ShantanuT01/DACTYL-Pretraining huggingface dataset:
A linear analytical solution is derived for the gravitational shock wave produced by a particle of mass $M$ that decays into a pair of null particles. The resulting space-time is shown to be unperturbed and isotropic, except for a discontinuous perturbation on a spherical null shell. Formulae are derived for the perturbation as a function of polar angle, as measured by an observer at the origin observing clocks on a sphere at distance $R$. The effect of the shock is interpreted physically as an instantaneous displacement in time and velocity when the shock passes the clocks. The time displacement is shown to be anisotropic, dominated by a quadrupole harmonic aligned with the particle-decay axis, with a magnitude $\delta \tau\sim GM/c^3$, independent of $R$. The velocity displacement is isotropic. The solution is used to derive the gravitational effect of a quantum state with a superposition of a large number of randomly oriented, statistically isotropic particle decays. This approach is shown to provide a well-controlled approximation to estimate the magnitude of gravitational fluctuations in systems composed of null point particles up to the Planck energy in a causal diamond of duration $\tau= 2R/c$, as well as quantum-gravitational fluctuations of black holes and cosmological horizons. Coherent large-angle quantum distortions of macroscopic geometry from fluctuations up to the Planck scale are shown to grow linearly with the duration, with a variance $\langle \delta \tau^2\rangle\sim \tau t_P$ much larger than that produced in models without causal quantum coherence.
We analyze the large $N$ spectrum of chiral primary operators of three dimensional fixed points of the renormalization group. Using the space-time picture of the fixed points and the correspondence between anti-de Sitter compactifications and conformal field theories we are able to extract the dimensions of operators in short superconformal multiplets. We write down some of these operators in terms of short distance theories flowing to these non-trivial fixed points in the infrared.
In the range of temperatures reached in future heavy ion collision experiments, hadronic pair annihilations and creations of charm quarks may take place within the lifetime of the plasma. As a result, charm quarks may increase the bulk viscosity affecting the early stages of hydrodynamic expansion. Assuming thermalization, we estimate the charm contribution to bulk viscosity within the same effective kinetic theory framework in which the light parton contribution has been computed previously. The time scale at which this physics becomes relevant is related to the width of the transport peak associated with the trace anomaly correlator, and is found to be < 20 fm/c for T > 600 MeV.
We present direct evidence for the contribution of local orbital moments to the damping of magnetization precession in magnetic thin films. Using x-ray magnetic circular dichroism (XMCD) characterization of rare-earth (RE) M$_{4,5}$ edges in Ni$_{81}$Fe$_{19}$ doped with $<$ 2% Gd and Tb, we show that the enhancement of GHz precessional relaxation is accompanied by a significant orbital moment fraction on the RE site. Tb impurities, which enhance the Landau-Lifshitz(-Gilbert) LL(-G) damping $\lambda(\alpha)$, show a spin to orbital number ratio of 1.5$\pm$0.3; Gd impurities, which have no effect on damping, show a spin to orbital number ratio of zero within experimental error. The results indicate that the dopant-based control of magnetization damping in RE-doped ferromagnets is an atomistic effect, arising from spin-lattice coupling, and thus scalable to nanometer dimensions.
Many astrochemical models of observed CO isotopologue line emission, earlier considered a good proxy measure of H$_2$ and hence disk gas mass, favor large deviations in the carbon and oxygen gas phase abundances and argue that severe gas phase CO depletion makes it a poor mass tracer. Here, we show that C$^{18}$O line emission is an effective measure of the gas mass, and despite its complex chemistry, a possibly better tracer than HD. Our models are able to reproduce C$^{18}$O emission from recent ALMA surveys and the TW Hya disk to within a factor of $\sim 2-3$ using carbon and oxygen abundances characteristic of the interstellar medium (C/H$=1.4 \times 10^{-4}$; O/H$=3.2\times 10^{-4}$) without having to invoke unusual chemical processing. Our gas and dust disk structure calculations considering hydrostatic pressure equilibrium and our treatment of the CO conversion on grains are primarily responsible for the very different conclusions on disk masses and CO depletion. As did previous studies, we find that a gas phase C/O of $\sim 1-2$ can explain observed hydrocarbon emission from the TW Hya disk; but significantly, we find that CO isotopologue emission is only marginally affected by the C/O ratio. We therefore conclude that C$^{18}$O emission provides estimates of disk masses that are uncertain only to within a factor of a few, and describe a simplified modeling procedure to obtain gas disk masses from C$^{18}$O emission lines.
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Our modification does not require additional ancilla qubits. Then, we demonstrate how many operations can be parallelized, leading to a further linear decrease in the parallel depth of the circuit, at the cost of a small constant factor increase in number of qubits required. Thirdly, we modify the term order in the Trotter-Suzuki decomposition, significantly reducing the error at given Trotter-Suzuki timestep. A final improvement modifies the Hamiltonian to reduce errors introduced by the non-zero Trotter-Suzuki timestep. All of these techniques are validated using numerical simulation and detailed gate counts are given for realistic molecules.
We constrain properties of cluster haloes by performing likelihood analysis using lensing shear and flexion data. We test our analysis using two mock cluster haloes: an isothermal ellipsoid (SIE) model and a more realistic elliptical Navarro-Frenk-White (eNFW) model. For both haloes, we find that flexion is more sensitive to the halo ellipticity than shear. The introduction of flexion information significantly improves the constraints on halo ellipticity, orientation and mass. We also point out that there is a degeneracy between the mass and the ellipticity of SIE models in the lensing signal.
A nonlinear model of the scalar field with a coupling between the field and its gradient is developed. It is shown, that such model is suitable for the description of phase transition accompanied by formation of spatial inhomogeneous distribution of the order parameter. The proposed model is analogous the mechanical nonlinear oscillator with the coordinate-dependent mass or velocity-dependent elastic module. Besides, for some value of energy the model under consideration possesses exact analytical solution. We assume that this model can related to the spinodal decomposition, quark confinement, or cosmological scenario. All predictions can be verified experimentally.
The magnetic field of the Sun is the underlying cause of the many diverse phenomena combined under the heading of solar activity. Here we describe the magnetic field as it threads its way from the bottom of the convection zone, where it is built up by the solar dynamo, to the solar surface, where it manifests itself in the form of sunspots and faculae, and beyond into the outer solar atmosphere and, finally, into the heliosphere. On the way it, transports energy from the surface and the subsurface layers into the solar corona, where it heats the gas and accelerates the solar wind.
We report the results of a new analysis of 13 wide band BeppoSAX observations of the BL Lac object Mkn 421. The data from LECS, MECS and PDS, covering an energy interval from 0.1 to over 100 keV, have been used to study the spectral variability of this source. We show that the energy distributions in different luminosity states can be fitted very well by a log-parabolic law F(E)=K*(E/E_1)^(-(a+b*Log(E/E_1))), which provides good estimates of the energy and flux of the synchrotron peak in the SED. In the first four short observations of 1997 Mkn 421 was characterized by a very stable spectral shape, with average values a=2.25 and b=0.45. In the observations of 1998 smaller values for both parameters, a~2.07 and b~0.34, were found and the peak energy in the SED was in the range 0.5-0.8 keV. Also in the observations of May 1999 and April-May 2000 the log-parabolic model gave a satisfactory description of the overall SED of Mkn 421. In particular, in the observations of spring 2000 the source was brighter than the other observations and showed a large change of the spectral curvature. Spectral parameters estimates gave a~1.8 and b~0.19 and the energy of the maximum in the SED moved to the range 1-5.5 keV. We give a possible interpretation of the log-parabolic spectral model in terms of particle acceleration mechanisms. An energy distribution of emitting particles with curvature close to the one observed can be explained by a simple model for statistical acceleration with the assumption that the probability for a particle to increase its energy is a decreasing function of the energy itself. A consequence of this mechanism is the existence of a linear relation between the spectral parameters a and b, well confirmed by the estimated values of these two parameters for Mkn421.(Abridged)
We propose an attention-based networks for transferring motions between arbitrary objects. Given a source image(s) and a driving video, our networks animate the subject in the source images according to the motion in the driving video. In our attention mechanism, dense similarities between the learned keypoints in the source and the driving images are computed in order to retrieve the appearance information from the source images. Taking a different approach from the well-studied warping based models, our attention-based model has several advantages. By reassembling non-locally searched pieces from the source contents, our approach can produce more realistic outputs. Furthermore, our system can make use of multiple observations of the source appearance (e.g. front and sides of faces) to make the results more accurate. To reduce the training-testing discrepancy of the self-supervised learning, a novel cross-identity training scheme is additionally introduced. With the training scheme, our networks is trained to transfer motions between different subjects, as in the real testing scenario. Experimental results validate that our method produces visually pleasing results in various object domains, showing better performances compared to previous works.
Fermion production by the electric field of a charge on de Sitter expanding universe is analyzed. The amplitude and probability of pair production are computed. We obtain from our calculations that the modulus of the momentum is no longer conserved and that there are probabilities for production processes where the helicity is no longer conserved. The rate of pair production in an electric field is found to be important in the early universe when the expansion factor was large comparatively with the particle mass.
We exploit our formula for the gravitational potential of finite size, power-law disks to derive a general expression linking the mass of the black hole in active galactic nuclei (AGN), the mass of the surrounding disk, its surface density profile (through the power index s), and the differential rotation law. We find that the global rotation curve v(R) of the disk in centrifugal balance does not obey a power law of the cylindrical radius R (except in the confusing case s = -2 that mimics a Keplerian motion), and discuss the local velocity index. This formula can help to understand how, from position-velocity diagrams, mass is shared between the disk and the black hole. To this purpose, we have checked the idea by generating a sample of synthetic data with different levels of Gaussian noise, added in radius. It turns out that, when observations are spread over a large radial domain and exhibit low dispersion (standard deviation less than 10% typically), the disk properties (mass and s-parameter) and black hole mass can be deduced from a non linear fit of kinematic data plotted on a (R, Rv 2)-diagram. For a deviation higher than 10%, masses are estimated fairly well from a linear regression (corresponding to the zeroth-order treatment of the formula), but the power index s is no longer accessible. We have applied the model to 7 AGN disks whose rotation has already been probed through water maser emission. For NGC3393 and UGC3789, the masses seem well constrained through the linear approach. For IC1481, the power-law exponent s can even be deduced. Because the model is scale-free, it applies to any kind of star/disk system. Extension to disks around young stars showing deviation from Keplerian motion is thus straightforward.
Frankl's union-closed sets conjecture states that in every finite union-closed set of sets, there is an element that is contained in at least half of the member-sets (provided there are at least two members). The conjecture has an equivalent formulation in terms of graphs: In every bipartite graph with least one edge, both colour classes contain a vertex belonging to at most half of the maximal stable sets.   We prove that, for every fixed edge-probability, almost every random bipartite graph almost satisfies Frankl's conjecture.
We present dynamical distance estimates for 15 Galactic globular clusters and use these to check the consistency of dynamical and photometric distance estimates. For most of the clusters, this is the first dynamical distance estimate ever determined. We extract proper-motion dispersion profiles using cleaned samples of bright stars from the Hubble Space Telescope proper-motion catalogs recently presented in Bellini et al. (2014) and compile a set of line-of-sight velocity-dispersion profiles from a variety of literature sources. Distances are then estimated by fitting spherical, non-rotating, isotropic, constant mass-to-light (M/L) dynamical models to the proper-motion and line-of-sight dispersion profiles together. We compare our dynamical distance estimates with literature photometric estimates from the Harris (1996, 2010 edition) globular cluster catalog and find that the mean fractional difference between the two types is consistent with zero at just $-1.9 \pm 1.7 \%$. This indicates that there are no significant biases in either estimation method and provides an important validation of the stellar-evolution theory that underlies photometric distance estimates. The analysis also estimates dynamical M/L ratios for our clusters; on average, the dynamically-inferred M/L ratios agree with existing stellar-population-based M/L ratios that assume a Chabrier initial mass function (IMF) to within $-8.8 \pm 6.4 \%$, implying that such an IMF is consistent with our data. Our results are also consistent with a Kroupa IMF, but strongly rule out a Salpeter IMF. We detect no correlation between our M/L offsets from literature values and our distance offsets from literature values, strongly indicating that our methods are reliable and our results are robust.
An action principle that applies uniformly to any number N of supercharges is proposed. We perform the reduction to the N=0 partition function by integrating out superpartner fields. As a new feature for theories of extended supersymmetry, the canonical Pfaffian measure factor is a result of a Gaussian integration over a superpartner. This is mediated through an explicit choice of direction n^a in the \theta-space, which the physical sector does not depend on. Also, we re-interpret the metric g^{ab} in the Susy algebra [D^a,D^b] = g^{ab}\partial_t as a symplectic structure on the fermionic \theta-space. This leads to a superfield formulation with a general covariant \theta-space sector.
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of probabilities and then use it to describe quantum dynamics? What is the origin of the probability distribution for a maximally specified quantum state?   Is quantum mechanics `local' or is there an essential nonlocality (nonseparability) inherent in quantum mechanics? These questions are discussed in this paper. The decay of an unstable quantum state and the time dependence of a minimum uncertainty states for future times as well as past times are also discussed.
We investigated interlayer phonon modes of mechanically exfoliated few-layer 2H-SnS2 samples by using room temperature low-frequency micro-Raman spectroscopy. Raman measurements were performed using laser wavelength of 441.6, 514.4, 532 and 632.8 nm with power below 100 uW and inside a vacuum chamber to avoid photo-oxidation. The intralayer Eg and A1g modes are observed at ~206 cm-1 and ~314 cm-1, respectively, but the Eg mode is much weaker for all excitation energies. The A1g mode exhibits strong resonant enhancement for the 532 nm (2.33 eV) laser. In the low-frequency region, interlayer vibrational modes of shear and breathing modes are observed. These modes show characteristic dependence on the number of layers. The strengths of the interlayer interactions are estimated by fitting the interlayer mode frequencies using the linear chain model and are found to be 1.64 x10^19 N.m-3 and 5.03 x10^19 N.m-3 for the shear and breathing modes, respectively.
We find a specific mechanism of background spin currents in two-dimensional electron systems with spatially nonuniform spin-orbit interaction (SOI) at thermodynamic equilibrium, in particular, in the systems consisting of regions with and without SOI. The spin density flows tangentially to the boundary in the normal and SOI regions within a layer of the width determined by the SOI strength. The density of these edge currents significantly exceeds the bulk spin current density. The spin current is polarized normally to the boundary. The spatial distribution of equilibrium spin currents is investigated in detail in the case of a step-like variation of the SOI strength and potential at the interface.
Utilizing low-luminosity star-forming systems discovered in the H$\alpha$ Dots survey, we present spectroscopic observations undertaken using the KPNO 4m telescope for twenty-six sources. With determinations of robust, "direct"-method metal abundances, we examine the properties of these dwarf systems, exploring their utility in characterizing starburst galaxies at low luminosities and stellar masses. We find that the H$\alpha$ Dots survey provides an effective new avenue for identifying star-forming galaxies in these regimes. In addition, we examine abundance characteristics and metallicity scaling relations with these sources, highlighting a flattening of both the luminosity-metallicity ($L$-$Z$) and stellar mass-metallicity ($M_{*}$-$Z$) relation slopes in these regimes as compared with those utilizing samples covering wider respective dynamic ranges. These local, accessible analogues to the kinds of star-forming dwarfs common at high redshift will help shed light on the building blocks which assembled into the massive galaxies common today.
We report the observation of a steepening in the cosmic ray energy spectrum of heavy primary particles at about $8 \times 10^{16}$ eV. This structure is also seen in the all-particle energy spectrum, but is less significant. Whereas the `knee' of the cosmic ray spectrum at $3-5 \times 10^{15}$ eV was assigned to light primary masses by the KASCADE experiment, the new structure found by the KASCADE-Grande experiment is caused by heavy primaries. The result is obtained by independent measurements of the charged particle and muon components of the secondary particles of extensive air showers in the primary energy range of $10^{16}$ to $10^{18}$ eV. The data are analyzed on a single-event basis taking into account also the correlation of the two observables.
Let $g$ be a dimension function. The Generalised Baker-Schmidt Problem (1970) concerns the $g$-dimensional Hausdorff measure ($\HH^g$-measure) of the set of $\Psi$-approximable points on nondegenerate manifolds. The problem relates the `size' of the set of $\Psi$-approximable points with the convergence or divergence of a certain series. In the dual approximation setting, the divergence case has been established by Beresnevich-Dickinson-Velani (2006) for any nondegenerate manifold. The convergence case, however, represents a major challenging open problem and progress thus far has been effectuated in limited cases only. In this paper, we discuss and prove several results on the $\HH^g$-measure on Veronese curves in any dimension $n$. As a consequence of one of our results, we generalize recent results of Pezzoni [Acta Arith. 193 (2020), no. 3, 269-281] regarding $n=3$. This improvement evolves from a deeper investigation on general irreducibility considerations applicable in arbitrary dimensions. We further investigate the $\HH^g$-measure for convergence on planar curves. We show that the monotonicity assumption on a multivariable approximating function cannot be removed for planar curves.
In this paper we construct a degeneration of Bott-Samelson-Demazure-Hansen varieties to toric varieties in an algebraic family and study the geometry of the resulting toric varieties. We give a natural set of torus invariant curves that generate the Chow group of $1$-cycles of the limiting toric variety and express the ample cone of this toric variety as a sub-cone of the ample cone of the corresponding Bott-Samelson-Demazure-Hansen variety. We also give a description of Extremal and Mori rays and determine when this toric variety is Fano.
The quantization of the family of linearly polarized Gowdy $T^3$ spacetimes is discussed in detail, starting with a canonical analysis in which the true degrees of freedom are described by a scalar field that satisfies a Klein-Gordon type equation in a fiducial time dependent background. A time dependent canonical transformation, which amounts to a change of the basic (scalar) field of the model, brings the system to a description in terms of a Klein-Gordon equation on a background that is now static, although subject to a time dependent potential. The system is quantized by means of a natural choice of annihilation and creation operators. The quantum time evolution is considered and shown to be unitary, allowing both the Schr\"odinger and Heisenberg pictures to be consistently constructed. This has to be contrasted with previous treatments for which time evolution failed to be implementable as a unitary transformation. Possible implications for both canonical quantum gravity and quantum field theory in curved spacetime are commented.
In this paper, we investigate the expanding patterns and spreading speed of solutions of farmer and hunter-gatherer model which is a three-component degenerate reaction-diffusion system. Ecologically speaking, since the lifestyle of agriculture and settlement allows for a larger population, after an initially localized population of farmers migrated into a region occupied by hunter-gatherers, the Neolithic transition from hunter-gatherers to farmers happened. This model was proposed by J. Elias, K. Humayun and M. Mimura in 2018. By numerical simulations, a travelling wave solution with a certain speed, depending on the parameter values, is observed. Despite such observation and studying on the well-posedness of the system, no mathematically rigorous studies on the spreading properties have been made. The main difficulty comes from the fact that the comparison principle does not hold for the whole system. In this paper, we give theoretical proof of the existence of two different expanding patterns. Furthermore, we show a lower estimate for the spreading speed.