ShantanuT01/DACTYL-Pretraining huggingface dataset:
Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper [1] is generalized and used to investigate superconducting state of this model. We use the notion of charge quantum number to describe the irreducible Green's function of the superconducting state. As in the previous paper we introduce the notion of tunneling Green's function and of its mass operator. This last quantity turns out to be equal to correlation function of the system. We proved the existence of exact relation between renormalized one-particle propagator and thermodynamic potential which includes integration over auxiliary interaction constant. The notion of skeleton diagrams of propagator and vacuum kinds were introduced. These diagrams are constructed from irreducible Green's functions and tunneling lines. Identity of this functional to the thermodynamic potential has been proved and the stationarity with respect to variation of the mass operator has been demonstrated.
(Abridged) We use optical spectroscopy to investigate the disk, wind, and accretion during the 2008 ZCMa NW outburst. Over 1000 optical emission lines reveal accretion, a variable, multi-component wind, and double-peaked lines of disk origin. The variable, non-axisymmetric, accretion-powered wind has slow ($\sim $0 km s$^{-1}$), intermediate ($\sim -$100 km s$^{-1}$) and fast ($\geq -$400 km s$^{-1}$) components. The fast components are of stellar origin and disappear in quiescence, while the slow component is less variable and could be related to a disk wind. The changes in the optical depth of the lines between outburst and quiescence are consistent with increased accretion being responsible for the observed outburst. We derive an accretion rate of 10$^{-4}$ M$_\odot$/yr in outburst. The Fe I and weak Fe II lines arise from an irradiated, flared disk at $\sim$0.5-3 $\times$M$_*$/16M$_\odot$ au with asymmetric upper layers, revealing that the energy from the accretion burst is deposited at scales below 0.5 au. Some line profiles have redshifted asymmetries, but the system is unlikely sustained by magnetospheric accretion, especially in outburst. The accretion-related structures extend over several stellar radii and, like the wind, are likely non-axisymmetric. The stellar mass may be $\sim$6-8 M$_\odot$, lower than previously thought ($\sim$16 M$_\odot$). Emission line analysis is found to be a powerful tool to study the innermost regions and accretion in stars within a very large range of effective temperatures. The density ranges in the disk and accretion structures are higher than in late-type stars, but the overall behavior, including the innermost disk emission and variable wind, is very similar independently of the spectral type. Our work suggests a common outburst behavior for stars with spectral types ranging from M-type to intermediate-mass stars.
For positive integers $n,r,k$ with $n\ge r$ and $k\ge2$, a set $\{(x_1,y_1),(x_2,y_2),\dots,(x_r,y_r)\}$ is called a $k$-signed $r$-set on $[n]$ if $x_1,\dots,x_r$ are distinct elements of $[n]$ and $y_1\dots,y_r\in[k]$. We say a $t$-intersecting family consisting of $k$-signed $r$-sets on $[n]$ is trivial if each member of this family contains a fixed $k$-signed $t$-set. In this paper, we determine the structure of large maximal non-trivial $t$-intersecting families. In particular, we characterize the non-trivial $t$-intersecting families with maximum size for $t\ge2$, extending a Hilton-Milner-type result for signed sets given by Borg.
In a ballistic two-dimensional electron gas, the Landau damping does not lead to plasmon attenuation in a broad interval of wave vectors q << k_F. Similarly, it does not contribute to the optical conductivity \sigma (\omega, q) in a wide domain of its arguments, E_F > \omega > qv_F, where E_F, k_F and v_F are, respectively, the Fermi energy, wavevector and velocity of the electrons. We identify processes that result in the plasmon attenuation in the absence of Landau damping. These processes are: the excitation of two electron-hole pairs, phonon-assisted excitation of one pair, and a direct plasmon-phonon conversion. We evaluate the corresponding contributions to the plasmon linewidth and to the optical conductivity.
Alpha Magnetic Spectrometer (AMS-02) is a general purpose high energy particle detector which will be deployed on the International Space Station (ISS) at the end of 2010 - beginning of 2011 to conduct a unique 10 to 18 year mission of fundamental physics research in space. Among the physics objectives of AMS are a search for an understanding of Dark Matter, Antimatter, the origin of cosmic rays and the exploration of new physics phenomena not possible to study from ground based experiments. This article reviews the status of the AMS-02 detector construction, detector calibration results as well as AMS physics potential for new phenomena searches.
We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that the field equations can be reduced to the Einstein equations with a two-fluid source and analyze the qualitative, asymptotic behavior of the models. Assuming an interaction of the two fluids we impose conditions so that the solutions of the corresponding dynamical system remain in the physically acceptable phase space. We show that in Weyl integrable spacetime, the corresponding scalar field acts as a phantom field and therefore, it may give rise to a late accelerated expansion of the Universe.
Richard Guy asked the following question: can we find a triangle with rational sides, medians, and area? Such a triangle is called a \emph{perfect triangle} and no example has been found to date. It is widely believed that such a triangle does not exist. Here we use the setup of Solymosi and de Zeeuw about rational distance sets contained in an algebraic curve, to show that for any angle $0<\theta < \pi$, the number of perfect triangles with an angle $\theta$ is finite. A \emph{rational median set} $S$ is a set of points in the plane such that for every three non collinear points $p_1,p_2,p_3$ in $S$ all medians of the triangle with vertices at $p_i$'s have rational length. The second result of this paper is that no irreducible algebraic curve defined over $\mathbb{R}$ contains an infinite rational median set.
The observed absence of gravitational aberration requires that ``Newtonian'' gravity propagate at a speed $c_g>2\times10^{10}c$. By evaluating the gravitational effect of an accelerating mass, I show that aberration in general relativity is almost exactly canceled by velocity-dependent interactions, permitting $c_g=c$. This cancellation is dictated by conservation laws and the quadrupole nature of gravitational radiation.
It has been conjectured that the internal energy density of the Potts model on a semi-infinite strip with a width $L$ does not have any finite-size corrections at the critical point $K=K_c$. By factorizing the transfer matrix for the kagome lattice with larger widths, we have found that this conjecture is not correct in that the internal energy density slightly varies with $L$ at the critical point. From this size dependence of the internal energy density, we obtain an upper bound as $K_c < 1.0565615$, which is close to a recent estimate $K_c^{\rm JS} = 1.0565600(7)$ by Jacobsen and Scullard [arXiv:1204.0622]. We also obtain a lower bound as $K_c > 1.0560$ by calculating the correlation length along the strips.
Since their discovery single-layer semiconducting transition metal dichalcogenides have attracted much attention thanks to their outstanding optical and mechanical properties. Strain engineering in these two-dimensional materials aims to tune their bandgap energy and to modify their optoelectronic properties by the application of external strain. In this paper we demonstrate that biaxial strain, both tensile and compressive, can be applied and released in a timescale of a few seconds in a reproducible way on transition metal dichalcogenides monolayers deposited on polymeric substrates. We can control the amount of biaxial strain applied by letting the substrate expand or compress. To do this we change the substrate temperature and choose materials with a large thermal expansion coefficient. After the investigation of the substrate-dependent strain transfer, we performed micro-differential spectroscopy of four transition metal dichalcogenides monolayers (MoS2, MoSe2, WS2, WSe2) under the application of biaxial strain and measured their optical properties. For tensile strain we observe a redshift of the bandgap that reaches a value as large as 95 meV/% in the case of single-layer WS2 deposited on polypropylene. The observed bandgap shifts as a function of substrate extension/compression follow the order MoSe2 < MoS2 < WSe2 < WS2. Theoretical calculations of these four materials under biaxial strain predict the same trend for the material-dependent rates of the shift and reproduce well the features observed in the measured reflectance spectra.
The lifetime of moving metallic components is often limited by accelerated oxidation. Yet, the mechanisms and pathways for oxidation during tribological loading are not well understood. Using copper as a model system, tribologically-induced oxidation is systematically investigated by varying the sliding speed and test duration under mild tribological loading. We demonstrate that tribo-oxidation is controlled by test duration rather than the number of cycles or the sliding speed. Plastic deformation from tribological loading creates dislocations, grain and phase boundaries that act as high diffusivity pathways. A combination of electron microscopy and atom probe tomography revealed significantly enhanced atomic concentration of the diffusing species around dislocations. Oxygen diffusion into the bulk as well as of copper towards the free surface along these defects control the oxide formation kinetics. Our work paves the way for formulating a physics-based understanding for tribo-oxidation, which is crucial to develop strategies to prevent oxidation and to strategically tailor surfaces to increase the lifetime of engineering systems.
Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the searcher alternates phases of slow motion allowing detection, and phases of fast motion without detection. We present full and systematic results for different modeling hypotheses of the detection mechanism in space dimension 1, 2 and 3. Our study completes and extends the results of our recent letter [Loverdo {\it et al.} Nature Physics {\bf 4}, 134 (2008)] and gives the necessary calculation details. In addition, a new modeling of the detection phase is presented. We show that the mean target detection time can be minimized as a function of the mean duration of each phase in dimension 1, 2 and 3. Importantly, this optimal strategy does not depend on the details of the modeling of the slow detection phase, which shows the robustness of our results. We believe that this systematic analysis can be used as a basis to study quantitatively various real search problems involving intermittent behaviors.
There are two effects of extra matter fields on the Lorentzian traversable wormhole. The ``primary effect'' says that the extra matter can afford to be a part of source or whole source of the wormhole when the wormhole is being formed. Thus the matter does not affect the stability of wormhole and the wormhole is still safe. If the extra matter is extotic, it can be the whole part of the source of the wormhole.   The ``auxiliary effect'' is that the extra matter plays the role of the additional matter to the stably-existed wormhole by the other exotic matter. This additional matter will change the geometry of wormhole enough to prevent from forming the wormhole by backreaction. In the minimally coupled massless scalar field case, the self-consistent solution was found. The backreaction of the scalar field can dominate the exotic matter part so that it will hinder the formation of the wormhole.
In this paper, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H.
Let $W\in \mathbb{C}[x_1,\cdots,x_N]$ be an invertible polynomial with an isolated singularity at origin, and let $G\subset {{\sf SL}}_N\cap (\mathbb{C}^*)^N$ be a finite diagonal and special linear symmetry group of $W$. In this paper, we use the category ${{\sf MF}}_G(W)$ of $G$-equivariant matrix factorizations and its associated VSHS to construct a $G$-equivariant version of Saito's theory of primitive forms. We prove there exists a canonical categorical primitive form of ${{\sf MF}}_G(W)$ characterized by $G_W^{{\sf max}}$-equivariance. Conjecturally, this $G$-equivariant Saito theory is equivalent to the genus zero part of the FJRW theory under LG/LG mirror symmetry. In the marginal deformation direction, we verify this for the FJRW theory of $\big(\frac{1}{5}(x_1^5+\cdots+x_5^5),\mathbb{Z}/5\mathbb{Z}\big)$ with its mirror dual B-model Landau-Ginzburg orbifold $\big(\frac{1}{5}(x_1^5+\cdots+x_5^5), (\mathbb{Z}/5\mathbb{Z})^4\big)$. In the case of the Quintic family $\mathcal{W}=\frac{1}{5}(x_1^5+\cdots+x_5^5)-\psi x_1x_2x_3x_4x_5$, we also prove a comparison result of B-model VSHS's conjectured by Ganatra-Perutz-Sheridan.
The star formation history and the internal dynamics of Milky Way satellite galaxies are often complicated. In the last years, a substantial fraction of the known faint dwarf satellites have been studied. Some of them show embedded stellar substructures, such as star clusters and even globular star clusters. In this work we study Eridanus II, a dwarf spheroidal satellite which hosts a star cluster, using published and archival data from the Hubble Space Telescope Advanced Camera for Surveys. We employ a Bayesian hierarchical method to infer the star formation history of Eridanus II. We find that the bulk of the stars in Eridanus II are very old ($13.5_{-1}^{+0.5}$ Gyr) and quite metal poor ($Z$\,=\,$0.00001$). We do not find any evidence of the presence of an intermediate age or young population in Eri II. We cannot date the embedded star cluster as a separate entity, but we find it likely that the cluster has a similar age and metallicity as the bulk of the stars in Eri II.   The existence of an old star cluster in a dark matter dominated old metal poor dwarf galaxy is of major importance to cast light on the dark matter distribution within dwarf galaxies. The existence of intermediate age stars is required by the recent detection of carbon stars in Eri II. Since no recent star formation is detected, {\it blue-straggler} fusions of lower mass stars are the most likely origin of the carbon star progenitors.
Can we relocalize in a scene represented by a single reference image? Standard visual relocalization requires hundreds of images and scale calibration to build a scene-specific 3D map. In contrast, we propose Map-free Relocalization, i.e., using only one photo of a scene to enable instant, metric scaled relocalization. Existing datasets are not suitable to benchmark map-free relocalization, due to their focus on large scenes or their limited variability. Thus, we have constructed a new dataset of 655 small places of interest, such as sculptures, murals and fountains, collected worldwide. Each place comes with a reference image to serve as a relocalization anchor, and dozens of query images with known, metric camera poses. The dataset features changing conditions, stark viewpoint changes, high variability across places, and queries with low to no visual overlap with the reference image. We identify two viable families of existing methods to provide baseline results: relative pose regression, and feature matching combined with single-image depth prediction. While these methods show reasonable performance on some favorable scenes in our dataset, map-free relocalization proves to be a challenge that requires new, innovative solutions.
In this paper, we develop a direct method of moving planes for the fractional Laplacian. Instead of conventional extension method introduced by Caffarelli and Silvestre, we work directly on the non-local operator. Using the integral defining the fractional Laplacian, by an elementary approach, we first obtain the key ingredients needed in the method of moving planes either in a bounded domain or in the whole space, such as strong maximum principles for anti-symmetric functions, narrow region principles, and decay at infinity. Then, using a simple example, a semi-linear equation involving the fractional Laplacian, we illustrate how this new method of moving planes can be employed to obtain symmetry and non-existence of positive solutions. We firmly believe that the ideas and methods introduced here can be conveniently applied to study a variety of nonlocal problems with more general operators and more general nonlinearities.
After a review of the canonical reduction to the rest-frame Wigner-covariant instant form of standard theories in Minkowski spacetime, a new formulation of tetrad gravity is introduced. Its canonical reduction, also in presence of N scalar particles, is done. The modification of the ADM formulation to solve the deparametrization problem of general relativity (how to recover the rest-frame instant form for G=0), is presented.
We have determined the Galactic rotation parameters and the solar Galactocentric distance $R_0$ by simultaneously solving Bottlinger's kinematic equations using data on masers with known line-of-sight velocities and highly accurate trigonometric parallaxes and proper motions measured by VLBI. Our sample includes 93 masers spanning the range of Galactocentric distances R from 3 to 15 kpc. The solutions found are   \Omega_0 = 29.7+/-0.5 km s^{-1} kpc^{-1},   \Omega'_0 = -4.20+/-0.11 km s^{-1} kpc^{-2},   \Omega"_0 =0.730+/-0.029 km s^{-1} kpc^{-3}, and   R_0=8.03+/-0.12 kpc. In this case, the linear rotation velocity at the solar distance R_0 is V_0=238+/-6 km s^{-1}.
Prior ultralow thermal conductivity materials are not suitable for thermoelectric applications due to the limited electronic transport in the materials. Here, we present a new class of ultralow thermal conductivity materials with substantial electronic heat transport. Our samples are graphene/metal heterostructures of transferred graphene and ultrathin metal films (Pd, Au and Ni) deposited by either thermal evaporation or rf magnetron sputtering. For the evaporated samples, we achieve an ultralow thermal conductivity of 0.06 W m-1 K-1, with phonons as the dominant heat carriers. The ultralow thermal conductivity is due to a huge disparity in phonon energy in graphene and metals. Interestingly, for the sputtered samples, we find that about 50 % of heat is carried by electrons, even when thermal conductivity is about 0.1 W m-1 K-1. We attribute the electronic contribution to transmission of electrons across atomic-scale pinholes in graphene. With the ultralow thermal conductivity and substantial electronic transport, the new materials could be explored for thermoelectric applications.
An optically and geometrically thick torus obscures the central engine of Active Galactic Nuclei (AGN) from some lines of sight. From a magnetohydrodynamical framework, the torus can be considered to be a particular region of clouds surrounding the central engine where the clouds are dusty and optically thick. In this framework, the magnetic field plays an important role in the creation, morphology and evolution of the torus. If the dust grains within the clouds are assumed to be aligned by paramagnetic alignment, then the ratio of the intrinsic polarisation and visual extinction, P(%)/Av, is a function of the magnetic field strength.   To estimate the visual extinction through the torus and constrain the polarisation mechanisms in the nucleus of AGN, we developed a polarisation model to fit both the total and polarised flux in a 1.2" (~263pc) aperture of the type 2 AGN, IC5063. The polarisation model is consistent with the nuclear polarisation observed at K being produced by dichroic absorption from aligned dust grains with a visual extinction through the torus of 48$\pm$2 mag. We estimated the intrinsic polarisation arising from dichroic absorption to be P$_{K}^{dic}$=12.5$\pm$2.7%.   We consider the physical conditions and environment of the gas and dust for the torus of IC5063. Then, through paramagnetic alignment, we estimate a magnetic field strength in the range of 12-128mG in the NIR emitting regions of the torus of IC5063. Alternatively, we estimate the magnetic field strength in the plane of the sky using the Chandrasekhar-Fermi method. The minimum magnetic field strength in the plane of the sky is estimated to be 13 and 41 mG depending of the conditions within the torus of IC5063. These techniques afford the chance to make a survey of AGN, to investigate the effects of magnetic field strength on the torus, accretion, and interaction to the host galaxy.
Following up on earlier work, I suggest why there are no mappings to infinity under the Collatz conjecture, nor under other mappings of the generalization $3n+p$, where $p$ is odd.
We present the results of a Suzaku spectroscopic study of the soft extended X-ray emission in the HII region M17. The spectrum of the extended emission was obtained with a high signal-to-noise ratio in a spatially-resolved manner using the X-ray Imaging Spectrometer (XIS). We established that the contamination by unresolved point sources, the Galactic Ridge X-ray emission, the cosmic X-ray background, and the local hot bubble emission is negligible in the background-subtracted XIS spectrum of the diffuse emission. Half a dozen of emission lines were resolved clearly for the first time, including K lines of highly ionized O, Ne, and Mg as well as L series complex of Fe at 0.5--1.5 keV. Based on the diagnosis of these lines, we obtained the following results: (1) the extended emission is an optically-thin thermal plasma represented well by a single temperature of 3.0 +/- 0.4 MK, (2) the abundances of elements with emission lines in the diffuse spectrum are 0.1--0.3 solar, while those of bright discrete sources are 0.3--1.5 solar, (3) the metal abundances relative to each other in the diffuse emission are consistent with solar except for a Ne enhancement of a factor of 2, (4) both the plasma temperature and the chemical composition of the diffuse emission show no spatial variation across the studied spatial scale of about 5 pc.
To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account. Here we present the field theory for finite spin chains at finite temperature and calculate experimentally measurable quantities like susceptibilities and nuclear magnetic resonance spectra. For the interchain couplings we concentrate on geometries relevant for cuprate spin chains like Sr$_2$CuO$_3$ and SrCuO$_2$. The field theoretical results are compared to experimental as well as numerical data obtained by the density matrix renormalization group.