ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic 2D Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo simulations on square lattices with linear sizes L ranging from 32 up to 512. The statistical weight of the Metropolis algorithm was changed according to the nonextensive statistics. Discontinuities in the m(T) curve are observed for $q\leq 0.5$. However, we have verified only one peak on the energy histograms at the critical temperatures, indicating the occurrence of continuous phase transitions. For the $0.5<q\leq 1.0$ regime, we have found continuous phase transitions between the ordered and the disordered phases, and determined the critical exponents via finite-size scaling. We verified that the critical exponents $\alpha $, $\beta $ and $\gamma $ depend on the entropic index $q$ in the range $0.5<q\leq 1.0$ in the form $\alpha (q)=(10 q^{2}-33 q+23)/20$, $\beta (q)=(2 q-1)/8$ and $\gamma (q)=(q^{2}-q+7)/4$. On the other hand, the critical exponent $\nu $ does not depend on $q$. This suggests a violation of the scaling relations $2 \beta +\gamma =d \nu $ and $\alpha +2 \beta +\gamma =2$ and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.
First passage percolation on $\mathbb{Z}^2$ is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is $\mathbf{E}[\min\{\tau_1,\ldots,\tau_4\}]$, where $\tau_1,\ldots,\tau_4$ are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.
Following conservative solutions of the two-component Camassa-Holm system $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x=0$, $\rho_t+(u\rho)_x=0$ along characteristics, we determine if wave breaking occurs in the nearby future or not, for initial data $u_0\in H^1(\mathbb R)$ and $\rho_0\in L^2(\mathbb R)$.
We perform high-resolution cosmological hydrodynamic simulations to study the formation of the first galaxies that reach the masses of $10^{8-9}~h^{-1}~M_\odot$ at $z=9$. The resolution of the simulations is high enough to resolve minihaloes and allow us to successfully pursue the formation of multiple Population (Pop) III stars, their supernova (SN) explosions, resultant metal-enrichment of the inter-galactic medium (IGM) in the course of the build-up of the system. Metals are ejected into the IGM by multiple Pop III SNe, but some of the metal-enriched gas falls back onto the halo after $\gtrsim 100~\rm Myr$. The star formation history of the first galaxy depends sensitively on the initial mass function (IMF) of Pop III stars. The dominant stellar population transits from Pop III to Pop II at $z\sim 12-15$ in the case of power-law Pop III IMF, ${\rm d}n/{\rm d}M \propto M^{-2.35}$ with the mass range $10-500~M_\odot$. At $z\lesssim 12$, stars are stably formed in the first galaxies with a star formation rate of $\sim 10^{-3}$-$10^{-1}~M_\odot/{\rm yr}$. In contrast, for the case with a flat IMF, gas-deprived first galaxies form due to frequent Pop III pair-instability SNe, resulting in the suppression of subsequent Pop II star formation. In addition, we calculate UV continuum, Ly$\alpha$- and H$\alpha$-line fluxes from the first galaxies. We show that the James Webb Space Telescope will be able to detect both UV continuum, Ly$\alpha$ and H$\alpha$ line emission from first galaxies with halo mass $\gtrsim 10^{9}~M_\odot$ at $z \gtrsim 10$.
Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot...\cdot(n_lg)$ where $g\in G$ and $n_1,\cdots,n_l\in[1,{\hbox{\rm ord}}(g)]$, and the index $\ind(S)$ of $S$ is defined to be the minimum of $(n_1+\cdots+n_l)/\hbox{\rm ord}(g)$ over all possible $g\in G$ such that $\langle g\rangle=G$. A conjecture says that if $G$ is finite such that $\gcd(|G|,6)=1$, then $\ind(S)=1$ for every minimal zero-sum sequence $S$. In this paper, we prove that the conjecture holds if $S$ is reduced and at least one $n_i$ coprime to $|G|$.
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.
Superconductivity with a remarkably high $T_c$ has recently been found in Sr-doped NdNiO$_2$ thin films. While this system bears strong similarities to the cuprates, some differences, such as a weaker antiferromagnetic exchange coupling and possible high-spin moments on the doped Ni sites have been pointed out. Here, we investigate the effect of Hund coupling and crystal field splitting in a simple model system and argue that a multiorbital description of nickelate superconductors is warranted, especially in the strongly hole-doped regime. We then look at this system from the viewpoint of the spin-freezing theory of unconventional superconductivity, which provides a unified understanding of unconventional superconductivity in a broad range of compounds. Sr$_{0.2}$Nd$_{0.8}$NiO$_2$ falls into a parameter regime influenced by two spin-freezing crossovers, one related to the emergent multi-orbital nature in the strongly doped regime and the other related to the single-band character and square lattice geometry in the weakly doped regime.
The requirement of t-b-\tau Yukawa coupling unification is common in simple grand unified models based on the gauge group SO(10), and it also places a severe constraint on the expected spectrum of superpartners. For Yukawa-unified models with \mu >0, the spectrum is characterized by three mass scales: {\it i}). first and second generation scalars in the multi-TeV range, {\it ii}). third generation scalars, \mu and m_A in the few-TeV range and {\it iii}). gluinos in the \sim 350-500 GeV range with chargino masses around 100-160 GeV. In such a scenario, gluino pair production should occur at large rates at the CERN LHC, followed by gluino three-body decays into neutralinos or charginos. Discovery of Yukawa-unified SUSY at the LHC should hence be possible with only 1 fb^{-1} of integrated luminosity, by tagging multi-jet events with 2--3 isolated leptons, without relying on missing E_T. A characteristic dilepton mass edge should easily be apparent above Standard Model background. Combining dileptons with b-jets, along with the gluino pair production cross section information, should allow for gluino and neutralino mass reconstruction. A secondary corroborative signal should be visible at higher integrated luminosity in the W1Z2-> 3\ell channel, and should exhibit the same dilepton mass edge as in the gluino cascade decay signal.
We demonstrate that the space formed by the star-formation rate (SFR), gas-phase metallicity (Z), and stellar mass (M), can be reduced to a plane, as first proposed by Lara-Lopez et al. We study three different approaches to find the best representation of this 3D space, using a principal component analysis, a regression fit, and binning of the data. The PCA shows that this 3D space can be adequately represented in only 2 dimensions, i.e., a plane. We find that the plane that minimises the chi^2 for all variables, and hence provides the best representation of the data, corresponds to a regression fit to the stellar mass as a function of SFR and $Z$, M=f(Z,SFR). We find that the distribution resulting from the median values in bins for our data gives the highest chi^2. We also show that the empirical calibrations to the oxygen abundance used to derive the Fundamental Metallicity Relation (Nagao et al.) have important limitations, which contribute to the apparent inconsistencies. The main problem is that these empirical calibrations do not consider the ionization degree of the gas. Furthermore, the use of the N2 index to estimate oxygen abundances cannot be applied for ~8.8 because of the saturation of the [NII]6584 line in the high-metallicity regime. Finally we provide an update of the Fundamental Plane derived by Lara-Lopez et al.
We state two conjectures that together allow one to describe the set of smoothing components of a Gorenstein toric affine 3-fold in terms of a combinatorially defined and easily studied set of Laurent polynomials called 0-mutable polynomials. We explain the origin of the conjectures in mirror symmetry and present some of the evidence.
We analyze numerically and analytically the non linear transport properties of a drift-diffusion equation in presence of a magnetic field and of a disorder potential. For a wide range of parameters this model exhibits a plateau where the drift velocity is almost independent on the applied electric field. This behavior has strong similarities with the zero differential resistance states observed experimentally in high mobility two dimensional systems. Performed numerical simulations are in a good global agreement with the developed analytical theory even if the later leads to overestimated negative differential resistance values.
We perform N-body simulations for $f(T)$ gravity using the ME-Gadget code, in order to investigate for the first time the structure formation process in detail. Focusing on the power-law model, and considering the model-parameter to be consistent within 1$\sigma$ with all other cosmological datasets (such as SNIa, BAO, CMB, CC), we show that there are clear observational differences between $\Lambda$CDM cosmology and $f(T)$ gravity, due to the modifications brought about the latter in the Hubble function evolution and the effective $Newton\prime s$ constant. We extract the matter density distribution, matter power spectrum, counts-in-cells, halo mass function and excess surface density (ESD) around low density positions (LDPs) at present time. Concerning the matter power spectrum we find a difference from $\Lambda$CDM scenario, which is attributed to about 2/3 to the different expansion and to about 1/3 to the effective gravitational constant. Additionally, we find a difference in the cells, which is significantly larger than the Poisson error, which may be distinguishable with weak-lensing reconstructed mass maps. Moreover, we show that there are different massive halos with mass $M>10^{14}M_{\odot}/h$, which may be distinguishable with statistical measurements of cluster number counting, and we find that the ESD around LDPs is mildly different. In conclusion, high-lighting possible smoking guns, we show that large scale structure can indeed lead us to distinguish General Relativity and $\Lambda$CDM cosmology from $f(T)$ gravity.
We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by product, we suggest some applications of our work in the task of calibrating Numerical Relativity complex codes, usually written in Cartesian coordinates.
We report extensive spectroscopic and differential photometric BVRI observations of the active, detached, 1.309-day double-lined eclipsing binary IM Vir, composed of a G7-type primary and a K7 secondary. With these observations we derive accurate absolute masses and radii of M(1) = 0.981 +/- 0.012 M(Sun), M(2) = 0.6644 +/- 0.0048 M(Sun), R(1) = 1.061 +/- 0.016 R(Sun), and R(2) = 0.681 +/- 0.013 R(Sun) for the primary and secondary, with relative errors under 2%. The effective temperatures are 5570 +/- 100 K and 4250 +/- 130 K. The significant difference in mass makes this a favorable case for comparison with stellar evolution theory. We find that both stars are larger than the models predict, by 3.7% for the primary and 7.5% for the secondary, as well as cooler than expected, by 100 K and 150 K, respectively. These discrepancies are in line with previously reported differences in low-mass stars, and are believed to be caused by chromospheric activity, which is not accounted for in current models. The effect is not confined to low-mass stars: the rapidly-rotating primary of IM Vir joins the growing list of objects of near-solar mass (but still with convective envelopes) that show similar anomalies. The comparison with the models suggests an age of 2.4 Gyr for the system, and a metallicity [Fe/H] of approximately -0.3 that is consistent with other indications, but requires confirmation.
A new version of the semiempirical formula based on fission approach of alpha decay is derived, by using the optimum values of the fitting parameters determined for even-even nuclei, combined with hindrance factors for even-odd, odd-even, and odd-odd nuclides. The deviations from experimental data for two regions of nuclear chart (493 alpha emitters with Z=52-118 and 142 transuranium nuclei including superheavies (Z=92-118), respectively) are compared with those obtained by using the universal curve and the Viola-Seaborg semiempirical relationship.
We show how the expectation values of geometrical quantities in 3d quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin expansion of this value is dominated by the classical expression, and we study the next to leading order quantum corrections.
It is shown that the structure of the generalized quadrangle of order two is fully encoded in the properties of the Desargues configuration. A point of the quadrangle is represented by a geometric hyperplane of the Desargues configuration and its line by a set of three hyperplanes such that one of them is the complement of the symmetric difference of the remaining two and they all share a pair of non-collinear points.
Suppose that $N_0$ independently diffusing particles, each with diffusivity $D$, are initially released at $x=\ell>0$ on the semi-infinite interval $0\leq x<\infty$ with an absorber at $x=0$. We determine the probability ${\cal P}(N)$ that $N$ particles survive until time $t=T$. We also employ macroscopic fluctuation theory to find the most likely history of the system, conditional on there being exactly $N$ survivors at time $t=T$. Depending on the basic parameter $\ell/\sqrt{4DT}$, very different histories can contribute to the extreme cases of $N=N_0$ (all particles survive) and $N=0$ (no survivors). For large values of $\ell/\sqrt{4DT}$, the leading contribution to ${\cal P}(N=0)$ comes from an effective point-like quasiparticle that contains all the $N_0$ particles and moves ballistically toward the absorber until absorption occurs.
We investigate nuclear matter properties in the relativistic Brueckner approach. The in-medium on-shell T-matrix is represented covariantly by five Lorentz invariant amplitudes from which we deduce directly the nucleon self-energy. We discuss the ambiguities of this approach and the failure of previously used covariant representations in reproducing the nucleon self-energies on the Hartree-Fock level. To enforce correct Hartree-Fock results we develop a subtraction scheme which treats the bare nucleon-nucleon potential exactly in accordance to the different types of meson exchanges. For the remaining ladder kernel, which contains the higher order correlations, we employ then two different covariant representations in order to study the uncertainty inherent in the approach. The nuclear matter bulk properties are only slightly sensitive on the explicit representation used for the kernel. However, we obtain new Coester lines for the various Bonn potentials which are shifted towards the empirical region of saturation. In addition the nuclear equation-of-state turns out to be significantly softer in the new approach.
In Dubouloz and Mangolte (Fake real planes: exotic affine algebraic models of $\mathbb{R}^{2}$, arXiv:1507.01574, 2015) we define and partially classify fake real planes, that is, minimal complex surfaces with conjugation whose real locus is diffeomorphic to the euclidean real plane $\mathbb{R}^{2}$. Classification results are given up to biregular isomorphisms and up to birational diffeomorphisms. In this note, we describe in an elementary way numerous examples of fake real planes and we exhibit examples of such planes of every Kodaira dimension $\kappa\in \{-\infty,0,1,2\}$ which are birationally diffeomorphic to $\mathbb{R}^{2}$.
We study Mott insulator - superfluid transition in a two-band boson Hubbard model, which can be mapped onto a spin-1/2 XY model with spins coupled to an additional Ising degree of freedom. By using a modified mean field theory that include the effects of phase fluctuations, we show that the transition is first order at both zero and finite temperatures. On the Mott insulator side, there may be reentrance in phase transition. These features are consequences of the underlying transition between competing defect poor and defect rich phases. The relevance of the model and our results to supersolid 4He and cold bosonic atoms in optical lattices are discussed.
Monolayer semiconductors are atomically thin quantum wells with strong confinement of electrons in two-dimensional (2D) plane. Here, we experimentally study the out-of-plane polarizability of excitons in hBN-encapsulated monolayer WSe$_{2}$ in strong electric fields of up to 1.6 V/nm (16 MV/cm). We monitor free and bound exciton photoluminescence peaks with increasing electric fields at a constant carrier density, carefully compensating for unintentional photodoping in our double-gated device at 4K. We show that the Stark shift is < 0.4 meV despite the large electric fields applied, yielding an upper limit of polarizability {\alpha}$_{z}$ to be ~ 10$^{-11}$ Dm/V. Such a small polarizability, which is nearly two orders of magnitude smaller than the previously reported value for MoS$_{2}$, indicates strong atomic confinement of electrons in this 2D system and highlights the unusual robustness of free excitons against surface potential fluctuations.
We prove Behrend's conjecture on the rationality of the canonical reduction of principal bundles and reductive group schemes for classical groups and give new bounds for the conjecture for exceptional groups. However we find a counterexample in the case of G_2-bundles in characteristic 2.
Semiconductor-based Josephson junctions provide a platform for studying proximity effect due to the possibility of tuning junction properties by gate voltage and large-scale fabrication of complex Josephson circuits. Recently Josephson junctions using InAs weak link with epitaxial aluminum contact have improved the product of normal resistance and critical current, $I_cR_N$, in addition to fabrication process reliability. Here we study similar devices with epitaxial contact and find large supercurrent and substantial product of $I_cR_N$ in our junctions. However we find a striking difference when we compare these samples with higher mobility samples in terms of product of excess current and normal resistance, $I_{ex}R_N$. The excess current is negligible in lower mobility devices while it is substantial and independent of gate voltage and junction length in high mobility samples. This indicates that even though both sample types have epitaxial contacts only the high-mobility one has a high transparency interface. In the high mobility short junctions, we observe values of $I_cR_N/\Delta \sim 2.2$ and $I_{ex}R_N/\Delta \sim 1.5$ in semiconductor weak links.
It is shown that every regular electromagnetic field in vacuum identically satisfy Maxwell equations in a new manifold where the roles of space and time have been exchanged. The new metric is Lorentzian, depends on the particular solution and forces the flow of time to tilt somehow in the direction of the field lines. We give a detailed description of the transformation and discuss several of its properties, both in the algebraic and differential settings. Examples are given where the new metrics are explicitly computed and carefully analyzed. We conclude with possible applications of the transformation as well as future perspectives.
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. We study the relationship between linear complexity and expansion complexity. In particular, we show that for purely periodic sequences both figures of merit provide essentially the same quality test for a sufficiently long part of the sequence. However, if we study shorter parts of the period or nonperiodic sequences, then we can show, roughly speaking, that the expansion complexity provides a stronger test. We demonstrate this by analyzing a sequence of binomial coefficients modulo $p$. Finally, we establish a probabilistic result on the behavior of the expansion complexity of random sequences over a finite field.
This paper has been withdrawn. A significantly revised version will be posted in the near future.
We study surfaces of general type $S$ with $p_g=0$ and $K^2=3$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$. It is shown that, if $S/i$ is not rational, then $S/i$ is birational to an Enriques surface or it has Kodaira dimension $1$ and the possibilities for the ramification divisor of the covering map $S\rightarrow S/i$ are described. We also show that these two cases do occur, providing an example. In this example $S$ has a hyperelliptic fibration of genus $3$ and the bicanonical map of $S$ is of degree $2$ onto a rational surface.