ShantanuT01/DACTYL-Pretraining huggingface dataset:
A program is outlined concerning the set of all solutions of the hyperbolic Ernst equation on a two-dimensional manifold whose underlying topological space is the same as the domain of all Ernst potentials for colliding plane gravitational wave pairs. The aim of the program is to construct and apply a non-trivial extension of the group of Kinnersley-Chitre transformations. This is to be done by employing the formalism of a homogeneous Hilbert problem. In this first paper of a series, the aforementioned program is completely carried out for the collinear polarization case.
Deep Very Large Array imaging of the binary X-ray source SS 433, sometimes classified as a microquasar, has been used to study the intrinsic brightness distribution and evolution of its radio jets. The intrinsic brightness of the jets as a function of age at emission of the jet material tau is recovered by removal of the Doppler boosting and projection effects. We find that intrinsically the two jets are remarkably similar when compared for equal tau, and that they are best described by Doppler boosting of the form D^{2+alpha}, as expected for continuous jets. The intrinsic brightnesses of the jets as functions of age behave in complex ways. In the age range 60 < tau < 150 days, the jet decays are best represented by exponential functions of tau, but linear or power law functions are not statistically excluded. This is followed by a region out to tau ~ 250 days during which the intrinsic brightness is essentially constant. At later times the jet decay can be fit roughly as exponential or power law functions of tau.
Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ``spiral surface'' in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomena called order-by-disorder. A broad ``spiral spin-liquid'' regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed via spin correlations. We discuss the agreement between these predictions and the well characterized spinel MnSc2S4.
This paper studies the regularity problem for the 3D incompress- ible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence predicts that there exists a critical wavenumber above which the high frequency part is dominated by the dissipation term in the fluid equation. Inspired by this idea, we apply an approach of splitting the wavenumber combined with an estimate of the energy flux to obtain a new regularity criterion. The regularity condition presented here is weaker than conditions in the existing criteria (Prodi-Serrin type criteria) for the 3D Hall-MHD system.
We have compared the occurrence of 6.7-GHz and 12.2-GHz methanol masers with 22-GHz water masers and 6035-MHz excited-state OH masers in the 100 square degree region of the southern Galactic plane common to the Methanol Multibeam (MMB) and H2O southern Galactic Plane surveys (HOPS). We find the most populous star formation species to be 6.7-GHz methanol, followed by water, then 12.2-GHz and, finally, excited-state OH masers. We present association statistics, flux density (and luminosity where appropriate) and velocity range distributions across the largest, fully surveyed portion of the Galactic plane for four of the most common types of masers found in the vicinity of star formation regions.   Comparison of the occurrence of the four maser types with far-infrared dust temperatures shows that sources exhibiting excited-state OH maser emission are warmer than sources showing any of the other three maser types. We further find that sources exhibiting both 6.7-GHz and 12.2-GHz methanol masers are warmer than sources exhibiting just 6.7-GHz methanol maser emission. These findings are consistent with previously made suggestions that both OH and 12.2-GHz methanol masers generally trace a later stage of star formation compared to other common maser types.
Chromospheric activities prior to solar flares provide important clues to solar flare initiation, but are as yet poorly understood. We report a significant and rapid H$\alpha$ line broadening before the solar flare SOL2011-09-29T18:08, that was detected using the unprecedented high-resolution H$\alpha$ imaging spectroscopy with the Fast Imaging Solar Spectrograph (FISS) installed on the 1.6 m New Solar Telescope (NST) at Big Bear Solar Observatory.The strong H$\alpha$ broadening extends as a blue excursion up to -4.5 A and as a red excursion up to 2.0 A, which implies a mixture of velocities in the range of -130 km/s to 38 km/s by applying the cloud model, comparable to the highest chromospheric motions reported before. The H$\alpha$ blueshifted broadening lasts for about 4 minutes, and is temporally and spatially correlated with the start of a rising filament, which is later associated with the main phase of the flare as detected by the Atmosphere Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO). The potential importance of this H$\alpha$ blueshifted broadening as a preflare chromospheric activity is briefly discussed within the context of the two-step eruption model.
Residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-$Z_2$-flux variables in Kitaev models, the freezing of one set of degrees of freedom and establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO$_4$ by Li et al, we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. We find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.
In existing image classification systems that use deep neural networks, the knowledge needed for image classification is implicitly stored in model parameters. If users want to update this knowledge, then they need to fine-tune the model parameters. Moreover, users cannot verify the validity of inference results or evaluate the contribution of knowledge to the results. In this paper, we investigate a system that stores knowledge for image classification, such as image feature maps, labels, and original images, not in model parameters but in external high-capacity storage. Our system refers to the storage like a database when classifying input images. To increase knowledge, our system updates the database instead of fine-tuning model parameters, which avoids catastrophic forgetting in incremental learning scenarios. We revisit a kNN (k-Nearest Neighbor) classifier and employ it in our system. By analyzing the neighborhood samples referred by the kNN algorithm, we can interpret how knowledge learned in the past is used for inference results. Our system achieves 79.8% top-1 accuracy on the ImageNet dataset without fine-tuning model parameters after pretraining, and 90.8% accuracy on the Split CIFAR-100 dataset in the task incremental learning setting.
The observations of external galaxies are projected to the 2D sky plane. Reconstructing the 3D intrinsic density distribution of a galaxy from the 2D image is challenging, especially for barred galaxies, but is a critical step for constructing galactic dynamical models. Here we present a method for deprojecting barred galaxies and we validate the method by testing against mock images created from an N-body simulation with a peanut-shaped bar. We decompose a galaxy image into a bulge (including a bar) and a disk. By subtracting the disk from the original image a barred bulge remains. We perform multi-Gaussian expansion (MGE) fit to each component, then we deproject them separately by considering the barred bulge is triaxial while the disk is axisymmetric. We restrict the barred bulge to be aligned in the disk plane and has a similar thickness to the disk in the outer regions. The 3D density distribution is thus constructed by combining the barred bulge and the disk. Our model can generally recover the 3D density distribution of disk and inner barred bulge regions, although not a perfect match to the peanut-shaped structure. By using the same initial conditions, we integrate the orbits in our model-inferred potential and the true potential by freezing the N-body simulation. We find that 85% of all these orbits have similar morphologies in these two potentials, and our model supports the orbits that generate a boxy/peanut-shaped structure and an elongated bar similar to these in the true potential.
In magnetically-doped quantum dots changing the carrier occupancy, from open to closed shells, leads to qualitatively different forms of carrier-mediated magnetic ordering. While it is common to study such nanoscale magnets within a mean field approximation, excluding the spin fluctuations can mask important phenomena and lead to spurious thermodynamic phase transitions in small magnetic systems. By employing coarse-grained, variational, and Monte Carlo methods on singly and doubly occupied quantum dots to include spin fluctuations, we evaluate the relevance of the mean field description and distinguish different finite-size scaling in nanoscale magnets.
We update phenomenological constraints on a Two Higgs Doublet Model with lepton flavour non-conserving Yukawa couplings. We review that $\tan \beta$ is ambiguous in such "Type III" models, and define it from the $\tau$ Yukawa coupling. The neutral scalars $\phi$ could be searched for at hadron colliders in $ \phi \to \tau \bar{\mu}$, and are constrained by the rare decay $\tau \to \mu \gamma$. The Feynman diagrams for the collider process, with Higgs production via gluon fusion, are similar to the two-loop "Barr-Zee" diagrams which contribute to $\tau \to \mu \gamma$. Some "tuning" is required to obtain a collider cross-section of order the Standard Model expectation for $\sigma (gg \to h_{SM} \to \tau^+ \tau^-)$, while agreeing with the current bound from $\tau \to \mu \gamma$.
Galactic interacting double white dwarfs (DWD) are guaranteed gravitational wave (GW) sources for the GW detector LISA, with more than 10^4 binaries expected to be detected over the mission's lifetime. Part of this population is expected to be eccentric, and here we investigate the potential for constraining the white dwarf (WD) properties through apsidal precession in these binaries. We analyze the tidal, rotational, and general relativistic contributions to apsidal precession by using detailed He WD models, where the evolution of the star's interior is followed throughout the cooling phase. In agreement with previous studies of zero-temperature WDs, we find that apsidal precession in eccentric DWDs can lead to a detectable shift in the emitted GW signal when binaries with cool (old) components are considered. This shift increases significantly for hot (young) WDs. We find that apsidal motion in hot (cool) DWDs is dominated by tides at orbital frequencies above ~10^{-4}Hz (10^{- 3}$Hz). The analysis of apsidal precession in these sources while ignoring the tidal component would lead to an extreme bias in the mass determination, and could lead us to misidentify WDs as neutron stars or black holes. We use the detailed WD models to show that for older, cold WDs, there is a unique relationship that ties the radius and apsidal precession constant to the WD masses, therefore allowing tides to be used as a tool to constrain the source masses.
The planetary nebula (PN) NGC 6778 harbors a binary central star with a short orbital period and displays two systems of fast collimated outflows. In order to assess the influence of the evolution through a common-envelope phase of the binary system of NGC 6778 on its formation and shaping, we have used narrow-band images and high-dispersion long-slit spectra of the nebula to investigate its detailed morphology and kinematics. We find that the overall structure of NGC 6778 can be described as a bipolar PN. The equatorial ring is highly disrupted and many radial features (filamentary wisps and cometary knots) also evidence strong dynamical effects. There are clear connections between the bipolar lobes and the fast collimated outflows: the collimated outflows seem to arise from bright knots at the tips of the bipolar lobes, whereas the kinematics of the bipolar lobes is distorted. We suggest that the interaction of the fast collimated outflows of NGC 6778 with its nebular envelope has resulted in the disruption of the nebular shell and equatorial ring.
The embedding of the SM hypercharge into an orientifold gauge group is studied. Possible embeddings are classified, and a systematic construction of bottom-up configurations and top-down orientifold vacua is achieved, solving the tadpole conditions in the context of Gepner orientifolds. Some hypercharge embeddings are strongly preferred compared to others. Configurations with chiral antisymmetric tensors are suppressed. We find among others, genuine examples of supersymmetric SU(5), flipped SU(5), Pati-Salam and trinification vacua with no chiral exotics.
A Mustafin variety is a degeneration of projective space induced by a point configuration in a Bruhat-Tits building. The special fiber is reduced and Cohen-Macaulay, and its irreducible components form interesting combinatorial patterns. For configurations that lie in one apartment, these patterns are regular mixed subdivisions of scaled simplices, and the Mustafin variety is a twisted Veronese variety built from such a subdivision. This connects our study to tropical and toric geometry. For general configurations, the irreducible components of the special fiber are rational varieties, and any blow-up of projective space along a linear subspace arrangement can arise. A detailed study of Mustafin varieties is undertaken for configurations in the Bruhat-Tits tree of PGL(2) and in the two-dimensional building of PGL(3). The latter yields the classification of Mustafin triangles into 38 combinatorial types.
In numerical simulations of black hole binaries, Pretorius and Khurana [Class. Quant. Grav. {\bf 24}, S83 (2007)] have observed critical behaviour at the threshold between scattering and immediate merger. The number of orbits scales as $n\simeq -\gamma\ln|p-p_*|$ along any one-parameter family of initial data such that the threshold is at $p=p_*$. Hence they conjecture that in ultrarelavistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent $\gamma$. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by $n_\infty\simeq 0.41/\eta$, where $\eta$ is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter.
The implications of the formation of a Bose condensate on one- and two-particle spectra are studied for ultrarelativistic nucleus-nucleus collisions in the framework of a hydrodynamic description. It is found that single particle spectra are considerably enhanced at low momenta. The Bose-Einstein correlation function has an intercept below two. For pion pairs in the central region a two-component structure may appear in the correlation function, which is different from that found in quantum optics. The chaoticity parameter is strongly momentum dependent.
Heavy nuclei exhibit a crossover from vibrational to rotational collectivity as the number of neutrons or protons increases from shell closure towards midshell, but the microscopic description of this crossover has been a major challenge. We apply the shell model Monte Carlo approach to families of even-even samarium and neodymium isotopes and identify a microscopic signature of the crossover from vibrational to rotational collectivity in the low-temperature behavior of $<\mathbf{J}^2>_T$, where $\bf J$ is the total spin and $T$ is the temperature. This signature agrees well with its values extracted from experimental data. We also calculate the state densities of these nuclei and find them to be in very good agreement with experimental data. Finally, we define a collective enhancement factor from the ratio of the total state density to the intrinsic state density as calculated in the finite-temperature Hartree-Fock-Bogoliubov approximation. The decay of this enhancement factor with excitation energy is found to correlate with the pairing and shape phase transitions in these nuclei.
We investigate the finite time thermodynamics of a single-level fermion system interacting with a thermal reservoir through a tunneling junction. The optimal protocol to extract the maximum work from the system when moving the single energy level between an initial higher value and a final lower value in a finite time is calculated from a quantum master equation. The calculation also yields the optimal protocol to raise the energy level with the expenditure of the least amount of work on the system. The optimal protocol displays discontinuous jumps at the initial and final times.
[Abridged] Recent studies revealed a strong correlation between the star formation rate (SFR) and stellar mass of star-forming galaxies, the so-called star-forming main sequence. An empirical modeling approach (2-SFM) which distinguishes between the main sequence and rarer starburst galaxies is capable of reproducing most statistical properties of infrared galaxies. In this paper, we extend this approach by establishing a connection between stellar mass and halo mass with the technique of abundance matching. Based on a few, simple assumptions and a physically motivated formalism, our model successfully predicts the (cross-)power spectra of the cosmic infrared background (CIB), the cross-correlation between CIB and cosmic microwave background (CMB) lensing, and the correlation functions of bright, resolved infrared galaxies measured by Herschel, Planck, ACT and SPT. We use this model to infer the redshift distribution these observables, as well as the level of correlation between CIB-anisotropies at different wavelengths. We also predict that more than 90% of cosmic star formation activity occurs in halos with masses between 10^11.5 and 10^13.5 Msun. Taking into account subsequent mass growth of halos, this implies that the majority of stars were initially (at z>3) formed in the progenitors of clusters, then in groups at 0.5<z<3 and finally in Milky-Way-like halos at z<0.5. At all redshifts, the dominant contribution to the star formation rate density stems from halos of mass ~10^12 Msun, in which the instantaneous star formation efficiency is maximal (~70%). The strong redshift-evolution of SFR in the galaxies that dominate the CIB is thus plausibly driven by increased accretion from the cosmic web onto halos of this characteristic mass scale. Material available at http://irfu.cea.fr/Sap/Phocea/Page/index.php?id=537.
We consider a model of star copolymers, based on self-avoiding walks, where the arms of the star can be chemically distinct. The copolymeric star is attached to an impenetrable surface at a vertex of unit degree and the different monomers constituting the star have different interaction strengths with the surface. When the star is adsorbed at the surface it can be desorbed by applying a force, either at a vertex of degree 1 or at the central vertex of the star. We give some rigorous results about the free energy of the system and use these to establish the general form of the phase diagrams, and the orders of certain phase transitions in the system. We also consider the special case of spiders, ie stars constrained to have all degree 1 vertices in the surface.
We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations $u_t=F(\n^2u, \n u, u, t)$ under a structural condition, and give a geometric lower bound of the principal curvature of the spatial level surfaces.
We develop a new mechanism for the accumulation of conserved numbers in the early Universe in Kaluza-Klein-like theories. The relaxation of the primordial extra space perturbations existing in the early Universe leads to the establishment of a symmetric final state and the appearance of Killing vectors. As a result, the initial non-zero value of symmetry associated numbers occurs after the inflation. We show this conceptual idea on a toy model of 2-dimensional apple-like extra space with U(1) symmetry. This mechanism naturally arises in the Kaluza-Klein theories and can be used to explain the observed cosmological baryon asymmetry.
We have studied the electronic structure of the Ni triangular lattice in NiGa$_2$S$_4$ using photoemission spectroscopy and subsequent model calculations. The cluster-model analysis of the Ni 2$p$ core-level spectrum shows that the S 3$p$ to Ni 3$d$ charge-transfer energy is $\sim$ -1 eV and the ground state is dominated by the $d^9L$ configuration ($L$ is a S 3$p$ hole). Cell perturbation analysis for the NiS$_2$ triangular lattice indicates that the strong S 3$p$ hole character of the ground state provides the enhanced superexchange interaction between the third nearest neighbor sites.
Many methods exist for the construction of the Hilbert series describing the moduli spaces of instantons. We explore some of the underlying group theoretic relationships between these various constructions, including those based on the Coulomb branches and Higgs branches of SUSY quiver gauge theories, as well as those based on generating functions derivable from the Weyl Character Formula. We show how the character description of the reduced single instanton moduli space of any Classical or Exceptional group can be deconstructed faithfully in terms of characters or modified Hall-Littlewood polynomials of its regular semi-simple subgroups. We derive and utilise Highest Weight Generating functions, both for the characters of Classical or Exceptional groups and for the Hall-Littlewood polynomials of unitary groups. We illustrate how the root space data encoded in extended Dynkin diagrams corresponds to relationships between the Coulomb branches of quiver gauge theories for instanton moduli spaces and those for T(SU(N)) moduli spaces.