ShantanuT01/DACTYL-Pretraining huggingface dataset:
The statistical model of Chase and Mekjian, which offers an analytic solution for the canonical ensemble of non-interacting fragments, is investigated for it's thermodynamic behavior. Various properties of the model, which exhibits a first-order phase transition, are studied. The effects of finite particle number are investigated. Three extensions of the model are considered, excluded volume, Coulomb effects and inclusion of isospin degrees of freedom. A formulation of a microcanonical version of the model is also presented.
Heterogeneous diffusion with spatially changing diffusion coefficient arises in many experimental systems like protein dynamics in the cell cytoplasm, mobility of cajal bodies and confined hard-sphere fluids. Here, we showcase a simple model of heterogeneous diffusion where the diffusion coefficient $D(x)$ varies in power-law way, i.e. $D(x) \sim |x|^{-\alpha}$ with the exponent $\alpha >-1$. This model is known to exhibit anomalous scaling of the mean squared displacement (MSD) of the form $\sim t^{\frac{2}{2+\alpha}}$ and weak ergodicity breaking in the sense that ensemble averaged and time averaged MSDs do not converge. In this paper, we look at the extreme value statistics of this model and derive, for all $\alpha$, the exact probability distributions of the maximum spatial displacement $M(t)$ and arg-maximum $t_m(t)$ (i.e. the time at which this maximum is reached) till duration $t$. In the second part of our paper, we analyze the statistical properties of the residence time $t_r(t)$ and the last-passage time $t_{\ell}(t)$ and compute their distributions exactly for all values of $\alpha$. Our study unravels that the heterogeneous version $(\alpha \neq 0)$ displays many rich and contrasting features compared to that of the standard Brownian motion (BM). For example, while for BM $(\alpha =0)$, the distributions of $t_m(t),~t_r(t)$ and $t_{\ell}(t)$ are all identical (\textit{\'{a} la} "arcsine laws" due to L\'{e}vy), they turn out to be significantly different for non-zero $\alpha$. Another interesting property of $t_r(t)$ is the existence of a critical $\alpha$ (which we denote by $\alpha _c=-0.3182$) such that the distribution exhibits a local maximum at $t_r = t/2$ for $\alpha < \alpha _c$
We develop a model-independent analysis of hadronic scattering data in the resonance region, where the resonance shape follows from the matrix elements of a Hamiltonian. We investigate the rho meson in the tau decay. We demonstrate that the rho meson resonance in the two-pion decay of the tau lepton is described well through the coupling of a bare rho meson to the two-pion and the four-pion continuum. Furthermore, this four-pion continuum corresponds with the data of the four-pion decay channel of the tau lepton at energies up to 1.1 GeV.
We prove the ill-posedness for the 3D incompressible inhomogeneous Navier-stokes equations in critical Besov space. In particular, a norm inflation happens in finite time with the initial data satisfying $$\|a_0\|_{\dot{B}_{p,1}^\frac{3}{p}}+\|u_0\|_{\dot{B}_{6,1}^{-\frac{1}{2}}}\le \delta,\ p>6$$ or $$\|a_0\|_{\dot{B}_{6,1}^\frac{1}{2}}+\|u_0\|_{\dot{B}_{p,1}^{\frac{3}{p}-1}}\le \delta,\ p>6.$$ To obtain the norm inflation, we construct a special class of initial data and introduce a modified pressure. Comparing with the classical Navier-Stokes equations in $L^\infty$ framework, we can obtain the ill-posedness for the inhomogeneous case in near $L^6$ framework.
Quasi-transverse-electric and -transverse-magnetic fundamental whispering gallery modes in a polymer-coated silica microtoroid are theoretically investigated and demonstrated to possess very high-quality factors. The existence of a nanometer-thickness layer not only evidently reduces the cavity mode volume but also draws the maximal electric field's position of the mode to the outside of the silica toroid, where single quantum dots or nanocrystals are located. Both effects result in a strongly enhanced coherent interaction between a single dipole (for example, a single defect center in a diamond crystal) and the quantized cavity mode. Since the coated microtoroid is highly feasible and robust in experiments, it may offer an excellent platform to study strong-coupling cavity quantum electrodynamics, quantum information, and quantum computation.
PSR B1259-63/LS 2883 is a binary system consisting of a 48 ms pulsar orbitting around a Be star with an orbital period of ~3.4 years. The system was detected at very high energies (VHE; E > 100 GeV) by the High Energy Stereoscopic System (H.E.S.S.) during its periastron passages in 2004 and 2007. Here we present new H.E.S.S. observations corresponding to its last periastron passage, which occurred on December 15th 2010. These new observations partially overlap with the beginning of a spectacular gamma-ray flare reported by the Fermi-LAT. The H.E.S.S. observations show both flux and spectral properties similar to those reported in previous periastron passages, without any signature of the emission enhancement seen at GeV energies. A careful statistical study based on the Fermi and H.E.S.S. lightcurves leads to the conclusion that the GeV and TeV emission during the flare have a different physical origin. This conlusion, in turn, allows to use Fermi-LAT measurements of the GeV flux as upper limits for the modeling of the VHE emission.
We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{\alpha_n}, {n-1}^{\alpha_{n-1}},..., 1^{\alpha_1})$, where $\alpha = (\alpha_1,...,\alpha_n)$ is a composition, or the $180^\circ$ rotation of such a diagram. If a diagram's skew Schur function is a linear combination of Schur functions of fat staircases, we call the diagram a sum of fat staircases. We prove a Schur-positivity result that is obtained each time we augment a sum of fat staircases with a skew diagram. We also determine conditions on which diagrams can be sums of fat staircases, including necessary and sufficient conditions in the special case when the diagram is a fat staircase skew a single row or column.
For a fixed set of positive integers $R$, we say $\mathcal{H}$ is an $R$-uniform hypergraph, or $R$-graph, if the cardinality of each edge belongs to $R$. For a graph $G=(V,E)$, a hypergraph $\mathcal{H}$ is called a Berge-$G$, denoted by $BG$, if there exists a bijection $f: E(G) \to E(\mathcal{H})$ such that for every $e \in E(G)$, $e \subseteq f(e)$. In this paper, we define a variant of Tur\'an number in hypergraphs, namely the cover Tur\'an number, denoted as $\hat{ex}_R(n, G)$, as the maximum number of edges in the shadow graph of a Berge-$G$ free $R$-graph on $n$ vertices. We show a general upper bound on the cover Tur\'an number of graphs and determine the cover Tur\'an density of all graphs when the uniformity of the host hypergraph equals to $3$.
Two photon collisions at high energy have an important theoretical advantage: the simplicity of the initial state, which gives us a unique opportunity to calculate these processes for large virtualities of both photons in perturbative QCD approach. In this paper we study QCD saturation in two photon collisions in the framework of the Glauber-Mueller approach. The Glauber-Mueller formula is derived emphasizing the impact parameter dependence ($b_t$) of the dipole-dipole amplitude. It is shown that non-perturbative QCD contributions are needed to describe large $b_t $-behaviour, and the way how to deal with them is suggested. Our approach can be viewed as the model for the saturation in which the entire impact parameter dependence is determined by the initial conditions. The unitarity bound for the total cross section, its energy dependence as well aspredictions for future experiments are discussed.It is argued that the total cross section increases faster than any power of $ \log(1/x)$ in a wide range of energy or $x$, namely $\sigma(\gamma^*-\gamma^*)   \propto (1/Q^2) exp(a \sqrt{\ln(1/x)}) \leq 1/m^2_{\pi}$ where $exp(a \sqrt{\ln(1/x)})$ reflects the $x$ dependence of the gluon density $xG \propto exp(2 a \sqrt{\ln(1/x)})$ and $m_{\pi}$ is the pion mass.
An approximate method to quantify the magnitude of the two-nucleon (2N) and three-nucleon (3N) short-range correlations (SRC) and their mass dependence is proposed. The proposed method relies on the concept of the "universality" or "local nuclear character" of the SRC. We quantify the SRC by computing the number of independent-particle model (IPM) nucleon pairs and triples which reveal beyond-mean-field behavior. It is argued that those can be identified by counting the number of nucleon pairs and triples in a zero relative orbital momentum state. A method to determine the quantum numbers of pairs and triples in an arbitrary mean-field basis is outlined. The mass dependence of the 2N and 3N SRC is studied. The predictions are compared to measurements. This includes the ratio of the inclusive inelastic electron scattering cross sections of nuclei to 2H and 3He at large values of the Bjorken variable. Corrections stemming from the center-of-mass motion of the pairs are estimated. We find that the relative probability per nucleon for 2N and 3N SRC has a soft dependence with mass number A and that the proton-neutron 2N SRC outnumber the proton-proton (neutron-neutron) 2N SRC. A linear relationship between the magnitude of the EMC effect and the predicted number of proton-neutron SRC pairs is observed. This provides support for the role of local nuclear dynamics on the EMC effect.
We tabulate the atomic mass excesses and binding energies, ground-state shell-plus-pairing corrections, ground-state microscopic corrections, and nuclear ground-state deformations of 9318 nuclei ranging from $^{16}$O to $A=339$. The calculations are based on the finite-range droplet macroscopic model and the folded-Yukawa single-particle microscopic model. Relative to our FRDM(1992) mass table in {\sc Atomic Data and Nuclear Data Tables} [{\bf 59} 185 (1995)], the results are obtained in the same model, but with considerably improved treatment of deformation and fewer of the approximations that were necessary earlier, due to limitations in computer power. The more accurate execution of the model and the more extensive and more accurate experimental mass data base now available allows us to determine one additional macroscopic-model parameter, the density-symmetry coefficient $L$, which was not varied in the previous calculation, but set to zero. Because we now realize that the FRDM is inaccurate for some highly deformed shapes occurring in fission, because some effects are derived in terms of perturbations around a sphere, we only adjust its macroscopic parameters to ground-state masses. The values of ten constants are determined directly from an optimization to fit ground-state masses of 2149 nuclei ranging from $^{16}$O to $^{265}_{106}$Sg and $^{264}_{108}$Hs. The error of the mass model is 0.5595~MeV. We also provide masses in the FRLDM, which in the more accurate treatments now has an error of 0.6618 MeV. But in contrast to the FRDM, it is suitable for studies of fission and has been extensively so applied elsewhere, with FRLDM(2002) constants. The FRLDM(2012) fits 31 fission barrier heights from $^{70}$Se to $^{252}$Cf with a root-mean-square deviation of 1.052 MeV.
Let $C$ be a convex $d$-dimensional body. If $\rho$ is a large positive number, then the dilated body $\rho C$ contains $\rho^{d}\left\vert C\right\vert +\mathcal{O}\left( \rho^{d-1}\right) $ integer points, where $\left\vert C\right\vert $ denotes the volume of $C$. The above error estimate $\mathcal{O}\left( \rho^{d-1}\right) $ can be improved in several cases. We are interested in the $L^{2}$-discrepancy $D_{C}(\rho)$ of a copy of $\rho C$ thrown at random in $\mathbb{R}^{d}$. More precisely, we consider \[ D_{C}(\rho):=\left\{ \int_{\mathbb{T}^{d}}\int_{SO(d)}\left\vert \textrm{card}\left( \left( \rho\sigma(C)+t\right) \cap\mathbb{Z}^d\right) - \rho^{d}\left\vert C\right\vert \right\vert ^{2}d\sigma dt\right\} ^{1/2}\ , \] where $\mathbb{T}^{d}=$ $\mathbb{R}^{d}/\mathbb{Z}^{d}$ is the $d$-dimensional flat torus and $SO\left( d\right) $ is the special orthogonal group of real orthogonal matrices of determinant $1$.   An argument of D. Kendall shows that $D_{C}(\rho)\leq c\ \rho^{(d-1)/2}$. If $C$ also satisfies the reverse inequality $\ D_{C}(\rho)\geq c_{1} \ \rho^{(d-1)/2}$, we say that $C$ is $L^{2}$\emph{-regular}. L. Parnovski and A. Sobolev proved that, if $d>1$, a $d$-dimensional unit ball is $L^{2}% $-regular if and only if $d\not \equiv 1\ (\operatorname{mod}4)$.   In this paper we characterize the $L^{2}$-regular convex polygons. More precisely we prove that a convex polygon is not $L^{2}$-regular if and only if it can be inscribed in a circle and it is symmetric about the centre.
We study the fate of the Kondo effect with one-dimensional conduction baths at very low densities, such that the system explores the bottom of the conduction band. This can involve either finite low densities, or a small number of fixed conduction electrons in a large system, i.e., the limit of large bath sizes can be taken with either fixed small density or with fixed number. We characterize the Kondo physics for such systems through the energy gain due to Kondo coupling, which is a general analog of the Kondo temperature scale, and through real-space profiles of densities and spin-spin correlation functions.
We construct an explicit PSp_4(3)-polynomial with 3 parameters of degree 40 by using some results of Siegel modular forms.
The exterior solution for an arbitrary charged, massive source, is studied as a static deviation from the Reissner-Nordstr\o m metric. This is reduced to two coupled ordinary differential equations for the gravitational and electrostatic potential functions. The homogeneous equations are explicitly solved in the particular case $q^2=m^2$, obtaining a multipole expansion with radial hypergeometric dependence for both potentials. In the limiting case of a neutral source, the equations are shown to coincide with recent results by Bondi and Rindler.
The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the theory is established for all such manifolds. Our results naturally incorporate and generalize the homogeneous measure and dimension theorems for non-degenerate manifolds established to date. The generality of the inhomogeneous aspect considered within enables us to make a new contribution even to the classical theory in R^n. Furthermore, the multivariable aspect considered within has natural applications beyond the standard inhomogeneous theory such as to Diophantine problems related to approximation by algebraic integers.
The cancellation problem asks if two complex algebraic varieties X and Y of the same dimension such that X\times\mathbb{C} and Y\times\mathbb{C} are isomorphic are isomorphic. Iitaka and Fujita established that the answer is positive for a large class of varieties of any dimension. In 1989, Danielewski constructed a famous counter-example using smooth affine surfaces with additive group actions. His construction was further generalized by Fieseler and Wilkens to describe a larger class of affine surfaces. Here we construct higher dimensional analogues of these surfaces. We study algebraic actions of the additive group \mathbb{C}\_{+} on certain of these varieties, and we obtain counter-examples to the cancellation problem in any dimension n\geq2 .
The electromagnetic form factors of the trinucleons 3H and 3He are calculated with wave functions obtained with the Argonne AV18 two-nucleon and Urbana IX three-nucleon interactions. Full account is taken of the two-body currents required by current conservation with the AV18 interaction as well as those associated with N-Delta transition currents and the currents of Delta resonance components in the wave functions. Explicit three-nucleon current operators associated with the two-pion exchange three-nucleon interaction arising from irreducible S-wave pion-nucleon scattering is constructed and shown to have very little effect on the calculated magnetic form factors. The calculated magnetic form factor of 3H, and charge form factors of both 3H and 3He are in satisfactory agreement with the experimental data. However, the position of the zero in the magnetic form factor of 3He is slightly underpredicted.
[abridged] Aims. We observed the outer parts of NGC 1569 and NGC 4449, two of the closest and strongest dwarf starburst galaxies in the local universe, to characterize their stellar density and populations, and obtain new insights into the structure, formation, and evolution of starburst galaxies and galaxy halos. Methods. We obtained HST/WFPC2 images between 5 and 8 scale radii from the center, along the intermediate and minor axes. We performed point-source photometry to determine color magnitude diagrams of I vs. V-I. We compared the results at different radii, including also our prior HST/ACS results for more centrally located fields. Results. We detect stars in the RGB and TP-AGB (carbon star) phases in all outer fields, but not younger stars such as those present at smaller radii. The RGB star density profile is well fit by either a de Vaucouleurs profile or a power-law profile, but has more stars at large radii than a single exponential. To within the uncertainties, there are no radial gradients in the RGB color or carbon-to-RGB-star ratio at large radii. Conclusions. The galaxies have faint outer stellar envelopes that are not tidally truncated within the range of radii addressed by our study. The density profiles suggest that these are not outward extensions of the inner disks, but are instead distinct stellar halos. This agrees with other work on galaxies of similar morphology. The presence of such halos is consistent with predictions of hierarchical galaxy formation scenarios. The halos consist of intermediate-age/old stars, confirming the results of other studies that have shown the starburst phenomenon to be very centrally concentrated. There is no evidence for stellar-population age/metallicity gradients within the halos themselves.
The spined cube $SQ_n$ is a variant of the hypercube $Q_n$, introduced by Zhou et al. in [Information Processing Letters 111 (2011) 561-567] as an interconnection network for parallel computing. A graph $\G$ is an $m$-Cayley graph if its automorphism group $\Aut(\G)$ has a semiregular subgroup acting on the vertex set with $m$ orbits, and is a Caley graph if it is a 1-Cayley graph. It is well-known that $Q_n$ is a Cayley graph of an elementary abelian 2-group $\mz_2^n$ of order $2^n$. In this paper, we prove that $SQ_n$ is a 4-Cayley graph of $\mz_2^{n-2}$ when $n\geq6$, and is a $\lfloor n/2\rfloor$-Cayley graph when $n\leq 5$. This symmetric property shows that an $n$-dimensional spined cube with $n\geq6$ can be decomposed to eight vertex-disjoint $(n-3)$-dimensional hypercubes, and as an application, it is proved that there exist two edge-disjoint Hamiltonian cycles in $SQ_n$ when $n\geq4$. Moreover, we determine the vertex-transitivity of $SQ_n$, and prove that $SQ_n$ is not vertex-transitive unless $n\leq3$.
This paper studies panoptic segmentation, a recently proposed task which segments foreground (FG) objects at the instance level as well as background (BG) contents at the semantic level. Existing methods mostly dealt with these two problems separately, but in this paper, we reveal the underlying relationship between them, in particular, FG objects provide complementary cues to assist BG understanding. Our approach, named the Attention-guided Unified Network (AUNet), is a unified framework with two branches for FG and BG segmentation simultaneously. Two sources of attentions are added to the BG branch, namely, RPN and FG segmentation mask to provide object-level and pixel-level attentions, respectively. Our approach is generalized to different backbones with consistent accuracy gain in both FG and BG segmentation, and also sets new state-of-the-arts both in the MS-COCO (46.5% PQ) and Cityscapes (59.0% PQ) benchmarks.
The AllWISE processing pipeline has measured motions for all objects detected on WISE images taken between 2010 January and 2011 February. In this paper, we discuss new capabilities made to the software pipeline in order to make motion measurements possible, and we characterize the resulting data products for use by future researchers. Using a stringent set of selection criteria, we find 22,445 objects that have significant AllWISE motions, of which 3,525 have motions that can be independently confirmed from earlier 2MASS images yet lack any published motions in SIMBAD. Another 58 sources lack 2MASS counterparts and are presented as motion candidates only. Limited spectroscopic follow-up of this list has already revealed eight new L subdwarfs. These may provide the first hints of a "subdwarf gap" at mid-L types that would indicate the break between the stellar and substellar populations at low metallicities (i.e., old ages). Another object in the motion list -- WISEA J154045.67-510139.3 -- is a bright (J ~ 9 mag) object of type M6; both the spectrophotometric distance and a crude preliminary parallax place it ~6 pc from the Sun. We also compare our list of motion objects to the recently published list of 762 WISE motion objects from Luhman (2014). While these first large motion studies with WISE data have been very successful in revealing previously overlooked nearby dwarfs, both studies missed objects that the other found, demonstrating that many other nearby objects likely await discovery in the AllWISE data products.
We theoretically study absorption by an undoped graphene layer decorated with arrays of small particles. We discuss periodic and random arrays within a common formalism, which predicts a maximum absorption of $50\%$ for suspended graphene in both cases. The limits of weak and strong scatterers are investigated and an unusual dependence on particle-graphene separation is found and explained in terms of the effective number of contributing evanescent diffraction orders of the array. Our results can be important to boost absorption by single layer graphene due to its simple setup with potential applications to light harvesting and photodetection based on energy (F\"orster) rather than charge transfer.
Motivated by the potential for cuprate-like superconductivity in monolayer rare-earth nickelate superlattices, we study the effects of crystal field splitting, lattice distortions and strain on the charge, magnetic, and orbital order in undoped two-dimensional (2D) nickelate monolayers $R$NiO$_3$. We use a two-band Hubbard model to describe the low-energy electron states, with correlations controlled by a effective Hubbard $U$ and Hund's $J$. The electrons are coupled to the octahedral breathing-mode lattice distortions. Treating the lattice semiclassically, we apply the Hartree-Fock approximation to obtain the phase diagram for the ground-state as a function of the various parameters. We find that the 2D confinement leads to strong preference for the planar $d_{x^2-y^2}$ orbital even in the absence of a crystal-field splitting. The $d_{x^2-y^2}$ polarization is enhanced by adding a crystal field splitting, whereas coupling to breathing-mode lattice distortions weakens it. However, the former effect is stronger, leading to $d_{x^2-y^2}$ orbital and antiferromagnetic (AFM) order at reasonable values of $U,J$ and thus to the possibility to realize cuprate-like superconductivity in this 2D material upon doping. We also find that the application of tensile strain enhances the cuprate-like phase and phases with orbital polarization in general, by reducing the $t_2 / t_1$ ratio of next-nearest to nearest neighbour hopping. On the contrary, systems with compressive stress have an increased hopping ratio and consequently show a preference for ferromagnetic (FM) phases, including, unexpectedly, the out-of-plane $d_{3z^2-r^2}$ FM phase.