ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose an experiment allowing an observation of Zitterbewegung (ZB, trembling motion) of electrons in graphene in the presence of a magnetic field. In contrast to the existing theoretical work we make no assumptions concerning shape of the electron wave packet. A femtosecond Gaussian laser pulse excites electrons from the valence $n=-1$ Landau level into three other levels, creating an oscillating electron wave packet with interband and intraband frequencies. Oscillations of an average position of the packet are directly related to the induced dipole moment and oscillations of the average packet's acceleration determine emitted electric field. Both quantities can be measured experimentally. A broadening of Landau levels is included to make the description of ZB as realistic as possible. Criteria of realization of a ZB experiment are discussed.
A set system is called union closed if for any two sets in the set system their union is also in the set system. Gilmer recently proved that in any union closed set system some element belongs to at least a $0.01$ fraction of sets, and conjectured that his technique can be pushed to the constant $\frac{3-\sqrt{5}}{2}$. We verify his conjecture; show that it extends to approximate union closed set systems, where for nearly all pairs of sets their union belong to the set system; and show that for such set systems this bound is optimal.
A number $n$ is practical if every integer in $[1,n]$ can be expressed as a subset sum of the positive divisors of $n$. We consider the distribution of practical numbers that are also shifted primes, improving a theorem of Guo and Weingartner. In addition, essentially proving a conjecture of Margenstern, we show that all large odd numbers are the sum of a prime and a practical number. We also consider an analogue of the prime $k$-tuples conjecture for practical numbers, proving the "correct" upper bound, and for pairs, improving on a lower bound of Melfi.
By investigating path-distribution dependent stochastic differential equations, the following type of nonlinear Fokker--Planck equations for probability measures $(\mu_t)_{t \geq 0}$ on the path space $\mathcal C:=C([-r_0,0];\mathbb R^d),$ is analyzed: $$\partial_t \mu(t)=L_{t,\mu_t}^*\mu_t,\ \ t\ge 0,$$ where $\mu(t)$ is the image of $\mu_t$ under the projection $\mathcal C\ni\xi\mapsto \xi(0)\in\mathbb R^d$, and $$L_{t,\mu}(\xi):= \frac 1 2\sum_{i,j=1}^d a_{ij}(t,\xi,\mu)\frac{\partial^2} {\partial_{\xi(0)_i} \partial_{\xi(0)_j}}   +\sum_{i=1}^d b_i(t,\xi,\mu)\frac{\partial}{\partial_{\xi(0)_i}},\ \ t\ge 0, \xi\in \mathcal C, \mu\in   \mathcal P^{\mathcal C}.$$ Under reasonable conditions on the coefficients $a_{ij}$ and $b_i$, the existence, uniqueness, Lipschitz continuity in Wasserstein distance, total variational norm and entropy, as well as derivative estimates are derived for the martingale solutions.
We show that the best variational ground state of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model with nearest-neighboring exchange coupling(NN-KAFH) is a $Z_{2}$ spin liquid state, rather than the widely believed $U(1)$ Dirac spin liquid state. The spinon excitation in the $Z_{2}$ spin liquid state has a small gap of about $1/40$ of the spinon band width. We find that while the $Z_{2}$ and the $U(1)$ spin liquid state have a large overlap on finite clusters and are thus very close in energy, they host totally different spinon excitation spectrum. The strength of the RVB theory becomes particularly clear in such a situation, as it provides not only a variational understanding of the ground state structure, but also a comprehensive picture for the excitation spectrum of the system. Our result indicates that the spin-$\frac{1}{2}$ NN-KAFH should be better understood as a nearly critical system, rather than a prototypical gapped $Z_{2}$ spin liquid system.
We investigate basic properties of uniformly rational varieties, i.e. those smooth varieties for which every point has a Zariski open neighborhood isomorphic to an open subset of A^n. It is an open question of Gromov whether all smooth rational varieties are uniformly rational. We discuss some potential criteria that might allow one to show that they form a proper subclass in the class of all smooth rational varieties. Finally we prove that small algebraic resolutions and big resolutions of nodal cubic threefolds are uniformly rational.
(Abridged) We present Herschel/HIFI spectra of the H2O 1113 GHz and H2O+ 1115 GHz lines toward five nearby prototypical starburst/AGN systems, and OH+ 971 GHz spectra toward three of these. The beam size of 20" corresponds to resolutions between 0.35 and 7 kpc. The observed line profiles range from pure absorption (NGC 4945, M82) to P-Cygni indicating outflow (NGC 253, Arp 220) and inverse P-Cygni indicating infall (Cen A). The similarity of the H2O, OH+, and H2O+ profiles to each other and to HI indicates that diffuse and dense gas phases are well mixed. We estimate column densities assuming negligible excitation (for absorption features) and using a non-LTE model (for emission features), adopting calculated collision data for H2O and OH+, and rough estimates for H2O+. Column densities range from ~10^13 to ~10^15 cm^-2 for each species, and are similar between absorption and emission components, indicating that the nuclear region does not contribute much to the emission in these ground-state lines. The N(H2O)/N(H2O+) ratios of 1.4-5.6 indicate an origin of the lines in diffuse gas, and the N(OH+)/N(H2O+) ratios of 1.6-3.1 indicate a low H2 fraction (~11%) in the gas.   Adopting recent Galactic values for the average gas density and the ionization efficiency, we find ionization rates for our sample galaxies of ~3x10^-16 s^-1 which are similar to the value for the Galactic disk, but ~10x below that of the Galactic Center and ~100x below estimates for AGN from excited-state H3O+ lines. We conclude that the ground-state lines of water and its associated ions probe primarily non-nuclear gas in the disks of these centrally active galaxies. Our data thus provide evidence for a decrease in ionization rate by a factor of ~10 from the nuclei to the disks of galaxies, as found before for the Milky Way.
Isotope thermometry, widely used to measure the temperature of a hot nuclear system formed in energetic nuclear collisions, is examined in the light of S-matrix approach to the nuclear equation of state of disassembled nuclear matter. Scattering between produced light fragment pairs, hitherto neglected, is seen to have an important bearing on the extraction of system temperature and volume at freeze-out from isotope thermometry. Taking due care of the scattering effects and decay of the primary fragments, a more reliable way to extract the nuclear thermodynamic parameters is suggested by exploiting least-squares fit to the observed fragment multiplicities.
We argue that the nearly 1/3 suppression of shot noise in nondegenerate diffusive contacts recently obtained by Gonzalez et al. (cond-mat/9803372) is due to the specific choice of the energy-independent elastic scattering time.
To study the role of protosellar jets and outflows in the time evolution of the parent cores and the protostars, the astronomical community needs a large enough data base of infrared images of protostars at the highest spatial resolution possible, to reveal the details of their morphology. Spitzer provides unprecedented sensitivity in the infrared to study both the jet and outflow features, however its spatial resolution is limited by its 0.85m mirror. Here we use a high resolution deconvolution algorithm, "HiRes", to improve the visualization of spatial morphology by enhancing resolution (to sub-arcsecond levels in the IRAC bands) and removing the contaminating sidelobes from bright sources in a sample of 89 protostellar objects. These reprocessed images are useful to detect: (i) wide angle outflow seen in scattered light; (ii) morphological details of H2 emission in jets and bow shocks; and (iii) compact features in MIPS 24 micron images as protostar/ disk and atomic/ionic line emissions associated with the jets. The HiRes fits image data of such a large homogeneous sample presented here will be useful to the community in studying these protostellar objects. To illustrate the utility of this HiRes sample, we show how the opening angle of the wide angle outflows in 31 sources, all observed in the HiRes processed Spitzer images, correlates with age. Our data suggest a power law fit to opening angle versus age with an exponent of ~0.32 and 0.02, respectively for ages less than 8000 yr and greater than 8000 yr.
We review a series of works describing thermoelectric effects in gated disordered nanowires (field effect transistor device configuration). After considering the elastic coherent regime characterizing sub-Kelvin temperatures, we study the inelastic activated regime occurring at higher temperatures, where electronic transport is dominated by phonon-assisted hops between localised states (Mott variable range hopping). The thermoelectric effects are studied as a function of the location of the Fermi level inside the nanowire conduction band, notably around its edges where they become very large. We underline the interest of using electron-phonon coupling around the band edges of large arrays of parallel nanowires for energy harvesting and hot spot cooling at small scales. Multiterminal thermoelectric transport and ratchet effects are eventually considered in the activated regime.
During the training for snowboard big air, one of the most popular winter sports, athletes and coaches extensively shoot and check their jump attempts using a single camera or smartphone. However, by watching videos sequentially, it is difficult to compare the precise difference in performance between two trials. Therefore, side-by-side display or overlay of two videos may be helpful for training. To accomplish this, the spatial and temporal alignment of multiple performances must be ensured. In this study, we propose a conventional but plausible solution using the existing image processing techniques for snowboard big air training. We conducted interviews with expert snowboarders who stated that the spatiotemporally aligned videos enabled them to precisely identify slight differences in body movements. The results suggest that the proposed method can be used during the training of snowboard big air.
We prove global well-posedness for a cubic, non-local Schr\"odinger equation with radially-symmetric initial data in the critical space $L^2(\R^2)$, using the framework of Kenig-Merle and Killip-Tao-Visan. As a consequence, we obtain a global well-posedness result for Schr\"odinger maps from $\R^2$ into $\S^2$ (Landau-Lifshitz equation) with radially symmetric initial data (with no size restriction).
We study the quasiparticle properties of two-dimensional massless Dirac Fermions when the many-body states possess a finite momentum density in the clean limit. The lack of Galilean invariance endows the many-body states at finite momentum density with qualitative differences from those of the system at rest. At finite carrier densities we demonstrate the appearance of a current-induced distortion of the pseudospin texture in momentum space that can be viewed as a drag of the Dirac point and the origin of which lies entirely in electron-electron interactions. We discuss the potential observation of this effect in graphene.
If every vertex in a map has one out of two face-cycle types, then the map is said to be $2$-semiequivelar. A 2-uniform tiling is an edge-to-edge tiling of regular polygons having $2$ distinct transitivity classes of vertices. Clearly, a $2$-uniform map is $2$-semiequivelar. The converse of this is not true in general. There are 20 distinct 2-uniform tilings (these are of $14$ different types) on the plane. In this article, we prove that a $2$-semiequivelar toroidal map $K$ has a finite $2$-uniform cover if the universal cover of $K$ is $2$-uniform except of two types.
In this paper, we study the deformations of Kolyvagin systems that are known to exist in a wide variety of cases, by the work of B. Howard, B. Mazur, and K. Rubin for the residual Galois representations, along the cyclotomic Iwasawa algebra. We prove, under certain technical hypotheses, that a cyclotomic deformation of a Kolyvagin system exists. We also briefly discuss how our techniques could be extended to prove that one could deform Kolyvagin systems for other deformations as well.   We discuss several applications of this result, particularly relation of these $\Lambda$-adic Kolyvagin systems to p-adic L-functions (in view of the conjectures of Perrin-Riou on p-adic L-functions) and applications to main conjectures; also applications to the study of Iwasawa theory of Rubin-Stark units.
Automated scene analysis has been a topic of great interest in computer vision and cognitive science. Recently, with the growth of crowd phenomena in the real world, crowded scene analysis has attracted much attention. However, the visual occlusions and ambiguities in crowded scenes, as well as the complex behaviors and scene semantics, make the analysis a challenging task. In the past few years, an increasing number of works on crowded scene analysis have been reported, covering different aspects including crowd motion pattern learning, crowd behavior and activity analysis, and anomaly detection in crowds. This paper surveys the state-of-the-art techniques on this topic. We first provide the background knowledge and the available features related to crowded scenes. Then, existing models, popular algorithms, evaluation protocols, as well as system performance are provided corresponding to different aspects of crowded scene analysis. We also outline the available datasets for performance evaluation. Finally, some research problems and promising future directions are presented with discussions.
The effective kinematic diagram technique is applied to study inelastic form factors of electron and quark in QED and QCD. The explicit expressions for these form factors in the double-logarithmic approximation are presented. The self-consistency of the results is shown by demonstrating the fulfillment of the Kinoshita-Lee-Nauenberg theorem.
The Faddeev equations for the three-body bound state are solved directly as thre e-dimensional integral equations without employing partial wave decomposition. Two-body forces of the Malfliet-Tjon type and simple spin independent genuine three-body forces are considered for the calculation of the three-body binding energy.
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time fractional equations in metric measure spaces.
Many scaling relations are observed for self-gravitating systems in the universe. We explore the consistent understanding of them from a simple principle based on the proposal that the collision-less dark matter fluid terns into a turbulent state, i.e. dark turbulence, after crossing the caustic surface in the non-linear stage. The dark turbulence will not eddy dominant reflecting the collision-less property. After deriving Kolmogorov scaling laws from Navier-Stokes equation by the method similar to the one for Smoluchowski coagulation equation, we apply this to several observations such as the scale-dependent velocity dispersion, mass-luminosity ratio, magnetic fields, and mass-angular momentum relation, power spectrum of density fluctuations. They all point the concordant value for the constant energy flow per mass: $0.3 cm^2/sec^3$, which may be understood as the speed of the hierarchical coalescence process in the cosmic structure formation.
The calculation results of the evolution of the cluster of primordial black holes based on the Fokker-Planck equation with neglecting of the gas accretion onto black holes are presented. In addition, we consider how a massive black hole located within the cluster center affects on its evolution. Despite it creates an additional potential in the central region of the cluster and might capture surrounding black holes, a negligible growth rate of a central black hole was shown for 1 Gyr. Furthermore, we find a significant (approximately tenfold) expansion of the cluster.
We briefly review and extend our discussion of the ROSAT detection of the extraordinarily luminous (>10^{42} erg/s) partly extended (> 30 kpc diameter) X-ray emission from the double-nucleus ultraluminous infrared galaxy NGC 6240. The ROSAT spectrum can be well fit by emission from two components in roughly equal proportions: a thermal optically thin plasma with kT \sim 0.6 keV and a hard component that can be represented by a canonical AGN powerlaw. Source counts appear to have dropped by 30% within a year. Altogether, these findings can be well explained by a contribution of radiation from an AGN essentially hidden at other wavelengths. Fits of ASCA spectra, conducted by various groups, corroborate this result, revealing a high-equivalent width FeK blend which again is straightforwardly interpreted by scattered AGN light.   If radiating at the Eddington limit, the central black hole mass does not exceed 10^7 M_sun. We discuss implications for the formation of this AGN. However, the luminosity in the remaining extended thermal component is still at the limits of a pure starburst-wind-induced source. We suggest that the deeply buried starburst has switched to a partially dormant phase so that heating of the outflow is diminished and a cooling flow could have been established. This flow may account for the extended shock heating traced by LINER-like emission line ratios and the extremely luminous H_2 emission from the central region of this galaxy. Next-generation X-ray telescopes will be able to test this proposal.
Transition voltage spectroscopy (TVS) has recently been introduced as a spectroscopic tool for molecular junctions where it offers the possibility to probe molecular level energies at relatively low bias voltages. In this work we perform extensive ab-initio calculations of the non-linear current voltage relations for a broad class of single-molecule transport junctions in order to assess the applicability and limitations of TVS. We find, that in order to fully utilize TVS as a quantitative spectroscopic tool, it is important to consider asymmetries in the coupling of the molecule to the two electrodes. When this is taken properly into account, the relation between the transition voltage and the energy of the molecular orbital closest to the Fermi level closely follows the trend expected from a simple, analytical model.
In this paper, we consider the uniqueness of solutions to the 3d Navier-Stokes equations with initial vorticity given by $\omega_0 = \alpha e_z \delta_{x = y = 0}$, where $\delta_{x=y= 0}$ is the one dimensional Hausdorff measure of an infinite, vertical line and $\alpha \in \mathbb R$ is an arbitrary circulation. This initial data corresponds to an idealized, infinite vortex filament. One smooth, mild solution is given by the self-similar Oseen vortex column, which coincides with the heat evolution. Previous work by Germain, Harrop-Griffiths, and the first author implies that this solution is unique within a class of mild solutions that converge to the Oseen vortex in suitable self-similar weighted spaces. In this paper, the uniqueness class of the Oseen vortex is expanded to include any solution that converges to the initial data in a sufficiently strong sense. This gives further evidence in support of the expectation that the Oseen vortex is the only possible mild solution that is identifiable as a vortex filament. The proof is a 3d variation of a 2d compactness/rigidity argument in $t \searrow 0$ originally due to Gallagher and Gallay.
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the authors prove that some associated estimators are unbiased, for each value of the size n of the systems of replicas and of resampling number k. Here we go beyond and prove these estimator's asymptotic normality when h goes to infinity, for any fixed value of k. The main ingredient is the asymptotic analysis of a functional equation on an appropriate characteristic function. Some numerical simulations illustrate the convergence to rely on Gaussian confidence intervals.
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through the spherical harmonic coefficients. We construct a couple of wavelets as an extension of the flat Mexican Hat Wavelet to the sphere and we apply them to the detection of sources on the sphere. We remark that no projections are used with this methodology.
Margot (1994) in his doctoral dissertation studied extended formulations of combinatorial polytopes that arise from "smaller" polytopes via some composition rule. He introduced the "projected faces property" of a polytope and showed that this property suffices to iteratively build extended formulations of composed polytopes.   For the composed polytopes, we show that an extended formulation of the type studied in this paper is always possible only if the smaller polytopes have the projected faces property. Therefore, this produces a characterization of the projected faces property.   Affinely generated polyhedral relations were introduced by Kaibel and Pashkovich (2011) to construct extended formulations for the convex hull of the images of a point under the action of some finite group of reflections. In this paper we prove that the projected faces property and affinely generated polyhedral relation are equivalent conditions.
This volume presents an overview of selected aspects of physical processes occurring in the inner regions of Active Galactic Nuclei (AGN). The observational evidence suggests that strong gravitational fields play a significant role in governing the energy output of AGN and their influence on the surrounding medium, possibly due to the presence of a supermassive black hole. In order to reduce an unnecessary overlap with numerous reviews on the subject of AGN, here we focus on several selected topics.
Supersymmetric (SUSY) models with R-parity generically predict sparticle decays with invisible neutralinos, which yield distinctive missing energy events at colliders. Since most LHC searches are designed with this expectation, the putative bounds on sparticle masses become considerably weaker if R-parity is violated so that squarks and gluinos decay to jets with large QCD backgrounds. Here we introduce a scenario in which baryonic R-parity violation (RPV) arises effectively from soft SUSY-breaking interactions, but leptonic RPV remains accidentally forbidden to evade constraints from proton decay and FCNCs. The model features a global R-symmetry that initially forbids RPV interactions, a hidden R-breaking sector, and a heavy mediator that communicates this breaking to the visible sector. After R-symmetry breaking, the mediator is integrated out and an effective RPV A-term arises at tree level; RPV couplings between quarks and squarks arise only at loop level and receive additional suppression. Although this mediator must be heavy compared to soft masses, the model introduces no new hierarchy since viable RPV can arise when the mediator mass is near the SUSY breaking scale. In generic regions of parameter space, a light thermally-produced gravitino is stable and can be a viable dark matter candidate.