ShantanuT01/DACTYL-Pretraining huggingface dataset:
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible rankings in an unfolding model and (ii) the number of ranking patterns generated by unfolding models. The paper is mostly expository but also contains some new results such as simple upper and lower bounds for the number of ranking patterns in the unidimensional case.
Jet precessions are widely involved in astrophysical phenomena from galaxies to X-ray binaries and gamma-ray bursts (GRBs). Polarization presents a unique probe of the magnetic fields in GRB jets. The precession of GRBs relativistic jets will change the geometry within the observable emitting region of the jet, which can potentially affect the polarization of the afterglow. In this paper, we take into account jet precession to study the polarization evolution and corresponding light curves in GRB early optical afterglows with ordered and random magnetic field geometries. We find that the jet precession in long-lived engines can significantly reduce the polarization degree (PD) regardless of the magnetic field structure. The strongest PD attenuation is found when the line of sight is aligned with the precession axis. Our results show that jet precession can provide new insight into the low PD measured in the early optical afterglows of GRBs.
For a smooth group scheme $G$ over an extension of $\mathbf{Z}_p$ such that the generic fiber of $G$ is reductive, we study the generic fiber of the Galois deformation ring for a $G$-valued mod $p$ representation of the absolute Galois group of a finite extension of $\mathbf{Q}_\ell$ with $\ell \neq p$. In particular, we show it admits a regular dense open locus, and that it is equidimensional of dimension $\dim G$.
Currently, the only known way to obtain experimental information about the space-time structure of a heavy-ion collision is through 2-particle momentum correlations. Azimuthally sensitive HBT interferometry (Hanbury Brown-Twiss intensity interferometry) can complement elliptic flow measurements by constraining the spatial deformation of the source and its time evolution. Performing these measurements on photons allows us to access the fireball evolution at earlier times than with hadrons. Using ideal hydrodynamics to model the space-time evolution of the collision fireball, we explore theoretically various aspects of 2-photon intensity interferometry with transverse momenta up to 2 GeV, in particular the azimuthal angle dependence of the HBT radii in non-central collisions. We highlight the dual nature of thermal photon emission, in both central and non-central collisions, resulting from the superposition of QGP and hadron resonance gas photon production. This signature is present in both the thermal photon source function and the HBT radii extracted from Gaussian fits of the 2-photon correlation function.
Based on the multiband semiconductor Bloch equations a microscopic approach to high-harmonic generation in crystalline solids which is able to properly describe degenerate bands and band crossings is presented and analyzed. It is well-known that numerical band structure calculations typically provide electronic wave functions with an undetermined k-dependent phase which results in matrix elements which contain arbitrary k-dependent phases. In addition, such approaches usually mix degenerate bands and bands with an energy difference smaller than the numerical precision in an arbitrary way for each point in k-space. These ambiguities are problematic if one considers the dynamics induced by electric fields since the matrix elements of the position operator involve a derivative of the wave functions with respect to k. When the light-matter interaction is described in the length gauge, the problem of arbitrary phases and degenerate subspace mixing of Bloch states is solved by adopting a smooth gauge transformation along the field direction. The results obtained within this method are validated by comparing with calculations in the velocity gauge. Although we obtain in both gauges the same overall result, the length gauge is advantageous since it converges with a smaller number of bands and thus requires significantly less numerical effort than the velocity gauge. Also an unique distinction between inter- and intraband contributions and thus an instructive physical interpretation is possible in the length gauge whereas in the velocity gauge this is unclear. The computed polarization-direction-dependent high-harmonic spectra agree well with experimental data reported for GaAs. Furthermore, it is demonstrated that, under proper conditions, the Berry curvature is largely responsible for the even-order harmonics which are polarized perpendicular to the driving field.
ATK-ForceField is a software package for atomistic simulations using classical interatomic potentials. It is implemented as a part of the Atomistix ToolKit (ATK), which is a Python programming environment that makes it easy to create and analyze both standard and highly customized simulations. This paper will focus on the atomic interaction potentials, molecular dynamics, and geometry optimization features of the software, however, many more advanced modeling features are available. The implementation details of these algorithms and their computational performance will be shown. We present three illustrative examples of the types of calculations that are possible with ATK-ForceField: modeling thermal transport properties in a silicon germanium crystal, vapor deposition of selenium molecules on a selenium surface, and a simulation of creep in a copper polycrystal.
In this paper we consider the stability for a type of stochastic McKean-Vlasov equations with non-Lipschitz coefficients. First, sufficient conditions are given for the exponential stability of the second moments for their solutions in terms of a Lyapunov function. Then we weaken the conditions and furthermore obtain exponentially 2-ultimate boundedness of their solutions. After this, the almost surely asymptotic stability of their solutions is proved. Finally we give an example to motivate the choice of Lyapunov functions.
We consider extensions of the Dirac equation with mass terms m1+i*gamma5*m2 and i*m_1+gamma*m2. The corresponding Hamiltonians are Hermitian and pseudo-Hermitian ("gamma5 Hermitian"), respectively. The fundamental spinor solutions for all generalized Dirac equations are found in the helicity basis and brought into concise analytic form. We postulate that the time-ordered product of field operators should yield the Feynman propagator (i*epsilon prescription), and we also postulate that the tardyonic as well as tachyonic Dirac equations should have a smooth massless limit. These postulates lead to sum rules that connect the form of the fundamental field anticommutators with the tensor sums of the fundamental plane-wave eigenspinors and the projectors over positive-energy and negative-energy states. In the massless case, the sum rules are fulfilled by two egregiously simple, distinguished functional forms. The first sum rule remains valid in the case of a tardyonic theory and leads to the canonical massive Dirac field. The second sum rule is valid for a tachyonic mass term and leads to a natural suppression of the right-handed helicity states for tachyonic particles, and left-handed helicity states for tachyonic spin-1/2 antiparticles. When applied to neutrinos, the theory contains a free tachyonic mass parameter. Tachyons are known to be repulsed by gravity. We discuss a possible role of a tachyonic neutrino as a contribution to the accelerated expansion of the Universe ("dark energy").
In this article, we calculate the period determinant of an irrgular singular connection d+dy on the legendre curve U: y^2 =x(x-1)(x- lambda). We calculate its de Rham cohomology and the cycles in the homology of the dual connection and describe the period matrix. Terasoma's work is introduced to approximate the direct image connection pi_*(\nabla) by a sequence of regular connections as an intermediate step where pi:U -> A^1(y), (x,y) |-> y. Finally, we will compare the period obtained by this approximation of the direct image connection and the original.
A generalized connection, including Christoffel coefficients, torsion, non-metricity tensor and metric-asymmetricity object, is analyzed according to the Schouten classification. The inverse structure matrix is found in the linearized regime, autoparallel trajectories are defined and the contribution of the components of the connection are clarified at first-order approximation.
Magnetic fields are a good tracer for gas compression by shock waves, which can be caused by interaction of star-formation driven outflows from individual star formation sites as described in the chimney model. We study the magnetic field structure in the central part of the nuclear starburst galaxy NGC 253 with spatial resolutions between 40 and 150 pc to detect any filamentary emission associated with the nuclear outflow. New VLA observations at 3 cm with 7.5" resolution were combined with archive data at 20 and 6 cm. We find filamentary radio continuum emission in a geometrical distribution that we interpret as the boundary of the northwestern nuclear outflow cone. The scaleheight of the continuum emission is 150+/-20 pc, regardless of the observing frequency. The equipartition magnetic field strength is 46+/-10 microG for the total field and 21+/-5 microG for the regular field in the filaments. The ordered magnetic field is aligned along the filaments, in agreement with amplification due to compression. The perpendicular diffusion coefficient across the filaments is kappa_perp = 1.5 x 10^28 cm^2 s^-1 E(GeV)^(0.5+/-0.7). In the SE part of the nuclear outflow cone the magnetic field is pointing away from the disc in form of a helix, with an azimuthal component increasing up to at least 1200 pc height, where it is about equal to the total component. The ordered magnetic field in the disc is anisotropic within a radius of 2.2 kpc. At larger radii, the large-scale field is regular and of even parity. The magnetic field is able to collimate the outflow, which can explain the observed small opening angle of ~26 degree. Due to angular momentum conservation, the field lines are frozen into the plasma and are wound up into a helix. Strong adiabatic losses of the cosmic-ray electrons can partly explain why the radio luminosity of the nucleus lies below the radio-FIR correlation.
We study three-leg antiferromagnetic Heisenberg model with the periodic boundary conditions in the rung direction. Since the rungs form regular triangles, spin frustration is induced. We use the density-matrix renormalization group method to investigate the ground state. We find that the spin excitations are always gapped to remove the spin frustration as long as the rung coupling is nonzero. We also visibly confirm spin-Peierls dimerization order in the leg direction. Both the spin gap and the dimerization order are basically enhanced as the rung coupling increases.
A general coupling of the Goldstino to the matter field and the weak gravitational field is constructed based on the standard and the nonlinear Volkov-Akulov realization of SUSY. The resulting Lagrangian, which is invariant under SUSY transformations, can give rise to explicit interactions which couple the helicity +-1/2 states of the gravitino with the gravitational field as well as the matter field.
We used high-quality Kepler photometry and spectroscopic data to investigate the Kepler binary candidate KIC 5988140. Using the spectrum synthesis method, we derived the fundamental parameters Teff, log g, [M/H], and v.sini and the abundances. Frequency analyses of both the photometric and the spectroscopic data were performed, revealing the same two dominant frequencies (F_1=0.688 and F_2=0.344 c/d). We also detected in the photometry the signal of nine more, significant frequencies located in the typical range of Delta Scuti pulsation. The light and radial velocity curves follow a similar, stable double-wave pattern which are not exactly in anti-phase but show a relative phase shift of about 0.1 period between the moment of minimum velocity and that of maximum light. We considered three different scenarios: binarity, co-existence of both Gamma Doradus and Delta Scuti pulsations and rotation of the stellar surface with an axisymmetric intensity distribution. However, none of these scenarios is capable of explaining all of the characteristics of the observed variations. We confirm the occurrence of various independent Delta Scuti-type pressure modes in the Kepler light curve. With respect to the low-frequency content, however, we argue that the physical cause of the remaining light and radial velocity variations of this late A-type star remains unexplained by any of the presently considered scenarios.
Context: Hadronic models, involving matter (proton or nuclei) acceleration in blazar jets, imply high energy photon and neutrino emissions due to interactions of high-energy protons with matter and/or radiation in the source environment. Aims: This paper shows that the sensitivity of the IceCube neutrino telescope in its 40-string configuration (IC-40) is already at the level of constraining the parameter space of purely hadronic scenarios of activity of blazars. Methods: Assuming that the entire source power originates from hadronic interactions, and assuming that the models describe the data, we estimate the expected neutrino flux from blazars based on the observed gamma-ray flux by Fermi, simultaneously with IC-40 observations. We consider two cases separately to keep the number of constrainable parameters at an acceptable level: proton-proton or proton-gamma interactions are dominant. Comparing the IC-40 sensitivity to the neutrino flux expected from some of the brightest blazars, we constrain model parameters characterizing the parent high-energy proton spectrum. Results: We find that when pp interactions dominate, some constraints on the primary proton spectrum can be imposed. For instance, for the tightest constrained source 3C 454.3, the very high energy part of the spectra of blazars is constrained to be harder than E^-2 with cut-off energies in the range of Ecut >10^18 eV. When interactions of high-energy protons on soft photon fields dominate, we can find similarly tight constraints on the proton spectrum parameters. [abridged]
Anions of the molecules ZnO, O2 and atomic Zn and O constitute mass spectra of the species sputtered from pellets of molecular solid of ZnO under Cs+ irradiation. Their normalized yields are independent of energy of the irradiating Cs+. Collision cascades cannot explain the simultaneous sputtering of atoms and molecules. We propose that the origin of the molecular sublimation, dissociation and subsequent emission is the result of localized thermal spikes induced by individual Cs+ ions. The fractal dimension of binary collision cascades of atomic recoils in the irradiated ZnO solid increases with reduction in the energy of recoils. Upon reaching the collision diameters of atomic dimensions, the space-filling fractal-like transition occurs where cascades transform into thermal spikes. These localized thermal spikes induce sublimation, dissociation and sputtering from the region. The calculated rates of the subliming and dissociating species due to localized thermal spikes agree well with the experimental results.
The isotropic diffuse $\gamma$-ray background (IGRB) has been detected by various experiments and recently the Fermi-LAT Collaboration has precisely measured its spectrum in a wide energy range. The origin of the IGRB is still unclear and we show in this paper the significative improvements that have been done, thanks to the new Fermi-LAT catalogs, to solve this mystery. We demonstrate that the $\gamma$-ray intensity and spectrum of the IGRB is fully consistent with the unresolved emission from extragalactic point sources, namely Active Galactic Nuclei and Star Forming Galaxies. We show also that the IGRB can be employed to derive sever constraints for the $\gamma$-ray emission from diffuse processes such as annihilation of Dark Matter (DM) particles. Our method is able to provide low bounds for the thermal annihilation cross section for a wide range of DM masses.
The surface brightness distribution in the majority of stellar galactic discs falls off exponentially. Often what lies beyond such a stellar disc is the neutral hydrogen gas whose distribution also follows a nearly exponential profile at least for a number of nearby disc galaxies. Both the stars and gas are commonly known to host lopsided asymmetry especially in the outer parts of a galaxy. The role of such asymmetry in the dynamical evolution of a galaxy has not been explored so far.   Following Lindblad's original idea of kinematic density waves, we show that the outer part of an exponential disc is ideally suitable for hosting lopsided asymmetry. Further, we compute the transport of angular momentum in the combined stars and gas disc embedded in a dark matter halo. We show that in a pure star and gas disc, there is a transition point where the free precession frequency of a lopsided mode, $\Omega -\kappa $, changes from retrograde to prograde and this in turn reverses the direction of angular momentum flow in the disc leading to an unphysical behaviour. We show that this problem is overcome in the presence of a dark matter halo, which sets the angular momentum flow outwards as required for disc evolution, provided the lopsidedness is leading in nature. This, plus the well-known angular momentum transport in the inner parts due to spiral arms, can facilitate an inflow of gas from outside perhaps through the cosmic filaments.
We explicitly compute the limiting transient distribution of the search-cost in the move-to-front Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a "law of large numbers for random partitions," a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting search-cost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one related to the initial ordering of the list. Our results ensure the stability of the limiting search-cost under general perturbations of the request probabilities. We provide the description of the limiting transient behavior in several examples where only the stationary regime is known, and discuss the range of validity of our scaling limit.
We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings, with and without diffusion.
The purpose of this paper is to investigate the spectral nature of the Neumann-Poincar\'e operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral resolution of the operator is derived, which shows in particular that it admits only the absolutely continuous spectrum, no singularly continuous spectrum and no pure point spectrum. We then quantitatively analyze using the spectral resolution the plasmon resonance at the absolutely continuous spectrum.
We describe an explicit symplectic resolution for the quotient singularity arising from the four-dimensional symplectic represenation of the binary tetrahedral group.
We analytically investigate the heat current $I$ and its thermal fluctuations $\Delta$ in a branching network without loops (Cayley tree). The network consists of two type of harmonic masses: vertex masses $M$ placed at the branching points where phononic scattering occurs and masses $m$ at the bonds between branching points where phonon propagation take place. The network is coupled to thermal reservoirs consisting of one-dimensional harmonic chains of coupled masses $m$. Due to impedance missmatching phenomena, both ${\cal I}$ and $\Delta$, are non-monotonic functions of the mass ratio $\mu=M/m$. In particular, there are cases where they are strictly zero below some critical value $\mu^*$.
I deduced a 3-D sunspot model that is in agreement with spectropolarimetric observations, to address the question of penumbral heating by the repetitive rise of flow channels. I performed inversions of data taken simultaneously in infrared and visible spectral lines. I used two independent magnetic components to reproduce the irregular Stokes profiles in the penumbra. I studied the averaged and individual properties of the two components. By integrating the field inclination to the surface, I developed a 3-D model of the spot from inversion results without intrinsic height information. I find that the Evershed flow is harbored by the weaker of the two field components. This component forms flow channels that show upstreams in the inner and mid penumbra, continue horizontally as slightly elevated loops throughout the penumbra, and finally bend down in the outer penumbra. I find several examples, where two or more flow channels are found along a radial cut from the umbra to the outer boundary of the spot. I find that a model of horizontal flow channels in a static background field is in good agreement with the observed spectra. The properties of the flow channels correspond very well to the simulations of Schlichenmaier et al. (1998). From the temporal evolution in intensity images and the properties of the flow channels in the inversion, I conclude that interchange convection of rising hot flux tubes in a thick penumbra still seems a possible mechanism for maintaining the penumbral energy balance.
We address the question of gravitino dark matter in the context of gauge mediated supersymmetry breaking models. A special emphasis is put on the role played by the MSSM singlet messenger in the case of SO(10) grand unification.
In the stochastic formulation of viscous hydrodynamics, the velocity of a fluid element fluctuates satisfying a similar relation to the quantum-mechanical uncertainty relation. Using a non-relativistic toy model, we show that the presence of such a velocity fluctuation increases the local anisotropy of the momentum distributions of produced hadrons, and thus the collective flow parameters such as $v_2$ is emphasized.
Shortly after the discovery of PSR J1906+0746, some hints of profile variations were already interpreted as first signs of relativistic spin-precession occuring. Using observations from the Nan\c{c}ay, Arecibo and Green Bank Radio Observatories, we report here the measurement of pulse profile and polarimetric variations. Using the Rotating Vector Model, we show that PSR J1906+0746 is likely to be an orthogonal rotator ($\alpha \simeq 80^\circ$). Fitting our polarimetric data to a precession model, we determined the geometry of the pulsar and found a wide misalignment angle ($\delta = 89_{-44}^{+85}$ deg, 95% C.L.), although the uncertainty is large. Assuming this geometry, we constructed the beam maps of both magnetic poles.