ShantanuT01/DACTYL-Pretraining huggingface dataset:
The cyclic Lotka-Volterra model in a $D$-dimensional regular lattice is considered. Its ``nucleus growth'' mode is analyzed under the scope of Tsallis' entropies $S_q=(1-\sum_i p_i^q)/(q-1)$, $q\in \mathbb{R}$. It is shown both numerically and by means of analytical considerations that a linear increase of entropy with time, meaning finite asymptotic entropy rate, is achieved for the entropic index $q_c=1-1/D$. Although the lattice exhibits fractal patterns along its evolution, the characteristic value of $q$ can be interpreted in terms of very simple features of the dynamics.
In this study, we develop a systematic weak localization/antilocalization theory fully considering the anisotropy and Berry phase of the system, and apply it to various phases of few-layer black phosphorus (BP), which has a highly anisotropic electronic structure with an electronic gap size tunable even to a negative value. The derivation of a Cooperon ansatz for the Bethe-Salpeter equation in a general anisotropic system is presented, revealing the existence of various quantum interference effects in different phases of few-layer BP, including a crossover from weak localization to antilocalization. We also predict that the magnetoconductivity at the semi-Dirac transition point will exhibit a nontrivial power-law dependence on the magnetic field, while following the conventional logarithmic field-dependence of 2D systems in the insulator and Dirac semimetal phases. Notably, the ratio between the magnetoconductivity and Boltzmann conductivity turns out to be independent of the direction, even in strongly anisotropic systems. Finally, we discuss the tunability of the quantum corrections of few-layer BP in terms of the symmetry class of the system.
I prove the existence, and describe the structure, of moduli space of pairs $(p,\Theta)$ consisting of a projective variety $P$ with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component of this moduli space is proper. A component containing a projective toric variety is described by a configuration of several polytopes, the main one of which is the secondary polytope. On the other hand, the component containing a principally polarized abelian variety provides a moduli compactification of $A_g$. The main irreducible component of this compactification is described by an "infinite periodic" analog of the secondary polytope and coincides with the toroidal compactification of $A_g$ for the second Voronoi decomposition.
We present the second catalog of serendipitously discovered compact extragalactic emission-line sources -- H$\alpha$ Dots. These objects have been discovered in searches of moderately deep narrow-band images acquired for the ALFALFA H$\alpha$ project (Van Sistine et al. 2016). In addition to cataloging 119 new H$\alpha$ Dots, we also present follow-up spectral data for the full sample. These spectra allow us to confirm the nature of these objects as true extragalactic emission-line objects, to classify them in terms of activity type (star forming or AGN), and to identify the emission line via which they were discovered. We tabulate photometric and spectroscopic data for the all objects, and present an overview of the properties of the full H$\alpha$ Dot sample. The H$\alpha$ Dots represent a broad range of star-forming and active galaxies detected via several different emission lines over a wide range of redshifts. The sample includes H$\alpha$-detected blue compact dwarf galaxies at low redshift, [\ion{O}{3}]-detected Seyfert 2 and Green Pea-like galaxies at intermediate redshifts, and QSOs detected via one of several UV emission lines, including Ly$\alpha$. Despite the heterogeneous appearance of the resulting catalog of objects, we show that our selection method leads to well-defined samples of specific classes of emission-line objects with properties that allow for statistical studies of each class.
Let K_4^- denote the diamond graph, formed by removing an edge from the complete graph K_4. We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of K_4^-. We show that, with probability tending to 1 as $n \to \infty$, the final size of the graph produced is $\Theta(\sqrt{\log(n)} \cdot n^{3/2})$. Our analysis also suggests that the graph produced after i edges are added resembles the random graph, with the additional condition that the edges which do not lie on triangles form a random-looking subgraph.
We study carrier transport through graphene on SrTiO$_3$ substrates by considering relative contributions of Coulomb and resonant impurity scattering to graphene resistivity. We establish that charged impurity scattering must dominate graphene transport as the charge neutrality point is approached by lowering the carrier density, and in the higher density regime away from the neutrality point a dual model including both charged impurities and resonant defects gives an excellent description of graphene transport on SrTiO$_3$ substrates. We further establish that the non-universal high-density behavior of $\sigma(n)$ in different graphene samples on various substrates arises from the competition among different scattering mechanisms, and it is in principle entirely possible for graphene transport to be dominated by qualitatively different scattering mechanisms at high and low carrier densities.
We perform a systematic study of the impact of the J^2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations, which covers a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants, with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of charge radii. Our main conclusion is that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.
A new way to define the operation of P-inversion in the theory with a magnetic charge is presented.
We consider double Dirichlet series associated with arithmetic functions such as the von Mangoldt function, the M\"obius function, and so on. We show analytic continuations of them by use of the Mellin-Barnes integral. Furthermore we observe their reverse values at non-positive integer points.
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind, respectively due to Simonyi and Tardos (Combinatorica, 2006), Simonyi, Tardif, and Zsb\'an (The Electronic Journal of Combinatorics, 2013), and Chen (Journal of Combinatorial Theory, Series A, 2011). As a consequence of the generalization of Chen's theorem, we get new families of graphs whose chromatic number equals their circular chromatic number and that satisfy Hedetniemi's conjecture for the circular chromatic number.
We discuss the Picard group of moduli space $\mathcal{K}_g$ of quasi-polarized K3 surfaces of genus $g\leq 12$ and $g\neq 11$. In this range, $\mathcal{K}_g$ is unirational and a general element in $\mathcal{K}_g$ is a complete intersection with respect to a vector bundle on a homogenous space, by the work of Mukai. In this paper, we find generators of the Picard group $Pic_\mathbb{Q}(\mathcal{K}_g)$ using Noether-Lefschetz theory. This verifies the Noether-Lefschetz conjecture on moduli of K3 surfaces in these cases.
We outline a generic ratchet mechanism for creating directed spin-polarized currents in ac-driven double well or double dot structures by employing resonant spin transfer through the system engineered by local external magnetic fields. We show its applicability to semiconductor nanostructures by considering coherent transport through two coupled lateral quantum dots, where the energy levels of the two dots exhibit opposite Zeeman spin splitting. We perform numerical quantum mechanical calculations for the I-V characteristics of this system in the nonlinear regime, which requires a self-consistent treatment of the charge redistribution due to the applied finite bias. We show that this setting enables nonzero averaged net spin currents in the absence of net charge transport.
We consider the extremal problem of maximizing a point value jf(z)j at a given point z 2 G by some positive definite and continuous function f on an Abelian group G, where for a given symmetric open set 3 z, f vanishes outside and is normalized by f(0) = 1. Denote the extremal value as CG(; z). This extremal problem was investigated in R and Rd and for a 0-symmetric convex body in a paper of Boas and Kac in 1943. Arestov and Berdysheva extended the investigation to Td, where T := R=Z. Kolountzakis and R?ev?esz gave a more general setting, considering arbitrary open sets, in all the classical groups above. Also they observed, that such extremal problems occurred in certain special cases and in a different, but equivalent formulation already a century ago in the work of Carath?eodory and Fej?er. Moreover, following observations of Boas and Kac, Kolountzakis and R?ev?esz showed how the general problem can be reduced to equivalent discrete problems of "Carath?eodory-Fej?er type" on Z or Zm := Z=mZ. We extend the results of Kolountzakis and R?ev?esz to locally compact Abelian groups.
Recent discovery of the X-ray neutral iron line (Fe I K\alpha at 6.40 keV) around several supernova remnants (SNRs) show that MeV cosmic-ray (CR) protons are distributed around the SNRs and are interacting with neutral gas there. We propose that these MeV CRs are the ones that have been accelerated at the SNRs together with GeV-TeV CRs. In our analytical model, the MeV CRs are still confined in the SNR when the SNR collides with molecular clouds. After the collision, the MeV CRs leak into the clouds and produce the neutral iron line emissions. On the other hand, GeV-TeV CRs had already escaped from the SNRs and emit gamma-rays through interaction with molecular clouds surrounding the SNRs. We apply this model to the SNRs W28 and W44 and show that it can reproduce the observations of the iron line intensities and the gamma-ray spectra. This can be another support of a hadronic scenario for the gamma-ray emissions from these SNRs.
The CCD photometric observations of the eclipsing binary PS Persei (PS Per) were obtained on two consecutive days in 2009. The 2003 version Wilson-Devinney code was used to analyze the first complete light curves in $V$ and $R$ bands. It is found that PS Per is a short-period Algol-type binary with the less massive component accurately filling its inner critical Roche lobe. The mass ratio of $q=0.518$ and the orbital inclination of $i=89.^{\circ}86$ are obtained. On the other hand, based on all available times of primary light minimum including two new ones, the orbital period has been improved.
The lensing and Einstein ring at the core of the galaxy cluster Abell 3827 are reproduced in the modified gravity theory MOG. The estimated effective lensing mass $M_L=(1+\alpha)M_b=5.2\times 10^{12} M_\odot$ within $R=18.3$~kpc for a baryon mass $M_b=1.0\times 10^{12} M_\odot$ within the same radius produces the observed Einstein ring angular radius $\theta_E=10''$. A detailed derivation of the total lensing mass is based on modeling of the cluster configuration of galaxies, intracluster light and X-ray emission. The MOG can fit the lensing and Einstein ring in Abell 3827 without dark matter as well as General Relativity with dark matter.
A model for the formation of supermassive primordial black holes in galactic nuclei with the simultaneous suppression of the formation of intermediate-mass black holes is presented. A bimodal mass function for black holes formed through phase transitions in a model with a "Mexican hat" potential has been found. The classical motion of the phase of a complex scalar field during inflation has been taken into account. Possible observational manifestations of primordial black holes in galaxies and constraints on their number are discussed.
The spin-Seebeck effect (SSE) in ferromagnetic metals and insulators has been investigated systematically by means of the inverse spin-Hall effect (ISHE) in paramagnetic metals. The SSE generates a spin voltage as a result of a temperature gradient in a ferromagnet, which injects a spin current into an attached paramagnetic metal. In the paramagnet, this spin current is converted into an electric field due to the ISHE, enabling the electric detection of the SSE. The observation of the SSE is performed in longitudinal and transverse configurations consisting of a ferromagnet/paramagnet hybrid structure, where thermally generated spin currents flowing parallel and perpendicular to the temperature gradient are detected, respectively. Our results explain the SSE in terms of a two-step process: (1) the temperature gradient creates a non-equilibrium state in the ferromagnet governed by both magnon and phonon propagations and (2) the non-equilibrium between magnons in the ferromagnet and electrons in the paramagnet at the contact interface leads to "thermal spin pumping" and the ISHE signal. The non-equilibrium state of metallic magnets (e.g. Ni81Fe19) under a temperature gradient is governed mainly by the phonons in the sample and the substrate, while in insulating magnets (e.g. Y3Fe5O12) both magnon and phonon propagations appear to be important. The phonon-mediated non-equilibrium that drives the thermal spin pumping is confirmed also by temperature-dependent measurements, giving rise to a giant enhancement of the SSE signals at low temperatures.
Plane perfect matchings of $2n$ points in convex position are in bijection with triangulations of convex polygons of size $n+2$. Edge flips are a classic operation to perform local changes both structures have in common. In this work, we use the explicit bijection from Aichholzer et al. (2018) to determine the effect of an edge flip on the one side of the bijection to the other side, that is, we show how the two different types of edge flips are related. Moreover, we give an algebraic interpretation of the flip graph of triangulations in terms of elements of the corresponding Temperley-Lieb algebra.
We prove estimates for solutions of the Cauchy problem for the inhomogeneous wave equation on $\R^{1+n}$ in a class of Banach spaces whose norms only depend on the size of the space-time Fourier transform. The estimates are local in time, and this allows one, essentially, to replace the symbol of the wave operator, which vanishes on the light cone in Fourier space, with an inhomogeneous symbol, which can be inverted. Our result improves earlier estimates of this type proved by Klainerman-Machedon. As a corollary, one obtains a rather general result concerning local well-posedness of nonlinear wave equations.
Many prominences are supported by magnetic flux ropes. One important question is how we can determine whether the flux rope is weakly-twisted or strongly-twisted. In this paper, we attempted to check whether prominences supported by weakly-twisted and strongly-twisted flux ropes can manifest different features so that we might distinguish the two types of magnetic structures by their appearance. We performed pseudo three-dimensional simulations of two magnetic flux ropes with different twists. We found that the resulting two prominences differ in many aspects. The prominence supported by a weakly-twisted flux rope is composed mainly of transient threads, forming high-speed flows inside the prominence. Its horns are evident. Conversely, the one supported by a highly-twisted flux rope consists mainly of stable quasi-stationary threads, including longer independently trapped threads and shorter magnetically connected threads. It is also revealed that the prominence spine deviates from the flux rope axis in the vertical direction and from the photospheric polarity inversion line projected on the solar surface, especially for the weakly-twisted magnetic flux rope. The two types of prominences differ significantly in appearance. It is also suggested that a piling-up of short threads in highly-twisted flux ropes might account for the vertical-like threads in some prominences.
The development of digitization methods for line drawings (especially in the area of electrical engineering) relies on the availability of publicly available training and evaluation data. This paper presents such an image set along with annotations. The dataset consists of 1152 images of 144 circuits by 12 drafters and 48 563 annotations. Each of these images depicts an electrical circuit diagram, taken by consumer grade cameras under varying lighting conditions and perspectives. A variety of different pencil types and surface materials has been used. For each image, all individual electrical components are annotated with bounding boxes and one out of 45 class labels. In order to simplify a graph extraction process, different helper symbols like junction points and crossovers are introduced, while texts are annotated as well. The geometric and taxonomic problems arising from this task as well as the classes themselves and statistics of their appearances are stated. The performance of a standard Faster RCNN on the dataset is provided as an object detection baseline.
Existence and uniqueness of a specific self-similar solution is established for the following reaction-diffusion equation with Hardy singular potential $$ \partial_tu=\Delta u^m+|x|^{-2}u^p, \qquad (x,t)\in \real^N\times(0,\infty), $$ in the range of exponents $1\leq p<m$ and dimension $N\geq3$. The self-similar solution is unbounded at $x=0$ and has a logarithmic vertical asymptote, but it remains bounded at any $x\neq0$ and $t\in(0,\infty)$ and it is a weak solution in $L^1$ sense, which moreover satisfies $u(t)\in L^p(\real^N)$ for any $t>0$ and $p\in[1,\infty)$. As an application of this self-similar solution, it is shown that there exists at least a weak solution to the Cauchy problem associated to the previous equation for any bounded, nonnegative and compactly supported initial condition $u_0$, contrasting with previous results in literature for the critical limit $p=m$.
Combining strong magnetic anisotropy with strong exchange interaction is a long standing goal in the design of quantum magnets. The lanthanide complexes, while exhibiting a very strong ionic anisotropy, usually display a weak exchange coupling, amounting to only a few wavenumbers. Recently, an isostructural series of mixed Ln$^{3+}$-N$_2^{3-}$-Ln$^{3+}$ (Ln $=$ Gd, Tb, Dy, Ho, Er) have been reported, in which the exchange splitting is estimated to reach hundreds wavenumbers. The microscopic mechanism governing the unusual exchange interaction in these compounds is revealed here by combining detailed modeling with density-functional theory and {\it ab initio} calculations. We find it to be basically kinetic and highly complex, involving non-negligible contributions up to seventh power of total angular momentum of each lanthanide site. The performed analysis also elucidates the origin of magnetization blocking in these compounds. Contrary to general expectations the latter is not always favored by strong exchange interaction.
In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the radius of convergence when one walk is averaged over and the other is kept fixed; z2, the radius of convergence when both walks are averaged over. While z2 can be easily computed, no explicit expression is available for z1. In [3] it was conjectured that z1 > z2 under a weak regularity assumption on the random walk. However, this gap was only proved for strongly transient random walk. Subsequently, in [1], [4] and [5] the gap was proved for a subclass of random walks that are transient but not strongly transient. In the present note we settle the full conjecture. The proof is based on a comparison of variational formulas for z1 and z2 derived in [3]. Under additional weak regularity assumptions on the random walk, we derive an upper bound for z1. We further show that the gap persists when the random walk has exponential waiting times. The gaps imply the presence of an intermediate phase for a model of two random walks with a pinning interaction. As explained in [3], they also imply the presence of intermediate phases in three classes of interacting stochastic systems: coupled branching processes, interacting diffusions, and directed polymers with bulk disorder.
The problem of long-range correlations of particles produced in high- energy collisions is discussed. Long-range correlations involve large groups of particles. Among them are, e.g., those correlations which lead to ring-like and elliptic flow shapes of individual high-multiplicity events in the polar+azimuthal angles plane. The \w method of \an which allows to disentangle various patterns has been proposed and applied to some central lead-lead collisions at energy 158 GeV per nucleon. Previous attempts to find out the ring-like correlations and recent results on \w \an of high- energy nuclei interactions are reviewed.
We study a non-uniformly rotating universe outside a Schwarzschild black hole by generating a time-dependent manifold of revolution around a straight line. In this simple model where layers of spherical shells of the universe non-uniformly rotate, the Einstein field equations require this phenomenon to be caused by a static mass-energy distribution with time-dependent $T^{\phi\phi}$ (quadratic with time) and $T^{r\phi}=T^{\phi r}$ (linear with time). This indicates that a time-dependent stress along a certain direction results in a spacetime shift in that direction. For this model however, such material violates the null energy condition. Incidentally, the various coordinate systems describing the Schwarzschild solution can be viewed as arising from the freedom in parametrising the straight line and the radial function in the general method of constructing spacetime by generating manifolds of revolution around a given curve.
We discuss junction conditions across null hypersurfaces in a class of scalar-tensor gravity theories with i) second order dynamics, ii) obeying the recent constraints imposed by gravitational wave propagation, and iii) allowing for a cosmologically viable evolution. These requirements select kinetic gravity braiding models with linear kinetic term dependence and scalar field-dependent coupling to curvature. We explore a pseudo-orthonormal tetrad and its allowed gauge fixing, with one null vector standing as the normal, the other being transversal to the hypersurface. We derive a generalization of the Lanczos equation in a 2+1 decomposed form, relating the energy density, current and isotropic pressure of a distributional source to the jumps in the transverse curvature and transverse derivative of the scalar. Additionally we discuss a scalar junction condition and its implications for the distributional source.
An initial-boundary value in a strip with homogeneous Dirichlet boundary conditions for two-dimensional Zakharov-Kuznetsov-Burgers equation is considered. Results on global well-posedness and long-time decay of solutions in Sobolev spaces are established.