ShantanuT01/DACTYL-Pretraining huggingface dataset:
The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general equation of motion and solve it in closed form for the case of parabolic motion. Especially the motion near the horizon and near the singularity are examined.
In this paper, we consider a simplified Ericksen-Leslie model for the nematic liquid crystal flow. The evolution system consists of the Navier-Stokes equations coupled with a convective Ginzburg-Landau type equation for the averaged molecular orientation. We suppose that the Navier-Stokes equations are characterized by a no-slip boundary condition and a time-dependent external force g(t), while the equation for the molecular director is subject to a time-dependent Dirichlet boundary condition h(t). We show that, in 2D, each global weak solution converges to a single stationary state when h(t) and g(t) converge to a time-independent boundary datum h_\infty and 0, respectively. Estimates on the convergence rate are also obtained. In the 3D case, we prove that global weak solutions are eventually strong so that results similar to the 2D case can be proven. We also show the existence of global strong solutions, provided that either the viscosity is large enough or the initial datum is close to a given equilibrium.
Moir\'e heterostructures are rapidly emerging as a tunable platform to study correlated electronic phenomena. Discovery of exotic quantum phases in moir\'e systems requires novel probes of charge and spin order. Unlike detection schemes which average over several moir\'e cells, local sensors can provide richer information with greater sensitivity. We study a WSe$_2$/MoSe$_2$/WSe$_2$ heterotrilayer which hosts excitons and electrons in distinct moir\'e lattices, and show that localized dipolar excitons are sensitive proximity charge sensors, uncovering numerous correlated electronic states at fractional fillings of the multi-orbital moir\'e lattice. In addition, the emission polarization can reveal the local electronic spin configuration at different fillings. Our results establish dipolar excitons as promising candidates to study emergent quantum matter and quantum magnetism in moir\'e crystals with higher spatial resolution.
We report on very long baseline interferometry (VLBI) observations of the radio emission from the inner region of the Crab Nebula, made at 1.6 GHz and 5 GHz after a recent high-energy flare in this object. The 5 GHz data have provided only upper limits of 0.4 milli-Jansky (mJy) on the flux density of the pulsar and 0.4 mJy/beam on the brightness of the putative flaring region. The 1.6 GHz data have enabled imaging the inner regions of the nebula on scales of up to ~40". The emission from the inner "wisps" is detected for the first time with VLBI observations. A likely radio counterpart (designated "C1") of the putative flaring region observed with Chandra and HST is detected in the radio image, with an estimated flux density of $0.5\pm 0.3$\,mJy and a size of 0.2-0.6". Another compact feature ("C2") is also detected in the VLBI image closer to the pulsar, with an estimated flux density of 0.4 +- 0.2 mJy and a size smaller than 0{\farcs}2. Combined with the broad-band SED of the flare, the radio properties of C1 yield a lower limit of ~0.5 mG for the magnetic field and a total minimum energy of 1.2*10^41 ergs vested in the flare (corresponding to using about 0.2% of the pulsar spin-down power). The 1.6 GHz observations provide upper limits for the brightness (0.2 mJy/beam) and total flux density (0.4 mJy) of the optical Knot 1 located at 0.6" from the pulsar. The absolute position of the Crab pulsar is determined, and an estimate of the pulsar proper motion is obtained.
In order to study the effects of internal extinction in spiral galaxies we search for correlations of near infrared (NIR) photometric parameters with inclination. We use data from the 2 Micron All-Sky Survey (2MASS) Extended Source Catalog (XSC) on 15,224 spiral galaxies for which we also have redshifts. For 3035 of the galaxies, I-band photometry is available which is included in the analysis. From the simple dependence of reddening on inclination we derive a lower limit to the difference in magnitude between the face-on and edge-on aspect of 0.9, 0.3 and 0.1 magnitudes in I (0.81 um), J (1.25 um) and H (1.65 um) bands. We find that the faintest isophotal radius reported in the XSC (at the 21st mag/arc sq level) is closer to the centers of the galaxies than other common isophotal measures (e.g. the 23.5 mag/arc sq radius in I-band), and argue that it should not be assumed to represent an outer isophote at which galaxies are transparent at all viewing angles. A simple linear extinction law (i.e. Delta M = gamma log(a/b)) is not adequate for the full range of disk inclinations and we adopt both a bi-linear and a quadratic law. A simple photometric model is used to explain the observed behavior. Internal extinction depends on galaxy luminosity. We show that for galaxies with a K total magnitude dimmer than -20, -20.7 and -20.9 the data indicates zero extinction in J, H and K respectively, while disk opacity increases monotonically with increasing disk luminosity.
We present a rigorous and computationally efficient method to do a parameter-free analysis of molecular wires connected to contacts. The self-consistent field approach is coupled with Non-equilibrium Green's Function (NEGF) formalism to describe electronic transport under an applied bias. Standard quantum chemistry software is used to calculate the self-consistent field using density functional theory (DFT). Such close coupling to standard quantum chemistry software not only makes the procedure simple to implement but also makes the relation between the I-V characteristics and the chemistry of the molecule more obvious. We use our method to interpolate between two extreme examples of transport through a molecular wire connected to gold (111) contacts: band conduction in a metallic (gold) nanowire, and resonant conduction through broadened, quasidiscrete levels of a phenyl dithiol molecule. We obtain several quantities of interest like I-V characteristic, electron density and voltage drop along the molecule.
This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for which only the information near the boundary are required and there might be no contrast of the coefficients on the boundary.
Very faint X-ray transients (VFXTs) are a group of X-ray binaries with low luminosities, the peak X-ray luminosities during their outbursts being only 10$^{34}$--10$^{36}$ erg\,s$^{-1}$. Using the $\gamma$-ray data obtained with the Large Area Telescope (LAT) onboard {\it Fermi Gamma-Ray Space Telescope}, we investigate their possible nature of containing rotation-powered pulsars, or more specifically being transitional millisecond pulsars (MSPs). Among more than 40 known VFXTs, we select 12 neutron star systems. We analyze the LAT data for the fields of the 12 VFXTs in 0.2--300 GeV energy range, but do not find any counterparts likely detected by {\it Fermi}. We obtain the luminosity upper limits for the 12 sources. While the distances to the sources are largely uncertain, the upper limits are comparable to the luminosities of two transitional systems PSR J1023$-$0038 and XSS J12270$-$4859. From our study, we conclude that no evidence is found at $\gamma$-rays for the suggestion that some of VFXTs could contain rotation-powered MSPs (or be transitional MSP systems).
To predict the outcome of (almost) any experiment we have to assume that our spacetime is globally hyperbolic. The wormholes, if they exist, cast doubt on the validity of this assumption. At the same time, no evidence has been found so far (either observational, or theoretical) that the possibility of their existence can be safely neglected.
We present a chrono-cosmography project, aiming at the inference of the four dimensional formation history of the observed large scale structure from its origin to the present epoch. To do so, we perform a full-scale Bayesian analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS) Data Release 7 main galaxy sample, relying on a fully probabilistic, physical model of the non-linearly evolved density field. Besides inferring initial conditions from observations, our methodology naturally and accurately reconstructs non-linear features at the present epoch, such as walls and filaments, corresponding to high-order correlation functions generated by late-time structure formation. Our inference framework self-consistently accounts for typical observational systematic and statistical uncertainties such as noise, survey geometry and selection effects. We further account for luminosity dependent galaxy biases and automatic noise calibration within a fully Bayesian approach. As a result, this analysis provides highly-detailed and accurate reconstructions of the present density field on scales larger than $\sim~3$ Mpc$/h$, constrained by SDSS observations. This approach also leads to the first quantitative inference of plausible formation histories of the dynamic large scale structure underlying the observed galaxy distribution. The results described in this work constitute the first full Bayesian non-linear analysis of the cosmic large scale structure with the demonstrated capability of uncertainty quantification. Some of these results will be made publicly available along with this work. The level of detail of inferred results and the high degree of control on observational uncertainties pave the path towards high precision chrono-cosmography, the subject of simultaneously studying the dynamics and the morphology of the inhomogeneous Universe.
The neutrinoless double beta decay ($\znbb$) induced by light Majorana neutrino exchange between decaying nucleons, accompanied by the squark exchange inside one nucleon, recently discussed by Babu and Mohapatra, is carefully analyzed both from the particle and nuclear physics sides. New nuclear matrix elements relevant to this mechanism are calculated. We extend the analysis to include mixing of light neutrinos with heavy and "sterile" neutrinos. It introduces another supersymmetric (SUSY) contribution to $\znbb$. We discuss constraints on the \rp MSSM parameters imposed by the current experimental limit on $\znbb$ decay half-life of $^{76}$Ge.
Stein's method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation the functional equation is a first order differential equation. Malliavin calculus is an infinite-dimensional differential calculus whose operators act on functionals of general Gaussian processes. Nourdin and Peccati (2009) established a fundamental connection between Stein's method for normal approximation and Malliavin calculus through integration by parts. This connection is exploited to obtain error bounds in total variation in central limit theorems for functionals of general Gaussian processes. Of particular interest is the fourth moment theorem which provides error bounds of the order $\sqrt{\mathbb{E}(F_n^4)-3}$ in the central limit theorem for elements $\{F_n\}_{n\ge 1}$ of Wiener chaos of any fixed order such that $\mathbb{E}(F_n^2) = 1$. This paper is an exposition of the work of Nourdin and Peccati with a brief introduction to Stein's method and Malliavin calculus. It is based on a lecture delivered at the Annual Meeting of the Vietnam Institute for Advanced Study in Mathematics in July 2014.
We study a class of second-order boundary-degenerate elliptic equations in two dimensions with minimal regularity assumptions. We prove a maximum principle and a Harnack inequality at the degenerate boundary, and assuming local boundedness, we prove continuity. On globally defined non-negative solutions we provide strong constraints on behavior at infinity, and prove a Liouville-type theorem for entire solutions on the closed half-plane. The class of PDE in question includes many from mathematical finance, Keldysh- and Tricomi-type PDE, and the 2nd order reduction of the fully non-linear 4th order Abreu equation from K\"ahler geometry.
Electron dynamics in quantum dots manifests itself in spin-flip spectra through electric dipole spin resonance (EDSR). Near a neutrality point separating two different singlet charged states of a double quantum dot, charge dynamics inside a $2\times2$ singlet manifold can be described by a 1/2-pseudospin. In this region, charge dynamics is highly nonlinear and strongly influenced by flopping its soft pseudospin mode. As a result, the responses to external driving include first and second harmonics of the driving frequency and their Raman satellites shifted by the pseudospin frequency. In EDSR spectra of a spin-orbit couplet doublet dot, they manifest themselves as charge satellites of spin-flip transitions. The theory describes gross features of the anomalous half-frequency EDSR in spin blockade spectra [Laird et al., Semicond. Sci. Techol. {\bf 24}, 064004 (2009)].
We perform a morphological study of 124 spectroscopically confirmed cluster galaxies in the z=0.84 galaxy cluster RX J0152.7-1357. Our classification scheme includes color information, visual morphology, and 1-component and 2-component light profile fitting derived from Hubble Space Telescope riz imaging. We adopt a modified version of a detailed classification scheme previously used in studies of field galaxies and found to be correlated with kinematic features of those galaxies. We compare our cluster galaxy morphologies to those of field galaxies at similar redshift. We also compare galaxy morphologies in regions of the cluster with different dark-matter density as determined by weak-lensing maps. We find an early-type fraction for the cluster population as a whole of 47%, about 2.8 times higher than the field, and similar to the dynamically young cluster MS 1054 at similar redshift. We find the most drastic change in morphology distribution between the low and intermediate dark matter density regions within the cluster, with the early type fraction doubling and the peculiar fraction dropping by nearly half. The peculiar fraction drops more drastically than the spiral fraction going from the outskirts to the intermediate-density regions. This suggests that many galaxies falling into clusters at z~0.8 may evolve directly from peculiar, merging, and compact systems into early-type galaxies, without having the chance to first evolve into a regular spiral galaxy.
We present the results from the high resolution Chandra observation of the Cartwheel galaxy. Many individual sources are resolved in the image, mostly associated with the outer ring. All detected sources have a very high X-ray luminosity ($\geq 10^{39}$ erg s$^{-1}$)that classifies them as Ultra Luminous X-ray sources (ULX). The brightest of them is possibly the most luminous individual non-nuclear source observed so far, with L$_X \sim 10^{41}$ erg s$^{-1}$ (at D=122 Mpc). The spatial extent of this source is consistent with a point source at the Chandra resolution. The luminosity function of individual X-ray sources extends about an order of magnitude higher than previously reported in other galaxies. We discuss this in the context of the "universal" luminosity function for High Mass X-ray Binaries and we derive a Star Formation Rate higher than in other starburst galaxies studied so far. A diffuse component, associated with hot gas, is present. However, deeper observations that we will obtain with XMM-Newton are needed to constrain its properties.
Let $n>1$, $e\geq 0$ and a prime number $p\geq 2^{n+2+2e}+3$, such that the index of regularity of $p$ is $\leq e$. We show that there are infinitely many irreducible Galois representations $\rho: Gal(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow {GL}_n(\mathbb{Q}_p)$ unramified at all primes $l\neq p$. Furthermore, these representations are shown to have image containing a fixed finite index subgroup of ${SL}_n(\mathbb{Z}_p)$. Such representations are constructed by lifting suitable residual representations $\bar{\rho}$ with image in the diagonal torus in ${GL}_n(\mathbb{F}_p)$, for which the global deformation problem is unobstructed.
Context: The optical ring like structure detected by Arp (1965) around M81 (commonly referenced as "Arp's loop") represents one of the most spectacular feature observed in nearby galaxies. Arp's loop is commonly interpreted as a tail resulting from the tidal interaction between M81 and M82. However, since its discovery the nature of this feature has remained controversial. Aims: Our primary purpose was to identify the sources of optical and infrared emission observed in Arp's loop. Methods: The morphology of the Arp's loop has been investigated with deep wide-field optical images. We also measured its colors using IRAS and Spitzer-MIPS infrared images and compared them with those of the disk of M81 and Galactic dust cirrus that fills the area where M81 is located. Results: Optical images reveal that this peculiar object has a filamentary structure characterized by many dust features overlapping M81's field. The ratios of far-infrared fluxes and the estimated dust-to-gas ratios indicate the infrared emission of Arp's loop is dominated by the contribution of cold dust that is most likely from Galactic cirrus. Conclusions: The above results suggest that the light observed at optical wavelengths is a combination of emission from i) a few recent star forming regions located close to M81, where both bright UV complexes and peaks in the HI distribution are found, ii) the extended disk of M81 and iii) scattered light from the same Galactic cirrus that is responsible for the bulk of the far infrared emission.
First, we present a Bell type inequality for n qubits, assuming that m out of the n qubits are independent. Quantum mechanics violates this inequality by a ratio that increases exponentially with m. Hence an experiment on n qubits violating of this inequality sets a lower bound on the number m of entangled qubits. Next, we propose a definition of maximally entangled states of n qubits. For this purpose we study 5 different criteria. Four of these criteria are found compatible. For any number n of qubits, they determine an orthogonal basis consisting of maximally entangled states generalizing the Bell states.
We show that in supersymmetric extensions of the Standard Model gluino box diagrams can yield a large CP-violating Delta(I)=3/2 contribution to s->d+q(bar)+q flavor-changing neutral current processes, which feeds into the I=2 isospin amplitude in K->pi+pi decays. This contribution only requires moderate mass splitting between the right-handed squarks u(tilde)_R and d(tilde)_R, and persists for squark masses of order 1 TeV. Taking into account current bounds on Im(delta_{sd}^{LL}) from K-K(bar) mixing, the resulting contribution to epsilon'/epsilon could naturally be an order of magnitude larger than the measured value.
A review of recent developments in the quantum differential calculus. The quantum group $GL_q(n)$ is treated by considering it as a particular quantum space. Functions on $SL_q(n)$ are defined as a subclass of functions on $GL_q(n)$. The case of $SO_q(n)$ is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992.
We discuss the Newtonian limit of boost-rotation symmetric spacetimes by means of the Ehler's frame theory. Conditions for the existence of such a limit are given and, in particular, we show that asymptotic flatness is an essential requirement for the existence of such a limit. Consequently, generalized boost-rotation symmetric spacetimes describing particles moving in uniform fields will not possess a Newtonian limit. In the cases where the boost-rotation symmetric spacetime is asymptotically flat and its Newtonian limit exists, then it is non-zero only for the instant of time symmetry and its value is given by a Poisson integral. The relation of this result with the (Newtonian) gravitational potential suggested by the weak field approximation is discussed. We illustrate our analysis through some examples: the two monopoles solution, the Curzon-Chazy particle solution, the generalized Bonnor-Swaminarayan solution, and the C metric.
The dynamical equation of the magnetization has been reconsidered with enlarging the phase space of the ferromagnetic degrees of freedom to the angular momentum. The generalized Landau-Lifshitz-Gilbert equation that includes inertial terms, and the corresponding Fokker-Planck equation, are then derived in the framework of mesoscopic non-equilibrium thermodynamics theory. A typical relaxation time $\tau$ is introduced describing the relaxation of the magnetization acceleration from the inertial regime towards the precession regime defined by a constant Larmor frequency. For time scales larger than $\tau$, the usual Gilbert equation is recovered. For time scales below $\tau$, nutation and related inertial effects are predicted. The inertial regime offers new opportunities for the implementation of ultrafast magnetization switching in magnetic devices.
We report on reactions producing two pions induced by real and virtual photons or nucleons. The role of different resonances in these reactions is emphasized. Novel results on coherent two pion photoproduction in nuclei are also reported.
This paper is part of a series discussing the results obtained in the framework of a wide international collaboration - the Lockman Hole Project - aimed at improving the extensive multiband coverage available in the Lockman Hole region, through novel deep, wide-area, multifrequency (60, 150, 350 MHz, and 1.4 GHz) radio surveys. This multifrequency, multi-band information will be exploited to get a comprehensive view of star formation and active galactic nucleus activities in the high-redshift Universe from a radio perspective. In this paper, we present novel 1.4 GHz mosaic observations obtained with the Westerbork Synthesis Radio Telescope. With an area coverage of 6.6 deg2, this is the largest survey reaching an rms noise of 11 uJy/beam. In this paper, we present the source catalogue (~6000 sources with flux densities S>55 uJy (5sigma), and we discuss the 1.4 GHz source counts derived from it. Our source counts provide very robust statistics in the flux range 0.1<S<1 mJy, and are in excellent agreement with other robust determinations obtained at lower and higher flux densities. A clear excess is found with respect to the counts predicted by the semi-empirical radio sky simulations developed in the framework of the Square Kilometre Array Simulated Skies project. A preliminary analysis of the identified (and classified) sources suggests this excess is to be ascribed to star-forming galaxies, which seem to show a steeper evolution than predicted.
Quantum chromodymamics (QCD) approach to the problem of multiplicity distributions in high energy particle collisions is described. The solutions of QCD equations for generating functions of the multiplicity distributions in gluon and quark jets are presented for both fixed and running coupling constants. The newly found characteristics very sensitive to distribution shapes is discussed. The predictions are confronted to experimental data. Evolution of the multiplicity distributions with decreasing phase space windows is considered and discussed in connection to the notions of intermittency and fractality. Some other QCD effects are briefly described.