ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce a new interacting particles model with blocking and pushing interactions. Particles evolve on the positive line jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q. We show that the model involves a Pieri-type formula for the orthogonal group. We prove that the two extreme cases - q=0 and q=1 - lead respectively to a random tiling model studied by Borodin and Kuan and to a random matrix model.
Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.
The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian. In this work the PQSCHA is reformulated in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the olomorphic path integral for the Weyl symbol of the density matrix, makes it possible to directly approach general Hamiltonians given in terms of bosonic creation and annihilation operators.
We present new off-shell formulations for the massive superspin-3/2 multiplet. In the massless limit, they reduce respectively to the old minimal (n=-1/3) and non-minimal ($n\neq -1/3, 0$) linearized formulations for 4D N=1 supergravity. Duality transformations, which relate the models constructed, are derived.
We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible than previous theorems along the same lines. We derive several applications. For instance we show that any irreducible, odd, essentially self-dual, regular, weakly compatible system of l-adic representations of the absolute Galois group of a totally real field is potentially automorphic, and hence is pure and its L-function has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.
The anomalous dimensions of high-twist operators in deeply inelastic scattering ($\gamma_{2n}$) are calculated in the limit when the moment variable $N \rightarrow 1$ (or $x_B\rightarrow 0$) and at large $Q^2$ (the double logarithmic approximation) in perturbative QCD. We find that the value of $\gamma_{2n}(N-1)$ in this approximation behaves as ${N_c \alpha_S \over \pi (N-1)} n^2(1 + {\delta \over 3} (n^2-1))$ where $\delta \approx 10^{-2}$. This implies that the contributions of the high-twist operators give rise to an earlier onset of shadowing than was estimated before. The derivation makes use of a Pomeron exchange approximation, with the Pomerons interacting attractively. We find that they behave as a system of fermions.
We present strong evidence that the broad, diffuse interstellar bands (DIBs) at 4881 and 5450\,\AA are caused by the $B\,^1$B$_1$\,$\leftarrow$\,$X\,^1$A$_1$ transition of H$_2$CCC (l-C$_3$H$_2$). The large widths of the bands are due to the short lifetime of the $B\,^1$B$_1$ electronic state. The bands are predicted from absorption measurements in a neon matrix and observed by cavity ring-down in the gas phase and show exact matches to the profiles and wavelengths of the two broad DIBs. The strength of the 5450\,\AA DIB leads to a l-C$_3$H$_2$ column density of $\sim5\times10^{14}$ cm$^{-2}$ towards HD\,183143 and $\sim2\times10^{14}$\,cm$^{-2}$ to HD\,206267. Despite similar values of $E$($B-V$), the 4881 and 5450\,\AA DIBs in HD\,204827 are less than one third their strength in HD\,183143, while the column density of interstellar C$_3$ is unusually high for HD\,204827 but undetectable for HD\,183143. This can be understood if C$_3$ has been depleted by hydrogenation to species such as l-C$_3$H$_2$ towards HD\,183143. There are also three rotationally resolved sets of triplets of l-C$_3$H$_2$ in the 6150$-$6330\,\AA region. Simulations, based on the derived spectroscopic constants and convolved with the expected instrumental and interstellar line broadening, show credible coincidences with sharp, weak DIBs for the two observable sets of triplets. The region of the third set is too obscured by the $\alpha$-band of telluric O$_2$.
We argue that the interpretation of the calorimetric data for disordered quantum antiferromagnets Tl$_{1-x}$K$_x$CuCl$_3$ in terms of Bose Glass physics by F. Yamada {\it et al.} in [Phys. Rev. B {\bf 83}, 020409(R) (2011)] is not unambiguous. A consistent analysis shows no difference in the crossover critical index for the disorder-free TlCuCl$_3$ and its disordered derivatives. Furthermore, we question the very existence of a proper field-induced thermodynamic phase transition in Tl$_{1-x}$K$_x$CuCl$_3$.
This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching color qubit preparation fidelity close to unity. We present the generalized rotation operator related to the DFG process, a methodology for the device design, and qubit preparation fidelity results as a function of user-accessible parameters.
The role of neutrinos in stars is introduced for students with little prior astrophysical exposure. We begin with neutrinos as an energy-loss channel in ordinary stars and conversely, how stars provide information on neutrinos and possible other low-mass particles. Next we turn to the Sun as a measurable source of neutrinos and other particles. Finally we discuss supernova (SN) neutrinos, the SN 1987A measurements, and the quest for a high-statistics neutrino measurement from the next nearby SN. We also touch on the subject of neutrino oscillations in the high-density SN context.
Recently, Giorgio Fusco and the author studied the system {\Delta}u - W_u (u) = 0 for a class of potentials that possess several global minima and are invariant under a general finite reflection group, and established existence of equivariant solutions connecting the minima in certain directions at infinity, together with an estimate. In this paper a new proof is given which, in particular, avoids the introduction of a pointwise constraint in the minimization process.
Shopping behaviour analysis through counting and tracking of people in shop-like environments offers valuable information for store operators and provides key insights in the stores layout (e.g. frequently visited spots). Instead of using extra staff for this, automated on-premise solutions are preferred. These automated systems should be cost-effective, preferably on lightweight embedded hardware, work in very challenging situations (e.g. handling occlusions) and preferably work real-time. We solve this challenge by implementing a real-time TensorRT optimized YOLOv3-based pedestrian detector, on a Jetson TX2 hardware platform. By combining the detector with a sparse optical flow tracker we assign a unique ID to each customer and tackle the problem of loosing partially occluded customers. Our detector-tracker based solution achieves an average precision of 81.59% at a processing speed of 10 FPS. Besides valuable statistics, heat maps of frequently visited spots are extracted and used as an overlay on the video stream.
Accretion powers relativistic jets in GRBs, similarly to other jet sources. Black holes that are at heart of long GRBs, are formed as the end product of stellar evolution. At birth, some of the black holes must be very rapidly spinning, to be able to power the GRBS. In some cases, the black holes may be born without formation of a disk/jet engine, and then the star will collapse without an electromagnetic transient. In this proceeding, we discuss the conditions for launching variable jets from the magnetized disk in an arrested state. We also discuss properties of collapsing massive stars as progenitors of GRBs, and the conditions which must be satisfied for the star in order for the collapsar to produce a bright gamma-ray transient. We find that the black hole rotation is further affected by self-gravity of the collapsing matter. Finally, we comment on the properties of the accretion disk under extreme conditions of nuclear densities and temperatures, while it can contribute to the kilonova accompanying short GRBs.
Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits, usually require the full measurement statistics, which can be challenging to access. In this work, we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources, and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial mode demultiplexing. For demultiplexing, our method is optimal, i.e. it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity and on the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise.
We investigate shear strength properties of wet granular materials in the pendular state (i.e. the state where the liquid phase is discontinuous) as a function of water content. Sand and glass beads were wetted and tested in a direct shear cell and under various confining pressures. In parallel, we carried out three-dimensional molecular dynamics simulations by using an explicit equation expressing capillary force as a function of interparticle distance, water bridge volume and surface tension. We show that, due to the peculiar features of capillary interactions, the major influence of water content over the shear strength stems from the distribution of liquid bonds. This property results in shear strength saturation as a function of water content. We arrive at the same conclusion by a microscopic analysis of the shear strength. We propose a model that accounts for the capillary force, the granular texture and particle size polydispersity. We find fairly good agreement of the theoretical estimate of the shear strength with both experimental data and simulations. From numerical data, we analyze the connectivity and anisotropy of different classes of liquid bonds according to the sign and level of the normal force as well as the bond direction. We find that weak compressive bonds are almost isotropically distributed whereas strong compressive and tensile bonds have a pronounced anisotropy. The probability distribution function of normal forces is exponentially decreasing for strong compressive bonds, a decreasing power-law function over nearly one decade for weak compressive bonds and an increasing linear function in the range of tensile bonds. These features suggest that different bond classes do not play the same role with respect to the shear strength.
We present a large scale survey of life-times for spontaneous fission in the regime of super-heavy elements (SHE), i.e. nuclei with Z=104-122. This is done on the basis of the Skyrme-Hartree-Fock model. The axially symmetric fission path is computed using a quadrupole constraint. Self-consistent cranking is used for the collective masses and associated quantum corrections. The actual tunneling probability is estimated by the WKB approximation. Three typical Skyrme forces are used to explore the sensitivity of the results. Benchmarks in the regime Z=104-108 show an acceptable agreement. The general systematics reflects nicely the islands of shell stabilization and the crossover from $\alpha$-decay to fission for the decay chains from the region of Z/N=118/176.
Quantum information resources quantified by non-zero discord are ubiquitous for the continuous-variables bipartite systems. Complementary to this, we formally construct a model characterized by zero two-way discord for arbitrarily long time interval. The model is classical in the sense it does not support quantum information processing. We point out some interesting physical features of the model.
We propose a general theoretical scheme for the investigation of light emitted from nano- and micrometric structures of arbitrary shape and composition. More specifically, the proposed fully three-dimensional approach allows to derive the light-intensity distributions around the emitting structures and their modifications in the presence of nearby scattering objects. Our analysis allows to better identify the non-trivial relationship between near-field images and fluorescent objects.
We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential energies of atomic groups that make up the total potential energy. It is shown that in the thermodynamic limit, the Born term, which depends on the second derivatives of potential energy, can be expressed exactly in terms of equilibrium averages that involve two types of atomic-group virials. As a result, the new form of the Born term involves only first derivatives of either atomic-group or total potential energies. The derived elastic constant expressions involving the two forms of the Born terms are tested and compared using molecular-dynamics simulations of crystalline argon and silicon. For both materials, the elastic constants obtained using the two forms of the Born term are in good agreement. In particular, the new form of the Born term converges to the same value as the original Born term but at a slower rate. The results for silicon also agree well with the results from the previous molecular-dynamics studies.
We study spin relaxation and dynamics of collective spin excitations in correlated double--exchange ferromagnets. For this, we introduce an expansion of the Green's functions equations of motion that treats non--perturbativerly all correlations between a given number of spin and charge excitations and becomes exact within a sub--space of states. Our method treats relaxation beyond Fermi's Golden Rule while recovering previous variational results for the spin--wave dispersion. We find that the momentum dependence of the spin--wave dephasing rate changes qualitatively due to the on--site Coulomb interaction, in a way that resembles experiment, and depends on its interplay with the magnetic exchange interaction and itinerant spin lifetime. We show that the collective spin relaxation and its dependence on the carrier concentration depends sensitively on three--body correlations between a spin excitation and a Fermi sea electron and hole. The above spin dynamics can be controlled via the itinerant carrier population.
We calculate the gravitational correction to the phase difference between neutrino mass eigenstates. There is a number of papers, where this correction was calculated for the spherically symmetric gravitational field described by the Schwarzschild metric. The results of these papers differ from each other. Our result is close to that of Bhattachary, Habib and Mottola (see ref. [3,6]) and differs only by a coefficient: our correction is twice smaller.
We study a group action on permutations due to Foata and Strehl and use it to prove that the descent generating polynomial of certain sets of permutations has a nonnegative expansion in the basis $\{t^i(1+t)^{n-1-2i}\}_{i=0}^m$, $m=\lfloor (n-1)/2 \rfloor$. This property implies symmetry and unimodality. We prove that the action is invariant under stack-sorting which strengthens recent unimodality results of B\'ona. We prove that the generalized permutation patterns $(13-2)$ and $(2-31)$ are invariant under the action and use this to prove unimodality properties for a $q$-analog of the Eulerian numbers recently studied by Corteel, Postnikov, Steingr\'{\i}msson and Williams.   We also extend the action to linear extensions of sign-graded posets to give a new proof of the unimodality of the $(P,\omega)$-Eulerian polynomials of sign-graded posets and a combinatorial interpretations (in terms of Stembridge's peak polynomials) of the corresponding coefficients when expanded in the above basis.   Finally, we prove that the statistic defined as the number of vertices of even height in the unordered decreasing tree of a permutation has the same distribution as the number of descents on any set of permutations invariant under the action. When restricted to the set of stack-sortable permutations we recover a result of Kreweras.
The geometry of the dust distribution within the inner regions of Active Galactic Nuclei (AGN) is still a debated issue and relates directly with the AGN unified scheme. Traditionally, models discussed in the literature assume one of two distinct dust distributions in what is believed to be a toroidal region around the Supermassive Black Holes: a continuous distribution, customarily referred to as smooth, and a concentration of dust in clumps or clouds, referred to as clumpy.   In this paper we perform a thorough comparison between two of the most popular models in the literature, namely the smooth models by Fritz. et al. 2006 and the clumpy models by Nenkova et al. 2008a, in their common parameters space. Particular attention is paid to the silicate features at ~9.7 and ~18 micron, the width of the infrared bump, the near-infrared index and the luminosity at 12.3 micron, all previously reported as possible diagnostic tools to distinguish between the two dust distributions. We find that, due to the different dust chemical compositions used in the two models, the behaviour of the silicate features at 9.7 and 18 micron is quite distinct between the two models. The width of the infrared bump and the peak of the infrared emission can take comparable values, their distributions do, however, vary. The near-infrared index is also quite different, due partly to the primary sources adopted by the two models. Models with matched parameters do not produce similar SEDs and virtually no random parameter combinations can result in seemingly identical SEDs.
We construct a new analytic solution of Einstein-Born-Infeld-dilaton theory in the presence of Liouville-type potentials for the dilaton field. These solutions describe dilaton black holes with nontrivial topology and nonlinear electrodynamics. Black hole horizons and cosmological horizons in these spacetimes, can be a two-dimensional positive, zero or negative constant curvature surface. The asymptotic behavior of these solutions are neither flat nor (A)dS. We calculate the conserved and thermodynamic quantities of these solutions and verify that these quantities satisfy the first law of black hole thermodynamics.
We present optical, near-infrared, and radio observations of the afterglow of GRB 120521C. By modeling the multi-wavelength dataset, we derive a photometric redshift of z~6.0, which we confirm with a low signal-to-noise ratio spectrum of the afterglow. We find that a model with a constant-density environment provides a good fit to the afterglow data, with an inferred density of 0.05/cm^3. The radio observations reveal the presence of a jet break at 7 d, corresponding to a jet opening angle of ~ 3 deg. The beaming-corrected gamma-ray and kinetic energies are both ~ 3e50 erg. We quantify the uncertainties in our results using a detailed Markov Chain Monte Carlo analysis, which allows us to uncover degeneracies between the physical parameters of the explosion. To compare GRB 120521C to other high-redshift bursts in a uniform manner we re-fit all available afterglow data for the two other bursts at z>6 with radio detections (GRBs 050904 and 090423). We find a jet break at ~ 15 d for GRB 090423, in contrast to previous work. Based on these three events, we find that GRBs at z>6 appear to explode in constant-density environments, and exhibit a wide range of energies and densities that span the range inferred for lower redshift bursts. On the other hand, we find a hint for narrower jets in the z>6 bursts, potentially indicating a larger true event rate at these redshifts. Overall, our results indicate that long GRBs share a common progenitor population at least to z~8.
Accretion disks around supermassive black holes have regions where the Rosseland mean opacity can be much larger than the electron scattering opacity primarily due to the large number of bound-bound transitions in iron. We study the effects of this iron opacity "bump" on the thermal stability and vertical structure of radiation pressure dominated accretion disks, utilizing three dimensional radiation magneto-hydrodynamic simulations in the local shearing box approximation. The simulations self-consistently calculate the heating due to MHD turbulence caused by magneto-rotational instability and radiative cooling by using the radiative transfer module based on a variable Eddington tensor in Athena. For a $5\times 10^8$ solar mass black hole with $\sim 3\%$ of the Eddington luminosity, a model including the iron opacity bump maintains its structure for more than $10$ thermal times without showing significant signs of thermal runaway. In contrast, if only electron scattering and free-free opacity are included as in the standard thin disk model, the disk collapses on the thermal time scale. The difference is caused by a combination of 1) an anti-correlation between the total optical depth and the temperature, and 2) enhanced vertical advective energy transport. These results suggest that the iron opacity bump may have a strong impact on the stability and structure of AGN accretion disks, and may contribute to a dependence of AGN properties on metallicity. Since this opacity is relevant primarily in UV emitting regions of the flow, it may help to explain discrepancies between observation and theory that are unique to AGNs.
Micromagnetic simulation results on dynamic hysteresis loops of clusters of iron oxide nanoparticles (NPs) with internal structure composed of nanorods are compared with the widely used macrospin approximation. Such calculations allowing for nanorod-composed NPs is facilitated by a previously developed coarse-graining method based on the renormalization group approach. With a focus on applications to magnetic hyperthermia, we show that magnetostatic interactions improve the heating performance of NPs in chains and triangles, and reduce heating performance in fcc arrangements. Hysteresis loops of triangular and fcc systems of complex NPs are not recovered within the macrospin approximation, especially at smaller interparticle distances. For triangular arrangements, the macrospin approximation predicts that magnetostatic interactions reduce loop area, in contrast to the complex NP case. An investigation of the local hysteresis loops of individual NPs and macrospins in clusters reveals the impact of the geometry of their neighbours on individual versus collective magnetic response, inhomogenous heating within clusters, and further differences between simulating NPs with internal structure and the use of the macrospin approximation. Capturing the internal physical and magnetic structure of NPs is thus important for some applications.