ShantanuT01/DACTYL-Pretraining huggingface dataset:
The nonequilibrium fluctuation theorems have paved the way for estimating equilibrium thermodynamic properties, such as free energy differences, using trajectories from driven nonequilibrium processes. While many statistical estimators may be derived from these identities, some are more efficient than others. It has recently been suggested that trajectories sampled using a particular time-dependent protocol for perturbing the Hamiltonian may be analyzed with another one. Choosing an analysis protocol based on the nonequilibrium density was empirically demonstrated to reduce the variance and bias of free energy estimates. Here, we present an alternate mathematical formalism for protocol postprocessing based on the Feynmac-Kac theorem. The estimator that results from this formalism is demonstrated on a few low-dimensional model systems. It is found to have reduced bias compared to both the standard form of Jarzynski's equality and the previous protocol postprocessing formalism.
We use a time-dependent hopping expansion technique to study the non-equilibrium dynamics of strongly interacting bosons in an optical lattice in the presence of a harmonic trap characterized by a force constant $K$. We show that after a sudden quench of the hopping amplitude $J$ across the superfluid (SF)-Mott insulator(MI) transition, the SF order parameter $|\Delta_{\bf r}(t)|$ and the local density fluctuation $\delta n_{\bf r}(t)$ exhibit sudden decoherence beyond a trap-induced time scale $T_0 \sim K^{-1/2}$. We also show that after a slow linear ramp down of $J$, $|\Delta_{\bf r}|$ and the boson defect density $P_{\bf r}$ display a novel non-monotonic spatial profile. Both these phenomena can be explained as consequences of trap-induced time and length scales affecting the dynamics and can be tested by concrete experiments.
We investigate the invariance principle for set-indexed partial sums of a stationary field $(X\_{k})\_{k\in\mathbb{Z}^{d}}$ of martingale-difference or independent random variables under standard-normalization or self-normalization respectively.
Within the scheme of quantum rate equations, we investigate the spin-resolved transport through a double quantum dot system with four ferromagnetic terminals. It is found that the injection efficiency of spin-polarized electrons can be significantly improved compared with single dot case. When the magnetization in one of four ferromagnetic terminals is antiparallel with the other three, the polarization rate of the current through one dot can be greatly enhanced, accompanied by the drastic decrease of the current polarization rate through the other one. The mechanism is the exchange interaction between electrons in the two quantum dots, which can be a promising candidate for the improvement of the spin injection efficiency.
We investigate magnetic activity properties of 21 stars via medium resolution optical spectra and long-term photometry. Applying synthetic spectrum fitting method, we find that all targets are cool giant or sub-giant stars possessing overall [M/H] abundances between $0$ and $-0.5$. We find that six of these targets exhibit only linear trend in mean brightness while eight of them clearly shows cyclic mean brightness variation. Remaining seven target appear to exhibit cyclic mean brightness variation but this can not be confirmed due to the long time scales of the predicted cycle compared to the current time range of the photometric data. We further determine seasonal photometric periods and compute average photometric period of each target. Analysed sample in this study provides a quantitative representation of a positive linear correlation between the inverse of the rotation period and the cycle period normalized to the rotation period, on the log-log scale. We also observe no correlation between the activity cycle length and the relative surface shear, indicating that the activity cycle must be driven by a parameter rather than the differential rotation. Our analyses show that the relative surface shear is positively correlated with the rotation period and there is a noticeable separation between main sequence stars and our sample. Compared to our sample, the relative surface shear of a main sequence star is larger for a given rotation period. However, dependence of the relative surface shear on the rotation period appears stronger for our sample. Analysis of the current photometric data indicates that the photometric properties of the observed activity cycles in 8 targets seem dissimilar to the sunspot cycle.
Making use of virtual observatory data, we present the first comprehensive sample of optical observations conducted before the explosion times of all gamma-ray bursts (GRBs) with known redshifts. In total, the fields of 11 such GRBs were observed by the Near-Earth Asteroid Tracking (NEAT) program from years to hours before the bursts. Though the typical limiting magnitudes from these observations are R~20 mag, we find no evidence for a significant detection of a precursor. The deepest non-detection of precursor emission is from GRB 030329, reaching down to an absolute B-band magnitude of M_B -18 mag from 6--1500 days (restframe) before the burst. This is of comparable brightness to supernovae, which, in some scenarios for GRB progenitors, are predicted to pre-date a GRB on similar timescales. Since sources cannot be localized to better than ~500 milliarcsecond (3 sigma) with current large-area surveys, unrelated supernovae or AGN activity in GRB hosts could be mistaken for genuine precursor emission. This possibility motivates the need for not only deep wide-field imaging, but imaging at high spatial resolution.
The main aim of this paper is to introduce the most important observables that help us to investigate stellar dynamos and compare those to the modeling results. We give an overview of the available observational methods and data processing techniques that are suitable for such purposes, with touching upon examples of inadequate interpretations as well. Stellar observations are compared to the solar data in such a way, which ensures that the measurements are comparable in dimension, wavelength, and timescale. A brief outlook is given to the future plans and possibilities. A thorough review of this topic was published nearly a decade ago (Berdyugina 2005), now we focus on the experience that have been gathered since that time.
We derive asymptote solution of a homogeneous and isotropic universe governed by the quadratic form of the field equation of $f(T)$ gravity. We explain how the higher order of the torsion can provide an origin for late accelerated phase of the universe in the FRW. The solution makes the scalar torsion $T$ to be a function of the cosmic time $t$. We show that for the equation of state $p=\omega \rho$ with $\omega\neq -1$ the scale factor represent late phase of universe. We perform the cosmological studies and show how the quadratic form of $f(T)$ effect on the behavior of these studies.
We present a complete theory for the full particle statistics of the positions of bulk and extremal particles in a one-dimensional Coulomb Gas (CG) with an arbitrary potential, in the typical and large deviations regimes. Typical fluctuations are described by a universal function which depends solely on general properties of the external potential. The rate function controlling large deviations is, rather unexpectedly, not strictly convex and has a discontinuous third derivative around its minimum for both extremal and bulk particles. This implies, in turn, that the rate function cannot predict the anomalous scaling of the typical fluctuations with the system size. Moreover, its asymptotic behavior for extremal particles differs from the predictions of the Tracy-Widom distribution. Thus many of the paradigmatic properties of the full particle statistics of two-dimensional systems do \emph{not} carry out into their one-dimensional counterparts, hence proving that 1d CG belongs to a different universality class. Our analytical expressions are thoroughly compared with Monte Carlo simulations showing excellent agreement.
The dynamics of magnetic fields in closed regions of solar and stellar coronae are investigated with a reduced magnetohydrodynamic (MHD) model in the framework of Parker scenario for coronal heating. A novel analysis of reduced MHD equilibria shows that their magnetic fields have an asymmetric structure in the axial direction with variation length-scale $z_\ell \sim \ell B_0/b$, where $B_0$ is the intensity of the strong axial guide field, $b$ that of the orthogonal magnetic field component, and $\ell$ the scale of $\mathbf{b}$. Equilibria are then quasi-invariant along the axial direction for variation scales larger than approximatively the loop length $z_\ell \gtrsim L_z$, and increasingly more asymmetric for smaller variation scales $z_\ell \lesssim L_z$. The $critical$ $length$ $z_\ell \sim L_z$ corresponds to the magnetic field intensity threshold $b \sim \ell B_0/L_z$. Magnetic fields stressed by photospheric motions cannot develop strong axial asymmetries. Therefore fields with intensities below such threshold evolve quasi-statically, readjusting to a nearby equilibrium, without developing nonlinear dynamics nor dissipating energy. But stronger fields cannot access their corresponding asymmetric equilibria, hence they are out-of-equilibrium and develop nonlinear dynamics. The subsequent formation of current sheets and energy dissipation is $necessary$ for the magnetic field to relax to equilibrium, since dynamically accessible equilibria have variation scales larger than the loop length $z_\ell \gtrsim L_z$, with intensities smaller than the threshold $b \lesssim \ell B_0/L_z$. The dynamical implications for magnetic fields of interest to solar and stellar coronae are investigated numerically and the impact on coronal physics discussed.
We report a numerical study of self-avoiding polymers on the square lattice, including an attractive potential between nonconsecutive monomers. Using Wang-Landau sampling (WLS) with adaptive windows, we obtain the density of states for chains of up to N=300 monomers and associated thermodynamic quantities. The method enables one to simulate accurately the low-temperature regime, which is virtually inaccessible using traditional methods. Instead of defining fixed energy windows, as in usual WLS, this method uses windows with boundaries that depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor $f$ is reduced, we eliminate border effects that arise in simulations using fixed windows.
In this paper, we are interested in the error estimates of the reiterated Stokes systems in a bounded $C^{1,1}$ domain with Dirichlet boundary conditions. And we have obtained the $O(\varepsilon)$ error estimates for the velocity term and $O(\varepsilon^{1/2})$ error estimates for the pressure term. Compared to the general homogenization of Stokes systems problems, the difficulty in the reiterated homogenization is that we need to handle the different scales of $x$. To overcome this difficulty, we use the Fourier transform methods which was firstly introduced by the author in [10] to separate these different scales. We also note that this method may be adapted to a more general multi-scale homogenization problem.
We have obtained echelle spectra with the Hubble Space Telescope (HST) of the MgII 2800A region of ten stars whose metallicities range from 1/300 to 1/3 that of the Sun, and whose space velocities suggest a halo or old thick-disk origin. Spectra of all ten show double-peaked emission in the MgII core, very much like the quiet Sun. A half-dozen non-rotating stars were observed more than once, and show at most a low level of variability in the emission flux, comparable to that of quiet stars of solar metallicity. For four stars, we have obtained Lyman-alpha spectra at 0.2A resolution; all four show emission. The data thus strongly suggest that chromospheric activity at a minimum level is present in all stars of near-solar temperature, regardless of age or metallicity. While this points to non-magnetic sources such as acoustic waves, a contribution from globally-organized magnetic fields is possible at a low level. We plan a longer series of MgII and Lyman alpha observations to constrain this.
Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators, but also as natural extensions of gradients of convex potentials. These vector fields are not always derived from potentials in the classical sense, and as such they are not always amenable to the standard methods of the calculus of variations. We describe here how the selfdual variational calculus developed recently by the author, provides a variational approach to PDEs and evolution equations driven by maximal monotone operators. To any such a vector field T on a reflexive Banach space X, one can associate a convex selfdual Lagrangian L_T on phase space X x X* that can be seen as a "potential" for T, in the sense that the problem of inverting T reduces to minimizing the convex energy L_T. This variational approach to maximal monotone operators allows their theory to be analyzed with the full range of methods --computational or not-- that are available for variational settings. Standard convex analysis (on phase space) can then be used to establish many old and new results concerned with the identification, superposition, and resolution of such vector fields.
Estimation of the B-mode angular power spectrum of polarized anisotropies of the cosmic microwave background (CMB) is a key step towards a full exploitation of the scientific potential of this probe. In the context of pseudo-spectrum methods the major challenge is related to a contamination of the B-mode spectrum estimate with residual power of much larger E-mode. This so-called E-to-B leakage is unavoidably present whenever an incomplete sky map is only available, as is the case for any realistic observation. The leakage has to be then minimized or removed and ideally in such a way that neither a bias nor extra variance is introduced. In this paper, we compare from these two perspectives three different methods proposed recently in this context Refs. Smith 2006, Zhao & Baskaran 2010, Kim & Naselsky 2010, which we first introduce within a common algebraic framework of the so-called chi-fields and then study their performance on two different experimental configurations - one corresponding to a small-scale experiment covering 1% of the sky motivated by current ground-based or balloon-borne experiments and another - to a nearly full-sky experiment, e.g., a possible CMB B-mode satellite mission. We find that though all these methods allow to reduce significantly the level of the E-to-B leakage, it is the method of Smith 2006, which at the same time ensures the smallest error bars in all experimental configurations studied here, owing to the fact that it permits straightforwardly for an optimization of the sky apodization of the polarization maps used for the estimation. For a satellite-like experiment, this method enables a detection of B-mode power spectrum at large angular scales but only after appropriate binning. The method of Zhao & Baskaran 2010 is a close runner-up in the case of a nearly full sky coverage.
We present new XSHOOTER spectra of NLTT5306, a 0.44 $\pm$ 0.04\msun white dwarf in a short period (101\,min) binary system with a brown dwarf companion that is likely to have previously undergone common envelope evolution. We have confirmed the presence of H$\alpha$ emission and discovered Na I absorption associated with the white dwarf. These observations are indicative of accretion. Accretion is typically evidenced by high energy emission in the UV and X-ray regime. However our \textit{Swift} observations covering the full orbital period in three wavebands (uvw1, uvm2, uvw2) revealed no UV excess or modulation. We used the X-ray non-detection to put an upper limit on the accretion rate of 2$\times$10$^{-15}$\msun yr$^{-1}$. We compare NLTT5306 to similar accreting binaries with brown dwarf donors and suggest the inferred accretion rate could be from wind accretion or accretion from a debris/dust disk. The lack of evidence for a disk implies NLTT5306 is magnetically funnelling a weak wind from a potentially low gravity brown dwarf. The upper limit on the accretion rate suggests a magnetic field as low as 0.45\,kG would be sufficient to achieve this. If confirmed this would constitute the first detection of a brown dwarf wind and could provide useful constraints on mass loss rates.
The recent discovery of a correlation between nuclear black hole mass, M_bh, and the stellar velocity dispersion (Gebhardt et al. 2000, Ferrarese and Merritt 2000), in elliptical galaxies and spiral bulges, has raised the question whether such a relationship exists for AGN. Estimates of M_bh for many AGN, made using reverberation mapping techniques, allow exploration of the relationship between black hole mass, the host galaxy and the energetics of nuclear emission. However, since only a few AGN have both M_bh and velocity dispersion measurements, we use the [OIII] 5007 emission line widths on the assumption that for most AGN the forbidden line kinematics are dominated by virial motion in the host galaxy bulge. We find that a relation does exist between M_bh and [OIII] line width for AGN which is similar to the one found by Gebhardt et al. 2000, although with more scatter as expected if secondary influences on the gas kinematics are also present. Our conclusion is that both active and inactive galaxies follow the same relationship between black hole mass and bulge gravitational potential. We find no compelling evidence for systematic differences in the mass estimates from reverberation mapping and stellar dynamics. We also find that for radio quiet AGN the radio power and black hole mass are highly correlated linking emission on scales of kiloparsecs with the nuclear energy source.
This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.
To investigate possible variations in the stellar initial mass function (IMF) in red-sequence galaxies, we have obtained infrared spectroscopy with Subaru/FMOS for a sample of 92 red-sequence galaxies in the Coma cluster. Velocity dispersions, ages and element abundances for these galaxies have been previously determined from optical data. By stacking the FMOS spectra in the rest frame, removing sky-subtraction residuals and other artefacts fixed in the observed frame, we derive composite spectra in the 9600-10500 Angstrom range for galaxies grouped according to their velocity dispersion or Mg/Fe ratio. We measure the Wing-Ford band of FeH and a new index centred on a CaI line at 10345 Angstrom; these features are strong in cool dwarf stars, and hence reflect the form of the IMF at low mass (<0.5M_sun) The CaI line, unlike the Wing-Ford band and other `classical' IMF indicators (NaI doublet, CaII triplet), is unaffected by the abundance of sodium. We compare the measured indices against predictions from spectral synthesis models matched to the element abundances estimated from the optical data. Binning galaxies by velocity dispersion, we find that both the Wing-Ford and CaI index measurements are best reproduced by models with the Salpeter IMF. There is no clear evidence for an increase in dwarf-star content with velocity dispersion. Binning the observed galaxies instead by Mg/Fe ratio, the behaviour of both indices implies a trend of IMF from Chabrier-like, at abundance ratios close to solar, to Salpeter or heavier for highly alpha-enhanced populations. At face value, this suggests that the IMF depends on the mode of star formation, with intense rapid star-bursts generating a larger population of low-mass stars.
The second known outburst of the WZ Sge type dwarf nova GW Lib was observed in April 2007. We have obtained unique multiwavelength data of this outburst which lasted ~ 26 days. AAVSO observers recorded the outburst in the optical, which was also monitored by WASP, with a peak V magnitude of ~ 8. The outburst was followed in the UV and X-ray wavelengths by the Swift UVOT and XRT telescopes. The X-ray flux at optical maximum was found to be three orders of magnitude above the pre-outburst quiescent level, whereas X-rays are normally suppressed during dwarf nova outbursts. A distinct supersoft X-ray component was also detected at optical maximum, which probably arises from an optically-thick boundary layer. Follow-up Swift observations taken one and two years after the outburst show that the post-outburst quiescent X-ray flux remains an order of magnitude higher than the pre-outburst flux. The long interoutburst timescale of GW Lib with no observed normal outbursts support the idea that the inner disc in GW Lib is evacuated or the disc viscosity is very low.
The main aim of this paper is studying the effect of toroidal magnetic field on the structure of Advection-Dominated Accretion Flows (ADAF) in the presence of the turbulence viscosity and diffusivity due to viscosity and magnetic field respectively. We use self-similar assumption in radial direction to solve the magnetohydrodynamic (MHD) equations for hot accretion disk. We use spherical coordinate $ (r, \theta, \varphi) $ to solve our equation. The toroidal component of magnetic field is considered and all three components of the velocity field $ \mathbf{v}\equiv (v_{r}, v_{\theta}, v_{\varphi}) $ are present in our work. We reduce the equations to a set of differential equations about $ \theta $ and apply the symmetric boundary condition at the equatorial plane of the disk. Our results indicate that the outflow region, where the redial velocity becomes positive in a certain inclination angle $ \theta_{0} $, always exist. The results represent that the stronger the magnetic field, the smaller the inclination angle, $ \theta_{0} $ becomes. It means that a magnetized disk is thinner compared to a non-magnetized disk. According to the work by \citealt{jw}, we can define three regions. The first one is called inflow region, which starts from the disk midplane to a certain inclination $ \theta_0 $ where $ v_{r}(\theta_{0}) = 0 $. In this region, the velocity has a negative value and the accretion material moves toward the central object. The outflow region, where $ v_{r}(\theta) > 0 $, is placed between $ \theta_{0} $ and surface of the disk, $ \theta_{0} < \theta < \theta_{s} $. In this area, the accretion flow moves away from the central object. The third region, which is located between the surface of the disk and the polar axis, is called wind region.