ShantanuT01/DACTYL-Pretraining huggingface dataset:
The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof. Somewhat surprisingly, the behavior in a generic direction is {\it better} than that in directions orthogonal to the symmetry axis. The geometric origin of this difference can be understood most clearly from the 3-dimensional perspective.
We compute the dimensions of spaces of sections of all powers of the Donaldson determinant bundle on the moduli space of rank 2 semi-stable sheaves on the projective plane, with zero first Chern class, and second Chern class equal to 3 or 4. We prove Le Potier's strange duality conjecture in some cases.
We investigate the properties of the hadron-quark mixed phase in compact stars using a Brueckner-Hartree-Fock framework for hadronic matter and the MIT bag model for quark matter. We find that the equation of state of the mixed phase is similar to that given by the Maxwell construction. The composition of the mixed phase, however, is very different from that of the Maxwell construction; in particular, hyperons are completely suppressed.
The aim of this paper is to revisit the implications of complementarity when we inject into a Mach Zehnder interferometer particles with internal structure, prepared in special translational-internal entangled (TIE) states. This correlation causes the path distinguishability to be phase dependent in contrast to the standard case. We show that such a TIE state permits us to detect small phase shifts along with almost perfect path distinguishability, beyond the constraints imposed by complementarity on simultaneous which-way and which-phase measurements for standard cases (when distinguishability is independent of interferometric phase).
We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the avalanches in the self-organized critical state. It does, however, introduce long-range spatial correlations within the metastable states. We find large scale networks of occupied sites whose density vanishes in the thermodynamic limit, for d>1.
We present a detailed discussion of extraordinary optoconductance (EOC). Experimental data was acquired via macroscopic metal-semiconductor hybrid structures composed of GaAs and In and subjected to illumination from an Ar ion laser. A drift diffusion model using the finite element method (FEM) provided a reasonable fit to the data. EOC is explored as a function of laser position, bias current, laser power density, and temperature. The positional dependence of the voltage is accounted for by the Dember effect, with the model incorporating the excess hole distribution based on the carrier mobility, and thus the mean free path. The bias current is found to produce a linear voltage offset and does not influence the EOC. A linear relationship is found between the laser power density and the voltage in the bare and hybrid devices. This dependence is reproduced in the model by a generation rate parameter which is related to the power density. Incorporating the mobility and diffusion temperature dependence, the model directly parallels the temperature dependence of the EOC without the use of fitting parameters.
We give a de Rham interpretation of Nahm's transform for certain parabolic harmonic bundles on the projective line and compare it to minimal Fourier--Laplace transform of $\mathcal{D}$-modules. We give an algebraic definition of a parabolic structure on the transformed bundle and show that it is compatible with the transformed harmonic metric.
We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: these relations allow us to show that competition for particles can have non-trivial effects on the phase behavior of individual lattices. For a system with non-identical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters, and could easily be extended beyond the mean-field case.
Within the finite-temperature Greens-function formalism we study the equation of state of a hot interacting pion gas at zero chemical potential. Employing realistic $\pi\pi$ meson-exchange interactions we selfconsistently calculate the in-medium single-pion selfenergy and the $\pi\pi$ scattering amplitude in the quasiparticle approximation. These quantities are then used to evaluate the thermodynamic potential, $\Omega_\pi$(T), from which the state variables: pressure-, entropy- and energy-density can be derived. In contrast to earlier calculations based on the low-energy Weinberg Lagrangian we find an overall increase as compared to the free-gas results. We also consider the possibility of a dropping $\rho$-meson mass as suggested by the 'Brown-Rho Scaling' law.
We explain how complexity of rational points on projective varieties can be interpreted via the theories of Chow forms and Okounkov bodies. Precisely, we study discrete measures on filtered linear series and build on work of Boucksom and Chen, Boucksom-et-al and Ferretti. For example, we show how asymptotic volume and Seshadri constants are related to the theories of Chow weights and Okounkov bodies for very ample linear series. We also consider arithmetic applications within the context of Diophantine approximation. In this direction, we establish Roth-type theorems which can be expressed in terms of normalized Chow weights and measures of local positivity.
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels satisfy suitable and explicit growth conditions, given in terms of their distribution functions; natural conditions for sharpness are also given. Most of the known results about Moser-Trudinger inequalities can be easily adapted to our unified scheme. We give some new applications of our theorems, including: sharp higher order Moser-Trudinger trace inequalities, sharp Adams/Moser-Trudinger inequalities for general elliptic differential operators (scalar and vector-valued), for sums of weighted potentials, and for operators in the CR setting.
In the framework of the study of supernova remnants and their complex interaction with the interstellar medium and the circumstellar material, we focus on the galactic supernova remnant W49B. Its morphology exhibits an X-ray bright elongated nebula, terminated on its eastern end by a sharp perpendicular structure aligned with the radio shell. The X-ray spectrum of W49B is characterized by strong K emission lines from Si, S, Ar, Ca, and Fe. There is a variation of the temperature in the remnant with the highest temperature found in the eastern side and the lowest one in the western side. The analysis of the recent observations of W49B indicates that the remnant may be the result of an asymmetric bipolar explosion where the ejecta are collimated along a jet-like structure and the eastern jet is hotter and more Fe-rich than the western one. Another possible scenario associates the X-ray emission with a spherical explosion where parts of the ejecta are interacting with a dense belt of ambient material. To overcome this ambiguity we present new results of the analysis of an XMM-Newton observation and we perform estimates of the mass and energy of the remnant. We conclude that the scenario of an anisotropic jet-like explosion explains quite naturally our observation results, but the association of W49B with a hypernova and a gamma-ray burst, although still possible, is not directly supported by any evidence.
Recently, D. S. Kim and T. Kim have studied applications of um- bral calculus associated with p-adic invariant integrals on Zp (see [6]). In this paper, we investigate some interesting properties arising from umbral calculus. These properties are useful in deriving some identities of Bernoulli polynomials.
Four nuclei which are proved to be $2\nu\beta\beta$ emitters ($^{76}$Ge, $^{82}$Se, $^{150}$Nd, $^{238}$U), and four suspected, due to the corresponding Q-values, to have this property ($^{148}$Nd, $^{154}$Sm, $^{160}$Gd, $^{232}$Th), were treated within a proton-neutron quasiparticle random phase approximation (pnQRPA) with a projected spherical single particle basis. The advantage of the present procedure over the ones using a deformed Woods Saxon or Nilsson single particle basis is that the actual pnQRPA states have a definite angular momentum while all the others provide states having only K as a good quantum number. The model Hamiltonian involves a mean field term yielding the projected single particle states, a pairing interaction for alike nucleons and a dipole-dipole proton-neutron interaction in both the particle-hole (ph) and particle-particle (pp) channels. The effect of nuclear deformation on the single beta strength distribution as well as on the double beta Gamow-Teller transition amplitude (M$_{{\rm GT}}$) is analyzed. The results are compared with the existent data and with the results from a different approach, in terms of the process half life T$_{1/2}$. The case of different deformations for mother and daughter nuclei is also presented.
The effects of feedback from high luminosity radio-loud AGN have been extensively discussed in the literature, but feedback from low-luminosity radio-loud AGN is less well understood. The advent of high sensitivity, high angular resolution, large field of view telescopes such as LOFAR is now allowing wide-area studies of such faint sources for the first time. Using the first data release of the LOFAR Two Metre Sky Survey (LoTSS) we report on our discovery of a population of 195 radio galaxies with 150 MHz luminosities between $3\times10^{22}$ and $1.5\times10^{25}\text{ W Hz}^{-1}$ and total radio emission no larger than 80 kpc. These objects, which we term galaxy-scale jets (GSJ), are small enough to be directly influencing the evolution of the host on galaxy scales. We report upon the typical host properties of our sample, finding that 9 per cent are hosted by spirals with the remainder being hosted by elliptical galaxies. Two of the spiral-hosted GSJ are highly unusual with low radio luminosities and FRII-like morphology. The host properties of our GSJ show that they are ordinary AGN observed at a stage in their life shortly after the radio emission has expanded beyond the central regions of the host. Based on our estimates, we find that about half of our GSJ have internal radio lobe energy within an order of magnitude of the ISM energy so that, even ignoring any possible shocks, GSJ are energetically capable of affecting the evolution of the host. The current sample of GSJ will grow in size with future releases of LoTSS and can also form the basis for further studies of feedback from low-luminosity radio sources.
We prove an expansion for densities in the free CLT and apply this result to an expansion in the entropic free central limit theorem assuming a moment condition of order 8 for the free summands.
Let M be a smooth complex projective variety and let L be a line bundle on it. Rays-positive manifolds, namely pairs (M,L) such that L is numerically effective and L\cdotR > 0 for all extremal rays R on M, are studied. Several illustrative examples and some applications are provided. In particular, projective varieties with crepant singularities and of small degree with respect to the codimension are classified, and the non-negativity of the sectional genus g(M,L) is proven, describing as well the pairs with g(M,L) = 0,1.
A microscopic view of the response of the electric dipoles to a dynamic external field in a ferroelectric (FE) chain has been studied by two spin dynamics methods. One is the prominent micromagnetic approach, and the other is the micromagnetic approach with a variable size of the pseudo-spin. The energy stored in the ferroelectric chain is described by the transverse Ising model (TIM) with electric pseudo-spins. The simulations are based on a modified Landau-Lifshitz-Gilbert (LLG) equation which is precession free. The results obtained are shown and compared with the result supplemented by Landau-Devonshire (L-D) theory in the Appendix.
Using the known connection between Schroedinger-like equations and Dirac-like equations in the supersymmetric context, we discuss an extension of FRW barotropic cosmologies in which a Dirac mass-like parameter is introduced. New Hubble cosmological parameters H_K(eta) depending on the Dirac-like parameter are plotted and compared with the standard Hubble case H_0(eta). The new H_K(eta) are complex quantities. The imaginary part is a supersymmetric way of introducing dissipation and instabilities in the barotropic FRW hydrodynamics
We suggest a method for probing the quark content of the photon using $b$ tagging at high energy $e^+e^-$ and $e\gamma$ colliders. We find that heavy quark tagging provides a sensitive and effective probe of the quark content of the photon especially in the low $x$-region where the various models differ the most. This process is complementary to others that have been studied in the literature and can contribute to more precise determinations of quark and gluon distributions inside the photon.
We report on systematic investigation of hot carrier dynamics in Ti4O7 by ultrafast time-resolved optical reflectivity. We find the transient indication for its two-step insulator-metal (I-M) transition, in which two phase transitions occur from long-range order bipolaron low-temperature insulating (LI) phase to disordered bipolaron high-temperature insulating (HI) phase at Tc1 and to free carrier metallic (M) phase at Tc2. Our results reveal that photoexcitation can effectively lower down both Tc1 and Tc2 with pump fluence increasing, allowing a light-control of I-M transition. We address a phase diagram that provides a framework for the photoinduced I-M transition and helps the potential use of Ti4O7 for photoelectric and thermoelectric devices.
We calculate the vector and scalar form factors of the pion to two loops in Chiral Perturbation Theory. We estimate the unknown O(p^6) constants using resonance exchange. We make a careful comparison to the available data and determine two O(p^4) constants rather precisely, and two O(p^6) constants less precisely. We also use Chiral Perturbation Theory to two loops to extract in a model--independent manner the charge radius of the pion from the available data, and obtain \rpiV=0.437\pm 0.016 fm^2.
TIGER integral-field spectrography and HST/WFPC2 imaging of the E3 galaxy NGC 2974 are used to derive the kinematics of the stellar and ionized gas components in its central 500 pc. We derive a numerical two-integral distribution function from a MGE mass model using the HQ formalism. The TIGER as well as published long-slit stellar kinematics are well fitted with this self-consistent model, requiring neither the addition of a significant mass contribution from a hidden disc structure, nor the presence of a central dark mass. The data reveal the presence of a striking, highly contrasted, two-arm gaseous spiral structure within a radius of ~200 pc, corresponding to a total mass of 6.8x10^4 Msun of ionized gas. We use a deconvolved TIGER datacube to probe its kinematics at a resolution of about 0.35 arcsec. Strong departures from circular motions are observed, as well as high velocity dispersion values on the inner side of the arms. We interpret the observed gas morphology and kinematics as the signature of streaming gas flows driven by a ~540 pc diameter bar with Ome=700+/-100 km/s/kpc. This hypothesis is strongly supported by the predictions of a density wave model. This model predicts that the bar should lie at about 35 degree from the line of nodes, and implies gas inflow towards the central ~50 pc. The quadrupole pertubation due to this bar is estimated to represent less than 2% of the underlying gravitational potential. Despite its weakness, the inner bar of NGC 2974 may be able to drive some gas within a 10 pc radius. We suggest that the presence of such inner bars might be more common among early-type disk galaxies than is generally thought, and that deep high-resolution emission-line imagery may be the best way to detect such structures.
We develop a model of early X-ray afterglows of gamma-ray bursts originating from the reverse shock (RS) propagating through ultra-relativistic, highly magnetized pulsar-like winds produced by long-lasting central engines. We first perform fluid and MHD numerical simulations of relativistic double explosions. We demonstrate that even for constant properties of the wind a variety of temporal behaviors can be produced, depending on the energy of the initial explosion and the wind power, the delay time for the switch-on of the wind, and magnetization of the wind. X-ray emission of the highly magnetized RS occurs in the fast cooling regime - this ensures high radiative efficiency and allows fast intensity variations. We demonstrate that: (i) RS emission naturally produces light curves showing power-law temporal evolution with various temporal indices; (ii) mild wind power, of the order of $\sim 10^{46}$ erg s$^{-1}$ (equivalent isotropic), can reproduce the afterglows' plateau phase; (iii) termination of the wind can produce sudden steep decays; (iv) short-duration afterglow flares are due to mild variations in the wind luminosity, with small total injected energy.
We prove the cohomological crepant resolution conjecture of Ruan for the weighted projective space P(1,3,4,4). To compute the quantum corrected cohomology ring we combine the results of Coates-Corti-Iritani-Tseng on P(1,1,1,3) and our previous results.
Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. In this work we introduce an extension of the Einstein-Cartan-Dirac theory with an electromagnetic (Maxwell) contribution minimally coupled to torsion. This contribution breaks the $U(1)$ gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe, yielding new physics in extreme (spin) density regimes. We obtain the generalized gravitational, electromagnetic and fermionic field equations for this theory, estimate the strength of the corrections, and discuss the corresponding phenomenology. In particular, we briefly address some astrophysical considerations regarding the relevance of the effects which might take place inside ultra-dense neutron stars with strong magnetic fields (magnetars).
CePdAl is a prototypical frustrated Kondo lattice with partial long-range order (LRO) at $T_\mathrm{N}=2.7$ K. Previous bulk experiments under hydrostatic pressure found signatures for a quantum critical regime that extends from $p_\mathrm{c} \approx 0.9$ GPa, where LRO disappears, up to $\sim 1.7$ GPa. We employed extensive muon spin relaxation and rotation ($\mu$SR) experiments under pressure. The continuous and complete suppression of LRO at $p_\mathrm{c}$ is confirmed. Above $T_\mathrm{N}(p)$ and beyond $p_\mathrm{c}$, an additional crossover scale $T^\ast(p)$ characterizes the change from pure to stretched exponential relaxation in zero field. Remarkably $T^\ast(p)$ agrees with previously determined signatures of entropy accumulation above LRO. This coincidence microscopically evidences fluctuating frustrated spins at $T\leq T^\ast$ with spin-liquid behavior. Power-law divergences of the temperature and longitudinal field dependences of the relaxation rate, with time-field scaling, at pressures between $p_c$ and 1.7 GPa characterize this regime as quantum critical.
We classify smooth toric Fano varieties of dimension $n\geq 3$ containing a toric divisor isomorphic to $\PP^{n-1}$. As a consequence of this classification, we show that any smooth complete toric variety $X$ of dimension $n\geq 3$ with a $T$-fixed point $x\in X$ such that the blow-up $B_x(X)$ of $X$ at $x$ is Fano is isomorphic either to $\PP^n$ or to the blow-up of $\PP^n$ along a $\PP^{n-2}$. As expected, such results are proved using toric Mori theory due to Reid.
We give necessary and sufficient conditions for the existence of positive radial solutions for a class of fully nonlinear uniformly elliptic equations posed in the complement of a ball in $\mathbb R^N$, and equipped with homogeneous Dirichlet boundary conditions.
We have studied the electronic structure of ferrimagnetic Mn2VAl single crystal by means of soft X-ray absorption spectroscopy (XAS), X-ray absorption magnetic circular dichroism (XMCD) and resonant soft X-ray inelastic scattering (RIXS). We have successfully observed the XMCD signals for all constitute elements, supporting the spin polarized states at the Fermi level. The Mn $L_{2,3}$ XAS and XMCD spectra are reproduced by the spectral simulation based on density-functional theory (DFT), indicating itinerant character of the Mn 3d states. On the other hand, V $3d$ electrons are rather localized since the ionic model can qualitatively explain the V $L_{2,3}$ XAS and XMCD spectra as well as the local dd excitation revealed by V $L_3$ RIXS.
We develop a new algorithm to compute a basis for $M_k(\Gamma_0(N))$, the space of weight $k$ holomorphic modular forms on $\Gamma_0(N)$, in the case when the graded algebra of modular forms over $\Gamma_0(N)$ is generated at weight two. Our tests show that this algorithm significantly outperforms a commonly used algorithm which relies more heavily on modular symbols.
Self-gravitating systems evolve toward the most tightly bound configuration that is reachable via available evolution processes. The inner parts shrink and the outer parts expand, provided that some physical process transports energy or angular momentum outward. The evolution of stars, star clusters, protostellar and protoplanetary disks, black hole accretion disks, and galaxy disks are all fundamentally similar. These processes for galaxy disks are the subjects of my lectures and of this Canary Islands Winter School. Part 1 discusses formation, growth, and death of bars. Part 2 details the slow ("secular") rearrangement of angular momentum that results from interactions between stars or gas and nonaxisymmetries such as bars. We have a heuristic understanding of how this forms outer rings, inner rings, and stuff dumped into the center. Observations show that barred galaxies have central concentrations of gas and star formation. Timescales imply that they grow central "pseudobulges" that get mistaken for elliptical-galaxy-like classical bulges but that formed gently out of disks. Part 3 shows how we distinguish between classical and pseudo bulges. Part 4 reviews how environmental secular evolution transforms gas-rich, star-forming spirals and irregulars into gas-poor, red and dead S0 and spheroidal ("Sph") galaxies. Sphs are not ellipticals; they have structural parameters like those of low-luminosity S+Im galaxies. So Sphs are bulgeless S0s. Part 5 combines hierarchical clustering and secular evolution into a comprehensive picture.