ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study numerically scaling properties of the distribution of cumulative energy dissipated in an avalanche and the dynamic phase transition in a stochastic directed cellular automaton [B. Tadi\'c and D. Dhar, Phys. Rev. Lett. {\bf 79}, 1519 (1997)] in d=1+1 dimensions. In the critical steady state occurring for the probability of toppling $p\ge p^\star$= 0.70548, the dissipated energy distribution exhibits scaling behavior with new scaling exponents $\tau_E $ and D_E for slope and cut-off energy, respectively, indicating that the sandpile surface is a fractal. In contrast to avalanche exponents, the energy exponents appear to be p- dependent in the region $p^\star \le p <1$, however the product $(\tau_E-1)D_E$ remains universal. We estimate the roughness exponent of the transverse section of the pile as $\chi =0.44\pm 0.04$. Critical exponents characterizing the dynamic phase transition at $p^\star $ are obtained by direct simulation and scaling analysis of the survival probability distribution and the average outflow current. The transition belongs to a new universality class with the critical exponents $\nu_\| =\gamma =1.22 \pm 0.02$, $\beta =0.56\pm 0.02$ and $\nu_\bot = 0.761 \pm 0.029$, with apparent violation of hyperscaling. Generalized hyperscaling relation leads to $\beta + \beta ^\prime = (d-1)\nu_\bot $, where $\beta ^\prime = 0.195 \pm 0.012$ is the exponent governed by the ultimate survival probability.
Herschel-HIFI spectra of H2O towards low-mass protostars show a distinct velocity component not seen in observations from the ground of CO or other species. The aim is to characterise this component in terms of excitation conditions and physical origin. A velocity component with an offset of ~10 km/s detected in spectra of the H2O 110-101 557 GHz transition towards six low-mass protostars in the 'Water in star-forming regions with Herschel' (WISH) programme is also seen in higher-excited H2O lines. The emission from this component is quantified and excitation conditions are inferred using 1D slab models. Data are compared to observations of hydrides (high-J CO, OH+, CH+, C+, OH) where the same component is uniquely detected. The velocity component is detected in all 6 targeted H2O transitions (Eup~50-250K), and in CO 16-15 towards one source, Ser SMM1. Inferred excitation conditions imply that the emission arises in dense (n~5x10^6-10^8 cm^-3) and hot (T~750K) gas. The H2O and CO column densities are ~10^16 and 10^18 cm^-2, respectively, implying a low H2O abundance of 10^-2 with respect to CO. The high column densities of ions such as OH+ and CH+ (both ~10^13 cm^-2) indicate an origin close to the protostar where the UV field is strong enough that these species are abundant. The estimated radius of the emitting region is 100AU. This component likely arises in dissociative shocks close to the protostar, an interpretation corroborated by a comparison with models of such shocks. Furthermore, one of the sources, IRAS4A, shows temporal variability in the offset component over a period of two years which is expected from shocks in dense media. High-J CO gas detected with Herschel-PACS with Trot~700K is identified as arising in the same component and traces the part of the shock where H2 reforms. Thus, H2O reveals new dynamical components, even on small spatial scales in low-mass protostars.
There has been a great deal of debate surrounding the issue of whether it is possible for a single photon to exhibit nonlocality. A number of schemes have been proposed that claim to demonstrate this effect, but each has been met with significant opposition. The objections hinge largely on the fact that these schemes use unobservable initial states and so, it is claimed, they do not represent experiments that could actually be performed. Here we show how it is possible to overcome these objections by presenting an experimentally feasible scheme that uses realistic initial states. Furthermore, all the techniques required for photons are equally applicable to atoms. It should, therefore, also be possible to use this scheme to verify the nonlocality of a single massive particle.
We present a reformulation of the canonical quantization of gravity, as referred to the minisuperspace; the new approach is based on fixing a Gaussian (or synchronous) reference frame and then quantizing the system via the reconstruction of a suitable constraint; then the quantum dynamics is re-stated in a generic coordinates system and it becomes dependent on the lapse function. The analysis follows a parallelism with the case of the non-relativistic particle and leads to the minisuperspace implementation of the so-called {\em kinematical action} as proposed in \cite{M02} (here almost coinciding also with the approach presented in \cite{KT91}). The new constraint leads to a Schr\"odinger equation for the system. i.e. to non-vanishing eigenvalues for the super-Hamiltonian operator; the physical interpretation of this feature relies on the appearance of a ``dust fluid'' (non-positive definite) energy density, i.e. a kind of ``materialization'' of the reference frame. As an example of minisuperspace model, we consider a Bianchi type IX Universe, for which some dynamical implications of the revised canonical quantum gravity are discussed. We also show how, on the classical limit, the presence of the dust fluid can have relevant cosmological issues. Finally we upgrade our analysis by its extension to the generic cosmological solution, which is performed in the so-called long-wavelength approximation. In fact, near the Big-Bang, we can neglect the spatial gradients of the dynamical variables and arrive to implement, in each space point, the same minisuperspace paradigm valid for the Bianchi IX model.
The first and second Born approximation are studied with the path integral representation for $ {\cal T} $ matrix. The $ {\cal T}$ matrix is calculated for Woods-Saxon potential scattering. To make corresponding integrals solvable analytically, an approximate function for the Woods-Saxon potential is used. Finally it shown that the Born series is converge at high energies and orders higher than two in Born approximation series can be neglected.
The suggestion that we occupy a privileged position near the centre of a large, nonlinear, and nearly spherical void has recently attracted much attention as an alternative to dark energy. Putting aside the philosophical problems with this scenario, we perform the most complete and up-to-date comparison with cosmological data. We use supernovae and the full cosmic microwave background spectrum as the basis of our analysis. We also include constraints from radial baryonic acoustic oscillations, the local Hubble rate, age, big bang nucleosynthesis, the Compton y-distortion, and for the first time include the local amplitude of matter fluctuations, \sigma_8. These all paint a consistent picture in which voids are in severe tension with the data. In particular, void models predict a very low local Hubble rate, suffer from an "old age problem", and predict much less local structure than is observed.
Two-dimensional hexagonal boron nitride (h-BN) single crystals with various shapes have been synthesized by chemical vapor deposition over the past several years. Here we report the formation of three-leaf dart (3LD)-shaped single crystals of h-BN on Cu foil by atmospheric-pressure chemical vapor deposition. The leaves of the 3LD-shaped h-BN are as long as 18 {\mu}m and their edges are smooth armchair on one side and stepped armchair on the other. Careful analysis revealed that surface oxygen plays an important role in the formation of the 3LD shape. Oxygen suppressed h-BN nucleation by passivating Cu surface active sites and lowered the edge attachment energy, which caused the growth kinetics to change to a diffusion-controlled mode.
Let $X$ be a normal noetherian scheme and $Z \subseteq X$ a closed subset of codimension $\geq 2$. We consider here the local obstructions to the map $\hat{\pi}_{1}(X\backslash Z) \to \hat{\pi}_{1}(X)$ being an isomorphism. Assuming $X$ has a regular alteration, we prove the equivalence of the obstructions being finite and the existence of a Galois quasi-\'{e}tale cover of $X$, where the corresponding map on fundamental groups is an isomorphism.
Present grids of stellar atmosphere models are the workhorses in interpreting stellar observations, and determining their fundamental parameters. These models rely on greatly simplified models of convection, however, lending less predictive power to such models of late type stars.   We present a grid of improved and more reliable stellar atmosphere models of late type stars, based on deep, 3D, convective, stellar atmosphere simulations. This grid is to be used in general for interpreting observations, and improve stellar and asteroseismic modeling.   We solve the Navier Stokes equations in 3D and concurrent with the radiative transfer equation, for a range of atmospheric parameters, covering most of stellar evolution with convection at the surface. We emphasize use of the best available atomic physics for quantitative predictions and comparisons with observations.   We present granulation size, convective expansion of the acoustic cavity, asymptotic adiabat, as function of atmospheric parameters. These and other results are also available in electronic form.
For a time-dependent classical quadratic oscillator we introduce pairs of real and complex invariants that are linear in position and momentum. Each pair of invariants realize explicitly a canonical transformation from the phase space to the invariant space, in which the action-phase variables are defined. We find the action operator for the time-dependent oscillator via the classical-quantum correspondence. Candidate phase operators conjugate to the action operator are discussed, but no satisfactory ones are found.
We provide a new proof of the known partial regularity result for the optimal transportation map (Brenier map) between two sets. Contrary to the existing regularity theory for the Monge-Amp{\`e}re equation, which is based on the maximum principle, our approach is purely variational. By constructing a competitor on the level of the Eulerian (Benamou-Brenier) formulation, we show that locally, the velocity is close to the gradient of a harmonic function provided the transportation cost is small. We then translate back to the Lagrangian description and perform a Campanato iteration to obtain an $\epsilon$-regularity result.
In 2000 Constantin showed that the incompressible Euler equations can be written in an "Eulerian-Lagrangian" form which involves the back-to-labels map (the inverse of the trajectory map for each fixed time). In the same paper a local existence result is proved in certain H\"older spaces $C^{1,\mu}$.   We review the Eulerian-Lagrangian formulation of the equations and prove that given initial data in $H^s$ for $n\geq2$ and $s>\frac{n}{2}+1$, a unique local-in-time solution exists on the $n$-torus that is continuous into $H^s$ and $C^1$ into $H^{s-1}$. These solutions automatically have $C^1$ trajectories.   The proof here is direct and does not appeal to results already known about the classical formulation. Moreover, these solutions are regular enough that the classical and Eulerian-Lagrangian formulations are equivalent, therefore what we present amounts to an alternative approach to some of the standard theory.
HD 110432 (BZ Cru; B1Ve) is the brightest member of a small group of "gamma Cas analogs" that emit copious hard X-ray flux, punctuated by ubiquitous "flares." To characterize the X-ray time history of this star, we made a series of six RXTE multi-visit observations in 2010 and an extended observation with the XMM-Newton in 2007. We analyzed these new light curves along with three older XMM-Newton observations from 2002--2003. Distributed over five months, the RXTE observations were designed to search for long X-ray modulations over a few months. These observations indeed suggest the presence of a long cycle with P = 226 days and an amplitude of a factor of two. We also used X-ray light curves constructed from XMM-Newton observations to characterize the lifetimes, strengths, and interflare intervals of 1615 flare-like events in the light curves. After accounting for false positive events, we infer the presence of 955 (2002-2003) and 386 (2007) events we identified as flares. Similarly, as a control we measured the same attributes for an additional group of 541 events in XMM-Newton light curves of gamma Cas, which after a similar correction yielded 517 flares. We found that the flare properties of HD 110432 are mostly similar to our control group. In both cases the distribution of flare strengths are best fit with log-linear relations. Both the slopes of these distributions and the flaring frequencies themselves exhibit modest fluctuations. We discovered that some flares in the hard X-ray band of HD 110432 were weak or unobserved in the soft band and vice versa. The light curves also occasionally show rapid curve drop offs that are sustained for hours. We discuss the existence of the long cycle and these flare properties in the backdrop of two rival scenarios to produce hard X-rays, a magnetic star-disk interaction and the accretion of blobs onto a secondary white dwarf.
Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.
Multi-label activity recognition is designed for recognizing multiple activities that are performed simultaneously or sequentially in each video. Most recent activity recognition networks focus on single-activities, that assume only one activity in each video. These networks extract shared features for all the activities, which are not designed for multi-label activities. We introduce an approach to multi-label activity recognition that extracts independent feature descriptors for each activity and learns activity correlations. This structure can be trained end-to-end and plugged into any existing network structures for video classification. Our method outperformed state-of-the-art approaches on four multi-label activity recognition datasets. To better understand the activity-specific features that the system generated, we visualized these activity-specific features in the Charades dataset.
In spatially resolved galaxy observations, star formation rate radial profiles are found to correlate with total specific star formation rates. A central depletion in star formation is thought to correlate with the globally depressed star formation rates of, for example, galaxies within the Green Valley. We present, for the first time, radial specific star formation rate profiles for a statistical sample of simulated galaxies from the Illustris and EAGLE large cosmological simulations. For galaxies on the star-forming sequence, simulated specific star formation rate profiles are in loose agreement with observations, although galaxies from the EAGLE simulation are too centrally peaked, and galaxies from Illustris have a steeper decline at large radii. However, both galaxy samples show centrally concentrated star formation for galaxies in the Green Valley at all galaxy stellar masses, indicating that quenching occurs from the outside-in, in strong conflict with observations of inside-out quenching. These results appear in spite of the different feedback models in these two simulations. We conclude that the distribution of star formation within galaxies is a strong additional constraint for star formation and feedback models in simulations, in particular related to the quenching of star formation.
We investigate the gyrokinetic limit for the Vlasov-Poisson system in two dimensions, in the regime studied by Golse and Saint-Raymond. We present another proof of convergence to the Euler equation under several assumptions on the energy and on the $L^\infty$ norms of the initial data.
We study the nonanalytic behavior of the static spin susceptibility of 2D fermions as a function of temperature and magnetic field. For a generic Fermi liquid, \chi_s (T, H)= const+c_1 max (T,\mu_B|H|), where c_1 is shown to be expressed via complicated combinations of the Landau parameters, rather than via the backscattering amplitude, contrary to the case of the specific heat. Near a ferromagnetic quantum critical point, the field dependence acquires a universal form \chi^{-1}_s(H)= const- c_2|H|^{3/2}$, with $c_2>0$. This behavior implies a first-order transition into a ferromagnetic state.   We establish a criterion for such a transition to win over the transition into an incommensurate phase.
We investigate the motion of the primary beam outside the light cylinder in the pulsar wind. Inside the light cylinder both primary and secondary plasma move along dipole magnetic field lines where their energies can be arbitrary. But at larger distances the theory predicts quasi-radial motion with the velocity exactly corresponding to the drift velocity which cannot be the same for primary and secondary plasma. Hence, the deceleration of the primary beam is to take place simultaneously resulting in the acceleration of the secondary plasma. We investigate this process in the three-fluid MHD approximation and demonstrate that for most pulsars the energy of the beam remains practically unchanged. Only for young radio pulsars (Crab, Vela) essential deceleration up to the energy of the secondary plasma takes place outside the fast magnetosonic surface $r_{\rm F} \sim (10$-$100) R_{\rm L}$, the energy of secondary plasma itself increasing insufficiently.
We consider the simple random walk on the $N$-dimensional integer lattice from the perspective of evaluating asymptotically the duration of play in the multidimensional gambler\apost s ruin problem. We show that, under suitable rescalings, all $p$-moments of exit-times from balls in the $L$-infinity metric, and all $p$-moments of partial-maxima values in this metric, possess associated asymptotic limit expressions, admitting two representations each. We derive for this purpose multidimensional refinements of the corresponding two-folded extension of Erd\H os-Kac theorem, which we revisit to this end. We show in particular a simplifying proof approach, which relies on an application of the optional stopping theorem, and yields the corresponding first-passage times asymptotics in parallel. We observe a direct manner of proof of the relation among the two limit expressions by Brownian motion scaling. We indicate in a manner intended to be brief and comprehensive other known proof approaches for the purposes of comparison and completeness.
We introduce twisted differential calculus of negative level and prove a descent theorem: Frobenius pullback provides an equivalence between finitely presented modules endowed with a topologically quasi-nilpotent twisted connection of level minus one and those of level zero. We explain how this is related to the existence of a Cartier operator on prismatic crystals. For the sake of readability, we limit ourselves to the case of dimension one.
This paper has been withdrawn by the authors. It has been superceded by an improved investigation: "Velocity statistics in vibrated granular media" W. Losert, D.G.W. Cooper, J. Delour, A. Kudrolli, and J.P. Gollub (submitted to Chaos for a special issue on Granular Materials) cond-mat/9901203
We present a new image of the 9.0 GHz radio emission from the extended Chandra Deep Field South. A total of 181 hours of integration with the Australia Telescope Compact Array has resulted in a 0.276 square degree image with a median sensitivity of $\sim$20 $\mu$Jy/beam rms, for a synthesised beam of 4.0 $\times$ 1.3 arcsec. We present a catalogue of the 9.0 GHz radio sources, identifying 70 source components and 55 individual radio galaxies. Source counts derived from this sample are consistent with those reported in the literature. The observed source counts are also generally consistent with the source counts from simulations of the faint radio population. Using the wealth of multiwavelength data available for this region, we classify the faint 9 GHz population and find that 91% are radio loud AGN, 7% are radio quiet AGN and 2% are star forming galaxies. The 9.0 GHz radio sources were matched to 5.5 and 1.4 GHz sources in the literature and we find a significant fraction of flat or inverted spectrum sources, with 36% of the 9 GHz sources having $\alpha_{5.5GHz}^{9.0GHz}$ $>$ -0.3 (for $S \propto \nu^\alpha$). This flat or inverted population is not well reproduced by current simulations of radio source populations.
It has been known for several decades that transport of chemical elements is induced by the process of microscopic atomic diffusion. Yet, the effect of atomic diffusion, including radiative levitation, has hardly been studied in the context of gravity mode pulsations of core-hydrogen burning stars. In this paper, we study the difference in the properties of such modes for models with and without atomic diffusion. We perform asteroseismic modeling of two slowly rotating A- and F-type pulsators, KIC11145123 ($f_{\rm rot} \approx0.010~{\rm d}^{-1}$) and KIC9751996 ($f_{\rm rot} \approx0.0696~{\rm d}^{-1}$), respectively, based on the periods of individual gravity modes. For both stars, we find models whose g-mode periods are in very good agreement with the {\it Kepler\/} asteroseismic data, keeping in mind that the theoretical/numerical precision of present-day stellar evolution models is typically about two orders of magnitude lower than the measurement errors. Using the Akaike Information Criterion (AIC) we have made a comparison between our best models with and without diffusion, and found very strong evidence for signatures of atomic diffusion in the pulsations of KIC11145123. In the case of KIC9751996 the models with atomic diffusion are not able to explain the data as well as the models without it. Furthermore, we compare the observed surface abundances with those predicted by the best fitting models. The observed abundances are inconclusive for KIC9751996, while those of KIC11145123 from the literature can better be explained by a model with atomic diffusion.
We present an improved way for imaging the local density of states with a scanning tunneling microscope, which consists in mapping the surface topography while keeping the differential conductance (d$I$/d$V$) constant. When archetypical C$_{60}$ molecules on Cu(111) are imaged with this method, these so-called iso-d$I$/d$V$ maps are in excellent agreement with theoretical simulations of the isodensity contours of the molecular orbitals. A direct visualization and unambiguous identification of superatomic C$_{60}$ orbitals and their hybridization is then possible.
We construct an Euler system -- a compatible family of global cohomology classes -- for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps holds, this Euler system is non-trivial, and we deduce bounds towards the Iwasawa main conjecture for these Galois representations.