ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate Nordstr\"om's second theory of gravitation, with a focus on utilizing it as a testbed for developing techniques in numerical relativity. Numerical simulations of inspiraling compact star binaries are performed for this theory, and compared to the predictions of semi-analytic calculations (which are similar to Peters and Mathews' results for GR). The simulations are based on a co-rotating spherical coordinate system, where both finite difference and pseudo-spectral methods are used. We also adopt the "Hydro without Hydro" approximation, and the Weak Radiation Reaction approximation when the orbital motion is quasi-circular. We evolve a binary with quasi-circular initial data for hundreds of orbits and find that the resulting inspiral closely matches the 1/4 power law profile given by the semi-analytical calculations. We additionally find that an eccentric binary circularizes and precesses at the expected rates. The methods investigated thus provide a promising line of attack for the numerical modeling of long binary inspirals in general relativity.
Using self-consistent, physically motivated models, we investigate the X-ray obscuration in 19 Type 2 [OIII] 5007 \AA\ selected AGN, 9 of which are local Seyfert 2 galaxies and 10 of which are Type 2 quasar candidates. We derive reliable line-of-sight and global column densities for these objects, which is the first time this has been reported for an AGN sample; 4 AGN have significantly different global and line-of-sight column densities. Five sources are heavily obscured to Compton-thick. We comment on interesting sources revealed by our spectral modeling, including a candidate ``naked'' Sy2. After correcting for absorption, we find that the ratio of the rest-frame, 2-10 keV luminosity (L$_{\rm 2-10keV,in}$) to L$_{\rm [OIII]}$ is 1.54 $\pm$ 0.49 dex which is essentially identical to the mean Type 1 AGN value. The Fe K$\alpha$ luminosity is significantly correlated with L$_{\rm [OIII]}$, but with substantial scatter. Finally, we do not find a trend between L$_{\rm 2-10keV,in}$ and global or line-of-sight column density, between column density and redshift, between column density and scattering fraction or between scattering fraction and redshift.
The model of random interlacements is a one-parameter family $\mathcal I^u,$ $u \ge 0,$ of random subsets of $\mathbb{Z}^d,$ which locally describes the trace of simple random walk on a $d$-dimensional torus run up to time $u$ times its volume. Its complement, the so-called vacant set $\mathcal V^u$, has been shown to undergo a non-trivial percolation phase-transition in $u;$ i.e., there exists $u_*(d) \in (0, \infty)$ such that for $u \in [0, u_*(d))$ the vacant set $\mathcal V^u$ contains a unique infinite connected component $\mathcal V_\infty^u,$ while for $u > u_*(d)$ it consists of finite connected components. Sznitman \cite{SZ11,SZ11B} showed that $u_*(d) \sim \log d,$ and in this article we show the existence of $u(d) > 0$ with $\frac{u(d)}{u_*(d)} \to 1$ as $d \to \infty$ such that $\mathcal V_\infty^{u}$ is transient for all $u \in [0, u(d)).$
Aims: We summarize the current observational picture of the outbursts of black-hole X-ray transients (BHTs), based on the evolution traced in a hardness-luminosity diagram (HLD), and we offer a physical interpretation.   Methods: The basic ingredient in our interpretation is the Poynting-Robertson Cosmic Battery (PRCB, Contopoulos & Kazanas 1998), which provides locally the poloidal magnetic field needed for the ejection of the jet. In addition, we make two assumptions, easily justifiable. The first is that the mass-accretion rate to the black hole in a BHT outburst has a generic bell-shaped form. This is guaranteed by the observational fact that all BHTs start their outburst and end it at the quiescent state. The second assumption is that at low accretion rates the accretion flow is geometrically thick, ADAF-like, while at high accretion rates it is geometrically thin.   Results: Both, at the beginning and the end of an outburst, the PRCB establishes a strong poloidal magnetic field in the ADAF-like part of the accretion flow, and this explains naturally why a jet is always present in the right part of the HLD. In the left part of the HLD, the accretion flow is in the form of a thin disk, and such a disk cannot sustain a strong poloidal magnetic filed. Thus, no jet is expected in this part of the HLD. The counterclockwise traversal of the HLD is explained as follows: the poloidal magnetic field in the ADAF forces the flow to remain ADAF and the source to move upwards in the HLD rather than to turn left. Thus, the history of the system determines the counterclockwise traversal of the HLD. As a result, no BHT is expected to ever traverse the entire HLD curve in the clockwise direction.   Conclusions: We offer a physical interpretation of accretion and ejection in BHTs with only one parameter, the mass transfer rate.
We consider a variation of the Hastings-Levitov model HL(0) for random growth in which the growing cluster consists of two competing regions. We allow the size of successive particles to depend both on the region in which the particle is attached, and the harmonic measure carried by that region. We identify conditions under which one can ensure coexistence of both regions. In particular, we consider whether it is possible for the process giving the relative harmonic measures of the regions to converge to a non-trivial ergodic limit.
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.
Pulsar wind nebulae (PWNe) are among the most extreme particle accelerators in galaxies, are recognized as multi-TeV electron/positron sources, and are one of the dominant classes of Galactic gamma-ray sources. Vela X is a nearby PWN at 290 pc from the Earth with large apparent size ($>1^\circ$). The H.E.S.S. array of imaging atmospheric Cherenkov telescopes has detected Vela X as one of the brightest known sources of TeV gamma rays. The bulk of the gamma-ray emission measured using H.E.S.S. coincides with an elongated structure known from X-ray observations and dubbed the cocoon, that seemingly emanates from the region of the pulsar wind termination shock. The spectral energy distribution of the cocoon peaks at around 10 TeV, and then presents a cutoff that can be precisely measured with H.E.S.S. owing to the extreme brightness of the source. Electrons radiating inverse-Compton gamma rays in the cutoff region are the same responsible for the X-ray synchrotron emission at energies $> 1$ keV. Therefore, Vela X provides a unique test case, in which we can constrain the densities and spectra of accelerated leptons in the cutoff regime, as well as the magnetic field properties, with minimal modeling assumptions. Thanks to the proximity/large apparent size of the source, this can be done in a spatially-resolved fashion across the PWN. We will present an analysis of H.E.S.S. data combined with X-ray data from the Suzaku space telescope. We will discuss implications for the mechanisms behind particle acceleration and transport, constrain the strength of the magnetic field in different locations in the nebula, and probe for magnetic field turbulence.
A detailed observation of microglitch phenomenon in relatively slow radio pulsars is presented. Our analyses for these small amplitude jumps in pulse rotation frequency ($\nu$) and/or spin down rate ($\dot{\nu}$) combine the traditional manual detection method (which hinges on careful visual inspections of the residuals of pulse phase residuals) and a new, and perhaps more objective, automated search technique (which exploits the power of the computer, rather than the eyes, for resolving discrete events in pulsar spin parameters). The results of the analyses of a sample of 26 radio pulsars reveal that: (i) only 20 pulsars exhibit significant fluctuations in their arrival times to be considered suitable for meaningful microglitch analyses; (ii) a phenomenal 299 microglitch events were identified in $\nu$ and/or $\dot{\nu}$: 266 of these events were found to be simultaneously significant in $\nu$ and $\dot{\nu}$, while 19 and 14 were noticeable only in $\nu$ and $\dot{\nu}$, respectively; (iii) irrespective of sign, the microglitches have fractional sizes which cover about 3 orders of magnitude in $\nu$ and $\dot{\nu}$ ($10^{-11} < |\Delta{\nu}/\nu| < 2.0\times10^{-8}$ and $5.0\times10^{-5} < |\Delta{\dot{\nu}}/\dot{\nu}| < 2.0\times10^{-2}$) with median values as $0.78\times10^{-9}$ and $0.36\times10^{-3}$, respectively.
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior at the edge, including the so called spectral gap. Results are obtained for two simple models with distinct limiting features. The first model is built on the complete graph while the second is a birth-and-death dynamics. Both models give rise to random matrices with non independent entries.
A storage system where a k units stock is replaced instantaneously, when required,is presented in this work. It is also supposed a Poisson demand. It is proved that the storage system replenishment cost expected present value function fulfills a defective renewal equation, being proposed for it an asymptotic expression.
In this revised reply to quant-ph/0211165, I address the question of the validity of my results in greater detail, by comparing my predictions to those of the Silberfarb-Deutsch model, and I deal at greater length with the beam area paradox. As before, I conclude that my previous results are an (order-of-magnitude) accurate estimate of the error probability introduced in quantum logical operations by the quantum nature of the laser field. While this error will typically (for a paraxial beam) be smaller than the total error due to spontaneous emission, a unified treatment of both effects reveals that they lead to formally similar constraints on the minimum number of photons per pulse required to perform an operation with a given accuracy; these constraints agree with those I have derived elsewhere.
The substructure of charged jets gets modified due to the presence of the medium in heavy-ion collisions which is an indication of redistribution of energy inside the jet cone. It helps to understand the energy loss mechanisms of jets in the medium. A model dependent study of the modification of differential jet shape $(\rho(r))$ and the angularity (g) due to medium, has been performed in the most central Pb-Pb collisions at 2.76 TeV in the jet range of 20-40 GeV/c.
$Gaia$ DR2 has provided an unprecedented wealth of information about the positions and motions of stars in our Galaxy, and has highlighted the degree of disequilibria in the disc. As we collect data over a wider area of the disc it becomes increasingly appealing to start analysing stellar actions and angles, which specifically label orbit space, instead of their current phase space location. Conceptually, while $\bar{x}$ and $\bar{v}$ tell us about the potential and local interactions, grouping in action puts together stars that have similar frequencies and hence similar responses to dynamical effects occurring over several orbits. Grouping in actions and angles refines this further to isolate stars which are travelling together through space and hence have shared histories. Mixing these coordinate systems can confuse the interpretation. For example, it has been suggested that by moving stars to their guiding radius, the Milky Way spiral structure is visible as ridge-like overdensities in the $Gaia$ data \citep{Khoperskov+19b}. However, in this work, we show that these features are in fact the known kinematic moving groups, both in the $L_z-\phi$ and the $v_{\mathrm{R}}-v_{\phi}$ planes. Using simulations we show how this distinction will become even more important as we move to a global view of the Milky Way. As an example, we show that the radial velocity wave seen in the Galactic disc in $Gaia$ and APOGEE should become stronger in the action-angle frame, and that it can be reproduced by transient spiral structure.
A truncation scheme for the Dyson-Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov-Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to vanish for small spacelike momenta whereas the ghost propagator is found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, alpha_c approximately 9.5. The results for the propagators obtained here compare favorably with recent lattice calculations.
For binary mixtures with fixed concentrations of the species, various relationships between the surface tensions and the concentrations are briefly reviewed.
We have imaged GM Aur with HST, detected its disk in scattered light at 1400A and 1650A, and compared these with observations at 3300A, 5550A, 1.1 microns, and 1.6 microns. The scattered light increases at shorter wavelengths. The radial surface brightness profile at 3300A shows no evidence of the 24AU radius cavity that has been previously observed in sub-mm observations. Comparison with dust grain opacity models indicates the surface of the entire disk is populated with sub-micron grains. We have compiled an SED from 0.1 microns to 1 mm, and used it to constrain a model of the star+disk system that includes the sub-mm cavity using the Monte Carlo Radiative Transfer code by Barbara Whitney. The best-fit model image indicates that the cavity should be detectable in the F330W bandpass if the cavity has been cleared of both large and small dust grains, but we do not detect it. The lack of an observed cavity can be explained by the presence of sub-microns grains interior to the sub-mm cavity wall. We suggest one explanation for this which could be due to a planet of mass <9 Jupiter masses interior to 24 AU. A unique cylindrical structure is detected in the FUV data from the Advanced Camera for Surveys/Solar Blind Channel. It is aligned along the system semi-minor axis, but does not resemble an accretion-driven jet. The structure is limb-brightened and extends 190 +/- 35 AU above the disk midplane. The inner radius of the limb-brightening is 40 +/- 10 AU, just beyond the sub-millimeter cavity wall.
We study analytic properties of the pair consisting of a rather general form of zeta-function with an Euler product and a periodic Hurwitz zeta-function with a transcendental parameter. We first survey briefly previous results, and then investigate the mixed joint discrete value distribution and prove the mixed joint discrete universality theorem for these functions, in the case when common differences of relevant arithmetic progressions are not necessarily the same. Also some generalizations are given. For this purpose, certain arithmetic conditions on the common differences are necessary.
The long-time asymptotics is analyzed for finite energy solutions of the 1D discrete Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group. For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schr\"odinger equation. The proofs use the strategy of Buslaev-Perelman: the linerization of the dynamics on the solitary manifold, the symplectic orthogonal projection, method of majorants, etc.
We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular epsilon-expansion, where epsilon is the distance to the upper critical dimension. Subsequently, we check the results by numerical simulations of spin models in the same universality class. Our systems offer the essential advantage that epsilon can be varied continuously, allowing an accurate examination of the region where epsilon is small. The numerical calculations turn out to be in striking disagreement with the predicted singularity.
A series of Co_xCu_{100-x} (x = 0, 40...75, 100) layers with thicknesses in-between 13 nm and 55 nm were prepared on silicon substrates using cross-beam pulsed laser deposition. Wide-angle X-ray diffraction (WAXRD), transmission electron microscopy (TEM) and electrical transport measurements revealed a structure consisting of decomposed cobalt and copper grains with grain sizes of about 10 nm. The influence of cobalt content and layer thickness on the grain size is discussed. Electron diffraction (ED) indicates the presence of an intermetallic Co-Cu phase of Cu3Au structure-type. Thermal treatment at temperatures between 525 K and 750 K results in the progressive decomposition of Co and Cu, with an increase of the grain sizes up to about 100 nm. This is tunable by controlling the temperature and duration of the anneal, and is directly observable in WAXRD patterns and TEM images. A careful analysis of grain size and the coherence length of the radiation used allows for an accurate interpretation of the X-ray diffraction patterns, by taking into account coherent and non-coherent scattering. The alloy films show a giant magnetoresistance of 1...2.3 % with the maximum obtained after annealing at around 725 K.
We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of Cavity Quantum Electrodynamics could be generalized to many other nanoscale circuits.
In this paper, we discuss the problem of whether the difference $[X]-[Y]$ of the classes of a Fourier--Mukai pair $(X, Y)$ of smooth projective varieties in the Grothendieck ring of varieties is annihilated by some power of the class $\mathbb{L} = [ \mathbb{A}^1 ]$ of the affine line. We give an affirmative answer for Fourier--Mukai pairs of very general K3 surfaces of degree 12. On the other hand, we prove that in each dimension greater than one, there exists an abelian variety such that the difference with its dual is not annihilated by any power of $\mathbb{L}$, thereby giving a negative answer to the problem. We also discuss variations of the problem.
We show that any smooth solution $(\mathbf{u},\mathbf{H})$ to the stationary equations of magneto-hydrodynamics (MHD) belonging to both spaces $L^6 (\mathbb{R}^3)$ and $BMO^{-1}(\mathbb{R}^3)$ must be identically zero. This is an extension of previous results, all of which systematically required stronger integrability and the additional assumption $\nabla \mathbf{u}, \nabla \mathbf{H} \in L^2 (\mathbb{R}^3) $, i.e., finite Dirichlet integral.
A fascinating conjectural connection between statistical mechanics and combinatorics has in the past five years led to the publication of a number of papers in various areas, including stochastic processes, solvable lattice models and supersymmetry. This connection, known as the Razumov-Stroganov conjecture, expresses eigenstates of physical systems in terms of objects known from combinatorics, which is the mathematical theory of counting. This note intends to explain this connection in light of the recent papers by Zinn-Justin and Di Francesco.
The molecular phase of the interstellar medium (ISM) in galaxies offers fundamental insight for understanding star-formation processes and how stellar feedback affects the nuclear activity of certain galaxies. We present here Large Millimeter Telescope spectra obtained with the Redshift Search Receiver, a spectrograph that cover simultaneously the 3 mm band from 74 to 111 GHz with a spectral resolution of around 100 km/s. The observed galaxies that have been detected previously in HCN, have different degrees of nuclear activity, one normal galaxy (NGC 6946), the starburst prototype (M 82) and two ultraluminous infrared galaxies (ULIRGs, IRAS 17208-0014 and Mrk 231). We plotted our data in the HCO+/HCN vs. HCN/13CO diagnostic diagram finding that NGC 6946 and M 82 are located close to other normal galaxies; and that both IRAS 17208-0014 and Mrk 231 are close to the position of the well known ULIRG Arp 220 reported by Snell et al. (2011). We found that in Mrk 231 -- a galaxy with a well known active galactic nucleus -- the HCO+/HCN ratio is similar to the ratio observed in other normal galaxies.
We study aspects of the propagation of strings on BTZ black holes. After performing a careful analysis of the global spacetime structure of generic BTZ black holes, and its relation to the geometry of the SL(2,R) group manifold, we focus on the simplest case of the massless BTZ black hole. We study the SL(2,R) Wess-Zumino-Witten model in the worldsheet minisuperspace limit, taking into account special features associated to the Lorentzian signature of spacetime. We analyse the two- and three-point functions in the pointparticle limit. To lay bare the underlying group structure of the correlation functions, we derive new results on Clebsch-Gordan coefficients for SL(2,R) in a parabolic basis. We comment on the application of our results to string theory in singular time-dependent orbifolds, and to a Lorentzian version of the AdS/CFT correspondence.
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or incomplete) equilibrium. One has a system of interest in equilibrium with the environment, and measures one of its quantities, for example its specific heat, by raising the temperature of the environment. However, within the observation time the global system settles down to a state of apparent equilibrium, so that the measured value of the specific heat is different from the equilibrium one. In such cases formulae for quantities such as the effective specific heat exist, which are provided by Fluctuation Dissipation theory. However, what is lacking is a proof that internal energy exists, i.e., that the fundamental differential form delta Q-delta W (difference between the heat absorbed by the system and the work performed by it) is closed. Here we show how the coefficients of the fundamental form can be expressed in such a way that the closure property of the form becomes manifest, so that the first principle is proven. We then show that the second principle too follows, and indeed as a consequence of microscopic time--reversibility. The treatment is given in a classical Hamiltonian setting. One has a global time--independent Hamiltonian system constituted by the system of interest and two auxiliary ones controlling temperature and pressure, and the occurring of a process due to a change in the thermodynamic parameters is implemented by a suitable choice of the measure for the initial data.