ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show the existence of L\'evy-type stochastic processes in one space dimension with characteristic triplets that are either discontinuous at thresholds, or are stable-like with stability index functions for which the closures of the discontinuity sets are countable. For this purpose, we formulate the problem in terms of a Skorokhod-space martingale problem associated with non-local operators with discontinuous coefficients. These operators are approximated along a sequence of smooth non-local operators giving rise to Feller processes with uniformly controlled symbols. They converge uniformly outside of increasingly smaller neighborhoods of a Lebesgue nullset on which the singularities of the limit operator are located.
Let $X$ be a smooth complex cubic fourfold and let $F$ be the variety of lines of $X$. The variety $F$ is known to be a smooth projective hyperkaehler fourfold, which is moreover endowed with a self rational map $\phi : F -\rightarrow F$ first constructed by C. Voisin. Here we define a filtration of Bloch--Beilinson type on the Chow group of zero-cycles $CH_0(F)$ which canonically splits under the action of $\phi$, thereby answering in this case a question of A. Beauville. Moreover, we show that this filtration is of motivic origin, in the sense that it arises from a Chow--Kuenneth decomposition of the diagonal.
We present the results of initiating a benchmarking scheme that allows for cross-comparison of the efficiencies of black holes used as working substances in heat engines. We use a circular cycle in the p-V plane as the benchmark engine. We test it on Einstein-Maxwell, Gauss-Bonnet, and Born-Infeld black holes. Also, we derive a new and surprising exact result for the efficiency of a special `ideal gas' system to which all the black holes asymptote.
We analyse the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, we show that the ground states form an (N+1) dimensional manifold. We show that the ensemble of ground states is equivalent to that of a solid-on-solid model with continuously variable heights and nearest neighbour interactions, at a finite temperature. For temperature T tending to zero, all ground states have equal weight, and there is no order-by-disorder in this model. We argue that the bond-energy bond-energy correlations at distance R decay as 1/R^2 at zero temperature. This is verified by Monte Carlo simulations. We also discuss the relation to the quantum spin-S Kitaev model for large S, and obtain lower and upper bounds on the ground state energy of the quantum model.
We show that the transverse momentum dependent elliptic flow $v_2(p_T)$ of thermal photons is quite sensitive to the initial formation time ($\tau_0$) of Quark Gluon Plasma (QGP) for semi-central collision of gold nuclei at RHIC \cite{tau}. A smaller value of the formation time or a larger initial temperature leads to a significant increase in the thermal photon radiation from QGP phase, which has a smaller $v_2$. The elliptic flow of thermal photon is dominated by the contribution from the quark matter at intermediate and high $p_T$ range and as a result sum $v_2$ decreases with smaller $\tau_0$ for $p_T \ge 1.5$ GeV. On the other hand we find that the elliptic flow parameter for hadrons depends only marginally on the value of $\tau_0$.
The Hubble Frontier Fields (HFF) are six clusters of galaxies, all showing indications of recent mergers, which have recently been observed for lensed images. As such they are the natural laboratories to study the merging history of galaxy clusters. In this work, we explore the 2D power spectrum of the mass distribution $P_{\rm M}(k)$ as a measure of substructure. We compare $P_{\rm M}(k)$ of these clusters (obtained using strong gravitational lensing) to that of $\Lambda$CDM simulated clusters of similar mass. To compute lensing $P_{\rm M}(k)$, we produced free-form lensing mass reconstructions of HFF clusters, without any light traces mass (LTM) assumption. The inferred power at small scales tends to be larger if (i)~the cluster is at lower redshift, and/or (ii)~there are deeper observations and hence more lensed images. In contrast, lens reconstructions assuming LTM show higher power at small scales even with fewer lensed images; it appears the small scale power in the LTM reconstructions is dominated by light information, rather than the lensing data. The average lensing derived $P_{\rm M}(k)$ shows lower power at small scales as compared to that of simulated clusters at redshift zero, both dark-matter only and hydrodynamical. The possible reasons are: (i)~the available strong lensing data are limited in their effective spatial resolution on the mass distribution, (ii)~HFF clusters have yet to build the small scale power they would have at $z\sim 0$, or (iii)~simulations are somehow overestimating the small scale power.
We use solar neutrino data to derive stringent bounds on Majorana neutrino transition moments (TMs). Such moments, if present, would contribute to the neutrino-electron scattering cross section and hence alter the signal observed in Super-Kamiokande. Using the latest solar neutrino data, combined with the results of the reactor experiment KamLAND, we perform a simultaneous fit of the oscillation parameters and TMs. Furthermore, we include data from the reactor experiments Rovno, TEXONO and MUNU in our analysis, improving significantly the current constraints on TMs. A comparison with previous works shows that our bounds are the strongest and most general results presented up to now. Finally, we perform a simulation of the future Borexino experiment and show that it will improve the bounds from today's data by order of magnitude.
The strong geodetic problem is a recent variation of the geodetic problem. For a graph $G$, its strong geodetic number ${\rm sg}(G)$ is the cardinality of a smallest vertex subset $S$, such that each vertex of $G$ lies on a fixed shortest path between a pair of vertices from $S$. In this paper, the strong geodetic problem is studied on the Cartesian product of graphs. A general upper bound for ${\rm sg}(G \,\square\, H)$ is determined, as well as exact values for $K_m \,\square\, K_n$, $K_{1, k} \,\square\, P_l$, and certain prisms. Connections between the strong geodetic number of a graph and its subgraphs are also discussed.
We consider nonlocal initial boundary value problems with integral boundary conditions for integro-differential first order hyperbolic systems. We prove a general regularity result stating that the $L^2$-generalized solutions become eventually continuous.
The electronic band structure of as-grown and doped graphene grown on the carbon face of SiC is studied by high-resolution angle-resolved photoemission spectroscopy, where we observe both rotations between adjacent layers and AB-stacking. The band structure of quasi-freestanding AB- bilayers is directly compared with bilayer graphene grown on the Si-face of SiC to study the impact of the substrate on the electronic properties of epitaxial graphene. Our results show that the C-face films are nearly freestanding from an electronic point of view, due to the rotations between graphene layers.
The quantum phases of superconductivity and superfluidity are characterised mathematically by the Yang concept of Off-Diagonal Long Range Order (ODLRO), related to the existence of a large eigenvalue of the density matrix. We analyse how the Yang criterion applies for various Hamiltonians commonly employed to describe superfluid-type correlations in atomic nuclei. For like-particle pairing Hamiltonians the behaviour of the largest eigenvalue of two-body density matrix shows a clear evidence for a transition between a normal to a paired phase. However, this is not the case for the isoscalar proton-neutron pairing interactions acting in self-conjugate nuclei.
We present magnetic torque measurements on the Shastry-Sutherland quantum spin system SrCu$_2$(BO$_3$)$_2$ in fields up to 31 T and temperatures down to 50 mK. A new quantum phase is observed in a 1 T field range above the 1/8 plateau, in agreement with recent NMR results. Since the presence of the DM coupling precludes the existence of a true Bose-Einstein condensation and the formation of a supersolid phase in SrCu$_2$(BO$_3$)$_2$, the exact nature of the new phase in the vicinity of the plateau remains to be explained. Comparison between magnetization and torque data reveals a huge contribution of the Dzyaloshinskii-Moriya interaction to the torque response. Finally, our measurements demonstrate the existence of a supercooling due to adiabatic magnetocaloric effects in pulsed field experiments.
The low-order kinematic moments of galaxies, namely bulk flow and shear, enables us to test whether theoretical models can accurately describe the evolution of the mass density field in the nearby Universe. We use the so-called etaMLE maximum likelihood estimator in logdistance space to measure thesemoments from a combined sample of the 2MASS Tully-Fisher (2MTF) survey and the COSMICFLOWS-3 (CF3) compilation. Galaxies common between 2MTF and CF3 demonstrate a small zero-point difference of -0.016+-0.002 dex.We test the etaMLE on 16 mock 2MTF survey catalogues in order to explore how well the etaMLE recovers the true moments, and the effect of sample anisotropy. On the scale size of 37 Mpc/h, we find that the bulk flow of the local Universe is 259 +- 15 km/h in the direction is (l,b)=(300+-4, 23+-3) (Galactic coordinates). The average shear amplitude is 1.7+-0.4 h km/s/Mpc. We use a variable window function to explore the bulk and shear moments as a function of depth. In all cases, the measurements are consistent with the predictions of the L cold dark matter (LCDM) model.
Synthetic antiferromagnets (SAF) have been proposed to replace ferromagnets in magnetic memory devices to reduce the stray field, increase the storage density and improve the thermal stability. Here we investigate the spin-orbit torque in a perpendicularly magnetized Pt/[Co/Pd]/Ru/[Co/Pd] SAF structure, which exhibits completely compensated magnetization and an exchange coupling field up to 2100 Oe. The magnetizations of two Co/Pd layers can be switched between two antiparallel states simultaneously by spin-orbit torque. The magnetization switching can be read out due to much stronger spin-orbit coupling at bottom Pt/[Co/Pd] interface compared to its upper counterpart without Pt. Both experimental and theoretical analyses unravel that the torque efficiency of antiferromagnetic coupled stacks is significantly higher than the ferromagnetic counterpart, making the critical switching current of SAF comparable to the conventional single ferromagnet. Besides adding an important dimension to spin-orbit torque, the efficient switching of completely compensated SAF might advance magnetic memory devices with high density, high speed and low power consumption.
Electric control of magnetism is a prerequisite for efficient and low power spintronic devices. More specifically, in heavy metal/ ferromagnet/ insulator heterostructures, voltage gating has been shown to locally and dynamically tune magnetic properties like interface anisotropy and saturation magnetization. However, its effect on interfacial Dzyaloshinskii-Moriya Interaction (DMI), which is crucial for the stability of magnetic skyrmions, has been challenging to achieve and has not been reported yet for ultrathin films. Here, we demonstrate 130% variation of DMI with electric field in Ta/FeCoB/TaOx trilayers through Brillouin Light Spectroscopy (BLS). Using polar- Magneto-Optical-Kerr-Effect microscopy, we further show a monotonic variation of DMI and skyrmionic bubble size with electric field, with an unprecedented efficiency. We anticipate through our observations that a sign reversal of DMI with electric field is possible, leading to a chirality switch. This dynamic manipulation of DMI establishes an additional degree of control to engineer programmable skyrmion based memory or logic devices.
We consider character sums determined by isogenies of elliptic curves over finite fields. We prove a congruence condition for character sums attached to arbitrary cyclic isogenies, and produce explicit formulas for isogenies of small degree.
We present a procedure for computing the log-canonical threshold of an arbitrary ideal generated by binomials and monomials.   The computation of the log canonical threshold is reduced to the problem of computing the minimum of a function, which is defined in terms of the generators of the ideal. The minimum of this function is attained at some ray of a fan which only depends on the exponents of the monomials appearing in the generators of the ideal.
Past imaging observations of a post-AGB star, HD 161796, have probed different parts of its circumstellar shell which correspond to different epochs of the star's AGB mass loss history. While the overall structure of the shell can be described by an axisymmetric model consisting of three layers of characteristic structure, the mass distribution in the shell appears to rotate its axis of symmetry in a continuous manner. It is thus interesting to observe the halo region of the shell using from far-IR to sub-mm wavelengths and increase the ``time resolution'' during this critical epoch of the star's mass loss history.
Field equations for n-frames h_a{}^\mu that are possible in the theory of absolute parallelism (AP) are considered. The methods of compatibility (or formal integrability) theory enable us to find the non-Lagrangian equation having unusual kind of compatibility conditions, guaranteed by two (not one) identities. This 'unique equation' was not noted explicitly in the classification by Einstein and Mayer of compatible second order equations of AP.   It is shown that some equations of AP (including 'unique equation') can be written in a trilinear form that contains only the matrix of frame density (of some weight) H_a{}^\mu and its derivatives and not inverse (coframe density) matrix. The equations are still regular and involutive for degenerate but finite matrices H_a{}^\mu if rank H_a{}^\mu > 1.
Extremely High Synchrotron Peak (EHSP) blazars are observed to form a small population of sources with high energy hump peaking at TeV energies in their broad-band spectral energy distributions. The observed gamma-ray emission from these sources at GeV-TeV energies is described by unusual hard spectral indices. The observed spectral and temporal characteristics of these sources challenge the standard leptonic models for the broad-band emissions from blazars. Therefore, such sources provide astrophysical sites to investigate directly the particle acceleration, cooling of relativistic particles and indirectly probe the cosmological quantities like extragalactic background light (EBL) and intergalactic magnetic field (IMF) in the Universe. In this study, we investigate the spectral properties of the gamma-ray emission from EHSP blazars using observations from the Fermi-LAT catalogues (3FGL and 3FHL) along with the TeV observations using ground based telescopes. The observed TeV gamma-ray spectra are corrected for the EBL absorption using the most recent and updated EBL models to determine the intrinsic spectrum at the source. The intrinsic TeV spectra are combined with the MeV-GeV observations from the Fermi-LAT to study the gamma-ray emission from EHSP blazars in the broad energy band. The intrinsic gamma-ray spectra are then used to estimate the position of high energy peak in the spectral energy distribution. We also present the qualitative description for the observed spectral properties of EHSP blazars using different physical scenarios and discuss their importance for the upcoming CTA observatory.
This paper addresses the existence and regularity of weak solutions for a fully parabolic model of chemotaxis, with prevention of overcrowding, that degenerates in a two-sided fashion, including an extra nonlinearity represented by a $p$-Laplacian diffusion term. To prove the existence of weak solutions, a Schauder fixed-point argument is applied to a regularized problem and the compactness method is used to pass to the limit. The local H\"older regularity of weak solutions is established using the method of intrinsic scaling. The results are a contribution to showing, qualitatively, to what extent the properties of the classical Keller-Segel chemotaxis models are preserved in a more general setting. Some numerical examples illustrate the model.
We present a catalog of sources detected above 10 GeV by the Fermi Large Area Telescope (LAT) in the first 7 years of data using the Pass 8 event-level analysis. This is the Third Catalog of Hard Fermi-LAT Sources (3FHL), containing 1556 objects characterized in the 10 GeV - 2 TeV energy range. The sensitivity and angular resolution are improved by factors of 3 and 2 relative to the previous LAT catalog at the same energies (1FHL). The vast majority of detected sources (79%) are associated with extragalactic counterparts at other wavelengths, including 16 sources located at very high redshift ($z>2$). Eight percent of the sources have Galactic counterparts and 13% are unassociated (or associated with a source of unknown nature). The high-latitude sky and the Galactic plane are observed with a flux sensitivity of 4.4 to 9.5$\times 10^{-11}$ ph cm$^{-2}$ s$^{-1}$, respectively (this is approximately 0.5% and 1% of the Crab Nebula flux above 10 GeV). The catalog includes 214 new $\gamma$-ray sources. The substantial increase in the number of photons (more than 4 times relative to 1FHL and 10 times to 2FHL) also allows us to measure significant spectral curvature for 32 sources and find flux variability for 163 of them. Furthermore, we estimate that for the same flux limit of $10^{-12}$ erg cm$^{-2}$ s$^{-1}$, the energy range above 10 GeV has twice as many sources as above 50 GeV, highlighting the importance, for future Cherenkov telescopes, of lowering the energy threshold as much as possible.
Synchrotron X-ray emission from the rims of young supernova remnants allows us to study the high-energy tail of the electrons accelerated at the shock front. The analysis of X-ray spectra can provide information on the physical mechanisms that limit the energy achieved by the electrons in the acceleration process. We aim at verifying whether the maximum electron energy in SN 1006 is limited by synchrotron losses and at obtaining information on the shape of the cutoff in the X-ray synchrotron emission. We analyzed the deep observations of the XMM-Newton SN 1006 Large Program. We performed spatially resolved spectral analysis of a set of small regions in the nonthermal limbs and studied the X-ray spectra by adopting models that assume different electron spectra. We found out that a loss-limited model provides the best fit to all the spectra and this indicates that the shape of the cutoff in the electron momentum (p) distribution has the form exp[-(p/p_cut)^2]. We also detected residual thermal emission from shocked ambient medium and confirmed the reliability of previous estimates of the post-shock density. Our results indicate that radiative losses play a fundamental role in shaping the electron spectrum in SN 1006.
We study the exterior product on 0-cycles modulo rational equivalence, and prove some nonvanishing results. The main tools used are higher cycle- and Abel-Jacobi- classes developed in articles of J. Lewis and the author. A theorem of Rosenschon-Saito (in the case of 0-cycles) is a special case of our results.
We examine high-resolution gravitational N-body simulations of the $\Omega=1$ cold dark matter (CDM) model in order to determine whether there is any normalization of the initial density fluctuation spectrum that yields acceptable results for galaxy clustering and velocities. Dense dark matter halos in the evolved mass distribution are identified with luminous galaxies; the most massive halos are also considered as sites for galaxy groups, with a range of possibilities explored for the group mass to light ratios. We verify the earlier conclusions of White et al. (1987) for the low amplitude (high bias) CDM model --- the galaxy correlation function is marginally acceptable but that there are too many galaxies. We also show that the peak biasing method does not accurately reproduce the results obtained using dense halos identified in the simulations themselves. The COBE anisotropy implies a higher normalization, resulting in problems with excessive pairwise galaxy velocity dispersion unless a strong velocity bias is present. Although we confirm the strong velocity bias of halos reported by Couchman \& Carlberg (1992), we show that the galaxy motions are still too large on small scales. We find no amplitude for which the CDM model can reconcile simultaneously the galaxy correlation function, the low pairwise velocity dispersion, and the richness distribution of groups and clusters. With the normalization implied by COBE, the CDM spectrum has too much power on small scales if $\Omega=1$.
The ground--state magnetic phase diagram is investigated for the two-- and three--dimensional $t$--$t'$ Hubbard model. We take into account commensurate ferro--, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often missed in previous investigations. We trace the influence of correlation effects on the stability of both spiral and collinear magnetic order by comparing the results of employing both the generalized non-correlated mean--field (Hartree--Fock) approximation and generalized slave boson approach by Kotliar and Ruckenstein with correlation effects included. We found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistic large Hubbard $U$, if the correlation effects are taken into account. The electronic phase separation plays an important role in the formation of magnetic states and corresponding regions are wide, especially in the vicinity of half--filling. The details of magnetic ordering for different cubic lattices are discussed.
Zeckendorf proved that every positive integer has a unique partition as a sum of non-consecutive Fibonacci numbers. Similarly, every natural number can be partitioned into a sum of non-consecutive terms of the Lucas sequence, although such partitions need not be unique. In this paper, we prove that a natural number can have at most two distinct non-consecutive partitions in the Lucas sequence, find all positive integers with a fixed term in their partition, and calculate the limiting value of the proportion of natural numbers that are not uniquely partitioned into the sum of non-consecutive terms in the Lucas sequence.
This submission to arXiv has been withdrawn by the authors
Geometrical properties of the extreme Kerr black holes in the topological sectors of nonextreme and extreme configurations are studied. We find that the Euler characteristic plays an essential role to distinguish these two kinds of extreme black holes. The relationship between the geometrical properties and the intrinsic thermodynamics are investigated.
The folded spinning string in AdS3 gives us an important insight into AdS/CFT duality. Recently its one-loop energy was analyzed in the context of AdS4/CFT3 by McLoughlin and Roiban arXiv:0807.3965, by Alday, Arutyunov and Bykov arXiv:0807.4400 and by Krishnan arXiv:0807.4561. They computed the spectrum of the fluctuations around the classical solution.   In this paper we reproduce their results using the algebraic curve technique and show that under some natural resummation of the fluctuation energies the one-loop energy agrees perfectly with the predictions of arXiv:0807.0777. This provides a further support of the all-loop Bethe equations and of the AdS4xCP3 algebraic curve developed in arXiv:0807.0437.