ShantanuT01/DACTYL-Pretraining huggingface dataset:
Severi varieties and Brill-Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface $S$ with polarization $L$ of type $(1,n)$, we prove nonemptiness and regularity of the Severi variety parametrizing $\delta$-nodal curves in the linear system $|L|$ for $0\leq \delta\leq n-1=p-2$ (here $p$ is the arithmetic genus of any curve in $|L|$). We also show that a general genus $g$ curve having as nodal model a hyperplane section of some $(1,n)$-polarized abelian surface admits only finitely many such models up to translation; moreover, any such model lies on finitely many $(1,n)$-polarized abelian surfaces. Under certain assumptions, a conjecture of Dedieu and Sernesi is proved concerning the possibility of deforming a genus $g$ curve in $S$ equigenerically to a nodal curve. The rest of the paper deals with the Brill-Noether theory of curves in $|L|$. It turns out that a general curve in $|L|$ is Brill-Noether general. However, as soon as the Brill-Noether number is negative and some other inequalities are satisfied, the locus $|L|^r_d$ of smooth curves in $|L|$ possessing a $g^r_d$ is nonempty and has a component of the expected dimension. As an application, we obtain the existence of a component of the Brill-Noether locus $\mathcal{M}^r_{p,d}$ having the expected codimension in the moduli space of curves $\mathcal{M}_p$. For $r=1$, the results are generalized to nodal curves.
Let $G = (V,E)$ be a finite graph and let $(\mathbb{A},+)$ be an abelian group with identity 0. Then $G$ is \textit{$\mathbb{A}$-magic} if and only if there exists a function $\phi$ from $E$ into $\mathbb{A} - \{0\}$ such that for some $c \in \mathbb{A}$, $\sum_{e \in E(v)} \phi(e) = c$ for every $v \in V$, where $E(v)$ is the set of edges incident to $v$. Additionally, $G$ is \textit{zero-sum $\mathbb{A}$-magic} if and only if $\phi$ exists such that $c = 0$. We consider zero-sum $\mathbb{A}$-magic labelings of graphs, with particular attention given to $\mathbb{A} = \mathbb{Z}_{2j}^k$. For $j \geq 1$, let $\zeta_{2j}(G)$ be the smallest positive integer $c$ such that $G$ is zero-sum $\mathbb{Z}_{2j}^c$-magic if $c$ exists; infinity otherwise. We establish upper bounds on $\zeta_{2j}(G)$ when $\zeta_{2j}(G)$ is finite, and show that $\zeta_{2j}(G)$ is finite for all $r$-regular $G$, $r \geq 2$. Appealing to classical results on the factors of cubic graphs, we prove that $\zeta_4(G) \leq 2$ for a cubic graph $G$, with equality if and only if $G$ has no 1-factor. We discuss the problem of classifying cubic graphs according to the collection of finite abelian groups for which they are zero-sum group-magic.
In this paper we propose a generalized model for the motion of a two-species self-driven objects ranging from a scenario of a completely random environment of particles of negligible excluded volume to a more deterministic regime of rigid objects in an environment. Each cell of the system has a maximum occupation level called $\sigma _{\max }$. Both species move in opposite directions. The probability of any given particle to move to a neighboring cell depends on the occupation of this cell according to a Fermi-Dirac like distribution, considering a parameter $\alpha $ that controls the system randomness. We show that for a certain $\alpha =\alpha _{c}$ the system abruptly transits from a mobile scenario to a clogged state which is characterized by condensates. We numerically describe the details of this transition by coupled partial differential equations (PDE) and Monte Carlo (MC) simulations that are in good agreement.
Colloidal semiconductor nanoplatelets exhibit quantum size effects due to their thickness of only few monolayers, together with strong optical band-edge transitions facilitated by large lateral extensions. In this article we demonstrate room temperature strong coupling of the light and heavy hole exciton transitions of CdSe nanoplatelets with the photonic modes of an open planar microcavity. Vacuum Rabi splittings of $66 \pm 1$ meV and $58 \pm 1$ meV are observed for the heavy and light hole excitons respectively, together with a polariton-mediated hybridisation of both transitions. By measuring the concentration of platelets in the film we compute the transition dipole moment of a nanoplatelet exciton to be $\mu = (575 \pm 110)$ D. The large oscillator strength and fluorescence quantum yield of semiconductor nanoplatelets provide a perspective towards novel photonic devices, combining polaritonic and spinoptronic effects.
A purported black hole solution in (2+1)-dimensions is shown to be nothing more than flat space viewed from an accelerated frame.
We model the stellar abundances and ages of two disrupted dwarf galaxies in the Milky Way stellar halo: Gaia-Sausage Enceladus (GSE) and Wukong/LMS-1. Using a statistically robust likelihood function, we fit one-zone models of galactic chemical evolution with exponential infall histories to both systems, deriving e-folding timescales of $\tau_\text{in} = 1.01 \pm 0.13$ Gyr for GSE and $\tau_\text{in} = 3.08^{+3.19}_{-1.16}$ Gyr for Wukong/LMS-1. GSE formed stars for $\tau_\text{tot} = 5.40^{+0.32}_{-0.31}$ Gyr, sustaining star formation for $\sim$$1.5 - 2$ Gyr after its first infall into the Milky Way $\sim$10 Gyr ago. Our fit suggests that star formation lasted for $\tau_\text{tot} = 3.36^{+0.55}_{-0.47}$ Gyr in Wukong/LMS-1, though our sample does not contain any age measurements. The differences in evolutionary parameters between the two are qualitatively consistent with trends with stellar mass $M_\star$ predicted by simulations and semi-analytic models of galaxy formation. Our fitting method is based only on poisson sampling from an evolutionary track and requires no binning of the data. We demonstrate its accuracy by testing against mock data, showing that it accurately recovers the input model across a broad range of sample sizes ($20 \leq N \leq 2000$) and measurement uncertainties ($0.01 \leq \sigma_\text{[$\alpha$/Fe]}, \sigma_\text{[Fe/H]} \leq 0.5$; $0.02 \leq \sigma_{\log_{10}(\text{age})} \leq 1$). Our inferred values of the outflow mass-loading factor reasonably match $\eta \propto M_\star^{-1/3}$ as predicted by galactic wind models. Due to the generic nature of our derivation, this likelihood function should be applicable to one-zone models of any parametrization and easily extensible to other astrophysical models which predict tracks in some observed space.
Let $Y\mathord{/\mkern-6mu/}_\theta G$ be a complete intersection in a GIT quotient $X\mathord{/\mkern-6mu/}_\theta G$ cut out by a $G$-representation $E$. We show that the $E$-twisted quasimap $I$-function recovers invariants of $(Y, G, \theta)$ if its nonequivariant limit exists before restriction to $Y\mathord{/\mkern-6mu/}_\theta G$. This corrects a conjecture credited to Coates-Corti-Iritani-Tseng. We explain how to correct computations in the literature based on the faulty conjecture.
We prove that rigid cohomology can be computed as the cohomology of a site analogous to the crystalline site. Berthelot designed rigid cohomology as a common generalization of crystalline and Monsky-Washnitzer cohomology. Unfortunately, unlike the former, the functoriality of the theory is not built-in. We defined somewhere else the "overconvergent site" which is functorially attached to an algebraic variety and proved that the category of modules of finite presentation on this ringed site is equivalent to the category of over- convergent isocrystals on the variety. We show here that their cohomology also coincides.
The previous version of this article gave erroneous predictions. The correct uptodate predictions can be found in the section devoted to gravitomagnetism in the living review of the Dark Gravity theory: gr-qc/0610079 The most natural prediction is zero frame dragging and the same geodetic effect as predicted by GR. However, a straightforward extension of the theory could lead to the same frame-dragging as in GR.
Based on the Sloan Digital Sky Survey DR 7, we investigate the environment, morphology and stellar population of bulgeless low surface brightness (LSB) galaxies in a volume-limited sample with redshift ranging from 0.024 to 0.04 and $M_r$ $\leq$ $-18.8$. The local density parameter $\Sigma_5$ is used to trace their environments. We find that, for bulgeless galaxies, the surface brightness does not depend on the environment. The stellar populations are compared for bulgeless LSB galaxies in different environments and for bulgeless LSB galaxies with different morphologies. The stellar populations of LSB galaxies in low density regions are similar to those of LSB galaxies in high density regions. Irregular LSB galaxies have more young stars and are more metal-poor than regular LSB galaxies. These results suggest that the evolution of LSB galaxies may be driven by their dynamics including mergers rather than by their large scale environment.
We report measurements of the low temperature (T = 0.5 K) oscillatory magnetization in a high-density array of 50 micron diameter wires of polycrystalline Bi utilizing a high sensitivity silicon cantilever magnetometer. We find that the magnetic response is strongly anisotropic, being much larger for magnetic field perpendicular than for fields parallel to the wire-axis. We argue that this is a geometric effect caused by the large aspect ratio of the individual microwires in the array. The magnetic response of the microwires is dominated by the light electrons due to the larger cyclotron orbits in comparison with the heavier holes. We find that de Haas - van Alphen oscillations are easily resolved, and discuss the application of this technique to the study of Bi nanowire arrays.
Classical novae are the result of thermonuclear flashes of hydrogen accreted by CO or ONe white dwarfs, leading eventually to the dynamic ejection of the surface layers. These are observationally known to be enriched in heavy elements, such as C, O and Ne that must originate in layers below the H-flash convection zone. Building on our previous work, we now present stellar evolution simulations of ONe novae and provide a comprehensive comparison of our models with published ones. Some of our models include exponential convective boundary mixing to account for the observed enrichment of the nova ejecta even when accreted material has a solar abundance distribution. Our models produce maximum temperature evolution profiles and nucleosynthesis yields in good agreement with models that generate enriched ejecta by assuming that the accreted material was pre-mixed. We confirm for ONe novae the result we reported previously, i.e.\ we found that $^3$He could be produced {\it in situ} in solar-composition envelopes accreted with slow rates ($\dot{M} < 10^{-10}\,M_\odot/\mbox{yr}$) by cold ($T_{\rm WD} < 10^7$ K) CO WDs, and that convection was triggered by $^3$He burning before the nova outburst in that case. In addition, we now find that the interplay between the $^3$He production and destruction in the solar-composition envelope accreted with an intermediate rate, e.g.\ $\dot{M} = 10^{-10}\,M_\odot/\mbox{yr}$, by the $1.15\,M_\odot$ ONe WD with a relatively high initial central temperature, e.g.\ $T_{\rm WD} = 15\times 10^6$ K, leads to the formation of a thick radiative buffer zone that separates the bottom of the convective envelope from the WD surface. (Abridged)
On the basis of experiments conducted in the 1970s and earlier, it is believed that, in a compound nucleus (CN), fluctuations in transition strengths are drawn from a Porter-Thomas distribution (PTD), a $\chi^2$ distribution of one degree of freedom. However, work done post-1990 at the Los Alamos Neutron Science Center (LANSCE) and Oak Ridge Electron Linear Accelerator (ORELA) facilities has yielded instances of neutron resonance data sets of superior quality that are inconsistent with the PTD. In view of the importance of the status of the PTD to the foundations of statistical reaction theory, the question arises whether other data acquired at these facilities can be mined for evidence of deviations from the PTD? To date, the focus has been on data taken in the regime of isolated resonances. In this letter, arguments are put forward in support of the analysis of measurements of the total cross section in the regime where resonances are weakly overlapping.
We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We solve this problem analytically in the frame of mean-field theory, which is then generalized using phenomenological scaling considerations. A large variety of interface critical behavior is obtained which is checked numerically on the example of two-dimensional q-state Potts models with q=2 to 4. Weak interface couplings are generally irrelevant, resulting in the same critical behavior at the interface as for a free surface. With strong interface couplings, the interface remains ordered at the bulk transition temperature. More interesting is the intermediate situation, the special interface transition, when the critical behavior at the interface involves new critical exponents, which however can be expressed in terms of the bulk and surface exponents of the two subsystems. We discuss also the smooth or discontinuous nature of the order parameter profile.
We carry out a complete birational classification of the degree g universal Jacobian P_g over the moduli space of curves, highlighting the transition cases g=10, 11. The universal Jacobian is unirational when g<10, has Kodaira dimension zero for g=10 and Kodaira dimension 19 for g=11. For g>11, the variety P_g has Kodaira dimension 3g-3, that is, the maximum allowed by Iitaka's easy addition formula for fibre spaces. In particular, we disprove the expectation that P_g and M_g have the same Kodaira dimension for all genera.
The Auxiliary Field Diffusion Monte Carlo method is applied to compute the spin susceptibility and the compressibility of neutron matter at zero temperature. Results are given for realistic interactions which include both a two-body potential of the Argonne type and the Urbana IX three-body potential. Simulations have been carried out for about 60 neutrons. We find an overall reduction of the spin susceptibilty by about a factor 3 with respect to the Pauli susceptibility for a wide range of densities. Results for the compressibility of neutron matter are also presented and compared with other available estimates obtained for semirealistic nucleon-nucleon interactions by using other techniques.
We present a computational framework (Rio) in the ADM 3+1 approach for numerical relativity. This work enables us to carry out high resolution calculations for initial data of two arbitrary black holes. We use the transverse conformal treatment, the Bowen-York and the puncture methods. For the numerical solution of the Hamiltonian constraint we use the domain decomposition and the spectral decomposition of Galerkin-Collocation. The nonlinear numerical code solves the set of equations for the spectral modes using the standard Newton-Raphson method, LU decomposition and Gaussian quadratures. We show the convergence of the Rio code. This code allows for easy deployment of large calculations. We show how the spin of one of the black holes is manifest in the conformal factor.
We study the mass distribution in six nearby (z<0.06) relaxed Abell clusters of galaxies A0262, A0496, A1060, A2199, A3158 and A3558. Given the dominance of dark matter in galaxy clusters we approximate their total density distribution by the NFW formula characterized by virial mass and concentration. We also assume that the anisotropy of galactic orbits is reasonably well described by a constant and that galaxy distribution traces that of the total density. Using the velocity and position data for 120-420 galaxies per cluster we calculate, after removal of interlopers, the profiles of the lowest-order even velocity moments, dispersion and kurtosis. We then reproduce the velocity moments by jointly fitting the moments to the solutions of the Jeans equations. Including the kurtosis in the analysis allows us to break the degeneracy between the mass distribution and anisotropy and constrain the anisotropy as well as the virial mass and concentration. The method is tested in detail on mock data extracted from N-body simulations of dark matter haloes. We find that the best-fitting galactic orbits are remarkably close to isotropic in most clusters. Using the fitted pairs of mass and concentration parameters for the six clusters we conclude that the trend of decreasing concentration for higher masses found in cosmological N-body simulations is consistent with the data. By scaling the individual cluster data by mass we combine them to create a composite cluster with 1465 galaxies and perform a similar analysis on such sample. The estimated concentration parameter then lies in the range 1.5 < c < 14 and the anisotropy parameter in the range -1.1 < \beta < 0.5 at the 95 percent confidence level.
We calculate the neutrino pair annihilation rate into electron pairs between two neutron stars in a binary system. We present a closed formula for the energy deposition rate at any point between the stars, where each neutrino of a pair derives from each star, and compare this result to that where all neutrinos derive from a single neutron star. An approximate generalization of this formula is given to include the relativistic effects of gravity. We find that this inter-star neutrino annihilation is a significant contributor to the energy deposition between heated neutron star binaries. In particular, for two neutron stars near their last stable orbit, inter-star neutrino annihilation energy deposition is almost equal to that of single star energy deposition.
We report a $^{35}$Cl nuclear magnetic resonance study in the honeycomb lattice, $\alpha$-RuCl$_3$, a material that has been suggested to potentially realize a Kitaev quantum spin liquid (QSL) ground state. Our results provide direct evidence that $\alpha$-RuCl$_3$ exhibits a magnetic field-induced QSL. For fields larger than $\sim 10$ T a spin-gap opens up while resonance lines remain sharp, evidencing that spins are quantum disordered and locally fluctuating. The spin gap increases linearly with increasing magnetic field, reaching $\sim50$ K at 15 T, and is nearly isotropic with respect to the field direction. The unusual rapid increase of the spin gap with increasing field and its isotropic nature are incompatible with conventional magnetic ordering and in particular exclude that the ground state is a fully polarized ferromagnet. The presence of such a field-induced, gapped QSL phase has indeed been predicted in the Kitaev model.
We present serendipitous detections of radio sources at 28.5 GHz (1 cm), which resulted from our program to image thermal Sunyaev-Zeldovich (SZ) effect in 56 galaxy clusters. We find 64 radio sources with fluxes down to 0.4 mJy, and within 250 arcseconds from the pointing centers. The spectral indices (S ~ \nu^-\alpha) of 54 sources with published low frequency flux densities range from -0.6 to 2 with a mean of 0.77, and a median of 0.84. Extending low frequency surveys of radio sources towards galaxy clusters CL 0016+16, Abell 665, and Abell 2218 to 28.5 GHz, and selecting sources with 1.4 GHz flux density greater than 7 mJy to form an unbiased sample, we find a mean spectral index of 0.71 and a median of 0.71. We find 4 to 7 times more sources predicted from a low frequency survey in areas without galaxy clusters. This excess cannot be accounted for by gravitational lensing of a background radio population by cluster potentials, indicating most of the detected sources are associated with galaxy clusters. For the cluster Abell 2218, the presence of unsubtracted radio sources with 28.5 GHz flux densities less than 0.5 mJy, can only contribute to temperature fluctuations at a level of 10 to 25 \muK. The corresponding error due to radio point source contamination in the Hubble constant derived through a combined analysis of 28.5 GHz SZ images and X-ray emission observations ranges from 1% to 6%.
Using a resimulation technique, we perform high-resolution cosmological simulations of dry mergers in a massive galaxy cluster identified in the Millennium Run. Our initial conditions include well resolved compound galaxy models consisting of dark matter halos and stellar bulges that are used to replace the most massive cluster progenitor halos at redshift z=3. By construction, our galaxy models obey the stellar mass-size relation initially. We demonstrate that the brightest cluster galaxy (BCG) evolves away from the Kormendy relation as defined by the smaller mass galaxies (i.e., the relation bends). As a result of the comparatively large number of mergers the BCG experiences, its total mass-to-light ratio becomes significantly higher than in typical elliptical galaxies. We also show that the mixing processes between dark matter and stars lead to a small but numerically robust tilt in the fundamental plane and that the BCG lies on the tilted plane. Our model is consistent with the observed steepening of the logarithmic mass-to-light gradient as a function of the stellar mass. Surprisingly, we find only tentative weak distortion in the Faber-Jackson relation that depends on the aperture size, unlike expected based on studies of isolated merger simulations. This may be due to differences in the distribution of galaxy orbits, which is given in our approach directly by the cosmological context while it has to be assumed in isolated merger simulations, and the fact that the BCG is located deep in the cluster potential well.
We present the discovery of a previously unknown member of the immediate solar neighbourhood, DENIS-P J104814.7-395606.1 (hereafter DENIS 1048-39), identified while mining the DENIS database for new nearby stars. A HIRES echelle spectrum obtained with the 10-m Keck telescope shows that it is an M9 dwarf. DENIS 1048-39 has a very bright apparent magnitude (I=12.67) for its spectral type and colour (I-J=3.07), and is therefore very nearby. If it is single its distance is only 4.1 +- 0.6pc, ranking it as between our twelfth and fortyth closest neighbour. It is also the closest star or brown dwarf with a spectral type later than M7V. Its proper motion was determined through comparison of Sky atlas Schmidt plates, scanned by the MAMA microdensitometer, with the DENIS images. At 1.53"/yr it further attests the closeness of DENIS 1048-39, and hence its dwarf status. These characteristics make it an obvious target for further detailed studies.
Let $p$ be a sufficiently large prime number, $r$ be any given positive integer. Suppose that $a_1,\,\dots,\,a_r$ are pairwise distinct and not zero modulo $p$. Let $N(a_1,\,\dots,\,a_r;\,p)$ denote the number of $\alpha_1,\,\dots,\,\alpha_r,\,\beta$, which are primitive roots modulo $p$, such that $\alpha_1+\beta\equiv a_1,\,\dots,\,\alpha_r+\beta\equiv a_r\,({\rm mod}\,p).$ In the first version of this paper, we proved an asymptotic formula for $N(a_1,\,\dots,\,a_r;\,p)$ so that we could answer an open problem of Wenpeng Zhang and Tingting Wang. But we found that our result had been included in a paper of L. Carlitz in 1956, which is explained in the additional remark below.
We present in this Letter the results from two high quality, low density GaAs quantum wells. In sample A of electron density n=5.0x10^10 cm^-2, anisotropic electronic transport behavior was observed at \nu=7/2 in the second Landau level. We believe that the anisotropy is due to the large Landau level mixing effect in this sample. In sample B of density 4.1x10^10 cm^-2, strong 8/3, 5/2, and 7/3 fractional quantum Hall states were observed. Furthermore, our energy gap data suggest that, similar to the 8/3 state, the 5/2 state may also be spin unpolarized in the low density limit. The results from both samples show that the strong electron-electron interactions and a large Landau level mixing effect play an import role in the competing ground states in the second landau level.