ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider a particle performing a stochastic motion on a one-dimensional lattice with jump widths distributed according to a power-law with exponent $\mu + 1$. Assuming that the walker moves in the presence of a distribution $a(x)$ of targets (traps) depending on the spatial coordinate $x$, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions $a(x) \sim x^{-\alpha}$ and we find that as long as $\mu < \alpha$ there is a finite probability that the walker will never be trapped, no matter how long the process is. This analytical result, valid on infinite chains, is corroborated by numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.
We investigate asymptotic behaviors of a metric viscosity solution of a Hamilton-Jacobi equation defined on a general metric space in Gangbo-\'{S}wi\c{e}ch sense. Our results include general stability and large time behavior of the solution.
We report the first result of weak gravitational lensing survey on a 2.1 sq deg Rc-band image taken with a wide field camera (Suprime-Cam) on the prime focus of 8.2 m Subaru Telescope. The weak lensing mass reconstruction is applied to the data to search for dark matter halos of cluster scale; M >= 10^14 solar mass. The reconstructed convergence field is divided by 1-sigma noise to obtain the signal-to-noise ratio map (S/N-map) of the detection. Local maxima and minima are searched on the S/N-map and the probability distribution function (PDF) of the peaks are created to compare with model predictions. We found excess over noise PDF created from the randomized realization on both positive and negative sides. Negative peaks imply the presence of voids in the dark matter distribution and this is the first report of the detection. Positive peaks, on the other hand, represent the dark matter halos and the number count of the halos on the 2.1 sq deg image is 4.9 +- 2.3 for S/N > 5 where the Gaussian smoothing radius of the convergence map is 1'. The result is consistent with the prediction assuming the Press-Schechter mass function and the NFW halo profile under the cluster normalized CDM cosmology. Although the present statistics is not enough due to the limited field of view, this work demonstrates that dark matter halo count via weak lensing is a promising way to test the paradigm of structure formation and cosmological model.
We prove existence of global in time strong solutions to the truncated thermo- visco-plasticity with an inelastic constitutive function of Norton-Hoff type. This result is a starting point to obtain renoramlised solutions for the considered model without truncations. The method of our proof is based on Yosida approximation of the maximal monotone term and a passage to the limit.
A class of exact solutions of the Einstein field equations representing non-static wormholes that obey the {\em weak and dominant energy conditions } is presented. Hence, in principle, these wormholes can be built with less exotic matter than the static ones.
In the framework of the simplest little Higgs model (SLHM), we study the production of a pair of neutral CP-even Higgs bosons at the LHC. First, we examine the production rate and find that it can be significantly larger than the SM prediction. Then we investigate the decays of the Higgs-pair and find that for a low Higgs mass their dominant decay mode is hh->\eta\eta\eta\eta (\eta is a CP-odd scalar) while hh->b\bar{b}\eta\eta and hh->\eta\eta WW may also have sizable ratios. Finally, we comparatively study the rates of pp-> hh -> b\bar{b}\tau^+ \tau^-, pp->hh->b\bar{b}\gamma\gamma, and pp->hh->WWWW in the SLHM and the littlest Higgs models (LHT). We find that for a light Higgs, compared with the SM predictions, all the three rates can be sizably enhanced in the LHT but severely suppressed in the SLHM; while for an intermediately heavy Higgs, both the LHT and SLHM can enhance sizably the SM predictions.
We study a duality that relates the T^6/Z_2 orientifold with N=2 flux to standard fluxless Calabi-Yau compactifications of type IIA string theory. Using the duality map, we show that the Calabi-Yau manifolds that arise are abelian surface (T^4) fibrations over P^1. We compute a variety of properties of these threefolds, including Hodge numbers, intersection numbers, discrete isometries, and H_1(X,Z). In addition, we show that S-duality in the orientifold description becomes T-duality of the abelian surface fibers in the dual Calabi-Yau description. The analysis is facilitated by the existence of an explicit Calabi-Yau metric on an open subset of the geometry that becomes an arbitrarily good approximation to the actual metric (at most points) in the limit that the fiber is much smaller than the base.
We present near-infrared interferometry of the carbon-rich asymptotic giant branch (AGB) star R Sculptoris.   The visibility data indicate a broadly circular resolved stellar disk with a complex substructure. The observed AMBER squared visibility values show drops at the positions of CO and CN bands, indicating that these lines form in extended layers above the photosphere. The AMBER visibility values are best fit by a model without a wind. The PIONIER data are consistent with the same model. We obtain a Rosseland angular diameter of 8.9+-0.3 mas, corresponding to a Rosseland radius of 355+-55 Rsun, an effective temperature of 2640+-80 K, and a luminosity of log L/Lsun=3.74+-0.18. These parameters match evolutionary tracks of initial mass 1.5+-0.5 Msun and current mass 1.3+-0.7 Msun. The reconstructed PIONIER images exhibit a complex structure within the stellar disk including a dominant bright spot located at the western part of the stellar disk. The spot has an H-band peak intensity of 40% to 60% above the average intensity of the limb-darkening-corrected stellar disk. The contrast between the minimum and maximum intensity on the stellar disk is about 1:2.5.   Our observations are broadly consistent with predictions by dynamic atmosphere and wind models, although models with wind appear to have a circumstellar envelope that is too extended compared to our observations. The detected complex structure within the stellar disk is most likely caused by giant convection cells, resulting in large-scale shock fronts, and their effects on clumpy molecule and dust formation seen against the photosphere at distances of 2-3 stellar radii.
The Time-dependent Hartree-Fock (TDHF) theory is applied to the study of heavy ion collisions at energies around the Coulomb barrier. The competition between fusion and nucleon transfer mechanisms is investigated. For intermediate mass systems such as 16O+208Pb, proton transfer favors fusion by reducing the Coulomb repulsion. A comparison with sub-barrier transfer experimental data shows that pairing correlations are playing an important role in enhancing proton pair transfer. For heavier and more symmetric systems, a fusion hindrance is observed due to the dominance of the quasi-fission process. Typical quasi-fission time of few zeptoseconds are obtained. Actinide collisions are also investigated both within the TDHF approach and with the Ballian-V\'en\'eroni prescription for fluctuation and correlation of one-body observables. The possible formation of new heavy neutron-rich nuclei in actinide collisions is discussed.
We investigate the details of the electronic structure in the neighborhoods of a carbon atom vacancy in graphene by employing magnetization-constrained density-functional theory on periodic slabs, and spin-exact, multi-reference, second-order perturbation theory on a finite cluster. The picture that emerges is that of two local magnetic moments (one \pi-like and one \sigma-like) decoupled from the \pi- band and coupled to each other. We find that the ground state is a triplet with a planar equilibrium geometry where an apical C atom opposes a pentagonal ring. This state lies ~0.2 eV lower in energy than the open-shell singlet with one spin flipped, which is a bistable system with two equivalent equilibrium lattice configurations (for the apical C atom above or below the lattice plane) and a barrier ~0.1 eV high separating them. Accordingly, a bare carbon-atom vacancy is predicted to be a spin-one paramagnetic species, but spin-half paramagnetism can be accommodated if binding to foreign species, ripples, coupling to a substrate, or doping are taken into account.
For some absolute constants $c$, $n_0$ and any $n\geq n_0$, we show that with probability close to one the convex hull of the $n$-dimensional Brownian motion ${\rm conv}\{BM_n(t):\, t\in[1,2^{cn}]\}$ does not contain the origin. The result can be interpreted as an estimate of the minimax of the Gaussian process $\{ \langle \bar{u},BM_n(t)\rangle,\, \bar{u}\in S^{n-1},\, t\in [1,2^{cn}]\}$.
This review discusses the structure and evolution of the Milky Way, in the context of opportunities provided by asteroseismology of red giants. The review is structured according to the main Galactic components: the thin disk, thick disk, stellar halo, and the Galactic bar/bulge. The review concludes with an overview of Galactic archaeology and chemical tagging, and a brief account of the upcoming HERMES survey with the AAT.
In the present paper, we investigate the complexity of infinite family of graphs $H_n=H_n(G_1,\,G_2,\ldots,G_m)$ obtained as a circulant foliation over a graph $H$ on $m$ vertices with fibers $G_{1},\,G_{2},\ldots,G_{m}.$ Each fiber $G_{i}=C_{n}(s_{i,1},\,s_{i,2},\ldots,s_{i,k_{i}})$ of this foliation is the circulant graph on $n$ vertices with jumps $s_{i,1},\,s_{i,2},\ldots,s_{i,k_{i}}.$ This family includes the family of generalized Petersen graphs, $I$-graphs, sandwiches of circulant graphs, discrete torus graphs and others.   We obtain a closed formula for the number $\tau(n)$ of spanning trees in $H_{n}$ in terms of Chebyshev polynomials, investigate some arithmetical properties of this function and find its asymptotics as $n\to\infty.$
In this paper we present a detailed study of the peculiar early-type galaxy NGC1947. The main goal of this work is to constrain the dynamical status and the formation history of NGC1947 by comparing the observed properties with the predictions derived from different galaxy formation scenarios. To this aim, we derived the photometric and kinematical properties of NGC1947. Due to the presence of an extended dust-lane, which crosses the galaxy center along the photometric minor axis, we used near-infrared images (J and K bands) to derive an accurate analysis of the stellar light distribution. Optical images (in the V and R bands) are used to derive the color profiles and color maps to study the structure of the dust-lane. The observed kinematics confirm the presence of two components with decoupled angular momentum: gas and dust rotate along the minor axis, while the rotation velocities of the stars are observed along the major axis. The complex structure observed in NGC1947 support the hypothesis that some kind of interactions happened in the evolution of this object. We analyzed two alternatives: a merging process and an accretion event. We discussed how the observed properties strongly suggest that the decoupled ring of gas and dust have been accreted from outside.
We present an evidence of isospin effects in nuclear fission by comparing the fission widths for reactions involving different isospin states of the same compound nucleus (CN). Yadrovsky suggested this possibility in 1975. Yadrovsky obtained the fission widths for two reaction data sets, namely $^{206}$Pb($\alpha$,f) and $^{209}$Bi(p,f), both leading to same CN, and concluded that "a nucleus remembers the isospin value of the nuclear states leading to fission". We obtain the fission decay widths for both the $T_0+1/2$ and $T_0-1/2$ states of CN by using two appropriate reaction data sets. We then compare the fission widths for the two isospin states of CN. More specifically, we have chosen the combination of $^{206}$Pb($\alpha$,f) and $^{209}$Bi(p,f) same as presented in Yadrovsky's paper and $^{235}$U(d,f) and $^{236}$U(p,f) reaction data sets in this study. A significant difference between the ratios of fission decay widths to total decay widths for different isospin values suggests that isospin plays an important role in fission.
We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.
Gravitational waves from inspiraling compact objects provide us with information of the distance scale since we can infer the absolute luminosity of the source from analysis of the wave form, which is known as standard sirens. The first detection of the gravitational wave signal of the binary black hole merger event by Advanced LIGO has opened up the possibility of utilizing standard sirens as cosmological probe. In order to extract information of the distance-redshift relation, we cross-correlate weak lensing, which is an unbiased tracer of matter distribution in the Universe, with the projected number density of gravitational wave sources. For weak lensing, we employ tomography technique to efficiently obtain information of large-scale structures at wide ranges of redshifts. Making use of the cross-correlations along with the auto-correlations, we present forecast of constraints on four cosmological parameters, i.e., Hubble parameter, matter density, the equation of state parameter of dark energy, and the amplitude of matter fluctuation. To fully explore the ability of cross-correlations, which require large overlapping sky coverage, we consider the specific case with the upcoming surveys by \textit{Euclid} for weak lensing and Einstein Telescope for standard sirens. We show that cosmological parameters can be tightly constrained solely by these auto- and cross-correlations of standard sirens and weak lensing. For example, the $1\text{-}\sigma$ error of Hubble parameter is expected to be $\sigma (H_0) = 0.33 \, \mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$. Thus, the proposed statistics will be a promising probe into the distance scale.
We theoretically examine the use of a statistical distance measure, the indistinguishability, as a generic tool for the identification of topological order. We apply this measure to the toric code and two fractional quantum Hall models. We find that topologically ordered states can be identified with the indistinguishability for both models. Calculations with the indistinguishability also underscore a key distinction between symmetries that underlie topological order in the toric code and quantum Hall models.
We study the late time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function $V(\phi) .$ We prove using a dynamical systems approach four general results for a large class of non-negative potentials which show that almost always the universe ever expands. In particular, for potentials having a local zero minimum, flat and negatively curved FRW models are ever expanding and the energy density asymptotically approaches zero. We investigate the conditions under which the scalar field asymptotically approaches the minimum of the potential. We discuss the question of whether a closed FRW with ordinary matter can avoid recollapse due to the presence of a scalar field with a non-negative potential.
The ultraviolet luminosity evolution of star-forming galaxies is explored from the theoretical point of view, especially focusing on the theory of UV energetics in simple and composite stellar populations and its relationship to the star formation rate and other main evolutionary parameters.   Galaxy emission below 3000 Angstroms directly correlates with actual star formation, not depending on the total mass of the system. A straightforward calibration is obtained, in this sense, from the theoretical models at 1600, 2000 and 2800 Angstroms, and a full comparison is carried out with IUE data and other balloon-borne observations for local galaxies.   The claimed role of late-type systems as prevailing contributors to the cosmic UV background is reinforced by our results; at 2000 Angstroms Im irregulars are found in fact nearly four orders of magnitude brighter than ellipticals, per unit luminous mass.   The role of dust absorption in the observation of high-redshift galaxies is assessed, comparing model output and observed spectral energy distribution of local galaxy samples. Similar to what we observe in our own galaxy, a quick evolution in the dust environment might be envisaged in primeval galaxies, with an increasing fraction of luminous matter that would escape the regions of harder and "clumpy" dust absorption on a timescale of some 10^7 yr, comparable with the lifetime of stars of 5-10 solar masses.
We provide a systematic measurement of the rest-frame UV continuum slope beta over a wide range in redshift (z~2-6) and rest-frame UV luminosity (0.1-2L*) to improve estimates of the SFR density at high redshift. We utilize the deep optical and infrared data (ACS/NICMOS) over the CDF-S and HDF-N GOODS fields, as well as the UDF for our primary UBVi "dropout" sample. We correct the observed distributions for selection biases and photometric scatter. We find that the UV-continuum slope of the most luminous galaxies is substantially redder at z~2-4 than it is at z~5-6. Lower luminosity galaxies are also found to be bluer than higher luminosity galaxies at z~2.5 and z~4. We do not find a large number of galaxies with beta's as red as -1 in our dropout selections at z~4, and particularly at z>~5, even though such sources could be readily selected from our data. This suggests that star-forming galaxies at z>~5 almost universally have very blue UV-continuum slopes, and that there are not likely to be a substantial number of dust-obscured galaxies at z>~5 that are missed in "dropout" searches. Using the same relation between UV-continuum slope and dust extinction as found to be appropriate at z~0 and z~2, we estimate the average dust extinction of galaxies as a function of redshift and UV luminosity in a consistent way. We find that the estimated dust extinction increases substantially with cosmic time for the most UV luminous galaxies, but remains small (<~2x) at all times for lower luminosity galaxies. Because these same lower luminosity galaxies dominate the luminosity density in the UV, the overall dust extinction correction remains modest at all redshifts. We include the contribution from ULIRGs in our SFR density estimates at z~2-6, but find that they contribute only ~20% of the total at z~2.5 and <~10% at z>~4.
Requiring the positivity and counting rule, we propose a new parametrization of the polarized parton distribution which reproduce the data well. We found that the NLO analysis is absolutely necessary to extract the correct information on the polarized gluon distributions. The calculated results of $x\Delta d_v(x)$ and $\Delta d_v(x)/d_v(x)$ seem to be consistent with the SMC data at $Q^2=$10GeV$^2$.
Context. More than ten Centaurs are now known to have cometary activity at large heliocentric distance (i.e. $\simeq$ 5-13 AU). Among these objects, 174P/Echeclus which showed cometary activity at 13 AU from the Sun, is a unique case, because of: (i) the amplitude of its outburst, (ii) the source of cometary activity that appears distinct from Echeclus itself.   Aims. This paper aims at investigating the physical conditions that have led to this unusual outburst. The purpose is also to quantify this phenomenon and to provide observational constraints for its modeling.   Methods. We use observations from different telescopes, performed before, during, and after the outburst. We performed the main observations on March 23 and 30, 2006, with the 8.2-m ESO Very Large Telescope and FORS 1 instrument. They consist of visible images and spectra.   Results. Our main results are: (i) a cometary source distinct from Echeclus itself that presents a brightness distribution compatible with a diffuse source; (ii) a total dust production rate Q_dust equal to about 86 kg.s^-1 and a parameter Afrho equal to 10,000cm; (iii) no emission lines (CN and C_2) can be detected in the visible range; (iv) the upper limits for the CN and C_2 production rates are about 3.8x10^25 and 10^26 molecules.s^-1 respectively; (v) we detected no Echeclus' satellite before the outburst up to M_R equal to about 26; (vi) the upper limit for the object generating the coma is about 8 km in diameter; (vii) and we detected no cometary activity one year later, in March 2007.
We use the motivic obstruction to stable rationality introduced by Shinder and the first-named author to establish several new classes of stably irrational hypersurfaces and complete intersections. In particular, we show that very general quartic fivefolds and complete intersections of a quadric and a cubic in $\mathbb P^6$ are stably irrational. An important new ingredient is the use of tropical degeneration techniques.
Gy\'{a}rf\'{a}s et al. determined the asymptotic value of the diagonal   Ramsey number of $\mathcal{C}^k_n$, $R(\mathcal{C}^k_n,\mathcal{C}^k_n),$ generating the same result for $k=3$ due to Haxell et al. Recently, the exact values of the Ramsey numbers of 3-uniform loose paths and cycles are completely determined. These results are motivations to conjecture that for every $n\geq m\geq 3$ and $k\geq 3,$ $$R(\mathcal{C}^k_n,\mathcal{C}^k_m)=(k-1)n+\lfloor\frac{m-1}{2}\rfloor,$$ as mentioned by Omidi et al. More recently, it is shown that this conjecture is true for $n=m\geq 2$ and $k\geq 7$ and for $k=4$ when $n>m$ or $n=m$ is odd. Here we investigate this conjecture for $k=5$ and demonstrate that it holds for $k=5$ and sufficiently large $n$.
Wigner symmetry in Nuclear Physics provides a unique example of a non-perturbative long distance symmetry, a symmetry strongly broken at short distances. We analyse the consequences of such a concept within the framework of One Boson Exchange Potentials in NN scattering and keeping the leading Nc contributions. Phenomenologically successful relations between singlet 1S0 and triplet 3S1 scattering phase shifts are provided in the entire elastic region. We establish symmetry breaking relations among non-central phase shifts which are successfully fulfilled by even-L partial waves and strongly violated by odd-L partial waves, in full agreement with large Nc requirements.