ShantanuT01/DACTYL-Pretraining huggingface dataset:
We derive corrections to atomic energy levels from disformal couplings in Galileon theories. Through Bayesian inference, we constrain the cutoff radii and Galileon scale via these corrections. To connect different atomic systems, we assume the various cutoff radii related by a one-parameter family of solutions. This introduces a new parameter $\alpha$ which is also constrained. In this model, we predict shifts to muonic helium of $\delta E_{He^3}=1.97^{+9.28}_{-1.87}$ meV and $\delta E_{He^4}=1.69^{+9.25}_{-1.61}$ meV as well as for true muonium, $\delta E_{TM}=0.06^{+0.46}_{-0.05}$ meV.
The Gepner-like models of $k^{K}$-type is considered. When $k+2$ is multiple of $K$ the elliptic genus and the Euler characteristic is calculated. Using free-field representation we relate these models with $\sigma$-models on hypersurfaces in the total space of anticanonical bundle over the projective space $\mathbb{P}^{K-1}$.
We show that certain models for neutrino masses that lead to the MSW explanation of the solar neutrino data and/or the hot dark matter component in the universe can also naturally allow for the successful generation of the cosmological baryon asymmetry at the electroweak scale. This follows either because the experimental Higgs boson mass limit is weakened due to the smaller production rate and the presence of sizeable invisible decays involving majoron emission, or due to the effect of additional electrically charged scalar bosons which substantially modify the condition for succesful baryogenesis.
We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.
We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 deg$^2$ SPTpol survey, the most precise CMB lensing measurement from the ground to date. We fit a flat $\Lambda$CDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO) as well as primary CMB spectra from Planck and SPTpol. The cosmological constraints based on SPTpol and Planck lensing band powers are in good agreement when analysed alone and in combination with Planck full-sky primary CMB data. With weak priors on the baryon density and other parameters, the CMB lensing data alone provide a 4\% constraint on $\sigma_8\Omega_m^{0.25} = 0.0593 \pm 0.025$.. Jointly fitting with BAO data, we find $\sigma_8=0.779 \pm 0.023$, $\Omega_m = 0.368^{+0.032}_{-0.037}$, and $H_0 = 72.0^{+2.1}_{-2.5}\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1} $, up to $2\,\sigma$ away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTpol and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat $\Lambda$CDM model. The SPTpol lensing spectrum constrains the spatial curvature to be $\Omega_K = -0.0007 \pm 0.0025$ and the sum of the neutrino masses to be $\sum m_{\nu} < 0.23$ eV at 95\% C.L. (with Planck primary CMB and BAO data), in good agreement with the Planck lensing results. With the differences in the $S/N$ of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement.
A laminar family is a collection $\mathscr{A}$ of subsets of a set $E$ such that, for any two intersecting sets, one is contained in the other. For a capacity function $c$ on $\mathscr{A}$, let $\mathscr{I}$ be $\{I:|I\cap A| \leq c(A)\text{ for all $A\in\mathscr{A}$}\}$. Then $\mathscr{I}$ is the collection of independent sets of a (laminar) matroid on $E$. We present a method of compacting laminar presentations, characterize the class of laminar matroids by their excluded minors, present a way to construct all laminar matroids using basic operations, and compare the class of laminar matroids to other well-known classes of matroids.
We analyse the cluster luminosity functions (CLFs) of the youngest star clusters in three galaxies exhibiting prominent circumnuclear starburst rings. We focus specifically on NGC 1512 and NGC 6951, for which we have access to H$\alpha$ data that allow us to unambiguously identify the youngest sample clusters. To place our results on a firm statistical footing, we first explore in detail a number of important technical issues affecting the process from converting the observational data into the spectral-energy distributions of the objects in our final catalogues. The CLFs of the young clusters in both galaxies exhibit approximate power-law behaviour down to the 90 per cent observational completeness limits, thus showing that star cluster formation in the violent environments of starburst rings appears to proceed similarly as that elsewhere in the local Universe. We discuss this result in the context of the density of the interstellar medium in our starburst-ring galaxies.
This article summarizes a new approach to quantum gravity based on the concepts of modular spacetime, Born geometry, and metastring theory and their applications to quantum gravity phenomenology. In particular, we discuss a new understanding of dark matter in terms of metaparticles (zero modes of the metastring) and its relation to dark energy (the curvature of dual spacetime) in view of the actual astronomical observations.
We present a multiwavelength examination of the supernova remnant (SNR) S26 in the nearby galaxy NGC 300 using data from Chandra X-ray Observatory, XMM-Newton X-ray Observatory, Hubble Space Telescope (HST), the Very Large Array, and the Australia Telescope Compact Array. We simultaneously fit all of the available X-ray data with a thermal plasma model and find a temperature of $0.77 \pm 0.13$ keV with a hydrogen column density of ($9.7^{+6.4}_{-4.8}$)$\times 10^{20}$ cm$^{-2}$. HST imaging allows us to measure a semimajor axis of $0.78 \pm 0.10$ arcsec ($7.5 \pm 1.0$ pc) and a semiminor axis of $0.69^{+0.14}_{-0.12}$ arcsec ($6.7^{+1.2}_{-1.4}$ pc). This precise size helps to constrain the age and velocity of the shock to be ($3.3^{+0.7}_{-0.6}$)$\times 10^{3}$ yr and $411^{+275}_{-122}$ km s$^{-1}$. We also fit photometry of the surrounding stars to infer the age and mass of the progenitor star to be $8 \pm 1$ Myr and $25^{+1}_{-5}$ M$_{\odot}$. Based on measured radio properties of the source and assuming equipartition, the estimated radio luminosity of $\sim 1.7 \times 10^{34}$ erg s$^{-1}$ over the $10^{8}-10^{11}$ Hz frequency range results in a minimum magnetic field associated with this SNR of $0.067$ mG and the minimum energy needed to power the observed synchrotron emission of $1.5 \times 10^{49}$ erg. The size and temperature of N300-S26 appear to be similar to the Galactic SNR G311.5-0.3 except that G311.5-0.3 has a significantly lower X-ray luminosity, is older, and has a slower shock velocity.
Gravitational radiation drives an instability in the r-modes of young rapidly rotating neutron stars. This instability is expected to carry away most of the angular momentum of the star by gravitational radiation emission, leaving a star rotating at about 100 Hz. In this paper we model in a simple way the development of the instability and evolution of the neutron star during the year-long spindown phase. This allows us to predict the general features of the resulting gravitational waveform. We show that a neutron star formed in the Virgo cluster could be detected by the LIGO and VIRGO gravitational wave detectors when they reach their ``enhanced'' level of sensitivity, with an amplitude signal-to-noise ratio that could be as large as about 8 if near-optimal data analysis techniques are developed. We also analyze the stochastic background of gravitational waves produced by the r-mode radiation from neutron-star formation throughout the universe. Assuming a substantial fraction of neutron stars are born with spin frequencies near their maximum values, this stochastic background is shown to have an energy density of about 10^-9 of the cosmological closure density, in the range 20 Hz to 1 kHz. This radiation should be detectable by ``advanced'' LIGO as well.
We used Early Release Science (ERS) observations taken with the Wide Field Camera 3 (WFC3) in the GOODS-S field to study the galaxy stellar mass function (GSMF) at 0.6<=z<4.5. Deep WFC3 near-IR data (for Y as faint as 27.3, J and H as faint as 27.4 AB mag at 5 sigma), as well as deep Ks (as faint as 25.5 at 5 sigma) Hawk-I band data, provide an exquisite data set with which determine in an unprecedented way the low-mass end of the GSMF, allowing an accurate probe of masses as low as M~7.6 10^9 Msun at z~3. Although the area used is relatively small (~33 arcmin^2), we found generally good agreement with previous studies on the entire mass range. Our results show that the slope of the faint-end increases with redshift, from alpha=-1.44+/-0.03 at z~0.8 to alpha=-1.86+/-0.16 at z~3, although indications exist that it does not steepen further between z~3 and z~4. This result is insensitive to any uncertainty in the M* parameter. The steepness of the GSMF faint-end solves the well-known disagreement between the stellar mass density (SMD) and the integrated star formation history at z>2. However, we confirm the that there appears to be an excess of integrated star formation with respect to the SMD at z<2, by a factor of ~2-3. Our comparison of the observations with theoretical predictions shows that the models forecast a greater abundance of low mass galaxies, at least up to z~3, as well as a dearth of massive galaxies at z~4 with respect to the data, and that the predicted SMD is generally overestimated at z<~2.
We consider a large black hole in asymptotically AdS spacetime of arbitrary dimension with a Minkowski boundary. By performing an appropriate slicing as we approach the boundary, we obtain via holographic renormalization a gauge theory fluid obeying Bjorken hydrodynamics in the limit of large longitudinal proper time. The metric we obtain reproduces to leading order the metric recently found as a direct solution of the Einstein equations in five dimensions. Our results are also in agreement with recent exact results in three dimensions.
A conjecture of Berge and Fulkerson (1971) states that every cubic bridgeless graph contains 6 perfect matchings covering each edge precisely twice, which easily implies that every cubic bridgeless graph has three perfect matchings with empty intersection (this weaker statement was conjectured by Fan and Raspaud in 1994). Let $m_t$ be the supremum of all reals $\alpha\le 1$ such that for every cubic bridgeless graph $G$, there exist $t$ perfect matchings of $G$ covering a fraction of at least $\alpha$ of the edges of $G$. It is known that the Berge-Fulkerson conjecture is equivalent to the statement that $m_5=1$, and implies that $m_4=\tfrac{14}{15}$ and $m_3=\tfrac45$. In the first part of this paper, we show that $m_4=\tfrac{14}{15}$ implies $m_3=\tfrac45$, and $m_3=\tfrac45$ implies the Fan-Raspaud conjecture, strengthening a recent result of Tang, Zhang, and Zhu. In the second part of the paper, we prove that for any $2\le t \le 4$ and for any real $\tau$ lying in some appropriate interval, deciding whether a fraction of more than (resp. at least) $\tau$ of the edges of a given cubic bridgeless graph can be covered by $t$ perfect matching is an NP-complete problem. This resolves a conjecture of Tang, Zhang, and Zhu.
A graph G is called (2k, k)-connected if G is 2k-edge-connected and G-v is k-edge-connected for every vertex v. The study of (2k, k)-connected graphs is motivated by a conjecture of Frank which states that a graph has a 2-vertex-connected orientation if and only if it is (4, 2)-connected. In this paper, we provide a construction of the family of (2k, k)-connected graphs for k even which generalizes the construction given by Jord\'an for k = 2. We also solve the corresponding connectivity augmentation problem: given a graph G and an integer k \geq 2, what is the minimum number of edges to be added to make G (2k, k)-connected. Both these results are based on a new splitting-off theorem for (2k, k)-connected graphs.
With a parallactic distance of 170 pc, PSR J2144-3933 is the closest isolated radio pulsar currently known. It is also the slowest (P = 8.51 s) and least energetic (Edot = 2.6E28 erg/s) radio pulsar; its radio emission is difficult to account for with standard pulsar models, since the position of PSR J2144-3933 in the period-period derivative diagram is far beyond the typical radio `death lines'. Here we present the first deep X-ray and optical observations of PSR J2144-3933, performed in 2009 with XMM-Newton and European Southern Observatory (ESO)/Very Large Telescope (VLT), from which we derive, assuming a blackbody emission spectrum, a surface temperature upper limit of 2.3E5 K for a 13 km radius neutron star, 4.4E5 K for a 500 m radius hot spot and 1.9E6 K for a 10 m radius polar cap. In addition, our non-detection of PSR J2144-3933 constrains its non-thermal luminosity to be <30 per cent and <2 per cent of the pulsar rotational energy loss in the 0.5-2 keV X-ray band and in the B optical band, respectively.
We investigate the first and second moments of shifted convolutions of the generalised divisor function $d_3(n)$.
Solute clusters affect the physical properties of alloys. Knowledge of the atomic structure of solute clusters is a prerequisite for material optimisation. In this study, solute clusters in a rapid-hardening Al-Cu-Mg alloy were characterised by a combination of atom probe tomography and density functional theory, making use of a hybrid data type that combines lattice rectification and data completion to directly input experimental data into atomistic simulations. The clusters input to the atomistic simulations are thus observed experimentally, reducing the number of possible configurations. Our results show that spheroidal, compact clusters are more energetically favourable and more abundant.
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the_averaged_ scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set. This averaged density falls short of a true structure determination (which would reveal the typical_unaveraged_ atomic patterns.) We discuss the problematic validity of inferring an ideal structure by simply factoring out a ``perp-space'' Debye-Waller factor, and we test this using simulations of rhombohedral tilings. A second, ``unified'' path is to relate the measured and modeled intensities directly, by adjusting parameters in a simulation to optimize the fit. This approach is well suited for unifying structural information from diffraction and from minimizing total energies derived ultimately from ab-initio calculations. Finally, we discuss the special pitfalls of fitting random-tiling decagonal phases.
Catalysis informatics is constantly developing, and significant advances in data mining, molecular simulation, and automation for computational design and high-throughput experimentation have been achieved. However, efforts to reveal the mechanisms of complex supported nanoparticle catalysts in cyberspace have proven to be unsuccessful thus far. This study fills this gap by exploring N$_2$ dissociation on a supported Ru nanoparticle as an example using a universal neural network potential. We calculated 200 catalyst configurations considering the reduction of the support and strong metal-support interaction (SMSI), eventually performing 15,600 calculations for various N$_2$ adsorption states. After successfully validating our results with experimental IR spectral data, we clarified key N$_2$ dissociation pathways behind the high activity of the SMSI surface and disclosed the maximum activity of catalysts reduced at 650 {\deg}C. Our method is well applicable to other complex systems, and we believe it represents a key first step toward the digital transformation of investigations on heterogeneous catalysis.
Temperature-independent magnetic viscosity in ferritin has been observed from 2 K down to 100 mK, proving that quantum tunneling plays the main role in these particles at low temperature. Magnetic relaxation has also been studied using the Landau-Zener method making the system crossing zero resonant field at different rates, alpha=dH/dt, ranging from 10^{-5} to 10^{-3} T/s, and at different temperatures, from 150 mK up to the blocking temperature. We propose a new Tln(Delta H_{eff}/tau_0 alpha) scaling law for the Landau-Zener probability in a system distributed in volumes, where Delta H_{eff} is the effective width of the zero field resonance.
We present new diagnostics of white dwarf (WD) cooling sequences and luminosity functions (LFs) in the near-infrared (NIR) bands that will exploit the sensitivity and resolution of future extremely large telescopes. The collision-induced absorption (CIA) of molecular hydrogen causes a clearly defined blue turn-off along the WD (WDBTO) cooling sequences and a bright secondary maximum in the WD LFs. These features are independent of age over a broad age range and are minimally affected by metal abundance. This means that the NIR magnitudes of the WDBTO are very promising distance indicators. The interplay between the cooling time of progressively more massive WDs and the onset of CIA causes a red turn-off along the WD (WDRTO) cooling sequences and a well defined faint peak in the WD LFs. These features are very sensitive to the cluster age, and indeed the K-band magnitude of the faint peak increases by 0.2--0.25 mag/Gyr for ages between 10 and 14 Gyr. On the other hand, the faint peak in the optical WD LF increases in the same age range by 0.17 (V band) and 0.15 (I band) mag/Gyr. Moreover, we also suggest to use the difference in magnitude between the main sequence turn-off and either the WDBTO (optical) or the WDRTO (NIR). This age diagnostic is also independent of distance and reddening. Once again the sensitivity in the K band (0.15-0.20 mag/Gyr) is on average a factor of two higher than in the optical bands (0.10 [V band], 0.07 [I band] mag/Gyr). Finally, we also outline the use of the new diagnostics to constrain the CO phase separation upon crystallization.
We point out the curious phenomenon of order by projection in a class of lattice Fermi systems near half filling. Enhanced pairing correlations of extended s-wave Cooper pairs result from the process of projecting out s-wave Cooper pairs, with negligible effect on the ground state energy. The Hubbard model is a particularly nice example of the above phenomenon, which is revealed with the use of rigorous inequalities including the Uncertainty Principle Inequality. In addition, we present numerical evidence that at half filling, a related but simplified model shows ODLRO of extended s-wave Cooper pairs.
We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes from a normal to an "inverted" type at a critical thickness $d_c$. We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss the methods for experimental detection of the QSH effect.
Inspired by a theorem of Gruson-Lazarsfeld-Peskine bounding the Castelnuovo-Mumford regularity of curves in projective spaces, we bound the Theta-regularity of curves in polarized abelian varieties.
Elementary excitations of an S = 1/2 antiferromagnetic Heisenberg chain KCuGaF6 were investigated through specific heat and electron spin resonance (ESR) measurements. In this compound, a staggered field is induced perpendicular to the external field because of the alternating g tensor and the Dzyaloshinsky-Moriya interaction with an alternating D vector. Such a spin system can be mapped onto the quantum sine-Gordon (SG) model, when subjected to the external magnetic field. Specific heat shows clear evidence of the field-induced gap, which is related to the elementary excitations, solitons and breathers, characteristic of the quantum SG model. q = 0 excitations originated from solitons and breathers were directly observed by high-frequency high-field ESR. These experimental results are well described by the quantum SG field theory.
The catenary degree is an invariant that measures the distance between factorizations of elements within a numerical semigroup. In general, all possible catenary degrees of the elements of the numerical semigroups occur as the catenary degree of one of its Betti elements. In this study, Betti elements of some telescopic numerical semigroup families with embedding dimension three were found and formulated. Then, with the help of these formulas, Frobenius numbers and genus of these families were obtained. Also, the catenary degrees of telescopic numerical semigroups were found with the help of factorizations of Betti elements of these semigroups
We consider a continuous analogue of the simulated annealing algorithm in $R^d$. We prove a convergence result, under hypotheses weaker than the usual ones. In particular, we cover cases where the gradient of the potential goes to zero at infinity. The proof follows an idea of L. Miclo, but we replace the Poincar\'e and log-Sobolev inequalities (which do not hold in our setting) by weak Poincar\'e inequalities. We estimate the latter with measure-capacity criteria. We show that, despite the absence of a spectral gap, the convergence still holds for the "classical" schedule t = c/ ln(t), if c is bigger than a constant related to the potential.
Using the mean-field approximation, we study the $k$-space spin textures and local spin currents emerged in the spin-triplet excitonic insulator states of the two-band Hubbard model defined on the square and triangular lattices. We assume a noninteracting band structure with a direct band gap and introduce $s$-, $p$-, $d$-, and $f$-type cross-hopping integrals, i.e., the hopping of electrons between different orbitals on adjacent sites with four different symmetries. First, we calculate the ground-state phase diagrams in the parameter space of the band filling and interaction strengths, whereby we present the filling dependence of the amplitude and phase of the excitonic order parameters. Then, we demonstrate that the spin textures (or asymmetric band structures) are emerged in the Fermi surfaces by the excitonic symmetry breaking when particular phases of the order parameter are stabilized. Moreover, in case of the $p$-type cross-hopping integrals, we find that the local spin current can be induced spontaneously in the system, which does not contradict the Bloch theorem for the absence of the global spin current. The proofs of the absence of the global spin current and the possible presence of the local spin currents are given on the basis of the Bloch theorem and symmetry arguments.