ShantanuT01/DACTYL-Pretraining huggingface dataset:
The metric outside a compact body deformed by a quadrupolar tidal field is universal up to its Love numbers, constants which encode the tidal response's dependence on the body's internal structure. For a non-rotating body, the deformed external geometry is characterized by the familiar gravitational Love numbers $K_2^{\text{el}}$ and $K_2^{\text{mag}}$. For a slowly rotating body, these must be supplemented by rotational-tidal Love numbers, which measure the response to couplings between the body's spin and the external tidal field. By integrating the interior field equations, I find that the response of a barotropic perfect fluid to spin-coupled tidal perturbations is described by two rotational-tidal Love numbers, which I calculate explicitly for polytropes. Two other rotational-tidal Love numbers identified in prior work are found to have a fixed, universal value for all barotropes. Equipped with the complete interior solution, I calculate the amplitude of the time-varying internal currents induced by the gravitomagnetic part of the tidal field. For a typical neutron star in an equal-mass binary system, the size of the equatorial velocity perturbation is on the order of kilometers per second.
We analyse a version of the policy iteration algorithm for the discounted infinite-horizon problem for controlled multidimensional diffusion processes, where both the drift and the diffusion coefficient can be controlled. We prove that, under assumptions on the problem data, the payoffs generated by the algorithm converge monotonically to the value function and an accumulation point of the sequence of policies is an optimal policy. The algorithm is stated and analysed in continuous time and state, with discretisation featuring neither in theorems nor the proofs. A key technical tool used to show that the algorithm is well-defined is the mirror coupling of Lindvall and Rogers.
We present optical and near-infrared integral field spectroscopy of the SCUBA galaxy SMM J163650.43+405734.5 (ELAIS N2 850.4) at z=2.385. We combine Ly-alpha and H-alpha emission line maps and velocity structure with high resolution HST ACS and NICMOS imaging to probe the complex dynamics of this vigorous star-burst galaxy. The imaging data shows a complex morphology, consisting of at least three components separated by ~1'' (8kpc) in projection. When combined with the H-alpha velocity field from UKIRT UIST IFU observations we identify two components whose redshifts are coincident with the systemic redshift, measured from previous CO observations, one of which shows signs of AGN activity. A third component is offset by 220+/-50km/s from the systemic velocity. The total star formation rate of the whole system (estimated from the narrow-line H-alpha and uncorrected for reddening) is 340+/-50Mo/yr. The Ly-alpha emission mapped by the GMOS IFU covers the complete galaxy and is offset by +270+/-40km/s from the systemic velocity. This velocity offset is comparable to that seen in rest-frame UV-selected galaxies at similar redshifts and usually interpreted as a star-burst driven wind. The extended structure of the Ly-alpha emission suggests that this wind is not a nuclear phenomenon, but is instead a galactic scale outflow. Our observations suggest that the vigorous activity in N2 850.4 is arising as a result of an interaction between at least two dynamically-distinct components, resulting in a strong starburst, a starburst-driven wind and actively-fuelled AGN activity. [abridged]
In this work, we extend double tensor integrals (DTI) from our previous work to parametrization double tensors integrals (PDTI) by applying integral kernel transform bounds to upper bound PDTI norm and establishing a new perturbation formula. Besides, the convergence property of random PDTI is investigated and this property is utilized to characterize the relation between the original derivative tensor and the action result of PDTI to the original derivative tensor. These tools help us to derive new tail bounds for random tensors according to more general operator inequalities, e.g., Heinz inequality and Birman-Koplienko-Solomyak inequality. Moreover, new tail bounds about random tensors are also obtained according to our new derived perturbation formula and integral kernel transform bounds.
We provide an explicit infinite family of integers $m$ such that all the polynomials of ${\mathbb F}_{2^n}[x]$ of degree $m$ have maximal differential uniformity for $n$ large enough. We also prove a conjecture of the third author in these cases.
Antiferromagnetic fluctuations in two dimensions cause a decrease in spectral weight at so-called hot spots associated with the pseudogap in electron-doped cuprates. In the 2D Hubbard model, these hot spots occur when the Vilk criterion is satisfied, namely when the spin correlation length exceeds the thermal de Broglie wavelength. Using the two-particle self-consistent approach, here we show that this criterion may be violated near the antiferromagnetic quantum critical point when sufficient disorder is added to the model. Static disorder decreases inelastic scattering, in contradiction with Matthiessen's rule, leading to a shift in the position of the quantum critical point and a modification of the conditions for the appearance of hot spots. This opens the road to a study of the interplay between disorder, antiferromagnetic fluctuations and superconductivity in electron-doped cuprates.
Photonic SUSY two-loop corrections to the muon magnetic moment are contributions from diagrams where an additional photon loop is attached to a SUSY one-loop diagram. These photonic corrections are evaluated exactly, extending a leading-log calculation by Degrassi and Giudice. Compact analytical expressions are provided and the numerical behaviour is discussed. The photonic corrections reduce the SUSY one-loop result by 7...9%. The new terms are typically around ten times smaller than the leading logarithms, but they can be larger and have either sign in cases with large SUSY mass splittings. We also provide details on renormalization and regularization and on how to incorporate the photonic corrections into a full SUSY two-loop calculation.
This article concerns the geometry of torsors under an elliptic curve. Let $\OO_K$ be a complete discrete valuation ring with algebraically closed residue field and function field $K$. Let $\pi$ be a generator of the maximal ideal of $\OO_K$, and $S=\mathrm{Spec}(\OO_K)$. Suppose that we are given $J_K$ an elliptic curve over $K$, with $J$ the connected component of the $S$-N?ron model of $J_K$. Given $X_K/K$ a torsor of order $d$ under $J_K$, let $X$ be the $S$-minimal regular proper model. Then there is an invertible id?al $\mathcal{I}\subset \OO_K$ such that $\mathcal{I}^{d}=\pi\OO_X\subset \OO_X$. Moreover, there exists a canonical morphism $q:\Pic^{\circ}_{X/S}\rightarrow J$ which induces a surjective map $q(S):\Pic^{\circ}(X)\rightarrow J(S)$. The purpose of the article is to prove this last morphism $q(S)$ is compatible with respect to the $\mathcal{I}$-adic filtration on $\Pic^{\circ}(X)$, and the $\pi$-adic filtration on $J(S)$. As a byproduct, we obtain {\textquotedblleft Herbrand functions\textquotedblright}, similar to those Serre used in his description of local class fields (\cite{Serre})
We study the acceleration, transport, and emission of particles in relativistic jets. Localized stochastic particle acceleration, spatial diffusion, and synchrotron as well as synchrotron self-Compton emission are considered in a leptonic model. To account for inhomogeneity, we use a 2D axi-symmetric cylindrical geometry for both relativistic electrons and magnetic field. In this first phase of our work, we focus on steady-state spectra that develop from a time-dependent model. We demonstrate that small isolated acceleration region in a much larger emission volume are sufficient to accelerate particles to high energy. Diffusive escape from these small regions provides a natural explanation for the spectral form of the jet emission. The location of the acceleration regions within the jet is found to affect the cooling break of the spectrum in this diffusive model. Diffusion-caused energy-dependent inhomogeneity in the jets predicts that the SSC spectrum is harder than the synchrotron spectrum. There can also be a spectral hardening towards the high-energy section of the synchrotron spectrum, if particle escape is relatively slow. These two spectral hardening effects indicate that the jet inhomogeneity might be a natural explanation for the unexpected hard {\gamma}-ray spectra observed in some blazars.
We estimate the gravitational radiation signature of the electron/positron annihilation-driven neutrino burst accompanying the asymmetric collapse of an initially hydrostatic, radiation-dominated supermassive object suffering the Feynman-Chandrasekhar instability. An object with a mass $5\times10^4\,M_\odot<M<5\times10^5\,M_\odot$, with primordial metallicity, is an optimal case with respect to the fraction of its rest mass emitted in neutrinos as it collapses to a black hole: lower initial mass objects will be subject to scattering-induced neutrino trapping and consequently lower efficiency in this mode of gravitational radiation generation; while higher masses will not get hot enough to radiate significant neutrino energy before producing a black hole. The optimal case collapse will radiate several percent of the star's rest mass in neutrinos and, with an assumed small asymmetry in temperature at peak neutrino production, produces a characteristic linear memory gravitational wave burst signature. The timescale for this signature, depending on redshift, is $\sim1{\rm~s}$ to $10{\rm~s}$, optimal for proposed gravitational wave observatories like DECIGO. Using the response of that detector, and requiring a signal-to-noise ratio SNR $>$ 5, we estimate that collapse of a $\sim 5\times10^4\,M_\odot$ supermassive star could produce a neutrino burst-generated gravitational radiation signature detectable to redshift $z\lesssim7$. With the envisioned ultimate DECIGO design sensitivity, we estimate that the linear memory signal from these events could be detectable with SNR $> 5$ to $z \lesssim13$.
Light curves in the B, V, and I_c passbands have been obtained for the type II Cepheids V154 in M3 and V42 and V84 in M5. Alternating cycle behavior, similar to that seen among RV Tauri variables, is confirmed for V84. Old and new observations, spanning more than a century, show that V154 has increased in period while V42 has decreased in period. V84, on the other hand, has shown large, erratic changes in period that do not appear to reflect the long term evolution of V84 through the HR diagram.
The synchrotron hump of the high energy peaked blazars generally lies in the 0.1-10 keV range and such sources show extreme flux and spectral variability in X-ray bands. Various spectral studies showed that the X-ray spectra of high energy peaked blazars are curved and better described by the log-parabolic model. The curvature is attributed to the energy dependent statistical acceleration mechanism. In this work, we review the X-ray spectral studies of high energy peaked blazars. It is found that the log-parabolic model well describes the spectra in a wide energy interval around the peak. The log-parabolic model provides the possibility of investigating the correlation between the spectral parameters derived from it. Therefore, we compiled the studies of correlations between the various parameters derived from the log-parabolic model and their implications to describe the variability mechanism of blazars.
We study scale dependence of the cosmic microwave background (CMB) power spectrum in a class of small, single-field models of inflation which lead to a high value of the tensor to scalar ratio. The inflaton potentials that we consider are degree 5 polynomials, for which we precisely calculate the power spectrum, and extract the cosmological parameters: the scalar index $n_s$, the running of the scalar index $n_{\mathrm{run}}$ and the tensor to scalar ratio $r$. We find that for non-vanishing $n_{\mathrm{run}}$ and for $r$ as small as $r=0.001$, the precisely calculated values of $n_s$ and $n_{\mathrm{run}}$ deviate significantly from what the standard analytic treatment predicts. We study in detail, and discuss the probable reasons for such deviations. As such, all previously considered models (of this kind) are based upon inaccurate assumptions. We scan the possible values of potential parameters for which the cosmological parameters are within the allowed range by observations. The 5 parameter class is able to reproduce all of the allowed values of $n_s$ and $n_{\mathrm{run}}$ for values of $r$ that are as high as 0.001. Subsequently this study at once refutes previous such models built using the analytical Stewart-Lyth term, and revives the small field brand, by building models that do yield an appreciable $r$ while conforming to known CMB observables.
Given a video of a person in action, we can easily guess the 3D future motion of the person. In this work, we present perhaps the first approach for predicting a future 3D mesh model sequence of a person from past video input. We do this for periodic motions such as walking and also actions like bowling and squatting seen in sports or workout videos. While there has been a surge of future prediction problems in computer vision, most approaches predict 3D future from 3D past or 2D future from 2D past inputs. In this work, we focus on the problem of predicting 3D future motion from past image sequences, which has a plethora of practical applications in autonomous systems that must operate safely around people from visual inputs. Inspired by the success of autoregressive models in language modeling tasks, we learn an intermediate latent space on which we predict the future. This effectively facilitates autoregressive predictions when the input differs from the output domain. Our approach can be trained on video sequences obtained in-the-wild without 3D ground truth labels. The project website with videos can be found at https://jasonyzhang.com/phd.
In this paper we prove that the SNIEP $\neq$ DNIEP, i.e. the symmetric and diagonalizable nonnegative inverse eigenvalue problems are different. We also show that the minimum $t>0$ for which $(3+t,3-t,-2,-2,-2)$ is realizable by a diagonalizable matrix is $t=1$, and we distinguish diagonalizably realziable lists from general realizable lists using the Jordan Normal Form
Electronic states and the Aharonov-Bohm effect in ZnO quantum dot-ring nanostructures containing few interacting electrons reveal several unique features. We have shown here that in contrast to the dot-rings made of conventional semiconductors, such as InAs or GaAs, the dot-rings in ZnO heterojunctions demonstrate several unique characteristics due to the unusual properties of quantum dots and rings in ZnO. In particular the energy spectra of the ZnO dot-ring and the Aharnov-Bohm oscillations are strongly dependant on the electron number in the dot or in the ring. Therefore even small changes of the confinement potential, sizes of the dot-ring or the magnetic field can drastically change the energy spectra and the behavior of Aharonov-Bohm oscillations in the system. Due to this interesting phenomena it is possible to effectively control with high accuracy the electron charge and spin distribution inside the dot-ring structure. This controlling can be achieved either by changing the magnetic field or the confinement potentials.
Standard methods for higher-order calculations of QCD cross sections in hadron-induced collisions are time-consuming. The fastNLO project uses multi-dimensional interpolation techniques to convert the convolutions of perturbative coefficients with parton distribution functions and the strong coupling into simple products. By integrating the perturbative coefficients for a given observable with interpolation kernels, fastNLO can store the results of the time-consuming folding integrals in tables, which subsequently are used for very fast rederivations of the same observable for arbitrary parton distribution functions, different scale choices, or alpha_s(M_Z). Various tables with code for their evaluation are available for numerous jet measurements at the LHC, the TeVatron, and HERA. FastNLO is used in publications of experimental results by the ATLAS, CMS, CDF, D0, and H1 collaborations, and in all recent global PDF analyses by MSTW, CTEQ, and NNPDF. This article focuses on developments implemented in the new version 2 of fastNLO, enhancing and broadening its functionality.
We find evidence that superconductivity intrudes into the paramagnetic-to-magnetic transition of the Kondo lattice model if magnetic frustration is added. Specifically, we study by variational method the model on a square lattice in the presence of both nearest- ($t$) and next-nearest-neighbor ($t^\prime$) hopping of the conduction electrons. We find that when $t^\prime/t$ is finite a $d$-wave superconducting dome emerges between the magnetic and paramagnetic metal phases and close to the compensated regime, i.e., the number of conduction electrons equal to the number of localized spin-1/2 moments. Superconductivity is further strengthened by a direct antiferromagnetic exchange between the localized moments, to such an extent that we even observe coexistence with magnetic order.
The Interstellar Boundary Explorer (IBEX) spacecraft is providing the first all-sky maps of the energetic neutral atoms (ENAs) produced by charge-exchange between interstellar neutral \HI\ atoms and heliospheric solar wind and pickup ions in the heliosphere boundary regions. The 'edge' of the interstellar cloud presently surrounding the heliosphere extends less than 0.1 pc in the upwind direction, terminating at an unknown distance, indicating that the outer boundary conditions of the heliosphere could change during the lifetime of the IBEX satellite. Using reasonable values for future outer heliosphere boundary conditions, ENA fluxes are predicted for one possible source of ENAs coming from outside of the heliopause. The ENA production simulations use three-dimensional MHD plasma models of the heliosphere that include a kinetic description of neutrals and a Lorentzian distribution for ions. Based on this ENA production model, it is then shown that the sensitivities of the IBEX 1.1 keV skymaps are sufficient to detect the variations in ENA fluxes that are expected to accompany the solar transition into the next upwind cloud. Approximately 20% of the IBEX 1.1 keV pixels appear capable of detecting the predicted model differences at the $ 3 \sigma$ level, with these pixels concentrated in the Ribbon region. Regardless of the detailed ENA production model, the success of the modeled \BdotR\ directions in reproducing the Ribbon locus, together with our results, indicate that the Ribbon phenomenon traces the variations in the heliosphere distortion caused by the relative pressures of the interstellar magnetic and gaseous components.
In a recent article [Phys. Rev. A 86, 024302 (2012)], the authors have derived some hierarchy relations between geometric discord and entanglement (measured by negativity and its square). We point out that these results are incorrect and give analytic counterexamples. We also discuss briefly the reason for such violations.
We report on an observation of the neutron star low-mass X-ray binary Serpens X-1, made with NuSTAR. The extraordinary sensitivity afforded by NuSTAR facilitated the detection of a clear, robust, relativistic Fe K emission line from the inner disk. A relativistic profile is required over a single Gaussian line from any charge state of Fe at the 5-sigma level of confidence, and any two Gaussians of equal width at the same confidence. The Compton back-scattering "hump" peaking in the 10-20 keV band is detected for the first time in a neutron star X-ray binary. Fits with relativistically-blurred disk reflection models suggest that the disk likely extends close to the innermost stable circular orbit (ISCO) or stellar surface. The best-fit blurred reflection models constrain the gravitational redshift from the stellar surface to be z > 0.16. The data are broadly compatible with the disk extending to the ISCO; in that case, z > 0.22 and R < 12.6 km (assuming M = 1.4 Msun and a=0, where a = cJ/GM^2). If the star is as large or larger than its ISCO, or if the effective reflecting disk leaks across the ISCO to the surface, the redshift constraints become measurements. We discuss our results in the context of efforts to measure fundamental properties of neutron stars, and models for accretion onto compact objects.
We test the modified Newtonian dynamics (MOND) theory with the velocity-dispersion profiles of Galactic globular clusters populating the outermost region of the Milky Way halo, where the Galactic acceleration is lower than the characteristic MOND acceleration a_0. For this purpose, we constructed self-consistent, spherical models of stellar systems in MOND, which are the analogues of the Newtonian King models. The models are spatially limited, reproduce well the surface-brightness profiles of globular clusters, and have velocity-dispersion profiles that differ remarkably in shape from the corresponding Newtonian models. We present dynamical models of six globular clusters, which can be used to efficiently test MOND with the available observing facilities. A comparison with recent spectroscopic data obtained for NGC2419 suggests that the kinematics of this cluster might be hard to explain in MOND.
In this paper we consider plane quartics with to involutions. We compute the Dixmier invariants, the bitangents and the Matrix representation problem of these curves, showing that they have symbolic solutions for the last two questions.
We investigate the physical properties of the Shastry-Sutherland lattice material BaNd$_2$ZnO$_5$. Neutron diffraction, magnetic susceptibility, and specific heat measurements reveal antiferromagnetic order below 1.65 K. The magnetic order is found to be a 2-$\boldsymbol{Q}$ magnetic structure with the magnetic moments lying in the Shastry-Sutherland lattice planes comprising the tetragonal crystal structure of BaNd$_2$ZnO$_5$. The ordered moment for this structure is 1.9(1) $\mu_B$ per Nd ion. Inelastic neutron scattering measurements reveal that the crystal field ground state doublet is well separated from the first excited state at 8 meV. The crystal field Hamiltonian is determined through simultaneous refinement of models with both the LS coupling and intermediate coupling approximations to the inelastic neutron scattering and magnetic susceptibility data. The ground state doublet indicates that the magnetic moments lie primarily in the basal plane with magnitude consistent with the size of the determined ordered moment.