measured a high-resolution (R = ~40 000) spectrum of V4332 Sgr obtained with VLT/UVES in April/May 2005. The spectrum comes from the ESO archives and is the best quality spectrum of the object ever obtained. We identified and measured over 200 emission features belonging to 11 elements and 6 molecules. The continuous, stellar-like component can be classified as ~M3. The interstellar reddening was estimated to be 0.35 < E(B-V) < 0.75. From radial velocities of interstellar absorption features in the NaI D lines, we estimated a lower limit of ~5.5 kpc to the distance of V4332 Sgr. The spectrum of V4332 Sgr considerably evolved between 2005 and 2009. The object significantly faded in the optical, which resulted from cooling of the main remnant by 300-350 K, corresponding to its spectral-type change from M3 to M5-6. The object increased in luminosity by ~50%, however, implying a significant expansion of its dimensions. Most of the emission features seen in 2005 significantly faded or even disappeared from the spectrum of V4332 Sgr in 2009. These resulted from fading of the optical central-star radiation and a decrease of the optical thickness of the cirumstellar matter. V4332 Sgr bears several resemblances to V1309 Sco, which erupted in 2008. This can indicate a similar nature of the eruptions of the two objects. The outburst resulted from merger of a contact binary in V1309 Sco.
We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov (LS) power-law growth in all the cases.
Ab initio theory describes nuclei from a fully microscopic formulation, with no presupposition of collective degrees of freedom, yet signatures of clustering and rotation nonetheless arise. We can therefore look to ab initio theory for an understanding of the nature of these emergent phenomena. To probe the nature of rotation in 10Be, we examine the predicted rotational spectroscopy from no-core configuration interaction (NCCI) calculations with the Daejeon16 internucleon interaction, and find spectra suggestive of coexisting rotational structures having qualitatively different intrinsic deformations: one triaxial and the other with large axial deformation arising primarily from the neutrons.
Lie group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein's field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three-dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi Type, as well as the scaling and the time reparametrization symmetry. A detailed application of the method is presented for Bianchi Type IV. The result is the acquisition of the general solution of Type IV in terms of sixth Painleve transcendent PVI, along with the known pp-wave solution. For Bianchi Types I, II, V the known entire solution space is attained and very briefly listed, along with two new Type V solutions of Euclidean and neutral signature and a Type I pp-wave metric.
The formation of galaxies and their various components can be stringent tests of dark matter models and of gravity theories. In the standard cold dark matter (CDM) model, spheroids are formed through mergers in a strongly hierarchical scenario, and also in the early universe through dynamical friction in clumpy galaxies. More secularly, pseudo-bulges are formed by the inner vertical resonance with bars. The high efficiency of bulge formation is in tension with observations in the local universe of a large amount of bulge-less spiral galaxies. In the present work, the formation of bulges in very gas-rich galaxies, as those in the early universe, is studied in the Milgrom's MOdified Newtonian Dynamics (MOND), through multi-grid simulations of the non-linear gravity, including the gas dissipation, star formation and feedback.   Clumpy disks are rapidly formed, as in their Newtonian equivalent systems. However, the dynamical friction is not as efficient, in the absence of dark matter halos, and the clumps have no time to coalesce into the center to form bulges, before they are eroded by stellar feedback and shear forces. Previous work has established that mergers are less frequent in MOND, and classical bulges are expected less massive. It is now shown that gas-rich clumpy galaxies in the early universe do not form bulges.   Since pseudo-bulges are formed with a similar rate as in the Newtonian equivalent systems, it can be expected that the contribution of pseudo-bulges is significantly higher in MOND.
Variations of total solar irradiance (TSI), magnetic field, Ca II K-flux, faculae and plage areas due to the number and the type of sunspots/sunspot groups (SGs) are well established by using Solar Irradiance Platform and ground based data from various centers such as Stanford Data (SFO), Kodaikanal data (KKL) and National Geographical Data Center (NGDC) Homepage, respectively. We applied time series analysis for extracting the data over the descending phases of solar activity cycles (SACs) 21, 22 and 23, and the ascending phases 22 and 23 of SACs, and analyzed the selected data using the Python programming language. Our detailed analysis results suggest that there is a stronger correlation between solar surface indices and the changes in the relative portion of the small and large SGs. This somewhat unexpected finding suggest that plage regions decreased in a lower values in spite of the higher number of large SGs in SAC 23 while Ca II K-flux did not decrease by large amount or it was comparable with SAC 22 for some years and relates with C type and DEF type SGs. Thus, increase of facular areas which are influenced by large SGs caused a small percentage decrease in TSI while decrement of plage areas triggered a higher decrease in the flux of magnetic field. Our results thus reveal the potential of such detailed comparison of SG analysis with solar surface indices for understanding and predicting future trends in the SAC.
We discuss possible signatures of the $CP$-odd scalar of two-doublet models at the LHC. We find that the inclusive two-photon decay mode and the decay sequence $A^0 \rightarrow Zh, h \rightarrow \gamma \gamma$, where $h$ is a $CP$-even neutral scalar, can give viable signals in fairly large and complementary regions of parameter space.
We study a two dimensional version of Neuhauser's long range sexual reproduction model and prove results that give bounds on the critical values $\lambda_f$ for the process to survive from a finite set and $\lambda_e$ for the existence of a nontrivial stationary distribution. Our first result comes from a standard block construction, while the second involves a comparison with the "generic population model" of Bramson and Gray (1991). An interesting new feature of our work is the suggestion that, as in the one dimensional contact process, edge speeds characterize critical values. We are able to prove the following for our quadratic contact process when the range is large but suspect they are true for two dimensional finite range attractive particle systems that are symmetric with respect to reflection in each axis. There is a speed $c(\theta)$ for the expansion of the process in each direction. If $c(\theta) > 0$ in all directions, then $\lambda > \lambda_f$, while if at least one speed is positive, then $\lambda > \lambda_e$. It is a challenging open problem to show that if some speed is negative, then the system dies out from any finite set.
In this paper, we study Mountain Pass Characterization of the second eigenvalue of the operator $-\De_p u -\De_{J,p}u$ and study shape optimization problems related to these eigenvalues.
Simulations of self-interacting dark matter (SIDM) predict that dark matter should lag behind galaxies during a collision. If the interaction is mediated by a high-mass force carrier, the distribution of dark matter can also develop asymmetric dark matter tails. To search for this asymmetry, we compute the gravitational lensing properties of a mass distribution with a free {\em skewness} parameter. We apply this to the dark matter around the four central galaxies in cluster Abell~3827. In the galaxy whose dark matter peak has previously been found to be offset, we tentatively measure a skewness $s=0.23^{+0.05}_{-0.22}$ in the same direction as the peak offset. Our method may be useful in future gravitational lensing analyses of colliding galaxy clusters and merging galaxies.
The theory of spaces with different (not only by sign) contravariant and covariant affine connections and metrics [}$(\bar{L}_n,g)$\QTR{it}{-spaces] is worked out within the framework of the tensor analysis over differentiable manifolds and in a volume necessary for the further considerations of the kinematics of vector fields and the Lagrangian theory of tensor fields over}$(\bar{L}_n,g)$\QTR{it}{-spaces. The possibility of introducing affine connections (whose components differ not only by sign) for contravariant and covariant tensor fields over differentiable manifolds with finite dimensions is discussed. The action of the deviation operator, having an important role for deviation equations in gravitational physics, is considered for the case of contravariant and covariant vector fields over differentiable manifolds with different affine connections A deviation identity for contravariant vector fields is obtained. The notions covariant, contravariant, covariant projective, and contravariant projective metrics are introduced in (}$\bar{L}_n,g$\{)-spaces. The action of the covariant and the Lie differential operators on the different type of metrics is found. The notions of symmetric covariant and contravariant (Riemannian) connections are determined and presented by means of the covariant and contravariant metrics and the corresponding torsion tensors. The different types of relative tensor fields (tensor densities) as well as the invariant differential operators acting on them are considered. The invariant volume element and its properties under the action of different differential operators are investigated.
In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a finite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global $L^2 $ a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially