ShantanuT01/DACTYL-Pretraining huggingface dataset:
This work contributes to the study of the non-trivial roots of the Riemann zeta function. In view of the Hilbert-Polya conjecture a series of self-adjoint operators on a Hilbert space is constructed whose eigenvalues approximate these roots.
A tope committee K* for a simple oriented matroid M is a subset of its maximal covectors such that every positive halfspace of M contains more than half of the covectors from K*. The structures of the family of all committees for M, and of the family of its committees that contain no pairs of opposites, are described. A Farey subsequence associated with the elements of the m-th layer of the Boolean lattice of rank 2m is explored.
Given the peculiar and (in spite of many efforts) unexplained quasi-periodic oscillation (QPO) twin peak phenomena in accretion disc PSD observations, the present exploratory analytical article tries to inquire deeper into the relationship between discoseismic modes and the underlying driving turbulence in order to assess its importance. We employ a toy model in the form of a Gaussian white noise driven damped harmonic oscillator with stochastic frequency. This oscillator represents the discoseismic mode. (Stochastic damping was also considered, but interestingly found to be less relevant for the case at hand.) In the context of this model, we find that turbulence interacts with disc oscillations in interesting ways. In particular, the stochastic part in the oscillator frequency behaves as a separate driving agent. This gives rise to 3:2 twin peaks for some values of the physical parameters, which we find. We conclude with the suggestion that the study of turbulence be brought to the forefront of disc oscillation dynamics, as opposed to being a mere background feature. This change of perspective carries immediate observable consequences, such as considerably shifting the values of the (discoseismic) oscillator frequencies.
We synthesized single crystals of composition Ba$_2$CuSi$_2$O$_6$Cl$_2$ and investigated its quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi$_2$O$_6$ also known as Han purple. Ba$_2$CuSi$_2$O$_6$Cl$_2$ has a singlet ground state with an excitation gap of ${\Delta}/k_{\rm B}\,{=}\,20.8$ K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the $g$-factor except for a small jump anomaly for a magnetic field perpendicular to the $c$ axis. The magnetization curve with a nonlinear slope above the critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. The magnetic-field-induced spin ordering in Ba$_2$CuSi$_2$O$_6$Cl$_2$ is described as the quasi-2D Bose-Einstein condensation of triplets.
We present final Spitzer trigonometric parallaxes for 361 L, T, and Y dwarfs. We combine these with prior studies to build a list of 525 known L, T, and Y dwarfs within 20 pc of the Sun, 38 of which are presented here for the first time. Using published photometry and spectroscopy as well as our own follow-up, we present an array of color-magnitude and color-color diagrams to further characterize census members, and we provide polynomial fits to the bulk trends. Using these characterizations, we assign each object a $T_{\rm eff}$ value and judge sample completeness over bins of $T_{\rm eff}$ and spectral type. Except for types $\ge$ T8 and $T_{\rm eff} <$ 600K, our census is statistically complete to the 20-pc limit. We compare our measured space densities to simulated density distributions and find that the best fit is a power law ($dN/dM \propto M^{-\alpha}$) with $\alpha = 0.6{\pm}0.1$. We find that the evolutionary models of Saumon & Marley correctly predict the observed magnitude of the space density spike seen at 1200K $< T_{\rm eff} <$ 1350K, believed to be caused by an increase in the cooling timescale across the L/T transition. Defining the low-mass terminus using this sample requires a more statistically robust and complete sample of dwarfs $\ge$Y0.5 and with $T_{\rm eff} <$ 400K. We conclude that such frigid objects must exist in substantial numbers, despite the fact that few have so far been identified, and we discuss possible reasons why they have largely eluded detection.
We present a microscopic treatment of current-induced torques and thermal fluctuations in itinerant ferromagnets based on a functional formulation of the Keldysh formalism. We find that the nonequilibrium magnetization dynamics is governed by a stochastic Landau-Lifschitz-Gilbert equation with spin transfer torques. We calculate the Gilbert damping parameter $\alpha$ and the non-adiabatic spin transfer torque parameter $\beta$ for a model ferromagnet. We find that $\beta \neq \alpha$, in agreement with the results obtained using imaginary-time methods of Kohno, Tatara and Shibata [J. Phys. Soc. Japan 75, 113706 (2006)]. We comment on the relationship between $s-d$ and isotropic-Stoner toy models of ferromagnetism and more realistic density-functional-theory models, and on the implications of these relationships for predictions of the $\beta/\alpha$ ratio which plays a central role in domain wall motion. Only for a single-parabolic-band isotropic-Stoner model with an exchange splitting that is small compared to the Fermi energy does $\beta/\alpha$ approach one. In addition, our microscopic formalism incorporates naturally the fluctuations needed in a nonzero-temperature description of the magnetization. We find that to first order in the applied electric field, the usual form of thermal fluctuations via a phenomenological stochastic magnetic field holds.
It has been observed in [Park 2014] that the physical states of the ADM formulation of 4D Einstein gravity holographically reduce and can be described by a 3D language. Obviously the approach poses the 4D covariance issue; it turns out that there are two covariance issues whose address is the main theme of the present work. Although the unphysical character of the trace piece of the fluctuation metric has been long known, it has not been taken care of in a manner suitable for the Feynman diagram computations; a proper handling of the trace piece through gauge-fixing is the key to more subtler of the covariance issues. As for the second covariance issue, a renormalization program can be carried out covariantly to any loop order at intermediate steps, thereby maintaining the 4D covariance; it is only at the final stage that one should consider the 3D physical external states. With the physical external states, the 1PI effective action reduces to 3D and renormalizability is restored just as in the entirely-3D approach of [Park 2014]. We revisit the one-loop two-point renormalization with careful attention to the trace piece of the fluctuation metric and in particular outline one-loop renormalization of the Newton's constant.
Aims. Adaptive optics images are used to test the hypothesis that the explosive BN/KL outflow from the Orion OMC1 cloud core was powered by the dynamical decay of a non-hierarchical system of massive stars. Methods. Narrow-band H2, [Fe II], and broad-band Ks obtained with the Gemini South multi-conjugate adaptive optics (AO) system GeMS and near-infrared imager GSAOI are presented. The images reach resolutions of 0.08 to 0.10", close to the 0.07" diffraction limit of the 8-meter telescope at 2.12 microns. Comparison with previous AO-assisted observations of sub-fields and other ground-based observations enable measurements of proper motions and the investigation of morphological changes in H2 and [Fe II] features with unprecedented precision. The images are compared with numerical simulations of compact, high-density clumps moving ~1000 times their own diameter through a lower density medium at Mach 1000. Results. Several sub-arcsecond H2 features and many [Fe II] 'fingertips' on the projected outskirts of the flow show proper motions of ~300 km/s. High-velocity, sub-arcsecond H2 knots ('bullets') are seen as far as 140" from their suspected ejection site. If these knots propagated through the dense Orion A cloud, their survival sets a lower bound on their densities of order 10^7 cm^-3, consistent with an origin within a few au of a massive star and accelerated by a final multi-body dynamic encounter that ejected the BN object and radio source I from OMC1 about 500 years ago. Conclusions. Over 120 high-velocity bow-shocks propagating in nearly all directions from the OMC1 cloud core provide evidence for an explosive origin for the BN/KL outflow triggered by the dynamic decay of a non-hierarchical system of massive stars. Such events may be linked to the origin of runaway, massive stars.
This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.
We present the stellar and gas kinematics of DDO 46 and DDO 168 from the LITTLE THINGS survey and determine their respective Vmax/sigma_z,0 values. We used the KPNO's 4-meter telescope with the Echelle spectrograph as a long-slit spectrograph. We acquired spectra of DDO 168 along four position angles by placing the slit over the morphological major and minor axes and two intermediate position angles. However, due to poor weather conditions during our observing run for DDO 46, we were able to extract only one useful data point from the morphological major axis. We determined a central stellar velocity dispersion perpendicular to the disk, sigma_z,0, of 13.5+/-8 km/s for DDO 46 and <sigma_z,0> of 10.7+/-2.9 km/s for DDO 168. We then derived the maximum rotation speed in both galaxies using the LITTLE THINGS HI data. We separated bulk motions from non-circular motions using a double Gaussian decomposition technique and applied a tilted-ring model to the bulk velocity field. We corrected the observed HI rotation speeds for asymmetric drift and found a maximum velocity, Vmax, of 77.4 +/- 3.7 and 67.4 +/- 4.0 km/s for DDO 46 and DDO 168, respectively. Thus, we derived a kinematic measure, Vmax/sigma_z,0, of 5.7 +/- 0.6 for DDO 46 and 6.3 +/- 0.3 for DDO 168. Comparing these values to ones determined for spiral galaxies, we find that DDO 46 and DDO 168 have Vmax/sigma_z,0 values indicative of thin disks, which is in contrast to minor-to-major axis ratio studies.
A formalism for the appearance of dark energy in the matter dominated era, leading to a persistent de Sitter expansion at the late time is proposed. Our framework is a hybrid quintessence model with a non-minimal coupling to the Ricci scalar. Coupling to the curvature triggers the dark energy evolution, while the coupling of scalar fields drives this evolution to a de Sitter stable fixed point. These occur via successive $Z_2$ symmetry breakings.
We investigate the effect of primordial non-Gaussianity on the cross-correlation between the CMB anisotropies and the 21 cm fluctuations from the epoch of reionization. We assume an analytic reionization model and an ionization fraction with $f_{\rm NL}$ induced scale dependent bias. We estimate the angular power spectrum of the cross-correlation of the CMB and 21 cm. In order to evaluate the detectability, the signal-to-noise (S/N) ratio for only a single redshift slice is also calculated for current and future observations, such as CMB observations by Planck satellite and 21 cm observations by Omniscope. The existence of the $f_{\rm NL}$ increases the signal of the cross-correlation at large scales and the amplification does not depend on the reionization parameters in our reionization model. However the cosmic variance is significant on such scales and the S/N ratio is suppressed. The obtained S/N ratio is 2.8 (2.4) for $f_{\rm NL}=10$ (100) in our fiducial reionization model. Our work suggests in the absence of significant foregrounds and systematics, the auto-correlations of 21 cm is a better probe of $f_{\rm NL}$ than the cross-correlations (as expected since it depends on $b^2$), while the cross-correlations contain only one factor of $b$. Nevertheless, it is interesting to examine the cross-correlations between 21 cm and CMB, as the signal-to-noise ratio is not negligible and it is more likely we can rid ourselves of systematics and foregrounds that are common to both CMB and 21 cm experiments than completely clean 21 cm of all of the possible foregrounds and systematics in large scales.
Time-delay interferometry (TDI) is a post-processing technique used to reduce laser noise in heterodyne interferometric measurements with unequal armlengths, a situation characteristic of space gravitational detectors such as Laser Interferometer Space Antenna (LISA). This technique consists in properly time-shifting and linearly combining the interferometric measurements in order to reduce the laser noise by several orders of magnitude and to detect gravitational waves. In this communication, we show that the Doppler shift due to the time evolution of the armlengths leads to an unacceptably large residual noise when using interferometric measurements expressed in units of frequency and standard expressions of the TDI variables. We also present a technique to mitigate this effect by including a scaling of the interferometric measurements in addition to the usual time-shifting operation when constructing the TDI variables. We demonstrate analytically and using numerical simulations that this technique allows one to recover standard laser noise suppression which is necessary to measure gravitational waves.
The INTEGRAL and Swift hard X-ray surveys have identified a large number of new sources, among which many are proposed as Cataclysmic Variables (CVs). Here we present the first detailed study of three X-ray selected CVs, Swift J1907.3-2050, IGRJ12123-5802, and IGRJ19552+0044 based on XMM-Newton, Suzaku, Swift observations and ground based optical and archival nIR/IR data. Swift J1907.3-2050 is highly variable from hours to months-years at all wavelengths. No coherent X-ray pulses are detected but rather transient features. The X-ray spectrum reveals a multi-temperature optically thin plasma absorbed by complex neutral material and a soft black body component arising from a small area. These characteristics are remarkably similar to those observed in magnetic CVs. A supra-solar abundance of nitrogen could arise from nuclear processed material from the donor star. Swift J1907.3-2050 could be a peculiar magnetic CV with the second longest (20.82 h) binary period. IGRJ12123-5802 is variable in the X-rays on a timescale of ~7.6 h. No coherent pulsations are detected, but its spectral characteristics suggest that it could be a magnetic CV of the Intermediate Polar (IP) type. IGRJ19552+0044 shows two X-ray periods, 1.38 h and 1.69 h and a X-ray spectrum characterized by a multi-temperature plasma with little absorption.We derive a low accretion rate, consistent with a CV below the orbital period gap. Its peculiar nIR/IR spectrum suggests a contribution from cyclotron emission. It could either be a pre-polar or an IP with the lowest degree of asynchronism.
The dynamics of coalescing compact binaries can be affected by the environment in which the systems evolve, leaving detectable signatures into the emitted gravitational signal. In this paper we investigate the ability of gravitational-wave detectors to constrain the nature of the environment in which compact binaries merge. We parametrize a variety of environmental effects by modifying the phase of the gravitational signal emitted by black hole and neutron star binaries. We infer the bounds on such effects by current and future generation of interferometers, studying their dependence on the binary's parameters. We show that the strong dephasing induced by accretion and dynamical friction can constraint the density of the surrounding medium to orders of magnitude below that of accretion disks. Planned detectors, such as LISA or DECIGO, will be able to probe densities typical of those of dark matter.
Starting from a collection of line bundles on a projective toric orbifold X, we introduce a stacky analogue of the classical linear series. Our first main result extends work of King by building moduli stacks of refined representations of labelled quivers. We associate one such stack to any collection of line bundles on X to obtain our notion of a stacky linear series; as in the classical case, X maps to the ambient stack by evaluating sections of line bundles in the collection. As a further application, we describe a finite sequence of GIT wall crossings between [A^n/G] and G-Hilb(A^n) for a finite abelian subgroup G of SL(n,k) where n is less than or equal to 3.
We study the twisted q-zeta functions and twisted q-Bernoulli polynomials
Besides the conventional transverse couplings between superconducting qubits (SQs) and electromagnetic fields, there are additional longitudinal couplings when the inversion symmetry of the potential energies of the SQs is broken. We study nonclassical-state generation in a SQ which is driven by a classical field and coupled to a single-mode microwave field. We find that the classical field can induce transitions between two energy levels of the SQs, which either generate or annihilate, in a controllable way, different photon numbers of the cavity field. The effective Hamiltonians of these classical-field-assisted multiphoton processes of the single-mode cavity field are very similar to those for cold ions, confined to a coaxial RF-ion trap and driven by a classical field. We show that arbitrary superpositions of Fock states can be more efficiently generated using these controllable multiphoton transitions, in contrast to the single-photon resonant transition when there is only a SQ-field transverse coupling. The experimental feasibility for different SQs is also discussed.
A search for matched circle pairs of similar temperature fluctuations in the final WMAP 9yr data is carried out. Such a signature is expected if the space of the Universe is multiply connected. We investigate the relation between the pixel resolution of cosmic microwave background (CMB) maps and a Gaussian smoothing in order to lower the probability for missing matched circle pairs. CMB maps having the 3-torus topology are generated with the characteristics of the WMAP satellite in order to determine how large the smoothing should be chosen in CMB maps disturbed by detector noise. The V- and W-band data are analysed with respect to matched circle pairs and a tentatively signal is found for a circle pair, which lies, however, close to the plane of the Galaxy. It is, however, inconclusive whether this signal is generated by chance, is due to residual foregrounds contained in the V- and W-band maps, or is due to a genuine topology.
The unexpected high bump in the UV part of the spectrum found in nearby giant elliptical galaxies, a.k.a. the UV upturn, has been a subject of debate. A remarkable progress has been made lately from the observational side, mainly involving space telescopes. The GALEX UV telescope has been obtaining thousands of giant ellipticals in the nearby universe, while HST is resolving local galaxies into stars and star clusters. An important clue has also been found regarding the origin of hot HB stars, and perhaps of sdB stars. That is, extreme amounts of helium are suspected to be the origin of the extended HB and even to the UV upturn phenomenon. A flurry of studies are pursuing the physics behind it. All this makes me optimistic that the origin of the UV upturn will be revealed in the next few years. I review some of the most notable progress and remaining issues.
The surface area of electrodeposited thin films of Ni, Co, and NiCo was evaluated using electrochemical double-layer capacitance, electrochemical area measurements using the [Ru(NH$_3$)$_6$]$^{3+}$/[Ru(NH$_3$)$_6$]$^{2+}$ redox couple, and topographic atomic force microscopy (AFM) imaging. These three methods were compared to each other for each composition separately and for the entire set of samples regardless of composition. Double-layer capacitance measurements were found to be positively correlated to the roughness factors determined by AFM topography. Electrochemical area measurements were found to be less correlated with measured roughness factors as well as applicable only to two of the three compositions studied. The results indicate that in situ double-layer capacitance measurements are a practical, versatile technique for estimating the accessible surface area of a metal sample.
The aspects of phase transitions in the two-dimensional Ising models modified by quenched and annealed site disorder are discussed in the framework of fermionic approach based on the reformulation of the problem in terms of integrals with anticommuting Grassmann variables.
The reconstruction of dense 3D models of face geometry and appearance from a single image is highly challenging and ill-posed. To constrain the problem, many approaches rely on strong priors, such as parametric face models learned from limited 3D scan data. However, prior models restrict generalization of the true diversity in facial geometry, skin reflectance and illumination. To alleviate this problem, we present the first approach that jointly learns 1) a regressor for face shape, expression, reflectance and illumination on the basis of 2) a concurrently learned parametric face model. Our multi-level face model combines the advantage of 3D Morphable Models for regularization with the out-of-space generalization of a learned corrective space. We train end-to-end on in-the-wild images without dense annotations by fusing a convolutional encoder with a differentiable expert-designed renderer and a self-supervised training loss, both defined at multiple detail levels. Our approach compares favorably to the state-of-the-art in terms of reconstruction quality, better generalizes to real world faces, and runs at over 250 Hz.
In this paper we present steady-state RMHD simulations that include a mass-load term to study the process of jet deceleration. The mass-load mimics the injection of a proton-electron plasma from stellar winds within the host galaxy into initially pair plasma jets, with mean stellar mass-losses ranging from $10^{-14}$ to $10^{-9}\,{M_\odot\,yr^{-1}}$. The spatial jet evolution covers $\sim 500\,{\rm pc}$ from jet injection in the grid at 10~pc from the jet nozzle. Our simulations use a relativistic gas equation of state and a pressure profile for the ambient medium. We compare these simulations with previous dynamical simulations of relativistic, non-magnetised jets. Our results show that toroidal magnetic fields can prevent fast jet expansion and the subsequent embedding of further stars via magnetic tension. In this sense, magnetic fields avoid a runaway deceleration process. Furthermore, when the mass-load is large enough to increase the jet density and produce fast, differential jet expansion, the conversion of magnetic energy flux into kinetic energy flux (i.e., magnetic acceleration), helps to delay the deceleration process with respect to non-magnetised jets. We conclude that the typical stellar population in elliptical galaxies cannot explain jet deceleration in classical FRI radio galaxies. However, we observe a significant change in the jet composition, thermodynamical parameters and energy dissipation along its evolution, even for moderate values of the mass-load.