ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an alternative proof to the Touchard-Kaplansky formula for the probl\`eme des m\'enages, which, we believe, is simpler than the extant ones and is in the spirit of the elegant original proof by Kaplansky (1943). About the latter proof, Bogart and Doyle (1986) argued that despite its cleverness, suffered from opting to give precedence to one of the genders for the couples involved (Bogart and Doyle supplied an elegant proof that avoided such gender-dependent bias).
We excite the gyrotropic mode of a magnetic vortex and observe the resulting effect on the spin state of a nearby nitrogen-vacancy (NV) defect in diamond. Thin permalloy disks fabricated on a diamond sample are magnetized in a vortex state in which the magnetization curls around a central core. The magnetization dynamics of this configuration are described by a discrete spectrum of confined magnon modes, as well as a low-frequency gyrotropic mode in which the vortex core precesses about its equilibrium position. Despite the spin transition frequencies being far-detuned from the modes of the ferromagnet, we observe enhanced relaxation of the NV spin when driving the gyrotropic mode. Moreover, we map the spatial dependence of the interaction between the vortex and the spin by translating the vortex core within the disk with an applied magnetic field, resulting in steplike motion as the vortex is pinned and de-pinned. The strong spin relaxation is observed when the vortex core is within approximately 250 nm of the NV center defect. We attribute this effect to the higher frequencies in the spectrum of the magnetic fringe field arising from the soliton-like nature of the gyrotropic mode when driven with sufficiently large amplitude.
The classical Dehn--Sommerville relations assert that the $h$-vector of an Eulerian simplicial complex is symmetric. We establish three generalizations of the Dehn--Sommerville relations: one for the $h$-vectors of pure simplicial complexes, another one for the flag $h$-vectors of balanced simplicial complexes and graded posets, and yet another one for the toric $h$-vectors of graded posets with restricted singularities. In all of these cases, we express any failure of symmetry in terms of "errors coming from the links." For simplicial complexes, this further extends Klee's semi-Eulerian relations.
We present an analysis of the dust continuum emission at 870 um in order to investigate the mass distribution of clumps within infrared dark clouds (IRDCs). We map six IRDCs with the Large APEX BOlometer CAmera (LABOCA) at APEX, reaching an rms noise level of 28-44 mJy/beam. The dust continuum emission coming from these IRDCs was decomposed by using two automated algorithms, Gaussclumps and Clumpfind. Moreover, we carried out single-pointing observations of the N_2H^+ (3-2) line toward selected positions to obtain kinematic information. The mapped IRDCs are located in the range of kinematic distances of 2.7-3.2 kpc. We identify 510 and 352 sources with Gaussclumps and Clumpfind, respectively, and estimate masses and other physical properties assuming a uniform dust temperature. The mass ranges are 6-2692 Msun (Gaussclumps) and 7-4254 Msun (Clumpfind) and the ranges in effective radius are around 0.10-0.74 pc (Gaussclumps) and 0.16-0.99 pc (Clumpfind). The mass distribution, independent of the decomposition method used, is fitted by a power law, dN/dM propto M^alpha, with an index of -1.60 +/- 0.06, consistent with the CO mass distribution and other high-mass star-forming regions.
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. The physical interpretation of the notion of relative velocity is discussed. The notions of deformation velocity tensor, shear velocity, rotation (vortex) velocity, and expansion velocity are introduced. Different types of flows are considered.   PACS numbers: 11.10.-z; 11.10.Ef; 7.10.+g; 47.75.+f; 47.90.+a; 83.10.Bb
It is shown that the true parameters of He-4-Sigma differ from the observed ones. The reason is that the amplitude of He-4-Sigma production in the reaction He-4(K-,pi-) sharply varies just in the corresponding mass region. It leads to the small, but noticeable shift of the binding energy and the width. Besides, the data at the threshold of Sigma-0 production is found to give an additional evidence that He-4-Sigma width cannot exceed 8.0 - 8.5 MeV.
Dynamic trajectories can be modeled with a Markov State Model (MSM). The reduction of continuous space coordinates to discretized coordinates can be done by statistical binning process. In addition to that, the transition probabilities can be determined by recording each event in the dynamic trajectory. This framework is put to a test by the electron spin resonance (ESR) spectroscopy of nitroxide spin label in X- and Q- bands. Calculated derivative spectra from MSM model with transition matrix obtained from a single Brownian trajectory by statistical binning process with the derivative spectra generated from the average of a large number of Brownian trajectories, are compared and yield a very good agreement. It is suggested that this method can be implemented to calculate absorption spectra from molecular dynamics (MD) simulation data. One of its advantages is that due to its reduction of computational effort, the parametrization process will be quicker. Secondly, the transition matrix defined in this manner, may indicate separable potential changes during the motion of the molecule and may have advantages when working with reducible set of coordinates. Thirdly, one can calculate the ESR spectra from a single MD trajectory directly without extending it artificially in the time axis. However, for short MD trajectories, the required statistical information can not be obtained depending on the timescale of transitions. Therefore, some statistical improvement will be needed in order to reach a better convergence.
Introducing a new notion of generalized suitable weak solutions, we first prove validity of the energy inequality for such a class of weak solutions to the Navier-Stokes equations in the whole space $\mathbb{R}^n$. Although we need certain growth condition on the pressure, we may treat the class even with infinite energy quantity except for the initial velocity. We next handle the equation for vorticity in 2D unbounded domains. Under a certain condition on the asymptotic behavior at infinity, we prove that the vorticity and its gradient of solutions are both globally square integrable. As their applications, Loiuville-type theorems are obtained.
We propose a superfield formalism of Lagrangian BRST-antiBRST quantization of arbitrary gauge theories in general coordinates with the base manifold of fields and antifields desribed in terms of both bosonic and fermionic variables.
Rigid tree honeycombs were introduced by Knutson, Tao, and Woodward and they were shown by Dykema, Collins, Timotin, and the authors to be sums of extreme rigid honeycombs, with uniquely determined summands up to permutations. Two extreme rigid honeycombs are essentially the same if they have proportional exit multiplicities and, up to this identification, there are countably many equivalence classes of such honeycombs. We describe two ways to approach the enumeration of these equivalence classes. The first method produces a (finite) list of all rigid tree honeycombs of fixed weight by looking at the locking patterns that can be obtained from a certain quadratic Diophantine equation. The second method constructs arbitrary rigid tree honeycombs from rigid overlays of two rigid tree honeycombs with strictly smaller weights. This allows, in principle, for an inductive construction of all rigid tree honeycombs starting with those of unit weight. We also show that some rigid overlays of two rigid tree honeycombs give rise to an infinite sequence of rigid tree honeycombs of increasing complexity but with a fixed number of nonzero exit multiplicities. This last result involves a new inflation/deflation construction that also produces other infinite sequences of rigid tree honeycombs.
We report deep imaging observations with DOLoRes@TNG of an ultra-faint dwarf satellite candidate of the Triangulum galaxy (M33) found by visual inspection of the public imaging data release of the DESI Legacy Imaging Surveys. Pisces VII/Triangulum (Tri) III is found at a projected distance of 72 kpc from M33, and using the tip of the red giant branch method we estimate a distance of D=1.0 +0.3,-0.2 Mpc, meaning the galaxy could either be an isolated ultra-faint or the second known satellite of M33. We estimate an absolute magnitude of M_V=-6.1+/-0.2 if Pisces VII/Tri II is at the distance of M33, or as bright as M_V=-6.8+/-0.2 if the galaxy is isolated. At the isolated distance, it has a physical half-light radius of r_h=131+/-61 pc consistent with similarly faint galaxies around the Milky Way. As the tip of the red giant branch is sparsely populated, constraining a precision distance is not possible, but if Pisces VII/Tri III can be confirmed as a true satellite of M33 it is a significant finding. With only one potential satellite detected around M33 previously (Andromeda XXII/Tri I), it lacks a significant satellite population in stark contrast to the similarly massive Large Magellanic Cloud. The detection of more satellites in the outskirts of M33 could help to better illuminate if this discrepancy between expectation and observations is due to a poor understanding of the galaxy formation process, or if it is due to the low luminosity and surface brightness of the M33 satellite population which has thus far fallen below the detection limits of previous surveys. If it is truly isolated, it would be the faintest known field dwarf detected to date.
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally coupled scalar field, within the Einstein-Christoffel symmetric hyperbolic formulation of Einstein's equations. By exploiting the characteristic propagation of the main variables and constraints, we are able to single out the only free modes at the outer boundary for these problems. In the vacuum case a single free modes exists which corresponds to a gauge freedom, while in the matter case an extra mode exists which is associated with the scalar field. We make use of the fact that the EC formulation has no superluminal characteristic speeds to excise the singularity. We present a second-order, finite difference discretization to treat these scenarios, where we implement these constraint-preserving boundary conditions, and are able to evolve the system for essentially unlimited times. As a test of the robustness of our approach, we allow large pulses of gauge and scalar field enter the domain through the outer boundary. We reproduce expected results, such as trivial (in the physical sense) evolution in the vacuum case (even in gauge- dynamical simulations), and the tail decay for the scalar field.
We study the stability of $D \geq 7$ asymptotically flat black holes rotating in a single two-plane against tensor-type gravitational perturbations. The extensive search of quasinormal modes for these black holes did not indicate any presence of growing modes, implying the stability of simply rotating Myers-Perry black holes against tensor-type perturbations.
We make explicit a theorem of Fromm and Goldmakher [arXiv:1706.03002], which states that one can improve Burgess' bound for short character sums simply by improving the leading constant in the P\'{o}lya-Vinogradov inequality. Towards achieving this, we establish explicit versions of several estimates related to the mean values of real multiplicative functions and the Dickman function.
In this paper, we use the type Ia supernovae data to constrain the holographic dark energy model proposed by Li. We also apply a cosmic age test to this analysis. We consider in this paper a spatially flat Friedmann-Robertson-Walker Universe with matter component and holographic dark energy component. The fit result shows that the case $c<1$ ($c=0.21$) is favored, which implies that the holographic dark energy behaves as a quintom-type dark energy. Furthermore, we also perform a joint analysis of SNe+CMB+LSS to this model; the result is well improved, and still upholds the quintom dark energy conclusion. The best fit results in our analysis are $c=0.81$, $\Omega_m^0=0.28$, and $h=0.65$, which lead to the present equation of state of dark energy $w_0=-1.03$ and the deceleration/acceleration transition redshift $z_T=0.63$. Finally, an expected SNAP simulation using $\Lambda$CDM as a fiducial model is performed on this model, and the result shows that the holographic dark energy model takes on $c<1$ ($c=0.92$) even though the dark energy is indeed a cosmological constant.
Based upon our recent study, we reveal the profound physical content of the longitudinal-Goldstone boson equivalence theorem as being able to discriminate physical processes which are sensitive/insensitive to probing the electroweak symmetry breaking (EWSB) sector. We then develop a precise electroweak power counting rule (a generalization from Weinberg's counting method) to `separately' count the power dependences on the energy E and all relevant mass scales. With these, we analyze the complete set of the bosonic operators in the electroweak chiral Lagrangian and systematically estimate and classify the sensitivities for testing all these effective operators at the CERN LHC via the weak-boson fusions and quark-anti-quark annihilations. These two kinds of processes are shown to be `complementary' in probing the EWSB mechanism.
We present mid-infrared spectral maps of the NGC 1333 star forming region, obtained with the the Infrared Spectrometer on board the Spitzer Space Telescope. Eight pure H2 rotational lines, from S (0) to S (7), are detected and mapped. The H2 emission appears to be associated with the warm gas shocked by the multiple outflows present in the region. A comparison between the observed intensities and the predictions of detailed shock models indicates that the emission arises in both slow (12 - 24 km/s) and fast (36 - 53 km/s) C-type shocks with an initial ortho-to-para ratio of ~ 1. The present H2 ortho-to-para ratio exhibits a large degree of spatial variations. In the post-shocked gas, it is usually about 2, i.e. close to the equilibrium value (~ 3). However, around at least two outflows, we observe a region with a much lower (~ 0.5) ortho-to-para ratio. This region probably corresponds to gas which has been heated-up recently by the passage of a shock front, but whose ortho-to-para has not reached equilibrium yet. This, together with the low initial ortho-to-para ratio needed to reproduce the observed emission, provide strong evidence that H2 is mostly in para form in cold molecular clouds. The H2 lines are found to contribute to 25 - 50% of the total outflow luminosity, and thus can be used to ascertain the importance of star formation feedback on the natal cloud. From these lines, we determine the outflow mass loss rate and, indirectly, the stellar infall rate, the outflow momentum and the kinetic energy injected into the cloud over the embedded phase. The latter is found to exceed the binding energy of individual cores, suggesting that outflows could be the main mechanism for core disruption.
Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped $^{111}$Cd$^+$ ion, and show that phase coherence of the resulting "Schr\"{o}dinger-cat" states of motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.
This study is aimed at investigating the physicochemical properties of low rank Nigerian coals. The coal samples were examined using bomb calorimetry, ultimate and proximate analyses to determine the heating value, elemental composition and physicochemical properties. The calorific values of the coals were; 23.74 MJ/kg for GMG; 27.34 MJ/kg for SKJ and 30.52 MJ/kg for AFZ. The results of elemental analysis showed high C, H, O and low N, and S content for the coals. The GMG coal displayed the lowest N, and S values emphasizing its low pollutant emission potential. The highest VM (51.16 %) and M (5.28 %) content was observed for GMG; AFZ coal displayed the highest ash content at 30.99 %; and SKJ the highest FC content. Consequently, the reactivity and maturity of the low rank Nigerian coals investigated increases in the order; GMG > SKJ > AFZ.   Keywords: Physicochemical, Characterization, Low rank, Nigeria, Coal, Energy
JEM-EUSO, on board of the Japanese Exploration Module of the International Space Station, is being proposed as the first space observatory devoted to UHECR. Its privileged position at 430 km above the Earth surface, combined with a large field of view, innovative optics and a high efficiency focal surface, results in an unprecedented exposure which significantly surpasses that of the largest ground observatories. The large number of events expected above the GZK threshold for photo-pion production by protons will allow the directional identification of individual sources and the determination of their spectra, i.e., doing astronomy and astrophysics through the particle channel. Similar goals can be achieved in the case of light UHECR nuclei. Furthermore, the atmospheric target volume ($\sim 10^{12}$ ton) makes the possibility of neutrino observation a highlight of the mission. Other exploratory objectives include the detection of extreme energy gammas and the study of Galactic magnetic fields as well as global observations of the earth's atmosphere, including clouds, night-glows, plasma discharges, and meteors. In this contribution we will describe the scientific objectives of JEM-EUSO.
A geometric relationship between loop quantum gravity and partitioned (triangulated) string theory is discussed. Combinatorial analysis reveals that three spatial and three curvature dimensions, intrinsic to the partitioned string, are necessary to replicate Standard Model particles and interactions. This analysis has established that particulate mass is determined by a functional relationship involving these six extra dimensions. The combinatorial analysis involves non-commutative 3D-matrix algebra which forms the mathematical underpinnings of Dirac notation. The functional relationship (symbolized by Beth) requires exponential, Randall-Sundrum, scaling to compute mass. Through the proper interpretation of complex gravity a cyclic cosmological model is developed. This formulation of cyclic cosmology inherently involves observed dark energy. Thus, a comprehensive theory is constructed from geometric fundamentals which models both massive, oscillating neutrinos and the current epoch of mini-inflation.
Many key features in photovoltaic perovskites occur in relatively long time scales and involve mixed compositions. This requires realistic but also numerically simple models. In this work we present a transferable classical force field to describe the mixed hybrid perovskite MA$_x$FA$_{1-x}$Pb(Br$_y$I$_{1-y}$)$_3$ for variable composition ($\forall x,y \in [0,1]$). The model includes Lennard-Jones and Buckingham potentials to describe the interactions between the atoms of the inorganic lattice and the organic molecule, and the AMBER model to describe intramolecular atomic interactions. Most of the parameters of the force field have been obtained by means of a genetic algorithm previously developed to parameterize the CsPb(Br$_x$I$_{1-x}$)$_3$ perovskite. The algorithm finds the best parameter set that simultaneously fits the DFT energies obtained for several crystalline structures with moderate degrees of distortion with respect to the equilibrium configuration. The resulting model reproduces correctly the XRD patterns, the expansion of the lattice upon I/Br substitution and the thermal expansion coefficients. We use the model to run classical molecular dynamics simulations with up to 8600 atoms and simulation times of up to 40~ns. From the simulations we have extracted the ion diffusion coefficient of the pure and mixed perovskites, presenting for the first time these values obtained by a fully dynamical method using a transferable model fitted to first principles calculations. The values here reported can be considered as the theoretical upper limit for ion migration dynamics induced by halide vacancies in photovoltaic perovskite devices under operational conditions.
Kondo insulators combine strong electronic correlations with spin orbit coupling and thereby provide a potential realization of correlated topological insulators. We present model calculations which allow us to study the onset of bulk coherence and concomitant topological edge states from the mixed valence to local moment regimes. Our real-space dynamical mean-field results include the detailed temperature dependence of the single particle spectral function on slab geometries as well as the temperature dependence of the topological invariant. The relevance of our calculations for candidate materials like SmB6 is discussed.
We present a multi-wavelength study of the massive ($M_{200\textrm{c}} \approx 1$-$2 \times 10^{15} M_\odot$) galaxy clusters RXC J2248.7$-$4431, MACS J0416.1$-$2403, and MACS J1206.2$-$0847 at $z \approx 0.4$. Using the X-ray surface brightness of the clusters from deep Chandra data to model their hot gas, we are able to disentangle this mass term from the diffuse dark matter in our new strong-lensing analysis, with approximately $50$-$100$ secure multiple images per cluster, effectively separating the collisional and collisionless mass components of the clusters. At a radial distance of $10\%$ of $R_{200\textrm{c}}$ (approximately $200$ kpc), we measure a projected total mass of $(0.129 \pm 0.001)$, $(0.131 \pm 0.001)$ and $(0.137 \pm 0.001)\times M_{200\textrm{c}}$, for RXC J2248, MACS J0416 and MACS J1206, respectively. These values are surprisingly similar, considering the large differences in the merging configurations, and, as a consequence, in the mass models of the clusters. Interestingly, at the same radii, the hot gas over total mass fractions differ substantially, ranging from $0.082 \pm 0.001$ to $0.133 \pm 0.001$, reflecting the various dynamical states of the clusters. Moreover, we do not find a statistically significant offset between the positions of the peak of the diffuse dark matter component and of the BCG in the more complex clusters of the sample. We extend to this sample of clusters previous findings of a number of massive sub-halos higher than in numerical simulations. These results highlight the importance of a proper separation of the different mass components to study in detail the properties of dark matter in galaxy clusters.
We consider the Y-junction, connecting three quantum wires, in the scattering states formalism. In the absence of fermionic interaction we analyze the restrictions on the values of conductance matrix, imposed by the unitarity of scattering S-matrix. Using the combination of numerical and analytical results, we describe the four-dimensional body of values of reduced conductance matrix. We show that this body touches the unit sphere at six points only, in accordance with Birkhoff-von Neumann theorem. It implies that the Abelian bosonization analysis for the vanishing interaction strength can be performed only in the vicinity of these six points.