ShantanuT01/DACTYL-Pretraining huggingface dataset:
Jets are defined as impulsive, well-collimated upflows, occurring in different layers of the solar atmosphere with different scales. Their relationship with coronal mass ejections (CMEs), another type of solar impulsive events, remains elusive. Using the high-quality imaging data of AIA/SDO, here we show a well-observed coronal jet event, in which part of the jets, with the embedding coronal loops, runs into a nearby coronal hole (CH) and gets bounced towards the opposite direction. This is evidenced by the flat-shape of the jet front during its interaction with the CH and the V-shaped feature in the time-slice plot of the interaction region. About a half-hour later, a CME initially with a narrow and jet-like front is observed by the LASCO C2 coronagraph, propagating along the direction of the post-collision jet. We also observe some 304 A dark material flowing from the jet-CH interaction region towards the CME. We thus suggest that the jet and the CME are physically connected, with the jet-CH collision and the large- scale magnetic topology of the CH being important to define the eventual propagating direction of this particular jet-CME eruption.
A dynamical model of electroweak pion production reactions in the Delta(1232) region has been extended to include the neutral current contributions for examining the local Quark-Hadron Duality in neutrino-induced reactions and for investigating how the axial N-Delta form factor can be determined by the parity violating asymmetry of N(\vec{e},e') reactions. We first show that the recent data of (e,e') structure functions F_1 and F_2, which exhibit the Quark-Hadron Duality, are in good agreement with our predictions. For possible future experimental tests, we then predict that the structure functions F_1, F_2, and F_3 for (\nu,e) and (\nu,\nu') processes also show the similar Quark-Hadron Duality. The spin dependent structure functions g_1 and g_2 of (e,e') have also been calculated from our model. It is found that the local Quark-Hadron Duality is not seen in the calculated g_1 and g_2, while our results for g_1 and some polarization observables associated with the exclusive p(\vec{e},e' pi) and \vec{p}(\vec{e},e' pi) reactions are in reasonably good agreement with the recent data. In the investigation of parity violating asymmetry A of N(\vec{e},e') reactions, it is found that the non-resonant contribution is small at the Delta peak and a measurement of A can be used to distinguish two previously determined axial N-Delta transition form factors. The predicted asymmetry A are also compared with the Parton Model predictions for future experimental investigations of Quark-Hadron Duality.
We analyze the geometrical structure of the passage times in the last passage percolation model. Viewing the passage time as a piecewise linear function of the weights we determine the domains of the various pieces, which are the subsets of the weight space that make a given path the longest one. We focus on the case when all weights are assumed to be positive, and as a result each domain is a pointed polyhedral cone. We determine the extreme rays, facets, and two-dimensional faces of each cone, and also review a well-known simplicial decomposition of the maximal cones via the so-called order cone. All geometric properties are derived using arguments phrased in terms of the last passage model itself. Our motivation is to understand path probabilities of the extremal corner paths on boxes in $\Z^2$, but all of our arguments apply to general, finite partially ordered sets.
Observations of a relation between continuum intensity and magnetic field strength in sunspots have been made during nearly five decades. This work presents full-Stokes measurements of the full-split (g = 3) line Fe I 1564.85 nm with spatial resolution of 0.5" obtained with the GREGOR Infrared Spectrograph in three large sunspots. The continuum intensity is corrected for instrumental scattered light and the brightness temperature is calculated. Magnetic field strength and inclination are derived directly from the line split and the ratio of Stokes components. The continuum intensity (temperature) relations to the field strength are studied separately in the umbra, light bridges, and penumbra. The results are consistent with previous studies and it was found that the scatter of values in the relations increases with increasing spatial resolution thanks to resolved fine structures. The observed relations show trends common for the umbra, light bridges, and the inner penumbra, while the outer penumbra has a weaker magnetic field compared to the inner penumbra at equal continuum intensities. This fact can be interpreted in terms of the interlocking comb magnetic structure of the penumbra. A comparison with data obtained from numerical simulations was made. The simulated data have a generally stronger magnetic field and a weaker continuum intensity than the observations, which may be explained by stray light and limited spatial resolution of the observations and by photometric inaccuracies of the simulations.
Motivated by the recent experiments indicating a spin-unpolarized \nu=0 quantum Hall state in graphene, we theoretically investigate the ground state based on the many-body problem projected onto the n=0 Landau level. For an effective model with the on-site Coulomb repulsion and antiferromagnetic exchange couplings, we show that the ground state is a doubly-degenerate spin-resolved chiral condensate in which all the zero-energy states with up spin are condensed into one chirality, while those with down spin to the other. This can be exactly shown for an Ising-type exchange interaction. The charge gap due to the on-site repulsion in the ground state is shown to grow linearly with the magnetic field, in qualitative agreement with the experiments.
Within the framework of the internal shock model, we study the luminosity and the variability in gamma-ray bursts from collimated fireballs. In particular we pay attention to the role of the photosphere due to $e^\pm$ pairs produced by internal shock synchrotron photons. It is shown that the observed Cepheid-like relationship between the luminosity and the variability can be interpreted as a correlation between the opening angle of the fireball jet and the mass included at the explosion with a standard energy output. We also show that such a correlation can be a natural consequence of the collapsar model. Using a multiple-shell model, we numerically calculate the temporal profiles of gamma-ray bursts. Collimated jets, in which the typical Lorentz factors are higher than in wide jets, can produce more variable temporal profiles due to smaller angular spreading time scales at the photosphere radius. Our simulations quantitatively reproduce the observed correlation.
The three--dimensional incompressible viscous Boussinesq equations, under the assumption of hydrostatic balance, govern the large scale dynamics of atmospheric and oceanic motion, and are commonly called the primitive equations. To overcome the turbulence mixing a partial vertical diffusion is usually added to the temperature advection (or density stratification) equation. In this paper we prove the global regularity of strong solutions to this model in a three-dimensional infinite horizontal channel, subject to periodic boundary conditions in the horizontal directions, and with no-penetration and stress-free boundary conditions on the solid, top and bottom, boundaries. Specifically, we show that short time strong solutions to the above problem exist globally in time, and that they depend continuously on the initial data.
The Bak-Tang-Wiesenfeld sandpile model provdes a simple and elegant system with which to demonstate self-organized criticality. This model has rather remarkable mathematical properties first elucidated by Dhar. I demonstrate some of these properties graphically with a simple computer simulation.
Millihertz quasi-periodic oscillations reported in three neutron-star low mass X-ray binaries have been suggested to be a mode of marginally stable nuclear burning on the neutron star surface. In this Letter, we show that close to the transition between the island and the banana state, 4U~1636--53 shows mHz QPOs whose frequency systematically decreases with time until the oscillations disappear and a Type I X-ray burst occurs. There is a strong correlation between the QPO frequency $\nu$ and the occurrence of X-ray bursts: when $\nu\gtrsim9$ mHz no bursts occur, while $\nu\lesssim9$ mHz does allow the occurrence of bursts. The mHz QPO frequency constitutes the first identified observable that can be used to predict the occurrence of X-ray bursts. If a systematic frequency drift occurs, then a burst happens within a few kilo-seconds after $\nu$ drops below 9 mHz. This observational result confirms that the mHz QPO phenomenon is intimately related with the processes that lead to a thermonuclear burst.
By means of a projector-operator formalism we derive an approximation based on a self consistent hybridization expansion to study the ground state properties of the Anderson Impurity model. We applied the approximation to the general case of finite Coulomb repulsion $U$, extending previous work with the same formalism in the infinite-$U$ case. The treatment provides a very accurate calculation of the ground state energy and their related zero temperature properties in the case in which $U$ is large enough, but still finite, as compared with the rest of energy scales involved in the model. The results for the valence of the impurity are compared with exact results that we obtain from equations derived using the Bethe ansatz and with a perturbative approach. The magnetization and magnetic susceptibility is also compared with Bethe ansatz results. In order to do this comparison, we also show how to regularize the Bethe ansatz integral equations necessary to calculate the impurity valence, for arbitrary values of the parameters.
The binary sum-of-digits function $s$ counts the number of ones in the binary expansion of a nonnegative integer. For any nonnegative integer $t$, T.~W.~Cusick defined the asymptotic density $c_t$ of integers $n\geq 0$ such that \[s(n+t)\geq s(n).\] In 2011, he conjectured that $c_t>1/2$ for all $t$ -- the binary sum of digits should, more often than not, weakly increase when a constant is added. In this paper, we prove that there exists an explicit constant $M_0$ such that indeed $c_t>1/2$ if the binary expansion of $t$ contains at least $M_0$ maximal blocks of contiguous ones, leaving open only the "initial cases" -- few maximal blocks of ones -- of this conjecture. Moreover, we sharpen a result by Emme and Hubert (2019), proving that the difference $s(n+t)-s(n)$ behaves according to a Gaussian distribution, up to an error tending to $0$ as the number of maximal blocks of ones in the binary expansion of $t$ grows.
Massive galaxies in the distant Universe form stars at much higher rates than today. Although direct resolution of the star forming regions of these galaxies is still a challenge, recent molecular gas observations at the IRAM Plateau de Bure interferometer enable us to study the star formation efficiency on subgalactic scales around redshift z = 1.2. We present a method for obtaining the gas and star formation rate (SFR) surface densities of ensembles of clumps composing galaxies at this redshift, even though the corresponding scales are not resolved. This method is based on identifying these structures in position-velocity diagrams corresponding to slices within the galaxies. We use unique IRAM observations of the CO(3-2) rotational line and DEEP2 spectra of four massive star forming distant galaxies - EGS13003805, EGS13004291, EGS12007881, and EGS13019128 in the AEGIS terminology - to determine the gas and SFR surface densities of the identifiable ensembles of clumps that constitute them. The integrated CO line luminosity is assumed to be directly proportional to the total gas mass, and the SFR is deduced from the [OII] line. We identify the ensembles of clumps with the angular resolution available in both CO and [OII] spectroscopy; i.e., 1-1.5". SFR and gas surface densities are averaged in areas of this size, which is also the thickness of the DEEP2 slits and of the extracted IRAM slices, and we derive a spatially resolved Kennicutt-Schmidt (KS) relation on a scale of ~8 kpc. The data generally indicates an average depletion time of 1.9 Gyr, but with significant variations from point to point within the galaxies.
Color transparency is the vanishing of initial and final state interactions, predicted by QCD to occur in high momentum transfer quasielastic nuclear reactions. For specific reactions involving nucleons, the initial and final state interactions are expected to be dominated by exchanges of pions. We argue that these interactions are also suppressed in high momentum transfer nuclear quasielastic reactions; this is ``chiral transparency". We show that studies of the $e ^3He \to e'\Delta^{++} nn$ reaction could reveal the influence of chiral transparency.
The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim$_b$, where $b$ is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force.
We propose a scenario to account for the surprising orbital properties of the planet orbiting the metal poor red horizontal branch star HIP 13044. The orbital period of 16.2 days implies that the planet went through a common envelope phase inside the red giant branch (RGB) stellar progenitor of HIP 13044. The present properties of the star imply that the star maintained a substantial envelope mass of 0.3Mo, raising the question of how the planet survived the common envelope before the envelope itself was lost? If such a planet enters the envelope of an RGB star, it is expected to spiral-in to the very inner region within <100yr, and be evaporated or destructed by the core. We speculate that the planet was engulfed by the star as a result of the core helium flash that caused this metal poor star to swell by a factor of ~3-4. The evolution following the core helium flash is very rapid, and some of the envelope is lost due to the interaction with the planet, and the rest of the envelope shrinks within about a hundred years. This is about equal to the spiraling-in time, and the planet survived.
The triaxial dynamics of the quadrupole-deformed rotor model of both the rigid and the irrotational type have been investigated in detail. The results indicate that level patterns and E2 transitional characters of the two types of the model can be matched with each other to the leading order of the deformation parameter $\beta$. Especially, it is found that the dynamical structure of the irrotational type with most triaxial deformation ($\gamma=30^\circ$) is equivalent to that of the rigid type with oblate deformation ($\gamma=60^\circ$), and the associated spectrum can be classified into the standard rotational bands obeying the rotational $L(L+1)$-law or regrouped into a new ground- and $\gamma$-band with odd-even staggering in the new $\gamma$-band commonly recognized as a signature of the triaxiality. The differences between the two types of the model in this case are emphasized especially on the E2 transitional characters.
We construct approximate transport maps for perturbative several-matrix models. As a consequence, we deduce that local statistics have the same asymptotic as in the case of independent GUE or GOE matrices, i.e., they are given by the Sine-kernel in the bulk and the Tracy-Widom distribution at the edge. Moreover, we prove universality for the local statistics of eigenvalues of self-adjoint polynomials in several independent GUE or GOE matrices which are close to the identity.
We present an analysis of K2 short cadence data of 34 M dwarfs which have spectral types in the range M0 - L1. Of these stars, 31 showed flares with a duration between $\sim$10-90 min. Using distances obtained from Gaia DR2 parallaxes, we determined the energy of the flares to be in the range $\sim1.2\times10^{29}-6\times10^{34}$ erg. In agreement with previous studies we find rapidly rotating stars tend to show more flares, with evidence for a decline in activity in stars with rotation periods longer than $\sim$10 days. The rotational modulation seen in M dwarf stars is widely considered to result from a starspot which rotates in and out of view. Flux minimum is therefore the rotation phase where we view the main starspot close to the stellar disk center. Surprisingly, having determined the rotational phase of each flare in our study we find none show any preference for rotational phase. We outline three scenarios which could account for this unexpected finding. The relationship between rotation phase and flare rate will be explored further using data from wide surveys such as NGTS and TESS.
We introduce the notion of lef line bundles on a complex projective manifold. We prove that lef line bundles satisfy the Hard Lefschetz Theorem, the Lefschetz Decomposition and the Hodge-Riemann Bilinear Relations. We study proper holomorphic semismall maps from complex manifolds and prove that, for constant coefficients, the Decomposition Theorem is equivalent to the non-degeneracy of certain intersection forms. We give a proof of the Decomposition Theorem for the complex direct image of the constant sheaf when the domain and the target are projective by proving that the forms in question are non-degenerate. A new feature uncovered by our proof is that the forms are definite.
Using the relativistic MHD code MPI-AMRVAC and a radiative transfer code in post-processing, we explore the influence of the magnetic-field configuration and transverse stratification of an over-pressured jet on its morphology, on the moving shock dynamics, and on the emitted radio light curve. First, we investigate different large-scale magnetic fields with their effects on the standing shocks and on the stratified jet morphology. Secondly, we study the interaction of a moving shock wave with the standing shocks. We calculate the synthetic synchrotron maps and radio light curves and analyse the variability at two frequencies 1 and 15.3 GHz and for several observation angles. Finally, we compare the characteristics of our simulated light curves with radio flares observed from the blazar 3C 273 with OVRO and VLBA in the MOJAVE survey between 2008 and 2019. We find that, in a structured, over-pressured relativistic jet, the presence of the large-scale magnetic field structure changes the properties of the standing shock waves and leads to an opening of the jet. When crossing such standing shocks, moving shock waves accompanying overdensities injected in the base of the jet are causing very luminous radio flares. The observation of the temporal structure of these flares under different viewing angles probes the jet at different optical depths. At 1 GHz and for small angles, the self-absorption caused by the moving shock wave becomes more important and leads to a drop in the observed flux after it interacts with the brightest standing knot. A weak asymmetry is seen in the shape of the simulated flares, resulting from the remnant emission of the shocked standing shocks. The characteristics of the simulated flares and the correlation of peaks in the light curve with the crossing of moving and standing shocks favor this scenario as an explanation of the observed radio flares of 3C 273.
Let $X(s,t), (s,t)\in E$, with $E\subset \mathbb{R}^2$ a compact set, be a centered two dimensional Gaussian random field with continuous trajectories and variance function $\sigma(s,t)$. Denote by $\mathcal{L}=\{(s,t): \sigma(s,t)=\max_{(s',t')\in E}\sigma(s',t')\}$. In this contribution, we derive the exact asymptotics of $\mathbb{P}\left(\sup_{(s,t)\in E}X(s,t)>u\right)$, as $u\to\infty$, under condition that $\mathcal{L}$ is a smooth curve. We illustrate our findings by an application concerned with extremes of the aggregation of two independent fractional Brownian motions.
We introduce a relative refined $\chi_y$-genus for sch\"on subvarieties of algebraic tori. These are rational functions of degree minus the codimension with coefficients in the ring of lattice polytopes. We prove that the relative refined $\chi_y$ turns sufficiently generic intersections into products, and that we can recover the ordinary $\chi_y$-genus by counting lattice points. Applying the tropical Chern character to the relative refined $\chi_y$-genus we obtain a refined tropicalization which is a tropical cycle having rational functions with $\mathbb Q$-coefficients as weights. We prove that the top-dimensional component of the refined tropicalization specializes to the unrefined tropicalization up to sign when setting $y=0$ and show that we can recover the $\chi_y$-genus by integrating the refined tropicalization with respect to a Todd measure.
Brownian dynamics is a popular fine-grained method for simulating systems of interacting particles, such as chemical reactions. Though the method is simple to simulate, it is generally assumed that the dynamics is impossible to solve exactly and analytically, aside from some trivial systems. We here give the first exact analytical solution to a non-trivial Brownian dynamics system: the reaction $A+B\xrightleftharpoons[]{}C$ in equilibrium in one-dimensional periodic space. The solution is a function of the particles' diffusion coefficients, radii, length of space and unbinding distance.
In a recent paper [D. Dantchev, J. Bergnoff, and J. Rudnick, Phys. Rev. E 89, 042116 (2014)] the problem of the Casimir force in the $O(n)$ model on a slab with free boundary conditions, investigated earlier by us [EPL 100, 10004 (2012)], is reconsidered using a mean spherical model with separate constraints for each layer. The authors (i) question the applicability of the Ginzburg-Landau-Wilson approach to the low-temperature regime, arguing for the superiority of their model compared to the family of $\phi^4$ models A and B whose numerically exact solutions we determined both for values of the coupling constant $0<g<\infty$ and $g=\infty$. They (ii) report consistency of their results with ours in the critical region and a strong manifestation of universality, but (iii) point out discrepancies with our results in the region below $T_{\mathrm{c}}$. We show here that (i) is unjustified and prove that our model B with $g=\infty$ is identical to their spherical model. Hence evidence for the reported universality is already contained in our work. Moreover, the results we determined for anyone of the models A and B for various thicknesses $L$ are all numerically exact. (iii) is due to their misinterpretation of our results for the scaling limit. We also show that their low-temperature expansion, which does not hold inside the scaling regime, is limited to temperatures lower than they anticipated.