ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus four, five, and six. We find that the only such curves with exceptional rational points are of levels $137$ and $311$. In particular there are no exceptional rational points on those curves of genus five and six. More precisely, we determine the rational points on the curves $X_0^+(N)$ for $N=137,173,199,251,311,157,181,227,263,163,197,211,223,269,271,359$.
A new generalization of the t-J model with a nearest-neigbor hopping is formulated and solved exactly by the Bethe-ansatz method. The model describes the dynamics of spin-S fermions with isotropic or anisotropic interactions. In the case S=1 the magnetic interaction is biquadratic in the spin operators. In contrast to the SU(N) generalization of the t-J model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.
N-body simulations have revealed a wealth of information about dark matter halos however their results are largely empirical. Using analytic means, we attempt to shed light on simulation results by generalizing the self-similar secondary infall model to include tidal torque. In this first of two papers, we describe our halo formation model and compare our results to empirical mass profiles inspired by N-body simulations. Each halo is determined by four parameters. One parameter sets the mass scale and the other three define how particles within a mass shell are torqued throughout evolution. We choose torque parameters motivated by tidal torque theory and N-body simulations and analytically calculate the structure of the halo in different radial regimes. We find that angular momentum plays an important role in determining the density profile at small radii. For cosmological initial conditions, the density profile on small scales is set by the time rate of change of the angular momentum of particles as well as the halo mass. On intermediate scales, however, $\rho\propto r^{-2}$, while $\rho\propto r^{-3}$ close to the virial radius.
We report the connection between the stacking order and magnetic properties of bilayer CrI$_3$ using first-principles calculations. We show that the stacking order defines the magnetic ground state. By changing the interlayer stacking order one can tune the interlayer exchange interaction between antiferromagnetic and ferromagnetic. To measure the predicted stacking-dependent magnetism, we propose using linear magnetoelectric effect. Our results not only gives a possible explanation for the observed antiferromagnetism in bilayer CrI$_3$ but also have direct implications in heterostructures made of two-dimensional magnets.
In this paper we study the asymptotic behavior of a Boltzmann type price formation model, which describes the trading dynamics in a financial market. In many of these markets trading happens at high frequencies and low transactions costs. This observation motivates the study of the limit as the number of transactions $k$ tends to infinity, the transaction cost $a$ to zero and $ka=const$. Furthermore we illustrate the price dynamics with numerical simulations.
We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that are accessible via the Shimura correspondence. This is a generalization of the result of Inam and Wiese to the setting of totally real number fields
Dopability in semiconductors plays a crucial role in device performance. Using the first-principles density-functional theory calculations, we investigate systematically the doping properties of layered MX2 (M= Mo, W; X=S, Te) by replacing M or X with the groups III, V and VII elements. It is found that the defect BM is hard to form in MX2 due to the large formation energy originating from the crystal distortion, while AlM is easy to realize compared to the former. In MoS2, WS2 and MoTe2, Al is the most desirable p-type dopant under anion-rich conditions among the group III components, since AlM has relatively low transition and formation energies. With respect to the doping of the group V elements, it is found that the substitutions on the cation sites have deeper defect levels than those on the anion sites due to the strong electronegativity. AsTe and SbTe in MoTe2 and WTe2 are trend to form shallow acceptors under cation-rich conditions, indicating high hole-concentrations for p-type doping, whereas SbS in MoS2 and PTe in WTe2 are shown to be good p-type candidates under cation-rich conditions. In despite of that the substitutions of group VII on X site have low formation energies, the transition energies are too high to achieve n-type MoS2 and WS2. Nevertheless, for MoTe2, the substitutions with the group VII elements on the anion sites are suitable for n-type doping on account of the shallow donor levels and low formation energies under Mo-rich condition. As to WTe2, F is the only potential donor due to the shallow transition energy of FTe. Our findings of filtering out unfavorable and identifying favorable dopants in MX2 are very valuable for experimental implementations.
We used density functional theory (DFT) calculations to investigate the physical origin of the mechano-chemical response of materials interfaces. Our results show that the mechano-chemical response can be decomposed into the contribution from the interface itself (deformation of interfacial bonds) and a contribution from the underlying solid. The relative contributions depend on the stiffness of these regions and the contact geometry, which affects the stress distribution within the bulk region. We demonstrate that, contrary to what is commonly assumed, the contribution to the activation volume from the elastic deformation of the surrounding bulk is significant and, in some case, may be dominant. We also show that the activation volume and the mechanochemical response of interfaces should be finite due to the effects on the stiffness and stress distribution within the near-surface bulk region. Our results indicate that the large range of activation volumes measured in the previous experiments even for the same material system might originate from the different degrees of contributions probed from the bulk vs. interface.
Motivated by observational and theoretical work which both suggest very small scale ($\lesssim 1\,$pc) structure in the circum-galactic medium of galaxies and in other environments, we study Lyman-$\alpha$ (Ly$\alpha$) radiative transfer in an extremely clumpy medium with many "clouds" of neutral gas along the line of sight. While previous studies have typically considered radiative transfer through sightlines intercepting $\lesssim 10$ clumps, we explore the limit of a very large number of clumps per sightline (up to $f_{\mathrm{c}} \sim 1000$). Our main finding is that, for covering factors greater than some critical threshold, a multiphase medium behaves similar to a homogeneous medium in terms of the emergent Ly$\alpha$ spectrum. The value of this threshold depends on both the clump column density and on the movement of the clumps. We estimate this threshold analytically and compare our findings to radiative transfer simulations with a range of covering factors, clump column densities, radii, and motions. Our results suggest that (i) the success in fitting observed Ly$\alpha$ spectra using homogeneous "shell models" (and the corresponding failure of multiphase models) hints towards the presence of very small-scale structure in neutral gas, in agreement within a number of other observations; and (ii) the recurrent problems of reproducing realistic line profiles from hydrodynamical simulations may be due to their inability to resolve small-scale structure, which causes simulations to underestimate the effective covering factor of neutral gas clouds.
We calculate positions of one- and two-particle, proton and neutron drip lines within the Hartree-Fock-Bogoliubov theory using Skyrme interaction. We also determine an approximate $r$-process path defined as a line where the neutron binding energy is equal to 2~MeV. A weakening of the nuclear shell structure at drip lines is found and interpreted as resulting from a coupling with continuum states.
We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively different types of fires that superimpose to give the effective exponents typically measured in simulations. We show that this explains not only why the exponent characterizing the fire-size distribution changes with increasing correlation length, but allows also to predict its asymptotic value. We support our arguments by computer simulations of a coarse-grained model, by scaling arguments and by analyzing states that are created artificially by superimposing the two types of fires.
In a recent paper it has been shown how to create a quantum state related to the prime number sequence using Grover's algorithm. Moreover, its multiqubit entanglement was analyzed. In the present work, we compare the multiqubit entanglement of several quantum sequence states as well we study the feasibility of producing such states using Grover's algorithm.
When dissipative particles are left alone, their fluctuation energy decays due to collisional interactions, clusters build up and grow with time until the system size is reached. When the effective dissipation is strong enough, this may lead to the `inelastic collapse', i.e. the divergence of the collision frequency of some particles. The cluster growth is an interesting physical phenomenon, whereas the inelastic collapse is an intrinsic effect of the inelastic hard sphere (IHS) model used to study the cluster growth - involving only a negligible number of particles in the system. Here, we extend the IHS model by introducing an elastic contact energy and the related contact duration t_c. This avoids the inelastic collapse and allows to examine the long-time behavior of the system. For a quantitative description of the cluster growth, we propose a burning - like algorithm in continuous space, that readily identifies all particles that belong to the same cluster. The criterion for this is here chosen to be only the particle distance.   With this method we identify three regimes of behavior. First, for short times a homogeneous cooling state (HCS) exists, where a mean-field theory works nicely, and the clusters are tiny and grow very slowly. Second, at a certain time which depends on the system's properties, cluster growth starts and the clusters increase in size and mass until, in the third regime, the system size is reached and most of the particles are collected in one huge cluster.
Since its early phases of operation, the AGILE mission is successfully observing Gamma Ray Bursts (GRBs) in the hard X-ray band with the SuperAGILE imager and in the MeV range with the Mini-Calorimeter. Up to now, three firm GRB detections were obtained above 25 MeV and some bursts were detected with lower statistical confidence in the same energy band. When a GRB is localized, either by SuperAGILE or Swift/BAT or INTEGRAL/IBIS or Fermi/GBM or IPN, inside the field of view of the Gamma Ray Imager of AGILE, a detection is searched for in the gamma ray band or an upper limit is provided. A promising result of AGILE is the detection of very short gamma ray transients, a few ms in duration and possibly identified with Terrestrial Gamma-ray Flashes. In this paper we show the current status of the observation of Gamma Ray Bursts and Terrestrial Gamma-ray Flashes with AGILE.
The impact of the magnetic field on postbounce supernova dynamics of non-rotating stellar cores is studied by performing three-dimensional magnetohydrodynamics simulations with spectral neutrino transport. The explodability of strongly and weakly magnetized models of $20$ and $27$ $M_{\odot}$ pre-supernova progenitors are compared. We find that although the efficiency for the conversion of the neutrino heating into turbulent energy including magnetic fields in the gain region is not significantly different between the strong and weak field models, the amplified magnetic field due to the neutrino-driven convection on large hot bubbles just behind stalled shock results in a faster and more energetic explosion in the strongly magnetized models. In addition, by comparing the difference between the 2nd- and 5th-order spatial accuracy of the simulation in the strong field model for $27$ $M_{\odot}$ progenitor, we also find that the higher order accuracy in space is beneficial to the explosion because it enhances the growth of neutrino-driven convection in the gain region. Based on our results of core-collapse supernova simulations for the non-rotating model, a new possibility for the origin of the magnetic field of the protoneutron star (PNS) is proposed. The magnetic field is accumulated and amplified to magnetar level, that is, $\mathcal{O}(10^{14})$ G, in the convectively stable shell near the PNS surface.
Aims. We aim at finding candidates of potential survivors of high-redshift compact galaxies in SDSS, as targets for more detailed follow-up observations.   Methods. From the virial theorem it is expected that for a given mass, compact galaxies have stellar velocity dispersion higher than the mean due to their smaller sizes. Therefore velocity dispersion coupled with size (or mass) is an appropriate method to select relics, independent of the stellar population properties. Based on these consideration we design a set of criteria using distribution of early-type galaxies from SDSS on the log$_{10}$(R$_{0}$)-log$_{10}$($\sigma_{0}$) plane to find the most extreme objects on it.   Results. We find 76 galaxies at 0.05 < z < 0.2, which have properties similar to the typical quiescent galaxies at high redshift. We study how well these galaxies fit on well-known local universe relations of early-type galaxies such as the fundamental plane, the red sequence or mass-size relations. As expected from the selection criteria, the candidates are located in an extreme corner of mass-size plane. However, they do not extend as deeply into the so-called zone of exclusion as some of the high-redshift compact galaxies ('red nuggets') found at high redshift, being a factor 2-3 less massive at a given intrinsic scale size. Our candidates are systematically offset from scaling relations of average early-type galaxies, while being in the mass-size range expected for passive evolution of the red nuggets from their high redshift to the present.   Conclusions. The 76 selected candidates form a well suited set of objects for further follow-up observations. We argue that selecting a high velocity dispersion is the best way to find analogues of compact high redshift galaxies in the local universe.
We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern character class of the sequence and its Chern character with supports on the finite fibers. Next, we compute these classes in the situation encountered by the second author when proving a "Kodaira vanishing theorem" for arithmetic surfaces.
We theoretically investigate the production of polarization-entangled photons through the biexciton cascade decay in a single semiconductor quantum dot. To accomplish a high degree of entanglement, despite the exciton finestructure splitting, one must either energetically align the two exciton states by means of external fields or erase the which-path information by post-selecting photons within the correct frequency range. Here we show that in the latter scheme, as well as in related proposals, the photon state becomes deteriorated through dephasing processes in the solid, and the degree of entanglement remains low despite filtering.
We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent).
A converse method to the Construction of Salem (1945) of convergent families of Salem numbers is investigated in terms of an association between Salem polynomials and Hurwitz quotients via expansive polynomials of small Mahler measure. This association makes use of Bertin-Boyd's Theorem A (1995) of interlacing of conjugates on the unit circle; in this context, a Salem number $\beta$ is produced and coded by an m-tuple of positive rational numbers characterizing the (SITZ) Stieltjes continued fraction of the corresponding Hurwitz quotient (alternant). The subset of Stieltjes continued fractions over a Salem polynomial having simple roots, not cancelling at $\pm 1$, coming from monic expansive polynomials of constant term equal to their Mahler measure, has a semigroup structure. The sets of corresponding generalized Garsia numbers inherit this semi-group structure.
We construct one dimensional families of Abelian surfaces with quaternionic multiplication which also have an automorphism of order three or four. Using Barth's description of the moduli space of (2,4)-polarized Abelian surfaces, we find the Shimura curve parametrizing these Abelian surfaces in a specific case. We explicitly relate these surfaces to the Jacobians of genus two curves studied by Hashimoto and Murabayashi. We also describe a (Humbert) surface in Barth's moduli space which parametrizes Abelian surfaces with real multiplication by Z[\sqrt{2}].
Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time-parameterizations. Using molecular dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time-parameterization, one can distinguish different types of soft ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time-parameterizations can potentially be useful in simulations that combine molecular dynamics algorithms with randomized particle creation, annihilation, or decay processes.
This paper is concerned with the convergence of the solution of general elliptic boundary value problems in cylindrical domain, when some directions of the domain go to infinity.
Diophantine problems involving recurrence sequences have a long history and is an actively studied topic within number theory. In this paper, we connect to the field by considering the equation \begin{align*} B_mB_{m+d}\dots B_{m+(k-1)d}=y^\ell \end{align*} in positive integers $m,d,k,y$ with $\gcd(m,d)=1$ and $k\geq 2$, where $\ell\geq 2$ is a fixed integer and $B=(B_n)_{n=1}^\infty$ is an elliptic divisibility sequence, an important class of non-linear recurrences. We prove that the above equation admits only finitely many solutions. In fact, we present an algorithm to find all possible solutions, provided that the set of $\ell$-th powers in $B$ is given. (Note that this set is known to be finite.) We illustrate our method by an example.
The dominant baryonic component of galaxy clusters is hot gas whose distribution is commonly probed through X-ray emission arising from thermal bremsstrahlung. The density profile thus obtained has been traditionally modeled with a beta-profile, a simple function with only three parameters. However, this model is known to be insufficient for characterizing the range of cluster gas distributions, and attempts to rectify this shortcoming typically introduce additional parameters to increase the fitting flexibility. We use cosmological and physical considerations to obtain a family of profiles for the gas with fewer parameters than the beta-model but which better accounts for observed gas profiles over wide radial intervals.
The moduli space describing the low-energy dynamics of BPS multi-monopoles for several charge configurations is presented. We first prove the conjectured form of the moduli space of $n-1$ distinct monopoles in a spontaneously broken SU(n) gauge theory. We further propose the solution where one of the charge components has two units, hence asymptotically corresponds to embeddings of two monopoles of one charge type and the rest different. The latter hyperk\"ahler metrics possess features of the two-monopole Atiyah-Hitchin metric. We also conjecture classes of solutions to multi-monopole moduli spaces with arbitrary charge and no more than two units in each component, which models the gluing together of Atiyah-Hitchin metrics. Our approach here uses the generalized Legendre transform technique to find the new hyperk\"ahler manifolds and rederive previously conjectured ones.
We present the analysis of a sub-DLA system (log N(H^0)=20.0+/-0.15, z_abs=2.69) toward SDSS J123714+064759 (z_em=2.78). Using the VLT/UVES and X-shooter spectrographs, we detect H2, HD and CO molecules in absorption with log N(H2,HD,CO)=(19.21,14.48,14.17). The overall metallicity of the system is super-solar ([Zn/H]=+0.34) and iron is highly depleted ([Fe/Zn]=-1.39), revealing metal-rich and dusty gas. The strongest H2 component does not coincide with the centre of the HI absorption. This implies that the molecular fraction in this component, f=2N(H2)/(2N(H2)+N(H^0)), is larger than the mean molecular fraction <f>=1/4 in the system. This is supported by the detection of Cl^0 associated with this H2-component having N(Cl^0)/N(Cl^+)>0.4. Since Cl^0 is tied up to H2 by charge exchange reactions, this means that the molecular fraction in this component is not far from unity. The size of the molecular cloud is probably smaller than 1pc. Both the CO/H2=10^-5 and CO/C^0~1 ratios for f>0.24 indicate that the cloud classifies as translucent, i.e., a regime where carbon is found both in atomic and molecular form. The corresponding extinction, Av=0.14, albeit lower than the definition of a translucent sightline (based on extinction properties), is high for the observed H^0 column density. This means that intervening clouds with similar local properties but with larger column densities could be missed by current magnitude-limited QSO surveys. The excitation of CO is dominated by radiative interaction with the Cosmic Microwave Background Radiation (CMBR) and we derive Tex(CO)=10.5+0.8-0.6 K when TCMBR(z=2.69)=10.05 K is expected. The astration factor of deuterium -with respect to the primordial D/H ratio- is only about 3. This can be the consequence of accretion of unprocessed gas from the intergalactic medium onto the associated galaxy. [abridged]
We examine a superpotential for an SO(10) GUT and show that if the parameters of the superpotential are in a certain region, the SO(10) GUT has an intermediate symmetry ${\rm SU(2)}_L \otimes {\rm SU(2)}_R \otimes {\rm SU(3)}_C \otimes {\rm U(1)}_{B-L}$ which breaks down to the group of the Standard Model at an intermediate scale $10^{10-12}$ GeV. In the model by the breakdown of the symmetry right-handed neutrinos acquire mass of the intermediate scale through a renormalizable Yukawa coupling.