ShantanuT01/DACTYL-Pretraining huggingface dataset:
The mixed spin-1/2 and spin-3/2 Ising model on the union jack lattice is solved by establishing a mapping correspondence with the eight-vertex model. It is shown that the model under investigation becomes exactly soluble as a free-fermion eight-vertex model when the parameter of uniaxial single-ion anisotropy tends to infinity. Under this restriction, the critical points are characterized by critical exponents from the standard Ising universality class. In a certain subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, the model becomes exactly soluble as a symmetric zero-field eight-vertex model. This surface is bounded by a line of bicritical points having interaction-dependent critical exponents that satisfy a weak universality hypothesis.
Originally selected as a neutron star (NS) candidate in the ROSAT All-Sky Survey, 1RXS J141256.0+792204 ("Calvera") was discovered to be a 59 ms X-ray pulsar in a pair of XMM-Newton observations (Zane et al. 2011). Surprisingly, their claimed detection of this pulsar in Fermi gamma-ray data requires no period derivative, severely restricting its dipole magnetic field strength, spin-down luminosity, and distance to small values. This implies that the cooling age of Calvera is much younger than its characteristic spin-down age. If so, it could be a mildly recycled pulsar, or the first "orphaned" central compact object (CCO). Here we show that the published Fermi ephemeris fails to align the pulse phases of the two X-ray observations with each other, which indicates that the Fermi detection is almost certainly spurious. Analysis of additional Fermi data also does not confirm the gamma-ray detection. This leaves the spin-down rate of Calvera less constrained, and its place among the families of NSs uncertain. It could still be either a normal pulsar, a mildly recycled pulsar, or an orphaned CCO.
We study the asymptotic behavior of solutions to the Schr{\"o}dinger equation with large-amplitude, highly oscillatory, random potential. In dimension $d<\mathfrak{m}$, where $\mathfrak{m}$ is the order of the leading operator in the Schr\"odinger equation, we construct the heterogeneous solution by using a Duhamel expansion and prove that it converges in distribution, as the correlation length $\varepsilon$ goes to 0, to the solution of a stochastic differential equation, whose solution is represented as a sum of iterated Stratonovich integral, over the space $C([0,+\infty),\mathcal{S}')$. The uniqueness of the limiting solution in a dense space of $L^2(\Omega\times\mathbb{R}^d)$ is shown by verifying the property of conservation of mass for the Schr\"odinger equation. In dimension $d>\mathfrak{m}$, the solution to the Schr{\"o}dinger equation is shown to converge in $L^2(\Omega\times\mathbb{R}^d)$ to a deterministic Schr{\"o}dinger solution in \cite{ZB-12}.
We examine the prospects for the next generation of surveys aimed at elucidating the nature of dark energy. We review the methods that can be used to determine the redshift evolution of the dark energy equation of state parameter w, highlighting their respective strengths and potential weaknesses. All of the attractive methods require surveys covering more than 5-10,000 square degrees of the sky. We examine the accuracy that each method is likely to deliver within a decade, and discuss the difficulties arising from systematic uncertainties associated with the techniques.   We conclude that the proposed photometric and redshift surveys have the potential of delivering measurements of w with percent accuracy at several redshifts out to z ~ 3 . Of particular interest will be the combination of weak lensing and baryonic acoustic oscillations measurements. This exquisite precision is likely to have a fundamental impact on our understanding of the nature of dark energy, providing the necessary guidance for its theoretical explanation.
The main objective of this work is to determine the character of orbits of stars moving in the meridional $(R,z)$ plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical dark matter halo component. In particular, we try to reveal the influence of the scale length of the dark matter halo on the different families of orbits of stars, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families evolve when this parameter varies. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our numerical computations reveal that when the dark matter halo is highly concentrated, that is when the scale length has low values the vast majority of star orbits move in regular orbits, while on the other hand in less concentrated dark matter halos the percentage of chaos increases significantly. We also compared our results with early related work.
We compute accurate redshift distributions to I(AB) = 24 and R(AB) = 24.5 using photometric redshifts estimated from six-band UBVRIZ photometry in the Canada-France Deep Fields-Photometric Redshift Survey (CFDF-PRS). Our photometric redshift algorithm is calibrated using hundreds of CFRS spectroscopic redshifts in the same fields. The dispersion in redshift is \sigma/(1+z) \la 0.04 to the CFRS depth of I(AB) = 22.5, rising to \sigma/(1+z) \la 0.06 at our nominal magnitude and redshift limits of I(AB) = 24 and z \le 1.3, respectively. We describe a new method to compute N(z) that incorporates the full redshift likelihood functions in a Bayesian iterative analysis and we demonstrate in extensive Monte Carlo simulations that it is superior to distributions calculated using simple maximum likelihood redshifts. The field-to-field differences in the redshift distributions, while not unexpected theoretically, are substantial even on 30' scales. We provide I(AB) and R(AB) redshift distributions, median redshifts, and parametrized fits of our results in various magnitude ranges, accounting for both random and systematic errors in the analysis.
Supersymmetric particles at the multi-TeV scale will escape direct detection at planned future colliders. However, such particles induce non-decoupling corrections in processes involving the accessible superparticles through violations of the supersymmetric equivalence between gauge boson and gaugino couplings. In a previous study, we parametrized these violations in terms of super-oblique parameters and found significant deviations in well-motivated models. Here, we systematically classify the possible experimental probes of such deviations, and present detailed investigations of representative observables available at a future linear collider. In some scenarios, the $e^-e^-$ option and adjustable beam energy are exploited to achieve high precision. It is shown that precision measurements are possible for each of the three coupling relations, leading to significant bounds on the masses and properties of heavy superparticles and possible exotic sectors.
Several hitherto unexplained features of thermal conductivity in group IV materials, such as the change in the slope as a function of sample size for pure vs. alloyed samples and the fast decay in thermal conductivity for low impurity concentration, are described in terms of a transition from a collective to kinetic regime in phonon transport. We show that thermal transport in pure bulk silicon samples is mainly collective, and that impurity/alloy and boundary scattering are responsible for the destruction of this regime with an associated strong reduction in thermal conductivity, leaving kinetic transport as the only one allowed when those resistive scattering mechanisms are dominant.
We present the results of timing analysis of the low-frequency Quasi-Periodic Oscillation (QPO) in the Rossi X-Ray Timing Explorer data of the black hole binary XTE J1550--564 during its 1998 outburst. The QPO frequency is observed to vary on timescales between $\sim$100 s and days, correlated with the count rate contribution from the optically thick accretion disk: we studied this correlation and discuss its influence on the QPO width. In all observations, the quality factors ($\nu_0$/FWHM) of the fundamental and second harmonic peaks were observed to be consistent, suggesting that the quasi-periodic nature of the oscillation is due to frequency modulation. In addition to the QPO and its harmonic peaks, a new 1.5$\nu$ component was detected in the power spectra. This component is broad, with a quality factor of $\sim$0.6. From this, we argue what the peak observed at half the QPO frequency, usually referred to as "sub-harmonic" could be the fundamental frequency, leading to the sequence 1:2:3:4. We also studied the energy dependence of the timing features and conclude that the two continuum components observed in the power spectrum, although both more intense at high energies, show a different dependence on energy. At low energies, the lowest-frequency component dominates, while at high energies the higher-frequency one has a higher fractional rms. An interplay between these two components was also observed as a function of their characteristic frequency. In this source, the transition between low/hard state and hard-intermediate state appears to be a smooth process.
Network data analysis methods are the only way to properly separate real gravitational wave (GW) transient events from detector noise. They can be divided into two generic classes: the coincidence method and the coherent analysis. The former uses lists of selected events provided by each interferometer belonging to the network and tries to correlate them in time to identify a physical signal. Instead of this binary treatment of detector outputs (signal present or absent), the latter method involves first the merging of the interferometer data and looks for a common pattern, consistent with an assumed GW waveform and a given source location in the sky. The thresholds are only applied later, to validate or not the hypothesis made. As coherent algorithms use a more complete information than coincidence methods, they are expected to provide better detection performances, but at a higher computational cost. An efficient filter must yield a good compromise between a low false alarm rate (hence triggering on data at a manageable rate) and a high detection efficiency. Therefore, the comparison of the two approaches is achieved using so-called Receiving Operating Characteristics (ROC), giving the relationship between the false alarm rate and the detection efficiency for a given method. This paper investigates this question via Monte-Carlo simulations, using the network model developed in a previous article.
This paper has been withdrawn by the author because Proposition 1 is not valid.
In this paper we stress the idea that new, more precise neutrino cross-sections measurements at low energies will be necessary to improve the results of future big neutrino detectors, which will be dominated by the contribution of the systematic errors. The use of a muon beam instead of the traditional pion beams is proposed. This choice allows the simultaneous measurement of both, numu and nue interactions and the two helicities, in a clean environment and with a precise knowledge of the beam flux. We show that with approx 10^{15} mu's/year and a moderate mass detector (approx 100 tons) placed close to the muon storage ring, precisions of the order of 10% in sigma(nu) (E_nu bin size of 100 MeV) can be reached for neutrino energies below 2 GeV.
Using shape measurement techniques developed for weak lensing surveys we have identified three new ultracool binaries in the Pan-STARRS1 survey. Binary companions which are not completely resolved can still alter the shapes of stellar images. These shape distortions can be measured if PSF anisotropy caused by the telescope is properly accounted for. We show using both a sample of known binary stars and simulated binaries that we can reliably recover binaries wider than around 0.3" and with flux ratios greater than around 0.1. We then applied our method to a sample of ultracool dwarfs within 30pc with 293 objects having sufficient Pan-STARRS1 data for our method. In total we recovered all but one of the 11 binaries wider than 0.3" in this sample. Our one failure was a true binary detected with a significant but erroneously high ellipticity which led it to be rejected in our analysis. We identify three new binaries, one a simultaneous discovery, with primary spectral types M6.5, L1 and T0.5. These latter two were confirmed with Keck/NIRC2 follow-up imaging. This technique will be useful for identifying large numbers of stellar and substellar binaries in the upcoming LSST and DES sky surveys.
We study QCD radiation in decay processes involving heavy particles. As input, the first-order gluon emission rate is calculated in a number of reactions, and comparisons of the energy flow patterns show a non-negligible process dependence. To proceed further, the QCD parton shower language offers a convenient approach to include multi-gluon emission effects, and to describe exclusive event properties. An existing shower algorithm is extended to take into account the process-dependent mass, spin and parity effects, as given by the matrix element calculations. This allows an improved description of multiple gluon emission effects off b and t quarks, and also off nonstandard particles like squarks and gluinos. Phenomenological applications are presented for bottom production at LEP, Higgs particle decay to heavy flavours, top production and decay at linear colliders, and some simple supersymmetric processes.
We use the Aubry-Perret bound for singular curves, a generalization of the Hasse-Weil bound, to prove the following curious result about rational functions over finite fields: Let $f(X),g(X)\in\Bbb F_q(X)\setminus\{0\}$ be such that $q$ is sufficiently large relative to $\text{deg}\, f$ and $\text{deg}\, g$, $f(\Bbb F_q)\subset g(\Bbb F_q\cup\{\infty\})$, and for ``most'' $a\in\Bbb F_q\cup\{\infty\}$, $|\{x\in \Bbb F_q:g(x)=g(a)\}|>(\text{deg}\, g)/2$. Then there exists $h(X)\in\Bbb F_q(X)$ such that $f(X)=g(h(X))$. A generalization to multivariate rational functions is also included.
Surprisingly little is known about the origin and evolution of the Milky Way's satellite galaxy companions. UV photoionisation, supernova feedback and interactions with the larger host halo are all thought to play a role in shaping the population of satellites that we observe today, but there is still no consensus as to which of these effects, if any, dominates. In this paper, we revisit the issue by re-simulating a Milky Way class dark matter (DM) halo with unprecedented resolution. Our set of cosmological hydrodynamic Adaptive Mesh Refinement (AMR) simulations, called the Nut suite, allows us to investigate the effect of supernova feedback and UV photoionisation at high redshift with sub-parsec resolution. We subsequently follow the effect of interactions with the Milky Way-like halo using a lower spatial resolution (50pc) version of the simulation down to z=0. This latter produces a population of simulated satellites that we compare to the observed satellites of the Milky Way and M31. We find that supernova feedback reduces star formation in the least massive satellites but enhances it in the more massive ones. Photoionisation appears to play a very minor role in suppressing star and galaxy formation in all progenitors of satellite halos. By far the largest effect on the satellite population is found to be the mass of the host and whether gas cooling is included in the simulation or not. Indeed, inclusion of gas cooling dramatically reduces the number of satellites captured at high redshift which survive down to z=0.
We have investigated several models of Pomeron and Odderon contributions to high energy elastic $pp$ and $\bar p p$ scattering. The questions we address concern their role in this field, the behavior of the scattering amplitude (or of the total cross-section) at high energy, and how to fit all high energy elastic data. The data are extremely well reproduced by our approach at all momenta and for sufficiently high energies. The relative virtues of Born amplitudes and of different kinds of eikonalizations are considered. An important point in this respect is that secondary structures are predicted in the differential cross-sections at increasing energies and these phenomena appear quite directly related to the procedure of eikonalizing the various Born amplitudes. We conclude that these secondary structures arise naturally within the eikonalized procedure (although their precise localization turns out to be model dependent). The fitting procedure naturally predicts the appearance of a zero at small $|t|$ in the real part of the even amplitude as anticipated by general theorems. We would like to stress, once again, how important it would be to have at LHC both $pp$ and $p \bar p$ options for many questions connected to the general properties of high energy hadronic physics and for a check of our predictions.
How do T Tauri disks accrete? The magneto-rotational instability (MRI) supplies one means, but protoplanetary disk gas is typically too poorly ionized to be magnetically active. Here we show that the MRI can, in fact, explain observed accretion rates for the sub-class of T Tauri disks known as transitional systems. Transitional disks are swept clean of dust inside rim radii of ~10 AU. Stellar coronal X-rays ionize material in the disk rim, activating the MRI there. Gas flows from the rim to the star, at a rate limited by the depth to which X-rays ionize the rim wall. The wider the rim, the larger the surface area that the rim wall exposes to X-rays, and the greater the accretion rate. Interior to the rim, the MRI continues to transport gas; the MRI is sustained even at the disk midplane by super-keV X-rays that Compton scatter down from the disk surface. Accretion is therefore steady inside the rim. Blown out by radiation pressure, dust largely fails to accrete with gas. Contrary to what is usually assumed, ambipolar diffusion, not Ohmic dissipation, limits how much gas is MRI-active. We infer values for the transport parameter alpha on the order of 0.01 for GM Aur, TW Hyd, and DM Tau. Because the MRI can only afflict a finite radial column of gas at the rim, disk properties inside the rim are insensitive to those outside. Thus our picture provides one robust setting for planet-disk interaction: a protoplanet interior to the rim will interact with gas whose density, temperature, and transport properties are definite and decoupled from uncertain initial conditions. Our study also supplies half the answer to how disks dissipate: the inner disk drains from the inside out by the MRI, while the outer disk photoevaporates by stellar ultraviolet radiation.
We study Markov chains formed by squared singular values of products of truncated orthogonal, unitary, symplectic matrices (corresponding to the Dyson index $\beta = 1,2,4$ respectively) where time corresponds to the number of terms in the product. More generally, we consider the $\beta$-Jacobi product process obtained by extrapolating to arbitrary $\beta > 0$. When the time scaling is preserved, we show that the global fluctuations are jointly Gaussian with explicit covariances. For time growing linearly with matrix size, we show convergence of moments after suitable rescaling. When $\beta = 2$, our results imply that the right edge converges to a process which interpolates between the Airy point process and a deterministic configuration. This process connects a time-parametrized family of point processes appearing in the works of Akemann-Burda-Kieburg and Liu-Wang-Wang across time. In the arbitrary $\beta > 0$ case, our results show tightness of the particles near the right edge. The limiting moment formulas correspond to expressions for the Laplace transform of a conjectural $\beta$-generalization of the interpolating process.
The bright, nearby (z=0.1685) gamma-ray burst of 29 March 2003 has presented us with the first opportunity to directly image the expansion of a GRB. This burst reached flux density levels at centimeter wavelengths more than 50 times brighter than any previously studied event. Here we present the results of a VLBI campaign using the VLBA, VLA, Green Bank, Effelsberg, Arecibo, and Westerbork telescopes that resolves the radio afterglow of GRB 030329 and constrains its rate of expansion. The size of the afterglow is found to be \~0.07 mas (0.2 pc) 25 days after the burst, and 0.17 mas (0.5 pc) 83 days after the burst, indicating an average velocity of 3-5 c. This expansion is consistent with expectations of the standard fireball model. We measure the projected proper motion of GRB 030329 in the sky to <0.3 mas in the 80 days following the burst. In observations taken 52 days after the burst we detect an additional compact component at a distance from the main component of 0.28 +/- 0.05 mas (0.80 pc). The presence of this component is not expected from the standard model.
Ice is one of the most important and interesting molecular crystals exhibiting a rich and evolving phase diagram. Recent discoveries mean that there are now twenty distinct polymorphs; a structural diversity that arises from a delicate interplay of hydrogen bonding and van der Waals dispersion forces. This wealth of structures provides a stern test of electronic structure theories, with Density Functional Theory (DFT) often not able to accurately characterise the relative energies of the various ice polymorphs. Thanks to recent advances that enable the accurate and efficient treatment of molecular crystals with Diffusion Monte Carlo (DMC), we present here the DMC-ICE13 dataset; a dataset of lattice energies of 13 ice polymorphs. This dataset encompasses the full structural complexity found in the ambient and high-pressure molecular ice polymorphs and when experimental reference energies are available our DMC results deliver sub-chemical accuracy. Using this dataset we then perform an extensive benchmark of a broad range of DFT functionals. Of the functionals considered, we find revPBE-D3 and RSCAN to reproduce reference absolute lattice energies with the smallest error, whilst optB86b-vdW and SCAN+rVV10 have the best performance on the relative lattice energies. Our results suggest that a single functional achieving reliable performance for all phases is still missing, and that care is needed in the selection of the most appropriate functional for the desired application. The insights obtained here may also be relevant to liquid water and other hydrogen bonded and dispersion bonded molecular crystals.