ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $W$ be the Weyl group of a simply-laced affine Kac-Moody Lie group, excepting $\tilde{A}_n$ for $n$ even. We construct a multiple Dirichlet series $Z(x_1, \ldots x_{n+1})$, meromorphic in a half-space, satisfying a group $W$ of functional equations. This series is analogous to the multiple Dirichlet series for classical Weyl groups constructed by Brubaker-Bump-Friedberg, Chinta-Gunnells, and others. It is completely characterized by four natural axioms concerning its coefficients, axioms which come from the geometry of parameter spaces of hyperelliptic curves. The series constructed this way is optimal for computing moments of character sums and L-functions, including the fourth moment of quadratic L-functions at the central point via $\tilde{D}_4$ and the second moment weighted by the number of divisors of the conductor via $\tilde{A}_3$. We also give evidence to suggest that this series appears as a first Fourier-Whittaker coefficient in an Eisenstein series on the twofold metaplectic cover of the relevant Kac-Moody group. The construction is limited to the rational function field $\mathbb{F}_q(t)$, but it also describes the $p$-part of the multiple Dirichlet series over an arbitrary global field.
Microlensing is increasingly gaining recognition as a powerful method for the detection and characterization of extra-solar planetary systems. Naively, one might expect that the probability of detecting the influence of more than one planet on any single microlensing light curve would be small. Recently, however, Griest & Safizadeh (1998) have shown that, for a subset of events, those with minimum impact parameter $u_{min} \lsim 0.1$ (high magnification events), the detection probability is nearly 100% for Jovian mass planets with projected separations in the range 0.6--1.6 of the primary Einstein ring radius $R_E$, and remains substantial outside this zone. In this Letter, we point out that this result implies that, regardless of orientation, all Jovian mass planets with separations near 0.6--1.6$R_E$ dramatically affect the central region of the magnification pattern, and thus have a significant probability of being detected (or ruled out) in high magnification events. The probability, averaged over all orbital phases and inclination angles, of two planets having projected separations within 0.6--$1.6R_E$ is substantial: 1-15% for two planets with the intrinsic orbital separations of Jupiter and Saturn orbiting around 0.3--1.0$M_\odot$ parent stars. We illustrate by example the complicated magnification patterns and light curves that can result when two planets are present, and discuss possible implications of our result on detection efficiencies and the ability to discriminate between multiple and single planets in high magnification events.
Based on original investigations into the stages of nucleation and growth of martensite, a consideration has been given to dynamic models of formation of martensite plates with a fine structure of transformation twins, which are compatible with the supersonic growth rate of martensite crystals. Along with relatively long quasi-longitudinal waves, which determine the orientation of the habit plane, the control wave process includes relatively short longitudinal waves, which act in synchronism and control the growth of the main component of a regular twin structure. Preference is given to a model containing, at the initial moment of time, the only active dynamic cell capable of periodic reproduction in the interphase region at the stage of the martensite crystal growth. Conditions providing the ratio between the components of the twin structure, which would be optimal for minimization of the transformation time, have been discussed. A transition to final deformations, which are two to three orders of magnitude larger than the threshold deformations, have been made. The calculated macroscopic morphological attributes, which were deduced from dynamic considerations, have been compared with the experimental data and crystallogeometrical calculation.
In the framework of the covariant Bethe-Salpeter formalism we calculate the amplitude of electrodisintegration of the deuteron near the threshold energy. Due to the small relative momentum of the final np-pair, the deuteron break-up process may be sufficiently described by a transition to the dominant 1S0 channel into the final state. Therefore only one unknown structure function (form factor) exists. The explicit formula for this form factor is given in terms of partial Bethe-Salpeter amplitudes. We compare our result to the usual non-relativistic calculations. The essential role of P-states as well as their possible link to mesonic exchange currents is discussed.
We measure the faint end slope of the galaxy luminosity function (LF) for cluster galaxies at 1<z<1.5 using Spitzer IRAC data. We investigate whether this slope, alpha, differs from that of the field LF at these redshifts, and with the cluster LF at low redshifts. The latter is of particular interest as low-luminosity galaxies are expected to undergo significant evolution. We use seven high-redshift spectroscopically confirmed galaxy clusters drawn from the IRAC Shallow Cluster Survey to measure the cluster galaxy LF down to depths of M* + 3 (3.6 microns) and M* + 2.5 (4.5 microns). The summed LF at our median cluster redshift (z=1.35) is well fit by a Schechter distribution with alpha[3.6] = -0.97 +/- 0.14 and alpha[4.5] = -0.91 +/- 0.28, consistent with a flat faint end slope and is in agreement with measurements of the field LF in similar bands at these redshifts. A comparison to alpha in low-redshift clusters finds no statistically significant evidence of evolution. Combined with past studies which show that M* is passively evolving out to z~1.3, this means that the shape of the cluster LF is largely in place by z~1.3. This suggests that the processes that govern the build up of the mass of low-mass cluster galaxies have no net effect on the faint end slope of the cluster LF at z<1.3.
For a rational prime $p \geq 3$ and an integer $n \geq 2$, we study the modularity of continuous 2-dimensional mod $p^n$ Galois representations of $\Gal(\bar{\Q}/\Q)$ whose residual representations are odd and absolutely irreducible. Under suitable hypotheses on the local structure of these representations and the size of their images we use deformation theory to construct characteristic 0 lifts. We then invoke modularity lifting results to prove that these lifts are modular. As an application, we show that certain unramified mod $p^n$ Galois representations arise from modular forms of weight $p^{n-1}(p-1)+1$.
New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein-Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the momentum basis is well-known from long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.
These notes describe several loop soup models and their {\it universal behaviour} in dimensions greater or equal to 3. These loop models represent certain classical or quantum statistical mechanical systems. These systems undergo phase transitions that are characterised by changes in the structures of the loops. Namely, long-range order is equivalent to the occurrence of macroscopic loops. There are many such loops, and the joint distribution of their lengths is always given by a {\it Poisson-Dirichlet distribution}.   This distribution concerns random partitions and it is not widely known in statistical physics. We introduce it explicitly, and we explain that it is the invariant measure of a mean-field split-merge process. It is relevant to spatial models because the macroscopic loops are so intertwined that they behave effectively in mean-field fashion. This heuristics can be made exact and it allows to calculate the parameter of the Poisson-Dirichlet distribution. We discuss consequences about symmetry breaking in certain quantum spin systems.
We investigate the effect of Coulomb interactions on the tunneling density of states (DOS) of granular metallic systems at the onset of Coulomb blockade regime in two and three dimensions. Using the renormalization group technique we derive the analytical expressions for the DOS as a function of temperature $T$ and energy $\epsilon$. We show that samples with the bare intergranular tunneling conductance $g^0_{\scriptscriptstyle T}$ less than the critical value $g_{\scriptscriptstyle T}^{\scriptscriptstyle C}=(1/2\pi d) \ln(E_{\scriptscriptstyle C}/\delta)$, where $E_{\scriptscriptstyle C}$ and $\delta$ are the charging energy and the mean energy level spacing in a single grain respectively, are insulators with a {\it hard gap} in the DOS at temperatures $T\to 0$. In 3d systems the critical conductance $g_{\scriptscriptstyle T}^{\scriptscriptstyle C}$ separates insulating and metallic phases at zero temperature, whereas in the granular films $g_{\scriptscriptstyle T}^{\scriptscriptstyle C}$ separates insulating states with the hard (at $g^0_{\scriptscriptstyle T}<g_{\scriptscriptstyle T}^{\scriptscriptstyle C}$) and soft (at $g^0_{\scriptscriptstyle T}>g_{\scriptscriptstyle T}^{\scriptscriptstyle C}$) gaps. The gap in the DOS begins to develop at temperatures $ T^* \sim E_{\scriptscriptstyle C} g_{\scriptscriptstyle T}^{\scriptscriptstyle 0} \exp (-2\pi d g_{\scriptscriptstyle T}^{\scriptscriptstyle 0})$ and reaches the value $\Delta \sim T^*$ at $T\to 0$.
In this paper we show that an affine space is determined by the abstract group structure of its group of regular automorphisms in the category of connected affine varieties. To prove this we study commutative subgroups of the group of automorphisms of affine varieties.
The spectroscopic variability of Arcturus hints at cyclic activity cycle and differential rotation. This could provide a test of current theoretical models of solar and stellar dynamos. To examine the applicability of current models of the flux transport dynamo to Arcturus, we compute a mean-field model for its internal rotation, meridional flow, and convective heat transport in the convective envelope. We then compare the conditions for dynamo action with those on the Sun. We find solar-type surface rotation with about 1/10th of the shear found on the solar surface. The rotation rate increases monotonically with depth at all latitudes throughout the whole convection zone. In the lower part of the convection zone the horizontal shear vanishes and there is a strong radial gradient. The surface meridional flow has maximum speed of 110 m/s and is directed towards the equator at high and towards the poles at low latitudes. Turbulent magnetic diffusivity is of the order $10^{15}$--$10^{16} {\rm cm^2/s}$. The conditions on Arcturus are not favorable for a circulation-dominated dynamo.
We study the exterior vacuum problem for first and second order stationary and axially symmetric perturbations of static bodies. The boundary conditions and their compatibility for the existence of an asymptotically flat exterior solution are discussed.
In search of a quantum phase transition between the two-dimensional ($2$D) ferromagnetism of CaCo$_{2-y}$As$_{2}$ and stripe-type antiferromagnetism in SrCo$_{2}$As$_{2}$, we rather find evidence for $1$D magnetic frustration between magnetic square Co layers. We present neutron diffraction data for Ca$_{1-x}$Sr$_{x}$Co$_{2-y}$As$_{2}$ that reveal a sequence of $x$-dependent magnetic transitions which involve different stacking of $2$D ferromagnetically-aligned layers with different magnetic anisotropy. We explain the $x$-dependent changes to the magnetic order by utilizing classical analytical calculations of a $1$D Heisenberg model where single-ion magnetic anisotropy and frustration of antiferromagnetic nearest- and next-nearest-layer exchange are all composition dependent.
The envelopes of stars near the Eddington limit are prone to various instabilities. A high Eddington factor in connection with the Fe opacity peak leads to convective instability, and a corresponding envelope inflation may induce pulsational instability. Here, we investigate the occurrence and consequences of both instabilities in models of Wolf-Rayet stars. We determine the convective velocities in the sub-surface convective zones to estimate the amplitude of the turbulent velocity at the base of the wind that potentially leads to the formation of small-scale wind structures, as observed in several WR stars. We also investigate the effect of mass loss on the pulsations of our models. We approximated solar metallicity WR stars by models of mass-losing helium stars, and we characterized the properties of convection in the envelope adopting the standard MLT. Our results show the occurrence of sub-surface convective regions in all studied models. Small surface velocity amplitudes are predicted for models with masses below 10Msun. For models with M>10Msun, the surface velocity amplitudes are of the order of 10km/s. Moreover we find the occurrence of pulsations for stars in the mass range 9-14Msun, while mass loss appears to stabilize the more massive WR stars. We confront our results with observationally derived line variabilities of 17 WN stars. The data suggest variability to occur for stars above 10Msun, which is increasing linearly with mass above this value, in agreement with our results. We further find some of our models to be unstable to radial pulsations, and predict local magnetic fields of the order of hundreds of Gauss in WR stars more massive than 10Msun. Our study relates the surface velocity fluctuations induced by sub-surface convection to the formation of clumping in the inner part of the wind. From this mechanism, we expect a stronger variability in more massive WR stars.
We construct initial data corresponding to a single perturbed Kerr black hole in vacuum. These data are defined on specific hyperboloidal ("ACMC-") slices on which the mean extrinsic curvature K asymptotically approaches a constant at future null infinity scri+. More precisely, we require that K obeys the Taylor expansion K=K0 + s^4 where K0 is a constant and s describes a compactified spatial coordinate such that scri+ is represented by s=0. We excise the singular interior of the black hole and assume a marginally outer trapped surface as inner boundary of the computational domain. The momentum and Hamiltonian constraints are solved by means of pseudo-spectral methods and we find exponential rates of convergence of our numerical solutions. Some physical properties of the initial data are studied with the calculation of the Bondi Mass, together with a multipole decomposition of the horizon. We probe the standard picture of gravitational collapse by assessing a family of Penrose-like inequalities and discuss in particular their rigidity aspects. Dynamical evolutions are planned in a future project.
The X-ray light-curves of the recurring outbursts observed in low-mass X-ray binaries provide strong test beds for constraining (still) poorly understood disc-accretion processes. These light-curves act as a powerful diagnostic to probe the physics behind the mechanisms driving mass inflow and outflow in these binary systems. We have thus developed an innovative methodology, combining a foundation of Bayesian statistics, observed X-ray light-curves, and accretion disc theory. With this methodology, we characterize the angular-momentum (and mass) transport processes in an accretion disc, as well as the properties of the X-ray irradiation-heating that regulates the decay from outburst maximum in low-mass X-ray transients. We recently applied our methodology to the Galactic black-hole low-mass X-ray binary population, deriving from their lightcurves the first-ever quantitative measurements of the $\alpha$-viscosity parameter in these systems \citep{tetarenko2018}. In this paper, we continue the study of these binaries, using Bayesian methods to investigate the X-ray irradiation of their discs during outbursts of strong accretion. We find that the predictions of the disc-instability model, assuming a source of X-ray irradiation proportional to the central accretion rate throughout outburst, do not adequately describe the later stages of BH-LMXB outburst light-curves. We postulate that the complex and varied light-curve morphology observed across the population is evidence for irradiation that varies in time and space within the disc, throughout individual transient outbursts. Lastly, we demonstrate the robustness of our methodology, by accurately reproducing the synthetic model light-curves computed from numerical codes built to simulate accretion flows in binary systems.
We consider a model of quantum electrodynamics (QED) on a graph. The one-loop divergences in the model are investigated by use of the background field method.
We propose a model to explore the dynamics of spin-systems coupled by exchange interaction to the conduction band electrons of a semiconductor material that forms the channel in a ferromagnet/semiconductor/ferromagnet spin-valve structure. We show that recent observation of the novel transient transport signature in a MnAs/GaAs/MnAs spin-valve structure with paramagnetic Mn impurities [D. Saha et al., Phys. Rev. Lett., 100, 196603 (2008)] can be quantitatively understood in terms of current driven dynamical polarization of Mn spins. Using our model of spin polarized transport through Schottky barriers at the two ferromagnet/semiconductor junctions in a spin-valve structure and a dynamical equation describing the paramagnetic impurities coupled to conduction band electrons we explain the scaling behaviour of observed transient features such as the magnitude and time-scale with temperature.
We combine HI 21cm observations of the Milky Way, M31, and the local galaxy population with QSO absorption-line measurements to geometrically model the three-dimensional distribution of infalling neutral gas clouds (HVCs) in the extended halos of low-redshift galaxies. We demonstrate that the observed distribution of HVCs around the Milky Way and M31 can be modeled by a radial exponential decline of the mean HI volume filling factor in their halos. Our model suggests a characteristic radial extent of HVCs of R_halo=50 kpc, a total HI mass in HVCs of ~10^8 M_sun, and a neutral-gas-accretion rate of ~0.7 M_sun/yr for M31/Milky-Way-type galaxies. Using a Holmberg-like luminosity scaling of the halo size of galaxies we estimate R_halo=110 kpc for the most massive galaxies. The total absorption-cross section of HVCs at z=0 most likely is dominated by galaxies with total HI masses between 10^8.5 and 10^10 M_sun. Our model indicates that the HI disks of galaxies and their surrounding HVC population can account for 30-100 percent of intervening QSO absorption-line systems with log N(HI)>17.5 at z=0. We estimate that the neutral-gas accretion rate density of galaxies at low redshift from infalling HVCs is dM_HI/dt/dV=0.022 M_sun/yr/Mpc^3, which is close to the measured star-formation rate density in the local Universe. HVCs thus may play an important role for the on-going formation and evolution of galaxies.
A non-equilibrium thermodynamics model able to analyze the combined effect of diffusion and adsorption in porous materials is proposed. The model considers the coupled dynamics of the diffusive phase, described by a diffusion type equation, and the adsorbed phase governed by a generalized Langmuir equation. It is shown that the combination of diffusion and adsorption can be treated as diffusion in an effective medium, with an effective diffusion coefficient depending on the characteristics of the adsorption kinetics. The interplay between these effects leads to the appearance of different regimes in which the effective diffusion coefficient exhibits peculiar behaviours such as a decrease due to the presence of the adsorption process and a non-monotonous behavior resulting from particle interactions. We outline applications of the model developed to diffusion in porous materials such as zeolites and bentonites, and to engineered highly porous materials.
This paper introduces a new empirical model for the rotational evolution of Sun-like stars -- those with surface convection zones and non-convective interior regions. Previous models do not match the morphology of observed (rotation period)-color diagrams, notably the existence of a relatively long-lived "C-sequence" of fast rotators first identified by Barnes(2003). This failure motivates the Metastable Dynamo Model (MDM) described here. The MDM posits that stars are born with their magnetic dynamos operating in a mode that couples very weakly to the stellar wind, so their (initially very short) rotation periods at first change little with time. At some point, this mode spontaneously and randomly changes to a strongly-coupled mode, the transition occurring with a mass-dependent lifetime that is of order 100 MYr. I show that with this assumption, one can obtain good fits to observations of young clusters, particularly for ages of 150 MYr to 200 MYr. Previous models and the MDM both give qualitative agreement with the morphology of the slower-rotating "I-sequence" stars, but none of them have been shown to accurately reproduce the stellar-mass-dependent evolution of the I-sequence stars, especially for clusters older than a few hundred MYr. I discuss observational experiments that can test aspects of the MDM, and speculate that the physics underlying the MDM may be related to other situations described in the literature, in which stellar dynamos may have a multi-modal character.
We prove a comparison theorem for the averages of the solutions of two exterior parabolic problems, the second being the "symmetrization" of the first one, by using approximation of the Schwarz symmetrization by polarizations, as it was introduced in [4]. This comparison provides an alternative proof, based on PDEs, of the isoperimetric inequality for the Wiener sausage, which was proved in [14].
We discuss high order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and absorption properties of these conditions. In the frozen coefficient approximation, with an appropriate first order pseudo-differential reduction, we show that the constraint subsystem is boundary stable on a four dimensional compact manifold. We analyze the remainder of the initial boundary value problem for a spherical reduction of the Z4c formulation with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions is presented in spherical symmetry.
In theories with three light neutrinos, a complete list of five zeroth-order textures for lepton mass matrices is found, which naturally yield: m_e = m_mu=0, m_tau \neq 0, Delta m^2_sun = 0, together with theta_{e tau} = 0, theta_{mu tau} approx 1. These textures provide suitable starting points for constructing theories which account for both atmospheric and solar neutrino fluxes. Using flavor symmetries, two schemes for such lepton masses are found, and example constructions exhibited.