ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the thermal phase transitions in a classical (hard-core) lattice gas model with nearest-neighbor three-body interactions on the honeycomb lattice, based on parallel tempering Monte Carlo simulations. This system realizes incompressible low-temperature phases at fractional fillings of 9/16, 5/8 and 3/4 that were identified in a previous study of a related quantum model. In particular, both the 9/16 and the 5/8 phase exhibit an extensive ground state degeneracy reflecting the frustrated nature of the three-body interactions on the honeycomb lattice. The thermal melting of the 9/16 phase is found to be a first-order, discontinuous phase transition. On the other hand, from the thermodynamic behavior we obtain indications for a four-states Potts-model thermal transition out of the 5/8 phase. Employing an exact mapping to a hard-core dimer model on an embedded honeycomb super-lattice, we find that this thermal Potts-model transition relates to the selection of one out of four extensive sectors within the low-energy manifold of the 5/8 phase.
We prove that there exists a constant $c > 0$ such that the vertices of every strongly $c \cdot kt$-connected tournament can be partitioned into $t$ parts, each of which induces a strongly $k$-connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of K\"uhn, Osthus and Townsend (2016).
We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension $d \geq 2$.
Context. The diffusive shock acceleration mechanism has been widely accepted as the acceleration mechanism for galactic cosmic rays. While self-consistent hybrid simulations have shown how power-law spectra are produced, detailed information on the interplay of diffusive particle motion and the turbulent electromagnetic fields responsible for repeated shock crossings are still elusive. Aims. The framework of test-particle theory is applied to investigate the effect of diffusive shock acceleration by inspecting the obtained cosmic-ray energy spectra. The resulting energy spectra can be obtained this way from the particle motion and, depending on the prescribed turbulence model, the influence of stochastic acceleration through plasma waves can be studied. Methods. A numerical Monte-Carlo simulation code is extended to include collisionless shock waves. This allows one to trace the trajectories of test particle while they are being accelerated. In addition, the diffusion coefficients can be obtained directly from the particle motion, which allows for a detailed understanding of the acceleration process. Results. The classic result of an energy spectrum with $E^{-2}$ is only reproduced for parallel shocks, while, for all other cases, the energy spectral index is reduced depending on the shock obliqueness. Qualitatively, this can be explained in terms of the diffusion coefficients in the directions that are parallel and perpendicular to the shock front.
Over the last number of years spectroscopic studies have strongly supported the assertion that protostellar accretion and outflow activity persists to the lowest masses. In this paper we present the results of our latest investigation of brown dwarf (BD) outflow activity and report on the discovery of two new outflows. Here ISO-Oph 32 is shown to drive a blue-shifted outflow with a radial velocity of 10-20 km/s and spectro-astrometric analysis constrains the position angle of this outflow to 240 +/- 7 degrees. The BD candidate ISO-Cha1 217 is found to have a bipolar outflow bright in several key forbidden lines (radial velocity = -20 km/s, +40 km/s) and with a PA of 190-210 degrees. A striking feature of the ISO-Cha1 217 outflow is the strong asymmetry between the red and blue-shifted lobes. This asymmetry is revealed in the relative brightness of the two lobes (red-shifted lobe is brighter), the factor of two difference in radial velocity (the red-shifted lobe is faster) and the difference in the electron density (again higher in the red lobe). Such asymmetries are common in jets from low mass protostars and the observation of a marked asymmetry at such a low mass supports the idea that BD outflow activity is scaled down from low mass protostellar activity.   In addition to presenting these new results, a comprehensive comparison is made between BD outflow activity and jets launched by CTTSs. In particular, the application of current methods for investigating the excitation conditions and mass loss rates in CTT jets to BD spectra is explored.
An important dynamic parameter of barred galaxies is the bar pattern speed. Among several methods that are used for the determination of the pattern speed the Tremaine-Weinberg method has the advantage of model independency and accuracy. In this work we apply the method to a simulated bar including gas dynamics and study the effect of 2D spectroscopy data quality on robustness of the method. We added a white noise and a Gaussian random field to the data and measured the corresponding errors in the pattern speed. We found that a signal to noise ratio in surface density ~5 introduces errors of ~20% for the Gaussian noise, while for the white noise the corresponding errors reach ~50%. At the same time the velocity field is less sensitive to contamination. On the basis of the performed study we applied the method to the NGC 3367 spiral galaxy using H{\alpha} Fabry-Perot interferometry data. We found for the pattern speed 43 \pm 6 km/s/kpc for this galaxy.
We study the systematics of the giant dipole resonance width $\Gamma$ in hot rotating nuclei as a function of temperature $T$, spin $J$ and mass $A$. We compare available experimental results with theoretical calculations that include thermal shape fluctuations in nuclei ranging from A=45 to A=208. Using the appropriate scaled variables, we find a simple phenomenological function $\Gamma(A,T,J)$ which approximates the global behavior of the giant dipole resonance width in the liquid drop model. We reanalyze recent experimental and theoretical results for the resonance width in Sn isotopes and $^{208}$Pb.
Utilizing the Haar transform, we study the higher order spectral properties of mean field avalanche models, whose avalanche dynamics are described by Poisson statistics at a critical point or critical depinning transition. The Haar transform allows us to obtain a time series of noise powers, $H(f_1,t)$, that gives improved time resolution over the Fourier transform. Using $H(f_1,t)$ we analytically calculate the Haar power spectrum, the real 1.5 spectra, the second spectra, and the real cross second spectra in mean field avalanche models. We verify our theoretical results with the numerical results from a simulation of the T=0 mean field nonequilibrium random field Ising model (RFIM). We also extend our higher order spectra calculation to data obtained from a numerical simulation of the T=0 infinite range RFIM for $d=3$, and experimental data obtained from an amorphous alloy, $Fe_{21}Co_{64}B_{15}$. We compare the results and obtain novel exponents.
We examine and quantify how hybrid (e.g., UV+IR) star formation rate (SFR) estimators and the $A_{\rm FUV}$-$\beta$ relation depend on inclination for disk-dominated galaxies using spectral energy distribution modeling that utilizes the inclination-dependent attenuation curves described in Doore et al. We perform this analysis on a sample of 133 disk-dominated galaxies from the CANDELS fields and 18 disk galaxies from the Spitzer Infrared Nearby Galaxies Survey and Key Insights on Nearby Galaxies: A Far-Infrared Survey with Herschel samples. We find that both the hybrid SFR estimators and the $A_{\rm FUV}$-$\beta$ relation present clear dependencies on inclination. To quantify this dependence in the hybrid SFR estimators, we derive an inclination and a far-UV and near-IR color-dependent parametric relation for converting observed UV and IR luminosities into SFRs. For the $A_{\rm FUV}$-$\beta$ relation, we introduce an inclination-dependent component that accounts for the majority of the inclination dependence with the scatter of the relation increasing with inclination. We then compare both of these inclination-dependent relations to similar inclination-independent relations found in the literature. From this comparison, we find that the UV+IR correction factor and $A_{\rm FUV}$ for our hybrid and $A_{\rm FUV}$-$\beta$ relations, respectively, result in a reduction in the residual scatter of our sample by approximately a factor of 2. Therefore, we demonstrate that inclination must be considered in hybrid SFR estimators and the $A_{\rm FUV}$-$\beta$ relation to produce more accurate SFR estimates in disk-dominated galaxies.
Amorphous films of tantalum oxide (Ta2O5) are widely applied to build highly reflective mirrors used in interferometric gravitational wave detectors, such as the Laser Interferometer Gravitational Wave Observatory (LIGO). Despite a large number of studies, the structural properties of amorphous Ta2O5 at the local scale still deserve several further investigations. Such information is essential to any attempt to understand the properties of this important material and no property modelling efforts can be expected to yield reliable information until the local structure in the amorphous phase is better understood. In this paper we report the results obtained by analysing the synchrotron X-ray pair distribution functions of pure and Ti-doped amorphous Ta2O5 film, deposited by ion beam sputtering, as prepared and after a thermal treatment. As a result, it is found that 1) the arrangement of Ta atoms in amorphous Ta2O5 strongly resembles that characterizing the high-pressure Z-Ta2O5 polymorph, whereas the topological properties of O atoms resembles that observed in delta-Ta2O5; 2) structural correlations in amorphous Ta2O5 start to vanish above ~ 5 Angstrom and are completely suppressed for r > 10 Angstrom on account of disorder; 3) Ti substitution retains the short-range topological ordering characterizing the as prepared Ta2O5 amorphous film even after thermal treatment; conversely, pure Ta2O5 films undergoes a significant rearrangement of the local structure after thermal treatment.
The paper describes behavior of log-inflection points of curves in $(\mathbb{C}^*)^2$ under passing to the tropical limit. We show that such points accumulate by pairs at the midpoints of bounded edges in the limiting tropical curve. Log-inflection points are points of inflection with respect to the parallelization of $(\mathbb{C}^*)^2$ given by the multiplicative group law.
It is well known that BRST symmetry plays a fundamental role in constructing quantum gauge theories. Yet, at the classical level, it constitutes the modern language to study constrained systems. First, this letter reviews the Sp(2) covariant quantisation of gauge theories, so that the geometrical interpretation of gauge theories in terms of quasi-principal fibre bundles Q(Ms, Gs) is the main scenario. It is then described the Sp(2) algebra for ordinary Yang-Mills theory. Some basic set theory and topology terms are reviewed to proceed then to use theorems on left inverse and right inverse of functions together with groups (Ms, Gs) to have triangular compositions of functions on manifolds. Henceforth, it is so the purpose of this letter to present topological structures to gauge theories, in particular to construct commutative diagrams for cocycle conditions of the Sp(2) symmetry.
We give new results on the growth of the number of particles in a dyadic branching Brownian motion which follow within a fixed distance of a path $f:[0,\infty)\to \mathbb{R}$. We show that it is possible to count the number of particles without rescaling the paths. Our results reveal that the number of particles along certain paths can oscillate dramatically. The methods used are entirely probabilistic, taking advantage of the spine technique developed by, amongst others, Lyons et al, Kyprianou, and Hardy & Harris.
This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued c\`adl\`ag weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process $A$ such that $[N,A] = 0$, for any continuous local martingale $N$. Given a function $u:[0,T] \times \mathbb{R} \to \mathbb{R}$, which is of class $C^{0,1}$ (or sometimes less), we provide a chain rule type expansion for $u(t,X_t)$ which stands in applications for a chain It\^o type rule.
We report a Raman scattering study of polycrystalline CaCu$_3$Ti$_4$O$_{12}$ (CCTO) under pressure up to 5.32 GPa. The pressure dependence of several Raman modes was investigated. No anomalies have been observed on the phonon spectra thereby indicating that the T$_{h}$ (Im$\bar 3$) structure remains stable for pressures up to 5.32 GPa. The pressure coefficients for the observed modes were determined. This set of parameters was used for evaluating the stress developed in CCTO thin films.
Nova outbursts take place in binary star systems comprising a white dwarf (WD) and either a low-mass Sun-like star (classical novae) or, a red giant. GeV gamma-ray emission has been detected from a dozen of classical novae and from one novae in symbiotic system (V407 Cyg) by Fermi-LAT. For classical novae, gamma-ray emission is generally thought to be related to internal shocks formed as fast outflow collides with the slow outflow. However, for V407 Cyg, the origin of the gamma-ray emission has been debated, as both internal shock and external shock, resulted from the collision between the nova ejecta and the ambient wind of the giant companion, were suggested to explain the gamma-ray data. Recently, bright GeV and TeV gamma-ray emission has been detected from a nova in symbiotic system, RS Ophiuchi, during its 2021 outburst, which shows a remarkably smooth power-law decay in time up to about one month after the outburst. We show that this temporal decay behavior can be interpreted as arising from an adiabatic external shock expanding in the red giant wind. In this interpretation, the gamma-rays are produced by shock-accelerated protons interacting with the dense wind through the hadronic process. We also derive the scaling relations for the decay slopes for both adiabatic and radiative nova shocks in the self-similar deceleration phase.
We present rigorous results on some open questions on NSRPS, non sequential recursive pairs substitution method (see Grassberger in \cite{G}). In particular, starting from the action of NSRPS on finite strings we define a corresponding natural action on measures and we prove that the iterated measure becomes asymptotically Markov. This certify the effectiveness of NSRPS as a tool for data compression and entropy estimation.
To investigate the magnetic properties of SmFe$_{12}$, we construct an effective spin model, where magnetic moments, crystal field (CF) parameters, and exchange fields at 0 K are determined by first principles. Finite temperature magnetic properties are investigated by using this model. We further develop an analytical method with strong mixing of states with different quantum number of angular momentum $J$ ($J$-mixing), which is caused by strong exchange field acting on spin component of 4$f$ electrons. Comparing our analytical results with those calculated by Boltzmann statistics, we clarify that the previous analytical studies for Sm transition metal compounds over-estimate the $J$-mixing effects. The present method enables us to make quantitative analysis of temperature dependence of magnetic anisotropy (MA) with high-reliability. The analytical method with model approximations reveals that the $J$-mixing caused by exchange field increases spin angular momentum, which enhances the absolute value of orbital angular momentum and MA constants via spin-orbit interaction. It is also clarified that these J-mixing effects remain even above room temperature. Magnetization of SmFe$_{12}$ shows peculiar field dependence known as first-order magnetization process (FOMP), where the magnetization shows an abrupt change at certain magnetic field. The result of the analysis shows that the origin of FOMP is attributed to competitive MA constants between positive $K_1$ and negative $K_2$. The sign of $K_{1(2)}$ appears due to an increase in CF potential denoted by the parameter $A_2^0\langle r^2\rangle$ ($A_4^0\langle r^4\rangle$) caused by hybridization between 3$d$-electrons of Fe on 8$i$ (8$j$) site and 5$d$ and 6$p$ valence electrons on Sm site. It is verified that the requirement for the appearance of FOMP is given as $-K_2<K_1<-6K_2$.
The experimental results on transverse momentum azimuthal hadron correlations at RHIC have opened a rich field for parton energy loss analysis in heavy-ion collisions. Recently, a considerable amount of work has beendevoted to study the shapes of the ``away-side'' jet which exhibit an interesting and unexpected ``double hump'' structure not observed in the analogous treatment of $pp$ data. Driven by the possibility that the latter result might just mean that such structure exists already in the case of $pp$ collisions, but that its relative intensity could be small, here we use the Event Shape Analysis to show that it is possible to identify and select well defined event topologies in $pp$ collisions, among which, a double hump structure for the away-side jet emerges. Using two shape parameters, the sphericity in the transverse plane and the recoil to analyze a sample of PYTHIA generated $pp$ collisions at $\sqrt{s_{NN}}=200$ GeV, we show that this structure corresponds to two jets emitted in the backward hemisphere. Finally, we show that Q-PYTHIA qualitatively reproduces the decrease in the yield of dijet events and the increase of the double hump structure in the away side observed in heavy ion collisions. The implications for the treatment of parton energy loss in heavy-ion collisions are discussed
Banded spherulitic growth of crystal is observed in some materials with spherically symmetric growth front and periodic radial variation of birefringence. This variation of birefringence in quasi two dimensional geometry produces concentric interference colour bands when viewed through crossed polarisers. In most materials, the banded spherulites are found to be formed by radially oriented periodically twisted fibrillar crystallites. Here, we report the formation of banded spherulites due to the rhythmic growth of concentric crystallite-rich and crystallite-poor bands for a pure compound consisting of strongly polar rod like molecules. The compound exhibits coexistence of untwisted fibrillar crystallites and an amorphous phase in its most stable solid state. On sufficient supercooling of the sample from its melting point, the banded spherulites are formed with a periodic variation of composition of untwisted radially aligned fibrillar crystallites and an amorphous solid phase. We have developed a time dependent Ginzburg-Landau model to account for the observed banded spherulitic growth.
We present detailed measurements of the redshift path density, equivalent width distribution, column density distribution, and redshift evolution of ${\MgII}$ absorbers as measured in archival spectra from the UVES spectrograph at the Very Large Telescope (VLT/UVES) and the HIRES spectrograph at the Keck Telescope (Keck/HIRES) to equivalent width detection limits below $0.01$~{\AA}. This survey examines 432 VLT/UVES spectra from the UVES SQUAD collaboration and 170 Keck/HIRES spectra from the KODIAQ group, allowing for detections of intervening ${\MgII}$ absorbers spanning redshifts $0.1 < z < 2.6$. We employ an accurate, automated approach to line detection which consistently detects redshifted absorption lines. We measure the equivalent widths, apparent optical depth column densities, and velocity widths for each absorbing system. Using our complete sample of all detectable ${\MgII}$ absorbers, we can accurately determine the redshift path density of absorbers across cosmic time. We measure evolution in the comoving ${\MgII}$ line density, $dN\,/dX$, finding more high equivalent width absorbers at $z = 2$ than at present. We also measure evolution in the equivalent width distribution, parameterized by a Schechter function fit, finding a shallower weak-end slope for absorbers at redshifts between $1.53 < z < 2.64$ as compared to lower redshifts. Finally, we calculate the cosmic mass fraction of ${\MgII}$ using the column density distribution. We find that weak ${\MgII}$ absorbers, those with equivalent widths less than $0.3$~{\AA}, are physically distinct and evolve separately from very strong ${\MgII}$ absorbers, which have equivalent widths greater than $1.0$~{\AA}.
We study the Persistence properties of the T=0 coarsening dynamics of one dimensional $q$-state Potts model using a modified mean-field approximation (MMFA). In this approximation, the spatial correlations between the interfaces separating spins with different Potts states is ignored, but the correct time dependence of the mean density $P(t)$ of persistent spins is imposed. For this model, it is known that $P(t)$ follows a power-law decay with time, $P(t)\sim t^{-\theta(q)}$ where $\theta(q)$ is the $q$-dependent persistence exponent. We study the spatial structure of the persistent region within the MMFA. We show that the persistent site pair correlation function $P_{2}(r,t)$ has the scaling form $P_{2}(r,t)=P(t)^{2}f(r/t^{{1/2}})$ for all values of the persistence exponent $\theta(q)$. The scaling function has the limiting behaviour $f(x)\sim x^{-2\theta}$ ($x\ll 1$) and $f(x)\to 1$ ($x\gg 1$). We then show within the Independent Interval Approximation (IIA) that the distribution $n(k,t)$ of separation $k$ between two consecutive persistent spins at time $t$ has the asymptotic scaling form $n(k,t)=t^{-2\phi}g(t,\frac{k}{t^{\phi}})$ where the dynamical exponent has the form $\phi$=max(${1/2},\theta$). The behaviour of the scaling function for large and small values of the arguments is found analytically. We find that for small separations $k\ll t^{\phi}, n(k,t)\sim P(t)k^{-\tau}$ where $\tau$=max($2(1-\theta),2\theta$), while for large separations $k\gg t^{\phi}$, $g(t,x)$ decays exponentially with $x$. The unusual dynamical scaling form and the behaviour of the scaling function is supported by numerical simulations.
This paper deals with an inverse problem for a non-self-adjoint Schr\"odinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to Neumann map. We establish in dimension n greater than 2, an H\"older type stability estimate for the inverse problem under study. The proof is mainly based on the reduction to an equivalent problem for an electro-magnetic Schr\"odinger equation and the use of a Carleman estimate designed for elliptic operators.
The deep-inelastic deuteron structure function (SF) $F_2^D(x_D,Q^2)$ in the covariant approach in light-cone variables is considered. The $x_D$ and $Q^2$-dependences of SF are calculated. The QCD analysis of generated data both for non-cumulative $x_D<1$ and cumulative $x_D>1$ ranges was performed. It was shown that $Q^2$-evolution of SF is valid for ranges $0.275<x_D<0.85$ and $1.1<x_D<1.4$ for the same value of QCD scale parameter ${\Lambda}$. It was found the $x_D$-dependence of SF for the ranges is essentially different.