ShantanuT01/DACTYL-Pretraining huggingface dataset:
We compare simple analytical closure models of homogeneous turbulent Boussinesq convection for stellar applications with three-dimensional simulations. We use simple analytical closure models to compute the fluxes of angular momentum and heat as a function of rotation rate measured by the Taylor number. We also investigate cases with varying angles between the angular velocity and gravity vectors, corresponding to locating the computational domain at different latitudes ranging from the pole to the equator of the star. We perform three-dimensional numerical simulations in the same parameter regimes for comparison. The free parameters appearing in the closure models are calibrated by two fitting methods using simulation data. Unique determination of the closure parameters is possible only in the non-rotating case or when the system is placed at the pole. In the other cases the fit procedures yield somewhat differing results. The quality of the closure is tested by substituting the resulting coefficients back into the closure model and comparing with the simulation results. To eliminate the possibilities that the results obtained depend on the aspect ratio of the simulation domain or suffer from too small Rayleigh numbers we performed runs varying these parameters. The simulation data for the Reynolds stress and heat fluxes broadly agree with previous compressible simulations. The closure works fairly well with slow and fast rotation but its quality degrades for intermediate rotation rates. We find that the closure parameters depend not only on rotation rate but also on latitude. The weak dependence on Rayleigh number and the aspect ratio of the domain indicates that our results are generally valid
Although Hinrichsen in his unpublished work theoretically rebutted the possibility of the discontinuous transition in one-dimensional nonequilibrium systems unless there are additional conservation laws, long-range interactions, macroscopic currents, or special boundary conditions, we have recently observed the resurrection of the claim that the triplet creation model (TC) introduced by Dickman and Tom\'e [Phys. Rev. E {\bf 44}, 4833 (1991)] would show the discontinuous transition. By extensive simulations, however, we find that the one-dimensional TC does belong to the directed percolation universality class even for larger diffusion constant than the suggested tricritical point in the literature. Furthermore, we find that the phase boundary is well described by the crossover from the mean field to the directed percolation, which supports the claim that the one-dimensional TC does not exhibit a discontinuous transition.
In the paper, the authors present several new relations and applications for the combinatorial sequence that counts the possible partitions of a finite set with the restriction that the size of each block is contained in a given set. One of the main applications is in the study of lonesum matrices.
This note announces the proof of a conjecture of H. Verlinde, according to which the spaces of Liouville conformal blocks and the Hilbert spaces from the quantization of the Teichm\"uller spaces of Riemann surfaces carry equivalent representations of the mapping class group. This provides a basis for the geometrical interpretation of quantum Liouville theory in its relation to quantized spaces of Riemann surfaces.
Under appropriate conditions controllable two-level systems can be used to detect the third moment of current fluctuations. We derive a Master Equation for a quantum system coupled to a bath valid to the third order in the coupling between the system and the environment. In this approximation the reduced dynamics of the quantum system depends on the frequency dependent third moment. Specializing to the case of a controllable two-level system (a qubit) and in the limit in which the splitting between the levels is much smaller than the characteristic frequency of the third moment, it is possible to show that the decay of the qubit has additional oscillations whose amplitude is directly proportional to the value of the third moment. We discuss an experimental setup where this effect can be seen.
We explore the reconstruction of the gravitational lensing field of the cosmic microwave background in real space showing that very little statistical information is lost when estimators of short range on the celestial sphere are used in place of the customary estimators in harmonic space, which are nonlocal and in principle require a simultaneous analysis of the entire sky without any cuts or excisions. Because virtually all the information relevant to lensing reconstruction lies on angular scales close to the resolution scale of the sky map, the gravitational lensing dilatation and shear fields (which unlike the deflection field or lensing potential are directly related to the observations in a local manner) may be reconstructed by means of quadratic combinations involving only very closely separated pixels. Even though harmonic space provides a more natural context for understanding lensing reconstruction theoretically, the real space methods developed here have the virtue of being faster to implement and are likely to prove useful for analyzing realistic maps containing a galactic cut and possibly numerous small excisions to exclude point sources that cannot be reliably subtracted.
Fix a prime number $\ell$. Graphs of isogenies of degree a power of $\ell$ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse graphs of so-called $\mathfrak l$-isogenies, resolving that they are (almost) volcanoes in any dimension. Specializing to the case of principally polarizable abelian surfaces, we then exploit this structure to describe graphs of a particular class of isogenies known as $(\ell, \ell)$-isogenies: those whose kernels are maximal isotropic subgroups of the $\ell$-torsion for the Weil pairing. We use these two results to write an algorithm giving a path of computable isogenies from an arbitrary absolutely simple ordinary abelian surface towards one with maximal endomorphism ring, which has immediate consequences for the CM-method in genus 2, for computing explicit isogenies, and for the random self-reducibility of the discrete logarithm problem in genus 2 cryptography.
A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.
We have studied the spectral time variations of candidate luminous blue variable stars (cLBV) in two low-metallicity blue compact dwarf galaxies, DDO 68 and PHL 293B. The LBV in DDO 68, located in HII region #3, shows an outburst, with an increase of more than 1000 times in Halpha luminosity during the period 2008-2010. The broad emission of the HI and HeI lines display a P Cygni profile, with a relatively constant terminal velocity of ~800 km/s, reaching a maximum luminosity L(Halpha) of ~2x10^38 erg/s, with a FWHM of ~1000-1200 km/s. On the other hand, since the discovery of a cLBV in 2001 in PHL 293B, the fluxes of the broad components and the broad-to-narrow flux ratios of the HI and HeI emission lines in this galaxy have remained nearly constant over 16 years, with small variations. The luminosity of the broad Halpha component varies between ~2x10^38 erg/s and ~10^39 erg/s, with the FWHM varying in the range ~500-1500 km/s. Unusually persistent P Cygni features are clearly visible until the end of 2020 despite a decrease of the broad-to-narrow flux ratio in the most recent years. A terminal velocity of ~800 km/s is measured from the P Cygni profile, similar to the one in DDO 68, although the latter is 3.7 more metal-deficient than PHL 293B. The relative constancy of the broad Halpha luminosity in PHL 293B suggests that it is due to a long-lived stellar transient of type LBV/SN IIn.
We establish a version of the Furstenberg-Katznelson multi-dimensional Szemer\'edi in the primes ${\mathcal P} := \{2,3,5,\ldots\}$, which roughly speaking asserts that any dense subset of ${\mathcal P}^d$ contains constellations of any given shape. Our arguments are based on a weighted version of the Furstenberg correspondence principle, relative to a weight which obeys an infinite number of pseudorandomness (or "linear forms") conditions, combined with the main results of a series of papers by Green and the authors which establish such an infinite number of pseudorandomness conditions for a weight associated with the primes. The same result, by a rather different method, has been simultaneously established by Cook, Magyar, and Titichetrakun.
In order to interface the DESY fieldbus adapter, SEDAC (SErial Data Acquisition and Control system), a full duplex device driver was developed for the Windows NT, Linux, VxWorks, and Solaris operating systems. Detailed driver development issues as well as a common user interface will be presented, along with a comparison of the device drivers among the different operating systems. In particular, we shall present benchmark results concerning general performance as well as ease of development.
Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive It\^{o}'s and Tanaka's formulas for the $d$-dimensional bifractional Brownian motion.
We present a detail study of dynamically generating a M2 brane from super-gravitons (or D0 branes) in a pp-wave background possessing maximal spacetime SUSY. We have three kinds of dynamical solutions depending on the excess energy which appears as an order parameter signalling a critical phenomenon about the solutions. As the excess energy is below a critical value, we have two branches of the solution, one can have its size zero while the other cannot for each given excess energy. However there can be an instanton tunnelling between the two. Once the excess energy is above the critical value, we have a single solution whose dynamical behavior is basically independent of the background chosen and whose size can be zero at some instant. A by product of this study is that the size of particles or extended objects can grow once there is a non-zero excess energy even without the presence of a background flux, therefore lending support to the spacetime uncertainty principle.
The deposition of one silicon monolayer on Ag(111) gives rise to a set of superstructures depending on growth conditions. These superstructures are correlated to the epitaxy between the honeycomb structure of silicon (so called silicene) and the silver substrate. In this paper, from a detailed re-analysis of experimental results, obtained by Scanning Tunneling Microscopy and by Low Energy Electron Diffraction on the (2R3x2R3)R30 structure, we propose a new atomic model of the silicene layer based on periodic arrangements of perfect areas of (2R3x2R3)R30 surrounded by defect areas. A generalization of this model explains the main experimental observations: deviation of the average direction, Moire patterns and apparent global disorder. In the frame of the proposed model, the apparent disorders observed on the STM images, would be topological effects, i.e. the silicene would keep a quasi-perfect honeycomb structure.
The critical dynamics of classical 3D Heisenberg model and complex model of the real antiferromagnetic Cr2O3 is investigated with use of the method of molecular dynamics. The dynamic critical exponent z are determined for these models on the basis of the theory dynamic finite-size scaling.
Understanding the formation of the extremely metal poor star SDSS-J102915+172927 is of fundamental importance to improve our knowledge on the transition between the first and second generation of stars in the Universe. In this paper, we perform three-dimensional cosmological hydrodynamical simulations of dust-enriched halos during the early stages of the collapse process including a detailed treatment of the dust physics. We employ the astrochemistry package \krome coupled with the hydrodynamical code \textsc{enzo} assuming grain size distributions produced by the explosion of core-collapse supernovae of 20 and 35 M$_\odot$ primordial stars which are suitable to reproduce the chemical pattern of the SDSS-J102915+172927 star. We find that the dust mass yield produced from Population III supernovae explosions is the most important factor which drives the thermal evolution and the dynamical properties of the halos. Hence, for the specific distributions relevant in this context, the composition, the dust optical properties, and the size-range have only minor effects on the results due to similar cooling functions. We also show that the critical dust mass to enable fragmentation provided by semi-analytical models should be revised, as we obtain values one order of magnitude larger. This determines the transition from disk fragmentation to a more filamentary fragmentation mode, and suggests that likely more than one single supernova event or efficient dust growth should be invoked to get such a high dust content.
Using a new method--statefinder diagnostic which can differ one dark energy model from the others, we investigate in this letter the dynamics of Born-Infeld(B-I) type dark energy model. The evolutive trajectory of B-I type dark energy with Mexican hat potential model with respect to $e-folding$ time $N$ is shown in the $r(s)$ diagram. When the parameter of noncanonical kinetic energy term $\eta\to0$ or kinetic energy $\dot{\phi}^2\to0$, B-I type dark energy(K-essence) model reduces to Quintessence model or $\Lambda$CDM model corresponding to the statefinder pair $\{r, s\}$=$\{1, 0\}$ respectively. As a result, the the evolutive trajectory of our model in the $r(s)$ diagram in Mexican hat potential is quite different from those of other dark energy models.
Information on dissipation in the entrance channel of heavy-ion collisions is extracted by macroscopic reduction procedure of Time-Dependent Hartree-Fock theory. The method gives access to a fully microscopic description of the friction coefficient associated with transfer of energy from the relative motion towards intrinsic degrees of freedom. The reduced friction coefficient exhibits a universal behavior, i.e. almost independent of systems investigated, whose order of magnitude is comparable with the calculations based on linear response theory. Similarly to nucleus-nucleus potential, especially close to the Coulomb barrier, there are sizable dynamical effects on the magnitude and form factor of friction coefficient.
In this paper we study the Dirichlet problem for Laplace's equation in a domain $\omega_{\epsilon, \eta}$ perforated periodically with small holes in $\mathbb{R}^d$, where $\epsilon$ represents the scale of the minimal distances between holes and $\eta$ the ratio between the scale of sizes of holes and $\epsilon$. We establish $W^{1, p}$ estimates for solutions with bounding constants depending explicitly on $\epsilon$ and $\eta$. The proof relies on a large-scale Lipschitz estimate for harmonic functions in perforated domains. The results are optimal for $d\ge 2$.
The CHIMERA code is a multi-dimensional multi-physics engine dedicated primarily to the simulation of core collapse supernova explosions. One of the most important aspects of these explosions is their capacity to produce gravitational radiation that is detectable by Earth-based laser-interferometric gravitational wave observatories such as LIGO and VIRGO. We present here preliminary gravitational signatures of two-dimensional models with non-rotating progenitors. These simulations exhibit explosions, which are followed for more than half a second after stellar core bounce.
Grain boundaries (GBs) can be used as traps for solute atoms and defects, and the interaction between segregants and GBs is crucial for understanding the properties of nanocrystalline materials. In this study, we have systematically investigated the tendency of Pt to segregate as well as the interaction between Pt and oxygen vacancies at the sigma 3/(111) GB of ceria (CeO2). The Pt atom has a stronger tendency to segregate to the sigma 3/(111) GB than to the (111) and (110) free-standing surfaces, but the tendency is weaker than to the (100) free-standing surface. Mechanic contributions (lattice distortion) play a dominant role in the strong tendency of Pt to segregate. At the Pt-segregated-GB (Pt@GB), oxygen vacancies prefer to form spontaneously near Pt in the GB region. However, at the pristine GB (no Pt and no vacancies), oxygen vacancies form only under O-poor conditions. Thus, Pt segregation to the GB promotes the formation of oxygen vacancies, and their strong interactions enhance the interfacial cohesion. We propose that GBs fabricated close to the surfaces of nanocrystalline ceria can trap Pt from the bulk or other types of surface, resulting in the suppression of the accumulation of Pt on the surface under redox reactions, especially under O-poor conditions.
We report the results of a study of neutrino-carbon interactions at beam energies ranging between few hundreds MeV and few tens of GeV, carried out within the framework of the impulse approximation using a realistic spectral function. The contributions of quasi elastic scattering, resonance production and deep inelastic scattering---consistently obtained, for first time, from a model based on a realistic description of the nuclear ground state---are compared and analyzed.
With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in terms of the corresponding solutions of the nonlinear integral equation. The analytic and asymptotic behaviours of the transfer matrix are studied and given.
We consider four norms on tensor product spaces that have appeared in quantum information theory and demonstrate duality relationships between them. We show that the product numerical radius is dual to the robustness of entanglement, and we similarly show that the S(k)-norm is dual to the projective tensor norm. We show that, analogous to how the product numerical radius and the S(k)-norm characterize k-block positivity of operators, there is a natural version of the projective tensor norm that characterizes Schmidt number. In this way we obtain an elementary new proof of the cross norm criterion for separability, and we also generalize both the cross norm and realignment criteria to the case of arbitrary Schmidt number.
New photometric material is presented for 6 outer disk supposedly old, Galact ic star clusters: Berkeley 76, Haffner 4, Ruprecht 10, Haffner 7, Haffner 11, and Haffner 15, that are projected against the rich and complex Canis Major overde nsity at $225^o \leq l \leq 248^o $, $-7^o \leq b \leq -2^o$. This CCD data-set, in the UBVI pass-bands, is used to derive their fundamental parameters, in particular age and distance. Four of the program clusters turn out to be older than 1 Gyr. This fact makes them ideal targets for future spectroscopic campaigns aiming at deriving their metal abundances. This, in turn, contributes to increase the number of well-studied outer disk o ld open clusters. Only Haffner 15, previously considered an old cluster, is found to be a young, significantly reddened cluster, member of the Perseus arm in the third Galactic quadrant.   As for Haffner~4, we suggest an age of about half a Gyr. The most interesting result we found is that Berkeley~76 is probably located at more than 17 kpc from the Galactic center, and therefore is among the most peripherical old open clusters so far detected. Besides, for Ruprecht~10 and Haffner~7, which were never studied before, we pr opose ages larger than 1 Gyr. All the old clusters of this sample are scarcely populated and show evidence o f tidal interaction with the Milky Way, and are therefore most probably in advanced st ages of dynamical dissolution.
We introduce two scalar leptoquarks, the SU$(2)_L$ isosinglet denoted $\phi\sim(\mathbf{3}, \mathbf{1}, -1/3)$ and the isotriplet $\varphi\sim(\mathbf{3}, \mathbf{3}, -1/3)$, to explain observed deviations from the standard model in semi-leptonic $B$-meson decays. We explore the regions of parameter space in which this model accommodates the persistent tensions in the decay observables $R_{D^{(*)}}$, $R_{K^{(*)}}$, and angular observables in $b\to s \mu\mu$ transitions. Additionally, we exploit the role of these exotics in existing models for one-loop neutrino mass generation derived from $\Delta L=2$ effective operators. Introducing the vector-like quark $\chi \sim (\mathbf{3}, \mathbf{2}, -5/6)$ necessary for lepton-number violation, we consider the contribution of both leptoquarks to the generation of radiative neutrino mass. We find that constraints permit simultaneously accommodating the flavour anomalies while also explaining the relative smallness of neutrino mass without the need for cancellation between leptoquark contributions. A characteristic prediction of our model is a rate of muon--electron conversion in nuclei fixed by the anomalies in $b \to s \mu \mu$ and neutrino mass; the COMET experiment will thus test and potentially falsify our scenario. The model also predicts signatures that will be tested at the LHC and Belle II.
Several sets of radially propagating null congruence generators are exploited in order to form 3-dimensional marginally trapped surfaces, referred to as black hole and cosmological apparent horizons in a Horava universe. Based on this method, we deal with the characteristics of the 2-dimensional space-like spheres of symmetry and the peculiarities of having trapping horizons. Moreover, we apply this method in standard expanding and contracting FLRW cosmological models of a Horava universe to investigate the conditions under which the extra parameters of the theory may lead to trapped/anti-trapped surfaces both in the future and in the past. We also include the cases of negative time, referred to as the finite past, and discuss the formation of anti-trapped surfaces inside the cosmological apparent horizons.
We obtain formulae for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a characterization of the distribution of the Hessian of the Gaussian field by means of the family of Gaussian orthogonally invariant (GOI) matrices, of which the Gaussian orthogonal ensemble (GOE) is a special case. The obtained formulae depend on the covariance function only through a single parameter (Euclidean space) or two parameters (sphere), and include the special boundary case of random Laplacian eigenfunctions.
New theorems characterizing analytically discs in the Euclidean plane $\RR^2$ are proved. Weighted mean value properties of solutions to the modified Helmholtz equation and harmonic functions are used for this purpose. The presence of a logarithmic weight diminish coefficients in the mean value identities. A weighted mean is also valid for solutions of the Helmholtz equation.