ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that particle positions and momenta grow unbounded as $t \to \infty$ and obtain sharp rates on the maximal values of these quantities on the support of the distribution function for each system. Furthermore, we establish nearly sharp rates of decay for the associated electric field, as well as upper and lower bounds on the decay rate of the charge density in the large time limit. We prove that, unlike (VP) in higher dimensions, smooth solutions do not scatter to their free-streaming profiles as $t \to \infty$ because nonlinear, long-range field interactions dominate the behavior of characteristics due to the exchange of energy from the potential to the kinetic term. In this way, the system may "forget" any previous configuration of particles.
We present a model to estimate the effect of differential magnification on the SED of high-z ULIRGs. It is found that the ratio of the high temperature component to the low temperature component can vary with up to a factor of ten with source position on very small angular scales ~0.01". This means that a correction for differential magnification is needed when deriving dust properties from strongly lensed sources.
For $\,0<\alpha\le \infty$, new subclasses $\,\mathcal{U}^{<\alpha>}$ of the class $\,\mathcal{U}$, of s-selfdecomposable probability measures, are studied. They are described by random integrals, by their characteristic functions and their L\'evy spectral measures. Also their relations with the classical L\'evy class $L$ of selfdecomposable distributions are investigated.
We present spectrophotometry of the eclipsing nova-like variable SW Sex. The continuum is deeply eclipsed and shows asymmetries due to the presence of a bright spot. We derive a new ephemeris and, by measuring the eclipse width, we are able to constrain the inclination to i > 75^o and the disc radius to R_D > 0.6 L_1. In common with other members of its class (of which it is the proto-type), SW Sex shows single-peaked emission lines which show transient absorption features and large phase shifts in their radial velocity curves. In addition, the light curves of the emission lines show a reduction in flux around phase 0.5 and asymmetric eclipse profiles which are not as deep as the continuum eclipse. Using Doppler tomography, we find that most of the line emission in SW Sex appears to originate from three sources: the secondary star, the accretion disc and an extended bright spot. The detection of the red star allows us to constrain the radial-velocity semi-amplitude of the secondary to K_R > 180 km/s and hence the component masses to M_1 = 0.3-0.7 Msun and M_2 < 0.3 Msun.
Magnetic activity in Sun-like and low-mass stars causes X-ray coronal emission, which is stronger for more rapidly rotating stars. This relation is often interpreted in terms of the Rossby number, i.e., the ratio of rotation period to convective overturn time. We reconsider this interpretation on the basis of the observed X-ray emission and rotation periods of 821 stars with masses below 1.4 Msun. A generalized analysis of the relation between X-ray luminosity normalized by bolometric luminosity, L_X/L_bol, and combinations of rotational period, P, and stellar radius, R, shows that the Rossby formulation does not provide the solution with minimal scatter. Instead, we find that the relation L_X/L_bol ~ P^{-2}R^{-4} optimally describes the non-saturated fraction of the stars. This relation is equivalent to L_X ~ P^{-2}, indicating that the rotation period alone determines the total X-ray emission. Since L_X is directly related to the magnetic flux at the stellar surface, this means that the surface flux is determined solely by the star's rotation and is independent of other stellar parameters. While a formulation in terms of a Rossby number would be consistent with these results if the convective overturn time scales exactly as L_bol^{-1/2}, our generalized approach emphasizes the need to test a broader range of mechanisms for dynamo action in cool stars.
A lot of efforts have been devoted to understanding the origin and effects of magnetic moments induced in graphene with carbon atom vacancy, or light adatoms like hydrogen or fluorine. At the meantime, the large negative magnetoresistance (MR) widely observed in these systems is not well understood, nor had it been associated with the presence of magnetic moments. In this paper, we study the systematic evolution of the large negative MR of in-situ hydrogenated graphene in ultra-high vacuum (UHV) environment. We find for most combination of electron density ($n_e$) and hydrogen density ($n_H$), MR at different temperature can be scaled to $\alpha=(\mu_BB)/[k_B(T-T^*)]$, where $T^*$ is the Curie-Weiss temperature. The sign of $T^*$ indicates the existence of tunable ferromagnetic-like ($T^* >0$) and anti-ferromagnetic-like ($T^* <0$) coupling in hydrogenated graphene. However, the lack of hysteresis of MR or anomalous Hall effect below $|T^*|$ points to the fact that long-range magnetic order did not emerge, which we attribute to the competition of different magnetic orders and disordered arrangement of magnetic moments on graphene. We also find that localized impurity states introduced by H adatoms could modify the capacitance of hydrogenated graphene. This work provides a new way to extract information from large negative MR behavior and can be a key to help understanding interactions of magnetic moments in graphene.
The Abel-Jacobi map of the family of elliptic quintics lying on a general cubic threefold is studied. It is proved that it factors through a moduli component of stable rank 2 vector bundles on the cubic threefold with Chern numbers c_1=0, c_2=2, whose general point represents a vector bundle obtained by Serre's construction from an elliptic quintic. The elliptic quintics mapped to a point of the moduli space vary in a 5-dimensional projective space inside the Hilbert scheme of curves, and the map from the moduli space to the intermediate Jacobian is \'etale. As auxiliary results, the irreducibility of families of elliptic normal quintics and of rational normal quartics on a general cubic threefold is proved. This implies the uniqueness of the moduli component under consideration. The techniques of Clemens-Griffiths and Welters are used for the calculation of the infinitesimal Abel-Jacobi map.
We present a complete analysis of the electric dipole moment (EDM) of the \rho-meson induced by CP violating operators of dimension 4 and 5 within the QCD sum rules approach. The set of CP-odd operators includes the theta term and the electric and chromoelectric dipole moments of the three light quarks. We find that the \rho-meson EDM induced purely by the EDMs of quarks is smaller, but still in reasonable agreement, with the predictions of a naive constituent quark model. However, the chromoelectric dipole moments, including that of the strange quark, give comparable and sometimes larger contributions. We also consider the effect on the hadronic EDM of the existence of Peccei-Quinn symmetry. When this symmetry is active, chromoelectric dipole moments induce a linear term in the axion potential which leads to a numerically important vacuum contribution to the hadronic EDM.
Based on the investigation of the multi-terminal conductance of a system composed of two graphene nanoribbons, in which one is on top of the other and rotated by 60 degrees, we propose a setup for a 50/50 electronic beam splitter that neither requires large magnetic fields nor ultra low temperatures. Our findings are based on an atomistic tight-binding description of the system and on the Green's function method to compute the Landauer conductance. We demonstrate that this system acts as a perfect 50/50 electronic beam splitter, in which its operation can be switched on and off by varying the doping (Fermi energy). We show that this device is robust against thermal fluctuations and long range disorder, as zigzag valley chiral states of the nanoribbons are protected against backscattering. We suggest that the proposed device can be applied as the fundamental element of the Hong-Ou-Mandel interferometer, as well as a building block of many devices in electron optics.
This article is divided in two parts. In the first part we endow a certain ring of ``Drinfeld quasi-modular forms'' for $\GL_2(\FF_q[T])$ (where $q$ is a power of a prime) with a system of "divided derivatives" (or hyperderivations). This ring contains Drinfeld modular forms as defined by Gekeler in \cite{Ge}, and the hyperdifferential ring obtained should be considered as a close analogue in positive characteristic of famous Ramanujan's differential system relating to the first derivatives of the classical Eisenstein series of weights 2, 4 and 6. In the second part of this article we prove that, when $q\not=2,3$, if ${\cal P}$ is a non-zero hyperdifferential prime ideal, then it contains the Poincar\'e series $h=P_{q+1,1}$ of \cite{Ge}. This last result is the analogue of a crucial property proved by Nesterenko \cite{Nes} in characteristic zero in order to establish a multiplicity estimate.
The precessional magnetization dynamics of GaMnAs thin films are characterized by broadband network analyzer ferromagnetic resonance (FMR) in a coplanar geometry at cryogenic temperatures. The FMR frequencies are characterized as function of in-plane field angle and field amplitude. Using an extended Kittel model of the FMR dispersion the magnetic film parameters such as saturation magnetization and anisotropies are derived. The modification of the FMR behavior and of the magnetic parameters of the thin film upon annealing is analyzed.
A Regge-inspired model is used to discuss the hard exclusive two-body hadronic reactions (pbar p ----> pi+ pi-, pi0 pi0, K+ K-, Kbar0 K0) for the FAIR facility project at GSI with the Panda detector. The comparison between the differential cross sections predictions and the available data is shown to determine the values of the few parameters of the model.
The relaxation process of electron spin in systems of electrons interacting with piezoelectric deformation phonons that are mediated through spin-orbit interactions was interpreted from a microscopic point of view using the formula for the electron spin relaxation times derived by a projection-reduction method. The electron spin relaxation times in two polymorphic structures of GaN were calculated. The piezoelectric material constant for the wurtzite structure obtained by a comparison with a previously reported experimental result was P_pe=1.5 x 10^29 eV/m. The temperature and magnetic field dependence of the relaxation times for both wurtzite and zinc-blende structures were similar, but the relaxation times in zinc-blende GaN were smaller and decreased more rapidly with increasing temperature and magnetic field than that in wurtzite GaN. This study also showed that the electron spin relaxation for wurtzite GaN at low density could be explained by the Elliot-Yafet process but not for zinc-blende GaN in the metallic regime.
For general N=5 and N=6 superconformal field theories in three dimensions, we compute the three-point correlation functions of the supercurrent multiplets. In each case, N=5 and N=6, the functional form of this correlator is uniquely fixed modulo an overall coefficient which is related, by superconformal Ward identities, to the parameter in the two-point function of the supercurrent. The structure of the correlation functions obtained is consistent with the property that every N=5 superconformal field theory, considered as a special N=4 theory, is invariant under the mirror map.
We consider geodesics for first passage percolation (FPP) on $\mathbb{Z}^d$ with iid passage times. As has been common in the literature, we assume that the FPP system satisfies certain basic properties conjectured to be true, and derive consequences from these properties. The assumptions are roughly as follows: (i) the fluctuation scale $\sigma(r)$ of the passage time on scale $r$ grows approximately as a positive power $r^\chi$, in the sense that two natural definitions of $\sigma(r)$ and $\chi$ yield the same value $\chi$, and (ii) the limit shape boundary has curvature uniformly bounded away from 0 and $\infty$ (a requirement we can sometimes limit to a neighborhood of some fixed direction.) The main a.s. consequences derived are the following, with $\nu$ denoting a subpolynomial function and $\xi=(1+\chi)/2$ the transverse wandering exponent: (a) for one-ended geodesic rays with a given asymptotic direction $\theta$, starting in a natural halfspace $H$, for the hyperplane at distance $r$ from $H$, the density of "entry points" where some geodesic ray first crosses the hyperplane is at most $\nu(r)/r^{(d-1)\xi}$, (b) the system has no bigeodesics, i.e. two-ended infinite geodesics, (c) given two sites $x,y$, and a third site $z$ at distance at least $\ell$ from $x$ and $y$, the probability that the geodesic from $x$ to $y$ passes through $z$ is at most $\nu(\ell)/\ell^{(d-1)\xi}$, and (d) in $d=2$, the probability that the geodesic rays in a given direction from two sites have not coalesced after distance $r$ decays like $r^{-\xi}$ to within a subpolynomial factor. Our entry-point density bound compares to a natural conjecture of $c/r^{(d-1)\xi}$, corresponding to a spacing of order $r^\xi$ between entry points, which is the conjectured scale of the transverse wandering.
We study a compactification of the configuration space of n distinct labeled points on an arbitrary nonsingular variety. Our construction provides a generalization of the original Fulton-MacPherson compactification that is parallel to the generalization of the moduli space of n-pointed stable curves carried out by Hassett.
A projective linear code over $\mathbb{F}_q$ is called $\Delta$-divisible if all weights of its codewords are divisible by $\Delta$. Especially, $q^r$-divisible projective linear codes, where $r$ is some integer, arise in many applications of collections of subspaces in $\mathbb{F}_q^v$. One example are upper bounds on the cardinality of partial spreads. Here we survey the known results on the possible lengths of projective $q^r$-divisible linear codes.
Recent radio VLBI observations of the ~parsec-scale nuclear region of the narrow line Seyfert 1 galaxy NGC 4051 hint toward the presence of outflowing plasma. From available literature we have collected high-quality, high-resolution broadband spectral energy distribution data of the nuclear region of NGC 4051 spanning from radio through X-rays, to test whether the broadband SED can be explained within the framework of a relativistically outflowing jet model. We show that once the contribution from the host galaxy is taken into account, the broadband emission from the active galactic nucleus of NGC 4051 can be well described by the jet model. Contributions from dust and ongoing star-formation in the nuclear region tend to dominate the IR emission even at the highest resolutions. In the framework of the jet model, the correlated high variability of the extreme ultraviolet and X-rays compared to other wavelengths suggests that the emission at these wavelengths is optically thin synchrotron originating in the particle acceleration site(s) in the jet very close (few $r_g=GM_{BH}/c^2$) to the central supermassive black hole of mass M_{BH}. Our conclusions support the hypothesis that narrow line Seyfert 1 galaxies (which NGC 4051 is a member of) harbor a "jetted" outflow with properties similar to what has already been seen in low-luminosity AGNs and stellar mass black holes in hard X-ray state.
A theory of electronic Raman scattering in nearly antiferromagnetic Fermi liquids is constructed using the phenomenological electron-electron interaction introduced by Millis, Monien, and Pines. The role of "hot spots" and their resulting signatures in the channel dependent Raman spectra is highlighted, and different scaling regimes are addressed. The theory is compared to Raman spectra taken in the normal state of overdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$, and it is shown that many features of the symmetry dependent spectra can be explained by the theory.
Attention is drawn to the role played by the size of the system in the thermodynamic analysis of particle yields in relativistic heavy ion collisions at SIS energies. This manifests itself in the non-linear dependence of K+ and K- yields in $AA$ collisions at 1 -- 2 A.GeV on the number of participants. It is shown that this dependence can be quantitatively well described in terms of a thermal model with a canonical strangeness conservation. The measured particle multiplicity ratios (pi+/p, pi-/pi+, d/p, K+/pi+ and K+/K- but not eta/pi0) in central Au-Au and Ni-Ni collisions at 0.8 -- 2.0 A.GeV are also explained in the context of a thermal model with a common freeze-out temperature and chemical potential. Including the concept of collective flow a consistent picture of particle energy distributions is derived with the flow velocity being strongly impact-parameter dependent.
Current lane detection methods are struggling with the invisibility lane issue caused by heavy shadows, severe road mark degradation, and serious vehicle occlusion. As a result, discriminative lane features can be barely learned by the network despite elaborate designs due to the inherent invisibility of lanes in the wild. In this paper, we target at finding an enhanced feature space where the lane features are distinctive while maintaining a similar distribution of lanes in the wild. To achieve this, we propose a novel Repainting and Imitating Learning (RIL) framework containing a pair of teacher and student without any extra data or extra laborious labeling. Specifically, in the repainting step, an enhanced ideal virtual lane dataset is built in which only the lane regions are repainted while non-lane regions are kept unchanged, maintaining the similar distribution of lanes in the wild. The teacher model learns enhanced discriminative representation based on the virtual data and serves as the guidance for a student model to imitate. In the imitating learning step, through the scale-fusing distillation module, the student network is encouraged to generate features that mimic the teacher model both on the same scale and cross scales. Furthermore, the coupled adversarial module builds the bridge to connect not only teacher and student models but also virtual and real data, adjusting the imitating learning process dynamically. Note that our method introduces no extra time cost during inference and can be plug-and-play in various cutting-edge lane detection networks. Experimental results prove the effectiveness of the RIL framework both on CULane and TuSimple for four modern lane detection methods. The code and model will be available soon.
We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem that apply to uniformly sheared granular systems in which microscopic time-reversal symmetry is broken. The former relation provides an exact representation of nonequilibrium steady-state properties as the integral of the time-correlation function describing transient dynamics from an initial quiescent towards a final sheared steady state. We also investigate implications of the integral fluctuation theorem on the approach towards the steady state and on the possible form of the steady-state distribution function in terms of the excess thermodynamic function.
We calculate the period integrals for a special class of affine hypersurfaces (deformed Delsarte hypersurfaces) in an algebraic torus by the aid of their Mellin transforms. A description of the relation between poles of Mellin transforms of period integrals and the mixed Hodge structure of the cohomology of the hypersurface is given. By interpreting the period integrals as solutions to Pochhammer hypergeometric differential equation, we calculate concretely the irreducible monodromy group of period integrals that correspond to the compactification of the affine hypersurface in a complete simplicial toric variety. As an application of the equivalence between oscillating integral for Delsarte polynomial and quantum cohomology of a weighted projective space $\mathbb{P}_{\bf B}$, we establish an equality between its Stokes matrix and the Gram matrix of the full exceptional collection on $\mathbb{P}_{\bf B}$.
The inner region of a luminous accretion disk is radiation pressure dominated. We estimate the surface temperature of a radiation pressure dominated accretion disk, \Theta=(c_s/r\Omega_K)^2<<(H/r)^2, which is significantly lower than that of a gas pressure dominated disk, \Theta (H/r)^2. This means that the outflow can be launched magnetically from the photosphere of the radiation pressure dominate disk only if the effective potential barrier along the magnetic field line is extremely shallow or no potential barrier is present. For the latter case, the slow sonic point in the outflow may probably be in the disk, which leads to a slow circular dense flow above the disk. This implies that hot gas (probably in the corona) is necessary for launching a jet from the radiation pressure dominated disk, which provides a natural explanation on the observational evidence that the relativistic jets are related to hot plasma in some X-ray binaries and active galactic nuclei. We investigate the outflows accelerated from the hot corona above the disk by the magnetic field and radiation force of the accretion disk. We find that, with the help of the radiation force, the mass loss rate in the outflow is high, which leads to a slow outflow. This may be the reason why the jets in radio-loud narrow-line Seyfert galaxies are in general mild relativistic compared with those in blazars.
We present the first Ga(4f) NMR study of the Cr susceptibility in the archetype of Kagome based frustrated antiferromagnets, SrCr$_{8}$Ga$_{4}$O$_{19}$. Our major finding is that the susceptibility of the frustrated lattice goes through a maximum around 50 K. Our data also supports the existence of paramagnetic ``clusters'' of spins, responsible for the Curie behavior observed in the macroscopic susceptibility at low T. These results set novel features for the constantly debated physics of geometrically frustrated magnets.
Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system tau using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth tau produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. The algorithm has been implemented in the XSPEC package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (> 10^{12} G), which is expected to be typical of accreting systems such as X-ray pulsars and supergiant fast X-ray transients.