ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using the random intensity of noise (RIN) approach to the one-dimensional Laval-Dubrulle-Nazarenko type model for the Lagrangian acceleration in developed turbulence [cond-mat/0305186, cond-mat/0305459] we study the probability density function and mean acceleration conditional on velocity fluctuations. The additive noise intensity and the cross correlation between the additive and multiplicative noises are assumed to be dependent on velocity fluctuations in an exponential way. The obtained fit results are found to be in a good qualitative agreement with the recent experimental data on the conditional acceleration statistics by Mordant, Crawford, and Bodenschatz. The fit to the observed conditional mean acceleration is of pure illustrative character which is performed to study influence of variation of the cross correlation parameter on the shape of conditional acceleration distribution and conditional acceleration variance. The conditional mean acceleration should be zero for homogeneous isotropic turbulence. The observed conditional mean acceleration increases for bigger velocity fluctuation amplitude and is associated to anisotropy of the studied flow.
The temperature of the low-density intergalactic medium (IGM) at high redshift is sensitive to the timing and nature of hydrogen and HeII reionization, and can be measured from Lyman-alpha forest absorption spectra. Since the memory of intergalactic gas to heating during reionization gradually fades, measurements as close as possible to reionization are desirable. In addition, measuring the IGM temperature at sufficiently high redshifts should help to isolate the effects of hydrogen reionization since HeII reionization starts later, at lower redshift. Motivated by this, we model the IGM temperature at z>5 using semi-numeric models of patchy reionization. We construct mock Lyman-alpha forest spectra from these models and consider their observable implications. We find that the small-scale structure in the Lyman-alpha forest is sensitive to the temperature of the IGM even at redshifts where the average absorption in the forest is as high as 90%. We forecast the accuracy at which the z~5 IGM temperature can be measured using existing samples of high resolution quasar spectra, and find that interesting constraints are possible. For example, an early reionization model in which reionization ends at z~10 should be distinguishable -- at high statistical significance -- from a lower redshift model where reionization completes at z~6. We discuss improvements to our modeling that may be required to robustly interpret future measurements.
CaFe$_{2}$O$_{4}$ is an $S=5/2$ antiferromagnet exhibiting two magnetic orders which shows regions of coexistence at some temperatures. Using a Green's function formalism, we model neutron scattering data of the spin wave excitations in this material, ellucidating the microscopic spin Hamiltonian. In doing so, we suggest that the low temperature A phase order $(\uparrow\uparrow\downarrow\downarrow)$ finds its origins in the freezing of antiphase boundaries created by thermal fluctuations in a parent B phase order $(\uparrow\downarrow\uparrow\downarrow)$. The low temperature magnetic order observed in CaFe$_{2}$O$_{4}$ is thus the result of a competition between the exchange coupling along $c$, which favors the B phase, and the single-ion anisotropy which stabilizes thermally-generated antiphase boundaries, leading to static metastable A phase order at low temperatures.
Compact analytical formulae for QED radiative corrections in the processes of elastic $e-p$ scattering are obtained in the case when kinematic variables are reconstructed from the recoil proton momentum measured. Numerical analysis is presented under kinematic conditions of current experiments at JLab.
Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell's inequalities is to assume existence of joint probability distribution for measurement results for all settings in the given experiment. However for spins-1, one faces the problem that eigenvalues of observables do not allow a consistent algebra if one allows all possible settings on each side (Bell 1966 contradiction), or some specific sets (leading to a Kochen-Specker 1967 contradiction). We show here that by choosing special set of settings which never lead to inconsistent algebra of eigenvalues, one can still derive multisetting Bell inequalities, and that they are robustly violated. Violation factors increase with the number of subsystems. The inequalities involve only spin observables, we do not allow all possible qutrit observables, still the violations are strong.
Ultra-luminous X-ray sources (ULXs) are off-nuclear point sources in nearby galaxies with luminosities well exceeding the Eddington limit for stellar-mass objects. It has been recognized after the discovery of pulsating ULXs (PULXs) that a fraction of these sources could be accreting neutron stars in high-mass X-ray binaries (HMXBs) though the majority of ULXs are lacking in coherent pulsations. The earliest stage of some HMXBs may harbor rapidly rotating neutron stars propelling out the matter transferred by the massive companion. The spin-down power transferred by the neutron-star magnetosphere to the accretion disk at this stage can well exceed the Eddington luminosities and the system appears as a non-pulsating ULX. In this picture, PULXs appear as super-critical mass-accreting descendants of non-pulsating ULXs. We present this evolutionary scenario within a self-consistent model of magnetosphere-disk interaction and discuss the implications of our results on the spin and magnetic field of the neutron star.
Active galactic nuclei host an accretion disc with an X-ray producing corona around a supermassive black hole. In bright sources, such as the Seyfert 1 galaxy Mrk 335, reflection of the coronal emission off the accretion disc has been observed. Reflection produces spectral features such as an iron emission line, which allow for properties of the inner accretion disc and the corona to be constrained. We perform a multi-epoch spectral analysis of all XMM-Newton, Suzaku, and NuSTAR observations of Mrk 335, and we optimize our fitting procedure to unveil correlations between the Eddington ratio and the spectral parameters. We find that the disc's ionization parameter correlates strongly with the Eddington ratio: the inner disc is more strongly ionized at higher flux. The slope of the correlation is less steep than previously predicted. Furthermore, the cut-off of the power-law spectrum increases in energy with the Eddington ratio, whereas the reflection fraction exhibits a decrease. We interpret this behaviour as geometrical changes of the corona as a function of the accretion rate. Below ~10% of the Eddington limit, the compact and optically thick corona is located close to the inner disc, whereas at higher accretion rates the corona is likely optically thin and extends vertically further away from the disc surface. Furthermore, we find a soft excess that consists of two components. In addition to a contribution from reflection in low ionization states, a second component is present that traces the overall flux.
Much of the interstellar medium in disk galaxies is in the form of neutral atomic hydrogen, H I. This gas can be in thermal equilibrium at relatively low temperatures, T < 300 K (the cold neutral medium, or CNM) or at temperatures somewhat less than 10^4 K (the warm neutral medium, or WNM). These two phases can coexist over a narrow range of pressures, P_min < P < P_max. We determine P_min and P_max in the plane of the Galaxy as a function of Galactocentric radius R using recent determinations of the gas heating rate and the gas phase abundances of interstellar gas. We provide an analytic approximation for P_min as a function of metallicity, far-ultraviolet radiation field, and the ionization rate of atomic hydrogen. Over most of the disk of the Galaxy, the H I must be in two phases: the weight of the H I in the gravitational potential of the Galaxy is large enough to generate thermal pressures exceeding P_min, so that turbulent pressure fluctuations can produce cold gas that is thermally stable; and the mean density of the H I is too low for the gas to be all CNM. Our models predict the presence of CNM gas to R = 16-18 kpc, somewhat farther than previous estimates. We also examine the potential impact of turbulent heating on our results and provide expressions for the heating rate as a function of Galactic radius.
We reconsider thin-disc global asymptotics for kinematic, axisymmetric mean-field dynamos with vacuum boundary conditions. Non-local terms arising from a small but finite radial field component at the disc surface are consistently taken into account for quadrupole modes. As in earlier approaches, the solution splits into a local part describing the field distribution along the vertical direction and a radial part describing the radial (global) variation of the eigenfunction. However, the radial part of the eigenfunction is now governed by an integro-differential equation whose kernel has a weak (logarithmic) singularity. The integral term arises from non-local interactions of magnetic fields at different radii through vacuum outside the disc. The non-local interaction can have a stronger effect on the solution than the local radial diffusion in a thin disc, however the effect of the integral term is still qualitatively similar to magnetic diffusion.
Ng and van Dam have argued that quantum theory and general relativity give a lower bound of L^{1/3} L_P^{2/3} on the uncertainty of any distance, where L is the distance to be measured and L_P is the Planck length. Their idea is roughly that to minimize the position uncertainty of a freely falling measuring device one must increase its mass, but if its mass becomes too large it will collapse to form a black hole. Here we show that one can go below the Ng-van Dam bound by attaching the measuring device to a massive elastic rod. Relativistic limitations on the rod's rigidity, together with the constraint that its length exceeds its Schwarzschild radius, imply that zero-point fluctuations of the rod give an uncertainty greater than or equal to L_P.
This paper focuses on vertices of the master corner polyhedra $P(G,g_0),$ the core of the group-theoretical approach to integer linear programming. We introduce two combinatorial operations that transform each vertex of $P(G,g_0)$ to adjacent ones. This implies that for any $P(G,g_0),$ there exists a subset of basic vertices, we call them support vertices, from which all others can be built. The class of support vertices is proved to be invariant under the automorphism group of $G,$ so this basis can be further reduced to a subset of pairwise non-equivalent support vertices. Among other results, we characterize irreducible points of the master corner polyhedra, establish relations between an integer point and the nontrivial facets that pass through it, construct complete subgraphs of the graph of $P(G,g_0),$ and show that these polyhedra are of diameter 2.
Sari, Piran, and Narayan have derived analytic formulas to model the spectra from gamma-ray burst blast waves that are energized by sweeping up material from the surrounding medium. We extend these expressions to apply to general radiative regimes and to include the effects of synchrotron self-absorption. Electron energy losses due to the synchrotron self-Compton process are also treated in a very approximate way. The calculated spectra are compared with detailed numerical simulation results. We find that the spectral and temporal breaks from the detailed numerical simulation are much smoother than the analytic formulas imply, and that the discrepancies between the analytic and numerical results are greatest near the breaks and endpoints of the synchrotron spectra. The expressions are most accurate (within a factor of ~ 3) in the optical/X-ray regime during the afterglow phase, and are more accurate when epsilon_e, the fraction of swept-up particle energy that is transferred to the electrons, is <~ 0.1. The analytic results provide at best order-of-magnitude accuracy in the self-absorbed radio/infrared regime, and give poor fits to the self-Compton spectra due to complications from Klein-Nishina effects and photon-photon opacity.
We study the distribution of 2-Selmer ranks in the family of quadratic twists of an elliptic curve E over an arbitrary number field K. Under the assumption that Gal(K(E[2])/K) = S_3 we show that the density (counted in a non-standard way) of twists with Selmer rank r exists for all positive integers r, and is given via an equilibrium distribution, depending only on a single parameter (the `disparity'), of a certain Markov process that is itself independent of E and K. More generally, our results also apply to p-Selmer ranks of twists of 2-dimensional self-dual F_p-representations of the absolute Galois group of K by characters of order p.
We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang-Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f -> f/2) each time the flat-histogram condition is satisfied, in the second f ~ 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1,...,L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E,t) -> const. as t -> infinity, so that the standard deviation sigma_g of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases sigma_g saturates at long times. In the 1/t algorithm, by contrast, sigma_g decays \propto 1/\sqrt{t}. Modified TS and 1/t procedures, in which f \propto 1/t^alpha, converge for alpha values between 0 and 1. There are two essential facets to convergence of flat-histogram methods: elimination of initial errors in g(E), and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f ~ 1/t^alpha with 0 < \alpha \leq 1. Convergence is optimal for alpha = 1. For alpha \leq 0 the sampling noise never decays, while for alpha > 1 the initial error is never completely eliminated.
We investigate how the shape of the galaxy two-point correlation function as measured in the zCOSMOS survey depends on local environment, quantified in terms of the density contrast on scales of 5 Mpc/h. We show that the flat shape previously observed at redshifts between z=0.6 and z=1 can be explained by this volume being simply 10% over-abundant in high-density environments, with respect to a Universal density probability distribution function. When galaxies corresponding to the top 10% tail of the distribution are excluded, the measured w_p(r_p) steepens and becomes indistinguishable from LCDM predictions on all scales. This is the same effect recognised by Abbas & Sheth in the SDSS data at z~0 and explained as a natural consequence of halo-environment correlations in a hierarchical scenario. Galaxies living in high-density regions trace dark matter halos with typically higher masses, which are more correlated. If the density probability distribution function of the sample is particularly rich in high-density regions because of the variance introduced by its finite size, this produces a distorted two-point correlation function. We argue that this is the dominant effect responsible for the observed "peculiar" clustering in the COSMOS field.
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse Fourier transform of the characteristic function of the respective process.
The bisymplectic Grassmannian I$_2$Gr$(k, V)$ parametrizes k-dimensional subspaces of a vector space V which are isotropic with respect to two general skew-symmetric forms; it is a Fano variety which admits an action of a torus with a finite number of fixed points. In this work we study its equivariant cohomology when $k = 2$; the central result of the paper is an equivariant Chevalley formula for the multiplication of the hyper-plane class by any Schubert class. Moreover, we study in detail the case of I$_2$Gr$(2, \mathbb{C}^6)$, which is a quasi-homogeneous variety, we analyze its deformations and we give a presentation of its cohomology.
I show that the application of the quantum-mechanical (QM) which-way weak measurement scheme of Vaidman may lead to logical inconsistencies. To this end, I study weak values of projection operators. Weak values are (normalized) amplitudes, operationally defined by a weak measurement followed by postselection. Projector weak values have a direct physical significance. This allows formulating an inconsistency in classical terms, viz., the contradiction in the readings of several measuring devices. To arrive at the contradiction, I also invoke the property of weak measurements not to collapse the wave function but to leave the state of the system unchanged (to lowest order in the weak measurement strength). My arguments rely entirely on basic QM rules plus commonly accepted weak QM measurement approximations. Therefore, the inconsistency challenges QM as such.
Relativistic heavy ion collisions generate nuclear-sized droplets of quark-gluon plasma (QGP) that exhibit nearly inviscid hydrodynamic expansion. Smaller collision systems such as p+Au, d+Au, and $^{3}$He+Au at the Relativistic Heavy Ion Collider, as well as p+Pb and high-multiplicity p+p at the Large Hadron Collider may create even smaller droplets of QGP. If so, the standard time evolution paradigm of heavy ion collisions may be extended to these smaller systems. These small systems present a unique opportunity to examine pre-hydrodynamic physics and extract properties of the QGP, such as the bulk viscosity, where the short lifetimes of the small droplets makes them more sensitive to these contributions. Here we focus on the influence of bulk viscosity, its temperature dependence, and cavitation effects on the dynamics in small and large systems using the publicly available hydrodynamic codes SONIC and MUSIC. We also compare pre-hydrodynamic physics in different frameworks including AdS/CFT strong coupling, IP-GLASMA weak coupling, and free streaming or no coupling.
We present new results on the shock around the southwest radio lobe of Centaurus A using data from the Chandra Very Large Programme observations. The X-ray spectrum of the emission around the outer southwestern edge of the lobe is well described by a single power-law model with Galactic absorption -- thermal models are strongly disfavoured, except in the region closest to the nucleus. We conclude that a significant fraction of the X-ray emission around the southwest part of the lobe is synchrotron, not thermal. We infer that in the region where the shock is strongest and the ambient gas density lowest, the inflation of the lobe is accelerating particles to X-ray synchrotron emitting energies, similar to supernova remnants such as SN1006. This interpretation resolves a problem of our earlier, purely thermal, interpretation for this emission, namely that the density compression across the shock was required to be much larger than the theoretically expected factor of 4. We estimate that the lobe is expanding to the southwest with a velocity of ~2600 km/s, roughly Mach 8 relative to the ambient medium. We discuss the spatial variation of spectral index across the shock region, concluding that our observations constrain gamma_max for the accelerated particles to be 10^8 at the strongest part of the shock, consistent with expectations from diffusive shock acceleration theory. Finally, we consider the implications of these results for the production of ultra-high energy cosmic rays (UHECRs) and TeV emission from Centaurus A, concluding that the shock front region is unlikely to be a significant source of UHECRs, but that TeV emission from this region is expected at levels comparable to current limits at TeV energies, for plausible assumed magnetic field strengths.
We present an instability occurring in the inner part of disks threaded by a moderately strong vertical (poloidal) magnetic field. Its mechanism is such that a spiral density wave in the disk, driven by magnetic stresses (rather than self-gravity as in galactic spirals), becomes unstable by exchanging angular momentum with a Rossby vortex it generates at its corotation radius. This angular momentum can then ``leak'' as Alfven waves emitted toward the corona of the disk thus providing, as an element of the accretion process, an energetic source for a wind or a jet. As galactic spirals, this instability forms low azimuthal wavenumber, standing spiral patterns which might provide an explanation for low-frequency QPOs in low-mass X-ray binaries.
We study isoperimetric problems with respect to infinite measures on $R ^n$. In the case of the measure $\mu$ defined by $d\mu = e^{c|x|^2} dx$, $c\geq 0$, we prove that, among all sets with given $\mu-$measure, the ball centered at the origin has the smallest (weighted) $\mu-$perimeter. Our results are then applied to obtain Polya-Szego-type inequalities, Sobolev embeddings theorems and a comparison result for elliptic boundary value problems.
We study the conormal sheaves and singular schemes of 1-dimensional foliations on smooth projective varieties $X$ of dimension 3 and Picard rank 1. We prove that if the singular scheme has dimension 0, then the conormal sheaf is $\mu$-stable whenever the tangent bundle $TX$ is stable, and apply this fact to the characterization of certain irreducible components of the moduli space of rank 2 reflexive sheaves on $\mathbb{P}^3$ and on a smooth quadric hypersurface $Q_3\subset\mathbb{P}^4$. Finally, we give a classification of local complete intersection foliations, that is, foliations with locally free conormal sheaves, of degree 0 and 1 on $Q_3$.
This paper presents a novel Robust Deep Appearance Models to learn the non-linear correlation between shape and texture of face images. In this approach, two crucial components of face images, i.e. shape and texture, are represented by Deep Boltzmann Machines and Robust Deep Boltzmann Machines (RDBM), respectively. The RDBM, an alternative form of Robust Boltzmann Machines, can separate corrupted/occluded pixels in the texture modeling to achieve better reconstruction results. The two models are connected by Restricted Boltzmann Machines at the top layer to jointly learn and capture the variations of both facial shapes and appearances. This paper also introduces new fitting algorithms with occlusion awareness through the mask obtained from the RDBM reconstruction. The proposed approach is evaluated in various applications by using challenging face datasets, i.e. Labeled Face Parts in the Wild (LFPW), Helen, EURECOM and AR databases, to demonstrate its robustness and capabilities.