ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity field. Furthermore, with additional regularity assumption on the initial velocity or on the initial density, we can also prove the uniqueness of such solution. We should mention that the classical maximal regularity theorem for the heat kernel plays an essential role in this context.
Crystallographic alignment between two-dimensional crystals in van der Waals heterostructures brought a number of profound physical phenomena, including observation of Hofstadter butterfly and topological currents, and promising novel applications, such as resonant tunnelling transistors. Here, by probing the electronic density of states in graphene using graphene-hexagonal boron nitride tunnelling transistors, we demonstrate a structural transition of bilayer graphene from incommensurate twisted stacking state into a commensurate AB stacking due to a macroscopic graphene self-rotation. This structural transition is accompanied by a topological transition in the reciprocal space and by pseudospin texturing. The stacking transition is driven by van der Waals interaction energy of the two graphene layers and is thermally activated by unpinning the microscopic chemical adsorbents which are then removed by the self-cleaning of graphene.
Precise stellar masses and radii can be determined using asteroseismology, but their accuracy must be tested against independent estimates. Using radii derived from Gaia DR2 parallaxes, we test the accuracy of asteroseismic radii for a sample of 93 dwarfs based on both individual frequency fitting and the seismic scaling relations. Radii from frequency fitting are about 1 per cent smaller than Gaia radii on average; however, this difference may be explained by a negative bias of 30 $\mu$as in the Gaia parallaxes. This indicates that the radii derived from frequency fitting are accurate to within 1 per cent. The scaling relations are found to overestimate radii by more than 5 per cent, compared to the Gaia radii, at the highest temperatures. We demonstrate that this offset is reduced to 3 per cent after applying corrections based on model frequencies to the scaling relation for $\Delta\nu$, but only when the model frequencies are corrected for the surface effect. With corrections to $\Delta\nu$, the scaling relation gives radii accurate to about 2--3 per cent for dwarfs in the temperature range $5400$--$6700$ K. The remaining offset at the highest temperatures may indicate the need for a correction to the scaling relation for $\nu_{\mathrm{max}}$.
The hypernuclear systems $NN\Xi $ and $\Xi\Xi N$ are considered as an analogue of $nnp$ ($^3$H) nuclear system (with the notation as $AAB$ system). We use the recently proposed modification for the $s$-wave Malfliet-Tjon potential. The modification simulates the Extended-Soft-Core model (ESC08c) for baryon-baryon interactions. The $\Xi N$ spin/isospin triplet $(S, I)=(1, 1)$ potential generates a bound state with the energy $B_2(AB)$=1.56~MeV. Three-body binding energy $B_3$ for the states with maximal total isospin is calculated employing the configuration-space Faddeev equations. Comparison with the results obtained within the integral representation for the equations is presented. The different types of the relation between $B_2$ and $B_3(V_{AA}=0)$ are discussed.
We study the role of closed string backgrounds in boundary string field theory. Background independence requires the introduction of dual boundary fields, which are reminiscent of the doubled field formalism. We find a correspondence between closed string backgrounds and collective excitations of open strings described by vertex operators involving dual fields. Renormalization group flow, solutions and stability are discussed in an example.
These notes were used in a short graduate course on branching processes the author gave in Beijing Normal University. The following main topics are covered: scaling limits of Galton--Watson processes, continuous-state branching processes, extinction probabilities, conditional limit theorems, decompositions of sample paths, martingale problems, stochastic equations, Lamperti's transformations, independent and dependent immigration processes. Some of the results are simplified versions of those in the author's book "Measure-valued branching Markov processes" (Springer, 2011). We hope these simplified results will set out the main ideas in an easy way and lead the reader to a quick access of the subject.
The goal of this paper is to extend the particle-like quantization scheme presented in Pacheco and Silk (2020), to extremal Kerr-de Sitter black holes in four spacetime dimensions, thereby obtaining various quantized parameters, like the black hole mass and angular momentum, consistent with existing results, in the proper limits. Moreover, we show numerically, that for such extremal quantum black holes, there is a root mean square deviation from the First Law of black hole thermodynamics, of the order $\mathcal{O}(\Lambda^{0.45 \pm 0.01})$, where $\Lambda$ denotes the Cosmological Constant.
We find that in general relativity slow down of the pulsar rotation due to the magnetodipolar radiation is more faster for the strange star with comparison to that for the neutron star of the same mass. Comparison with astrophysical observations on pulsars spindown data may provide an evidence for the strange star existence and, thus, serve as a test for distinguishing it from the neutron star.
A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large class of unbounded collision kernels and daughter distribution functions, assuming the collision kernel $K$ to be given by $K(x,y)= x^{\alpha} y^{\beta} + x^{\beta} y^{\alpha}$ with $\alpha \le \beta \le 1$. When $\alpha + \beta \in [1,2]$, it is shown that there exists at least one weak mass-conserving solution for all times. In contrast, when $\alpha + \beta \in [0,1)$ and $\alpha \ge 0$, global mass-conserving weak solutions do not exist, though such solutions are constructed on a finite time interval depending on the initial condition. The question of uniqueness is also considered. Finally, for $\alpha <0$ and a specific daughter distribution function, the non-existence of mass-conserving solutions is also established.
I present three methods to determine the distance to the Galactic centre R0, the solar azimuthal velocity in the Galactic rest frame Vg,\odot and hence the local circular speed Vc at R0. These simple, model-independent strategies reduce the set of assumptions to near axisymmetry of the disc and are designed for kinematically hot stars, which are less affected by spiral arms and other effects. The first two methods use the position-dependent rotational streaming in the heliocentric radial velocities U. The resulting rotation estimate {\theta} from U velocities does not depend on Vg,\odot. The first approach compares this with rotation from the galactic azimuthal velocities to constrain Vg,\odot at an assumed R0. Both Vg,\odot and R0 can be determined using the proper motion of Sgr A\ast as a second constraint. The second strategy makes use of {\theta} being roughly proportional to R0. Therefore a wrong R0 can be detected by an unphysical trend of Vg,\odot with the intrinsic rotation of different populations. From these two strategies I estimate R0 = (8.27 \pm 0.29) kpc and Vg,\odot = (250 \pm 9) kms-1 for a stellar sample from SEGUE, or respectively Vc = (238 \pm 9) kms-1. The result is consistent with the third estimator, where I use the angle of the mean motion of stars, which should follow the geometry of the Galactic disc. This method also gives the Solar radial motion with high accuracy. The rotation effect on U velocities must not be neglected when measuring the Solar radial velocity U\odot. It biases U\odot in any extended sample that is lop-sided in position angle {\alpha} by of order 10 kms-1. Combining different methods I find U\odot \sim 14 kms-1, moderately higher than previous results from the Geneva-Copenhagen Survey.
Generalized Navier-Stokes equations which were proposed recently to describe active turbulence in living fluids are analyzed rigorously. Results on wellposedness and stability in the $L^2(\mathbb{R}^n)$-setting are derived. Due to the presence of a Swift-Hohenberg term global wellposedness in a strong setting for arbitrary initial data in $L^2_\sigma(\mathbb{R}^n)$ is available. Based on the existence of global strong solutions, results on linear and nonlinear (in-) stability for the disordered steady state and the manifold of ordered polar steady states are derived, depending on the involved parameters.
We present new estimates of the luminosity function (LF) and star formation rate density (SFRD) for an H$\alpha$ selected sample at $z\sim0.62$ from the Deep And Wide Narrow-band (DAWN) survey. Our results are based on a new H$\alpha$ sample in the extended COSMOS region (compared to Coughlin et al. 2018) with the inclusion of flanking fields, resulting in a total area coverage of $\sim$1.5 deg$^2$. A total of 241 H$\alpha$ emitters were selected based on robust selection criteria using spectro-photometric redshifts and broadband color-color classification. We explore the effect of different dust correction prescriptions by calculating the LF and SFRD using a constant dust extinction correction, A{$_{\textrm{H}\alpha}=1$} mag, a luminosity-dependent correction, and a stellar-mass dependent correction. The resulting H$\alpha$ LFs are well fitted using Schechter functions with best-fit parameters: L$^*=10^{42.24}$ erg s$^{-1}$, $\phi^*=10^{-2.85}$ Mpc$^{-3}$, $\alpha = -1.62$ for constant dust correction, L$^*=10^{42.31}$ erg s$^{-1}$, $\phi^*=10^{-2.8}$ Mpc$^{-3}$, $\alpha=-1.39$ for luminosity-dependent dust correction, and L$^*=10^{42.36}$ erg s$^{-1}$, $\phi^*=10^{-2.91}$ Mpc$^{-3}$, $\alpha = -1.48$, for stellar mass-dependent dust correction. The deep and wide nature of the DAWN survey effectively samples H$\alpha$ emitters over a wide range of luminosities, thereby providing better constraints on both the faint and bright end of the LF. Also, the SFRD estimates $\rho_{\textrm{SFR}}=10^{-1.39}$ M$_{\odot}$yr$^{-1}$Mpc$^{-3}$ (constant dust correction), $\rho_{\textrm{SFR}}=10^{-1.47}$ M$_{\odot}$yr$^{-1}$Mpc$^{-3}$ (luminosity-dependent dust correction), and $\rho_{\textrm{SFR}}=10^{-1.49}$ M$_{\odot}$yr$^{-1}$Mpc$^{-3}$ (stellar mass-dependent dust correction) are in good agreement with the evolution of SFRD across redshifts ($0 < z < 2$) seen from previous H$\alpha$ surveys.
The density driven Mott transition is studied by means of Dynamical Mean-Field Theory in the Hubbard-Holstein model, where the Hubbard term leading to the Mott transition is supplemented by an electron-phonon (e-ph) term. We show that an intermediate e-ph coupling leads to a first-order transition at T=0, which is accompanied by phase separation between a metal and an insulator. The compressibility in the metallic phase is substantially enhanced. At quite larger values of the coupling a polaronic phase emerges coexisting with a non-polaronic metal.
Raman scattering in the three-dimensional Dirac semimetal Cd3As2 shows an intricate interplay of electronic and phonon degrees of freedom. We observe resonant phonon scattering due to interband transitions, an anomalous anharmonicity of phonon frequency and intensity, as well as quasielastic (E~0) electronic scattering. The latter two effects are governed by a characteristic temperature scale T* ~ 100 K that is related to mutual fluctuations of lattice and electronic degrees of freedom. A refined analysis shows that this characteristic temperature corresponds to the energy of optical phonons which couple to interband transitions in the Dirac states of Cd3As2. As electron-phonon coupling in a topological semimetal is primarily related to phonons with finite momenta, the back action on the optical phonons in only observed as anharmonicities via multi-phonon processes involving a broad range of momenta. The resulting energy density fluctuations of the coupled system have previously only been observed in low dimensional or frustrated spin systems with suppressed long range ordering.
In this paper we investigate how well Planck and Lyman-Alpha forest data will be able to constrain the sum of the neutrino masses, and thus, in conjunction with flavour oscillation experiments, be able to determine the absolute masses of the neutrinos. It seems possible that Planck, together with a Lyman-Alpha survey, will be able to put pressure on an inverted hierarchial model for the neutrino masses. However, even for optimistic assumptions of the precision of future Lyman-Alpha datasets, it will not be possible to confirm a minimal-mass normal hierarchy.
The mini-proceedings of the 15th Meeting of the "Working Group on Rad. Corrections and MC Generators for Low Energies" held in Mainz on April 11, 2014, are presented. These meetings, started in 2006, have as aim to bring together experimentalists and theorists working in the fields of meson transition form factors, hadronic contributions to $(g-2)_\mu$ and the effective fine structure constant, and development of Monte Carlo generators and Radiative Corrections for precision e+e- and tau physics.
In this paper, we find all integers $c$ having at least two representations as a difference between a Fibonacci number and a Tribonacci number.
The presence of dark matter (DM) is suggested by a wealth of astrophysical and cosmological measurements. However, its underlying nature is yet unknown. Among the most promising candidates are weakly interacting massive particles (WIMPs): particles with mass and coupling strength at the electroweak scale and thermally produced in the early universe have a present relic density consistent with that observed today. WIMP self-annihilation would produce Standard Model particles including gamma-rays, which have been long-time recognized as a prime messenger to indirectly detect dark matter signals. The centre of the Milky Way is predicted as the brightest source of DM annihilations. The H.E.S.S. collaboration is currently performing a survey of the inner region of the Milky Way, the Inner Galaxy Survey (IGS), intended to achieve the best sensitivity to faint and diffuse emissions in a region of several degrees around the Galactic Centre. We analyzed 2014-2020 observations taken with the five-telescope array to search for a DM annihilation signal. With the current dataset of about 550 hours, we found no significant excess and therefore derived strong constraints on the velocity-weighted annihilation cross-section. TeV thermal WIMPs can be probed in different annihilation channels.
The use of Levi-Civita transformation allows us to formulate the problem of two-dimensional screened donor states in a magnetic field as that of two-dimensional anharmonic oscillator. Therefore, the operator method can be directly used for the first problem and the exact solutions of Schrodinger equation are obtained correspondently. In our approach, wave-functions are constructed in the representation of annihilation and creation operators, which permits one to use purely algebraic method in further calculations of other characteristics. The considered problem is related to the motion of 2D electron gas in GaAs/AlGaAs multiple-quantum well structures with the presence of a magnetic field, which continues to provide new and fascinating phenomena.
We present a method for segmenting an arbitrary number of moving objects in image sequences using the geometry of 6 points in 2D to infer motion consistency. The method has been evaluated on the Hopkins 155 database and surpasses current state-of-the-art methods such as SSC, both in terms of overall performance on two and three motions but also in terms of maximum errors. The method works by finding initial clusters in the spatial domain, and then classifying each remaining point as belonging to the cluster that minimizes a motion consistency score. In contrast to most other motion segmentation methods that are based on an affine camera model, the proposed method is fully projective.
It is conjectured that every integer N>454 is the sum of seven nonnegative cubes. We prove the conjecture when N is a multiple of 4.
We consider linear arrays of cells of volume $V_\mathrm{c}$ populated by monodisperse rods of size $\sigma V_\mathrm{c}$, $\sigma=1,2,\ldots$, subject to hardcore exclusion interaction. Each rod experiences a position-dependent external potential. In one application we also examine effects of contact forces between rods. We employ two distinct methods of exact analysis with complementary strengths and different limits of spatial resolution to calculate profiles of pressure and density on mesoscopic and microscopic length scales at thermal equilibrium. One method uses density functionals and the other statistically interacting vacancy particles. The applications worked out include gravity, power-law traps, and hard walls. We identify oscillations in the profiles on a microscopic length scale and show how they are systematically averaged out on a well-defined mesoscopic length scale to establish full consistency between the two approaches. The continuum limit, realized as $V_\mathrm{c}\to0$, $\sigma\to\infty$ at nonzero and finite $\sigma V_\mathrm{c}$, connects our highest-resolution results with known exact results for monodisperse rods in a continuum. We also compare the pressure profiles obtained from density functionals with the average microscopic pressure profiles derived from the pair distribution function.
Polarimetry is one of the most informative techniques of studying magnetic fields in molecular clouds. How reliable the interpretation of the polarization maps in terms of magnetic fields is the issue that the grain alignment theory addresses.   We show that grain alignment involves several processes acting simultaneously, but on different time-scales. We explain that rotating dust grains get substantial magnetic moment that allows them precess fast about magnetic field lines. As the result, grains preserve their orientation to magnetic field when the magnetic field direction fluctuates. We point out to the importance of internal alignment, i.e. the process forces grain axes to be aligned in respect to the grain angular momentum. We show that subtle quantum effects, in particular relaxation related to nuclear magnetic moments of atoms composing the grain, brings to live complex grain motions, e.g. flips. These flips substantially alter the dynamics of grain and limit the applicability of earlier theories that did not account for them. We also briefly review basic physical processes involved in the alignment of grain angular momentum in respect to interstellar magnetic field. We claim that the bulk of existing observational data is consistent with the radiative torque alignment mechanism. In particular, we show that large grains that are known to exist in the cores of molecular clouds may be aligned by the attenuated external interstellar radiation field.
Steingrimsson has recently introduced a partition analogue of Foata-Zeilberger's mak statistic for permutations and conjectured that its generating function is equal to the classical q-Stirling numbers of second kind. In this paper we prove a generalization of Steingrimsson's conjecture.
Macroscopic plasma polarization, which is created by gravitation and other mass-acting (inertial) forces in massive astrophysical objects (MAO) is under discussion. Non-ideality effect due to strong Coulomb interaction of charged particles is introduced into consideration as a new source of such polarization. Simplified situation of totally equilibrium isothermal star without relativistic effects and influence of magnetic field is considered. The study is based on conditions of constancy for generalized (electro)chemical potentials and/or conditions of equilibrium for the forces acting on each charged specie. New "non-ideality force" appears in this consideration. Hypothetical sequences of gravitational, inertial and non-ideality polarization on thermo- and hydrodynamics of MAO are under discussion.
Fluctuations of the amplitude of the order parameter govern the properties of superconducting systems close to the critical transition temperature. In the BCS regime we examine the contribution of these pairing fluctuations to the superfluid order parameter for harmonically confined atomic Fermi gases. In the limit of small systems we obtain an expression for the space dependence of the fluctuations, in good agreement with the results of numerical calculations. In this limit we also predict a parity effect, i.e. that pairing fluctuations should show a maximum or a minimum at the centre of the trap, depending on the value of the last occupied shell being even or odd. We finally propose to detect pairing fluctuations by measuring the density-density correlation function as evaluated after a ballistic expansion of the gas.
Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three-Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations---3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations---predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame ($T_{\rm Lab}$) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which $T_{\rm Lab}>$ 220 MeV/n.
It is shown that the notion of W_\infty-algebra originally carried out over a (compact) Riemann surface can be extended to n complex dimensional (compact) manifolds within a symplectic geometrical setup. The relationships with the Kodaira-Spencer deformation theory of complex structures are discussed. Subsequently, some field theoretical aspects at the classical level are briefly underlined.