ShantanuT01/DACTYL-Pretraining huggingface dataset:
The phase diagram for the interacting fermions in weak coupling is described by the perturbative renormalization group equations. Due to the lack of analytic solutions for these coupled non-linear differential equations, it is rather subtle to tell which couplings are relevant or irrelevant. We propose a powerful classification scheme to build up the hierarchy of the relevant couplings by a scaling Ansatz found numerically. To demonstrate its superiority over the conventional classification for the relevant couplings, we apply this scheme to a controversial phase transition in the two-leg ladder and show that it should be a non-trivial crossover instead. The scaling Ansatz we propose here can classify the relevant couplings in hierarchical order without any ambiguity and can improve significantly how we interpret the numerical outcomes in general renormalization group methods.
We prove that, under certain conditions on the function pair $\varphi_1$ and $\varphi_2$, bilinear average $p^{-1}\sum_{y\in \mathbb{F}_p}f_1(x+\varphi_1(y)) f_2(x+\varphi_2(y))$ along curve $(\varphi_1, \varphi_2)$ satisfies certain decay estimate. As a consequence, Roth type theorems hold in the setting of finite fields. In particular, if $\varphi_1,\varphi_2\in \mathbb{F}_p[X]$ with $\varphi_1(0)=\varphi_2(0)=0$ are linearly independent polynomials, then for any $A\subset \mathbb{F}_p, |A|=\delta p$ with $\delta>c p^{-\frac{1}{12}}$, there are $\gtrsim \delta^3p^2$ triplets $x,x+\varphi_1(y), x+\varphi_2(y)\in A$. This extends a recent result of Bourgain and Chang who initiated this type of problems, and strengthens the bound in a result of Peluse, who generalized Bourgain and Chang's work. The proof uses discrete Fourier analysis and algebraic geometry.
SGR J1745$-$2900 is a magnetar near the Galactic center. X-ray observations of this source found a decreasing X-ray luminosity accompanied by an enhanced spindown rate. This negative correlation between X-ray luminosity and spindown rate is hard to understand. The wind braking model of magnetars is employed to explain this puzzling spindown behavior. During the release of magnetic energy of magnetars, a system of particles may be generated. Some of these particles remain trapped in the magnetosphere and may contribute to the X-ray luminosity. The rest of the particles can flow out and take away the rotational energy of the central neutron star. A smaller polar cap angle will cause the decrease of X-ray luminosity and enhanced spindown rate of SGR J1745$-$2900. This magnetar is expected to have a maximum spindown rate shortly.
We present a framework for the detection and estimation of deformations applied to a grid of sources. Our formalism uses the Hamiltonian formulation of the quantum Fisher information matrix (\textsc{qfim}) as the figure of merit to quantify the amount of information we have on the deformation matrix. Quantum metrology for grid deformations provides an ideal testbed to examine multi-parameter estimations for arbitrarily parameterised channel evolutions with generally non-commuting Hermitian generators. We generalise the local generator of translations for deformation parameters to multi-parameter estimations and use it to explore how well different deformations can be detected and corrected for. This approach holds for any deformation. We explore the application of our theory to the set of affine geometry maps. Both the configuration of the grid and the properties of the sources help to maximise the sensitivity of the \textsc{qfim} to changes in the deformation parameters. For the non-multiplicative Hamiltonian parameterisations resulting from grid rotations about any chosen axis, oscillatory dependence of the \textsc{qfi} surfaces for a specific interplay between mutual source separation distances and grid configurations.
In this note, we consider radio characteristics of three proton flares that caused discrete enhancements of solar energetic particles (SEPs) near Earth. The analysis confirmed that the flux density and frequency spectrum of microwave bursts, although the latter are generated by electrons propagating to the photosphere, reflect the number and energy spectrum of accelerated particles, including the 10-100 MeV protons coming to Earth.
This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic arrangements to Dirichlet arrangements, including characteristic polynomials and supersolvability. We apply these results to visibility sets of order polytopes and fixed-energy harmonic functions on electrical networks.
We present a theory of cooperative light scattering valid in any dimension: connecting theories for an open line, open plane, and open space in the non-relativistic regime. This theory includes near-field and dipole-orientation effects, highlighting how field mode confinement controls the phenomena. We present a novel experimental implementation for planar collective effects.
We present observations of 18 galaxies from the Galaxy And Mass Assembly (GAMA) survey made with the SPIRAL optical integral field unit (IFU) on the Anglo-Australian Telescope. The galaxies are selected to have a narrow range in stellar mass (6x10^9Msolar < M* <2x10^10 Msolar) in order to focus on the effects of environment. Local galaxy environments are measured quantitatively using 5th nearest neighbour surface densities. We find that the total star formation rates (SFR) measured from the IFU data are consistent with total SFRs measured from aperture correcting either GAMA or Sloan Digital Sky Survey single-fibre observations. The mean differences are SFR_GAMA/SFR_IFU = 1.26+/-0.23, sigma=0.90 and for the Sloan Digital Sky Survey we similarly find SFR_Brinchmann/SFR_IFU = 1.34+/-0.17, sigma=0.67. Examining the relationships with environment, we find off-centre and clumpy Halpha emission is not significantly dependent on environment, being present in 2/7 (29^+20_-11 per cent) galaxies in high-density environments (>0.77 Mpc^-2), and 5/11 (45^+15_-13 per cent) galaxies in low-density environments (<0.77 Mpc^-2). We find a weak but not significant relationship of the total star formation rates of star-forming galaxies with environment. Due to the size of our sample and the scatter observed we do not draw a definitive conclusion about a possible SFR dependence on environment. Examining the spatial distribution of the Halpha emission, we find no evidence for a change in shape or amplitude of the radial profile of star-forming galaxies with environment. If these observations are borne out in larger samples this would infer that any environment-driven star-formation suppression must either act very rapidly (the `infall-and-quench' model) or that galaxies must evolve in a density-dependent manner (an `in-situ evolution' model).
Texture analysis and classification are some of the problems which have been paid much attention by image processing scientists since late 80s. If texture analysis is done accurately, it can be used in many cases such as object tracking, visual pattern recognition, and face recognition.Since now, so many methods are offered to solve this problem. Against their technical differences, all of them used same popular databases to evaluate their performance such asBrodatz or Outex, which may be made their performance biased on these databases. In this paper, an approach is proposed to collect more efficient databases of texture images. The proposed approach is included two stages. The first one is developing feature representation based on gray tone difference matrixes and local binary patterns features and the next one is consisted an innovative algorithm which is based on K-means clustering to collect images based on evaluated features. In order to evaluate the performance of the proposed approach, a texture database is collected and fisher rate is computed for collected one and well known databases. Also, texture classification is evaluated based on offered feature extraction and the accuracy is compared by some state of the art texture classification methods.
We determine the spectra of cubic plane graphs whose faces have sizes 3 and 6. Such graphs, "(3,6)-fullerenes", have been studied by chemists who are interested in their energy spectra. In particular we prove a conjecture of Fowler, which asserts that all their eigenvalues come in pairs of the form $\{\lambda,-\lambda\}$ except for the four eigenvalues $\{3,-1,-1,-1\}$. We exhibit other families of graphs which are "spectrally nearly bipartite" in this sense. Our proof utilizes a geometric representation to recognize the algebraic structure of these graphs, which turn out to be examples of Cayley sum graphs.
We consider the couplings of RR fields with open string sector for $Dp$-${\overline{Dp}}$ backgrounds of various $p$. Proposed approach, based on the approximation of the open string algebra by the algebra of differential operators, provides the unified description of these couplings and their interrelations.
Background : Several recent experiments report significant low-energy isoscalar monopole strength, below the giant resonance, in various nuclei. In light $\alpha$-conjugate nuclei, these low-energy resonances were recently interpreted as cluster vibration modes. However, the nature of these excitations in neutron-rich nuclei remain elusive.   Purpose : The present work provides a systematic analysis of the low-energy monopole strength in isotopic chains, from Neon to Germanium, in order to monitor and understand its nature and conditions of emergence.   Methods : We perform covariant quasiparticle random phase approximation (QRPA) calculations, formulated within the finite amplitude method (FAM), on top of constrained relativistic Hartree-Bogoliubov (RHB) reference states.   Results : Neutron excess leads to the appearance of low-energy excitations according to a systematic pattern reflecting the single-particle features of the underlying RHB reference state. With the onset of deformation, these low-energy resonances get split and give rise to more complex patterns, with possible mixing with the giant resonance. At lower energy, cluster-like excitations found in $N=Z$ systems survive in neutron-rich nuclei, with valence neutrons arranging in molecular-like orbitals. Finally, at very low energy, pair excitations are also found in superfluid nuclei, but remain negligible in most of the cases.   Conclusions : The low-energy part of the monopole strength exhibits various modes, from cluster vibrations ($\sim$ 5-10 MeV) to components of the giant resonance downshifted by the onset of deformation, including soft modes ($\sim$ 10-15 MeV) as well as pair excitation ($<$ 5 MeV), with possible mixing, depending on neutron-excess, deformation, and pairing energy.
The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. Here we elucidate the behavior of the trace distance, the Hilbert- Schmidt distance, the Bures distance, the Hellinger distance and the quantum Jensen-Shannon divergence for two system-environment setups, namely a qubit bi-linearly coupled to an infinite and a finite size environment with the latter composed of harmonic oscillators.
We present optical spectra of the Type Ic supernova 1994I in M51 and preliminary non-LTE analysis of the spectra. Our models are not inconsistent with the explosions of C+O cores of massive stars. While we find no direct evidence for helium in the optical spectra, our models cannot rule out small amounts of helium. More than 0.1~\msol\ of helium seems unlikely.
Adopting a spherically symmetric steady-state ballistic inflow as the kinematic model for the gas distribution responsible for producing the H{\alpha} emission line and a central black hole (BH) mass of 1.7 x10^6 M_sun, determined from prior reverberation mapping, leads to the following dimensions for the size of the broad line region (BLR) in NGC 4051; an inner radius ~3 lt-days and a lower limit to the outer radius ~ 475 lt-days. Thus, the previously determined reverberation size for the BLR marks just the inner radius of a much larger volume of ionized gas. The number of ionizing photons required to sustain the H{\alpha} emission line luminosity exceeds the number observed to be available from the central AGN by a factor of 3 - 4. Such a large ionizing deficit can be reconciled if the BLR is ionized by a 10^5 K accretion disk that is hidden from direct view by the high opacity of intervening H gas. A new definition is introduced for the ionization parameter that acknowledges the fact that H opacity significantly attenuates the flux of ionizing photons in the large, partially ionized, nebula surrounding the AGN. Collectively, these results have important implications for BH masses estimated using reverberation radii and the structure of the BLR inferred from velocity-delay maps.
We present a specially designed evolutionary algorithm for the prediction of surface reconstructions. This new technique allows one to automatically explore all the low-energy configurations with variable surface atoms and variable surface unit cells through the whole chemical potential range. The power of evolutionary search is demonstrated by the efficient identification of diamond 2*1 (100) and 2*1 (111) surfaces with a fixed number of surface atom and a fixed cell size. With further variation of surface unit cells, we study the reconstructions of the polar surface MgO (111). Experiment has detected an oxygen trimer (ozone) motif (Plass et al, 1998). We predict a new version of this motif which can be thermodynamically stable at extreme oxygen rich condition. Finally, we perform a variable stoichiometry search for a complex ternary system: semi-polar GaN (101bar1) with and without adsorbed oxygen. The search yields a non-intuitive reconstruction based on N3-trimers. These examples demonstrate that an automated scheme to explore the energy landscape of surfaces will improve our understanding of surface reconstructions. The method presented in this report can be generally applied to binary and multi-component systems.
With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistic physics. These relations are proved through the MaxEnt approach once again. It is found that for a reversible isothermal process, the information contained in the first and second laws of thermodynamics and the MaxEnt approach is equivalent. Moreover, these relations are used to derive the probability distribution functions in nonextensive and extensive statistics and calculate the generalized forces of some interesting systems. The results obtained are of universal significance.
We prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This result extends in some ways a classical result of Lions and Malgrange [12] and a recent result of the authors [10].
Near-infrared spectroscopy from APOGEE and wide-field optical photometry from Pan-STARRS1 have recently made possible precise measurements of the shape of the extinction curve for tens of thousands of stars, parameterized by R(V). These measurements revealed structures in R(V) with large angular scales, which are challenging to explain in existing dust paradigms. In this work, we combine three-dimensional maps of dust column density with R(V) measurements to constrain the three-dimensional distribution of R(V) in the Milky Way. We find that variations in R(V) are correlated on kiloparsec scales. In particular, most of the dust within one kiloparsec in the outer Galaxy, including many local molecular clouds (Orion, Taurus, Perseus, California, Cepheus), has a significantly lower R(V) than more distant dust in the Milky Way. These results provide new input to models of dust evolution and processing, and complicate application of locally derived extinction curves to more distant regions of the Milky Way and to other galaxies.
Four quantities deducible from nuclear structure experiments have been claimed to correlate to the slope parameter $L$ of the symmetry energy; the neutron skin thickness, the cross section of low-energy dipole (LED) mode, dipole polarizability $\alpha_D$, and $\alpha_D S_0$ (i.e. product of $\alpha_D$ and the symmetry energy $S_0$). By the calculations in the Hartree-Fock plus random-phase approximation with various effective interactions, we compare the correlations between $L$ and these four quantities. The correlation derived from different interactions and the correlation from a class of interactions that are identical in the symmetric matter as well as in $S_0$ are simultaneously examined. These two types of correlations may behave differently, as exemplified in the correlation of $\alpha_D$ to $L$. It is found that the neutron skin thickness and $\alpha_DS_0$ correlate well to $L$, and therefore are suitable for narrowing down the value of $L$ via experiments. The LED emergence and upgrowth makes the $\alpha_DS_0$-$L$ correlation strong, although these correlations are disarranged when neutron halo appears in the ground state.
In this paper we characterise univariate rational functions over a number field $\K$ having infinitely many points in the cyclotomic closure $\K^c$ for which the orbit contains a root of unity. Our results are similar to previous results of Dvornicich and Zannier describing all polynomials having infinitely many preperiodic points in $\K^c$.
In minimal SUSY-GUT models with $M_{SUSY}\ltap 1$ TeV, the renormalization group equations have a solution dominated by the infrared fixed point of the top Yukawa coupling. This fixed point predicts $m_t=(200\; {\rm GeV})\sin \beta $; combined with the LEP results it excludes $m_t\ltap 130$ GeV. For $m_t$ in the range 130-160 GeV, we discuss the sensitivity of the $m_t$ fixed point result to GUT threshold corrections and point out the implications for Higgs boson searches. The lightest scalar $h$ has mass 60-85 GeV and will be detectable at LEPII. At SSC/LHC, each of the five scalars $h$, $H$, $A$, $H^{\pm }$ may be detectable, but not all of them together; in one parameter region none will be detectable.
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\chi$D) phenomenon. The existence of M$\chi$D phenomenon in $^{105}$Rh is highly expected.
We present a comprehensive timing and spectral studies of Be/X-ray binary pulsar EXO 2030+375 using extensive Rossi X-ray Timing Explorer observations from 1995 till 2011, covering numerous Type I and 2006 Type II outbursts. Pulse profiles of the pulsar were found to be strongly luminosity dependent. At low luminosity, the pulse profile consisted of a main peak and a minor peak that evolved into a broad structure at high luminosity with a significant phase shift. A narrow and sharp absorption dip, also dependent on energy and luminosity, was detected in the pulse profile. Comparison of pulse profiles showed that the features at a particular luminosity are independent of type of X-ray outbursts. This indicates that the emission geometry is solely a function of mass accretion rate. The broadband energy spectrum was described with a partial covering high energy cutoff model as well as a physical model based on thermal and bulk Comptonization in accretion column. We did not find any signature of cyclotron resonance scattering feature in the spectra obtained from all the observations. A detailed analysis of spectral parameters showed that, depending on source luminosity, the power-law photon index was distributed in three distinct regions. It suggests the phases of spectral transition from sub-critical to super-critical regimes in the pulsar as proposed theoretically. A region with constant photon index was also observed in ~(2-4) x 10^37 erg/s range, indicating critical luminosity regime in EXO 2030+375.
The standard diffusion processes are known to be obtained as the limits of appropriate random walks. These prelimiting random walks can be quite different however. The diffusion coefficient can be made responsible for the size of jumps or for the intensity of jumps. The "rough" diffusion limit does not feel the difference. The situation changes, if we model jump-type approximations via CTRW with non-exponential waiting times. If we make the diffusion coefficient responsible for the size of jumps and take waiting times from the domain of attraction of an $\alpha$-stable law with a constant intensity $\al$, then the standard scaling would lead in the limit of small jumps and large intensities to the most standard fractional diffusion equation. However, if we choose the CTRW approximations with fixed jump sizes and use the diffusion coefficient to distinguish intensities at different points, then we obtain in the limit the equations with variable position-dependent fractional derivatives. In this paper we build rigorously these approximations and prove their convergence to the corresponding fractional equations for the cases of multidimensional diffusions and more general Feller processes.
Let $(A,\Theta)$ be a complex principally polarized abelian variety of dimension $g\geq 4$. Based on vanishing theorems, differentiation techniques and intersection theory, we show that whenever the theta divisor $\Theta$ is irreducible, its multiplicity at any point is at most $g-2$. This improves work of Koll\'ar, Smith-Varley, and Ein-Lazarsfeld. We also introduce some new ideas to study the same type of questions for pluri-theta divisors.
We report the detection of a strong submillimeter wavelength HCN laser line at a frequency near 805 GHz toward the carbon star IRC+10216. This line, the J=9-8 rotational transition within the (04(0)0) vibrationally excited state, is one of a series of HCN laser lines that were first detected in the laboratory in the early days of laser spectroscopy. Since its lower energy level is 4200 K above the ground state, the laser emission must arise from the inner part of IRC+10216's circumstellar envelope. To better characterize this environment, we observed other, thermally emitting, vibrationally excited HCN lines and find that they, like the laser line, arise in a region of temperature approximately 1000 K that is located within the dust formation radius; this conclusion is supported by the linewidth of the laser. The (04(0)0), J=9-8 laser might be chemically pumped and may be the only known laser (or maser) that is excited both in the laboratory and in space by a similar mechanism.
We investigate the velocity dependence of kinetic friction with a model which makes minimal assumptions on the actual mechanism of friction so that it can be applied at many scales provided the system involves multi-contact friction. Using a recently developed master equation approach we investigate the influence of two concurrent processes. First, at a nonzero temperature thermal fluctuations allow an activated breaking of contacts which are still below the threshold. As a result, the friction force monotonically increases with velocity. Second, the aging of contacts leads to a decrease of the friction force with velocity. Aging effects include two aspects: the delay in contact formation and aging of a contact itself, i.e., the change of its characteristics with the duration of stationary contact. All these processes are considered simultaneously with the master equation approach, giving a complete dependence of the kinetic friction force on the driving velocity and system temperature, provided the interface parameters are known.