ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper presents the theoretical basis of the fireball/blast wave model, and some implications of recent results on GRB source models and cosmic-ray production from GRBs. BATSE observations of the prompt gamma-ray luminous phase, and Beppo-SAX and long wavelength afterglow observations of GRBs are briefly summarized. Derivation of spectral and temporal indices of an adiabatic blast wave decelerating in a uniform surrounding medium in the limiting case of a nonrelativistic reverse shock, both for spherical and collimated outflows, is presented as an example of the general theory. External shock model fits for the afterglow lead to the conclusion that GRB outflows are jetted. The external shock model also explains the temporal duration distribution and clustering of peak energies in prompt spectra of long-duration GRBs, from which the redshift dependence of the GRB source rate density can be derived. Source models are reviewed in light of the constant energy reservoir result of Frail et al. that implies a total GRB energy of a few times 10^{51} ergs and an average beaming fraction of ~1/500 of full sky. Paczynski's isotropic hypernova model is ruled out. The Vietri-Stella model two-step collapse process is preferred over a hypernova/collapsar model in view of the X-ray observations of GRBs and the constant energy reservoir result. Second-order processes in GRB blast waves can accelerate particles to ultra-high energies. GRBs may be the sources of UHECRs and cosmic rays with energies above the knee of the cosmic ray spectrum. High-energy neutrino and gamma-ray observations with GLAST and ground-based gamma-ray telescopes will be crucial to test GRB source models.
We studied the total magnetic field strength in normal star-forming galaxies estimated using energy equipartition assumption. Using the well known radio--far infrared correlation we demonstrate that the equipartition assumption is valid in galaxies at sub-kpc scales. We find that the magnetic field strength is strongly correlated with the surface star formation rate in the galaxies NGC 6946 and NGC 5236. Further, we compare the magnetic field energy density to the total (thermal + turbulent) energy densities of gas (neutral + ionized) to identify regions of efficient field amplification in the galaxy NGC 6946. We find that in regions of efficient star formation, the magnetic field energy density is comparable to that of the total energy density of various interstellar medium components and systematically dominates in regions of low star formation efficiency.
Three related topics on the quantum-vacuum geometric phases in a noncoplanarly curved optical fiber is presented: (i) a brief review: the investigation of vacuum effect and its experimental realization; (ii) the sequence of ideas of geometric phases in the fiber; (iii) three derivations of effective Hamiltonian that describes the wave propagation of photon field in a curved fiber.
We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the derivatives of double and triple Eisenstein series.
We perform numerical simulations of the growth of a Population III stellar system under photodissociating feedback. We start from cosmological initial conditions at z = 100, self-consistently following the formation of a minihalo at z = 15 and the subsequent collapse of its central gas to high densities. The simulations resolve scales as small as ~ 1 AU, corresponding to gas densities of 10^16 cm^-3. Using sink particles to represent the growing protostars, we evolve the stellar system for the next 5000 years. We find that this emerging stellar group accretes at an unusually low rate compared with minihalos which form at earlier times (z = 20 - 30), or with lower baryonic angular momentum. The stars in this unusual system will likely reach masses ranging from < 1 M_sun to 5 M_sun by the end of their main-sequence lifetimes, placing them in the mass range for which stars will undergo an asymptotic giant branch (AGB) phase. Based upon the simulation, we predict the rare existence of Population III stars that have survived to the present day and have been enriched by mass overflow from a previous AGB companion.
We present factorization theorems for two exclusive heavy-quarkonium production processes: production of two quarkonia in e^+e^- annihilation and production of a quarkonium and a light meson in B-meson decays. We describe the general proofs of factorization and supplement them with explicit one-loop analyses, which illustrate some of the features of the soft-gluon cancellations. We find that violations of factorization are generally suppressed relative to the factorized contributions by a factor v^2m_c/Q for each S-wave charmonium and a factor m_c/Q for each L-wave charmonium with L>0. Here, v is the velocity of the heavy quark or antiquark in the quarkonium rest frame, Q=sqrt{s} for e^+e^- annihilation, Q=m_B for B-meson decays, sqrt{s} is the e^+e^- center-of-momentum energy, m_c is the charm-quark mass, and m_B is the B-meson mass. There are modifications to the suppression factors if quantum-number restrictions apply for the specific process.
In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform ringdown simulations that resemble the experimental setup using both in-plane and out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and discuss the possible reversal mode of skyrmionic states. We compare the power spectral densities of incomplete skyrmion and isolated skyrmion states and observe several key differences that can contribute to the experimental identification of the state present in the sample. We measure the FeGe Gilbert damping, and using its value we determine what eigenmodes can be expected to be observed in experiments. Finally, we show that neglecting the demagnetisation energy contribution or ignoring the magnetisation variation in the out-of-film direction - although not changing the eigenmode's magnetisation dynamics significantly - changes their resonance frequencies substantially. Apart from contributing to the understanding of skyrmionic states physics, this systematic work can be used as a guide for the experimental identification of skyrmionic states in confined helimagnetic nanostructures.
Photometric surveys of galaxy clusters have revealed a large number of ultra compact dwarfs (UCDs) around predominantly massive elliptical galaxies. Their origin is still debated as some UCDs are considered to be the remnant nuclei of stripped dwarf galaxies while others seem to mark the high-mass end of the star cluster population. We aim to characterise the properties of a UCD found at very close projected distance (1.1 kpc) from the centre of the low-mass (M~10^10 M_sun) early-type galaxy FCC47. This is a serendipitous discovery from MUSE adaptive optics science verification data. We explore the potential origin of this UCD as either a massive cluster or the remnant nucleus of a dissolved galaxy. We use archival Hubble Space Telescope data to study the photometric and structural properties of FCC47-UCD1. In the MUSE data, the UCD is unresolved, but we use its spectrum to determine the radial velocity and metallicity. FCC47-UCD1's surface brightness is best described by a single King profile with low concentration C = R_t/R_c ~ 10 and large effective radius (r_e = 24pc). Its integrated magnitude and a blue colour (G = -10.6 mag, g-z = 1.46 mag) combined with with a metallicity of [M/H] = -1.12+-0.10 dex and an age > 8 Gyr obtained from the full fitting of the MUSE spectrum suggests a stellar population mass of M_star = 4.87x10^6 M_sun. The low S/N of the MUSE spectrum prevents detailed stellar population analysis. Due to the limited spectral resolution of MUSE, we can only give an upper limit on the velocity dispersion (sig < 17km/s), and consequently on its dynamical mass (M_dyn < 1.3x10^7 M_sun). The origin of the UCD cannot be constrained with certainty. The low metallicity, old age and magnitude are consistent with a star cluster origin, whereas the extended size is consistent with an origin as the stripped nucleus of a dwarf galaxy with a initial stellar mass of a few 10^8 M_sun.
A combination of three-dimensional (3D) magnetohydrodynamics (MHD) and synthetic numerical simulations are presented to follow the evolution of a randomly magnetised plasma that models the intra-cluster medium (ICM), under the isolated effects of powerful, light, hypersonic and bipolar Fanaroff-Riley class II (FR II) jets. We prescribe the cluster magnetic field (CMF) as a Gaussian random field with a Kolmogorov-like energy spectrum. Both the power of the jets and the viewing angle that is used for the synthetic Rotation Measure (RM) observations are investigated. We find the model radio sources introduce and amplify fluctuations on the RM statistical properties which we analyse as a function of time as well as the viewing angle. The average RM and the RM standard deviation are increased by the action of the jets. Energetics, RM statistics and magnetic power spectral analysis consistently show that the effects also correlate with the jets' power, and that the lightest, fastest jets produce the strongest changes in their environment. We see jets distort and amplify the CMFs especially near the edges of the lobes and the jets' heads. This process leads to a flattening of the RM structure functions at scales comparable to the source size. The edge features we find are similar to ones observed in Hydra A. The results show that jet-produced RM enhancements are more apparent in quasars than in radio galaxies. Globally, jets tend to enhance the RM standard deviation which may lead to overestimations of the CMFs' strength by about 70%. This study means to serve as a pathfinder for the SKA, EVLA and LOFAR to follow the evolution of cosmic magnetic fields.
We study congruences of lines $X_\omega$ defined by a sufficiently general choice of an alternating 3-form $\omega$ in $n+1$ dimensions, as Fano manifolds of index $3$ and dimension $n-1$. These congruences include the $\mathrm{G}_2$-variety for $n=6$ and the variety of reductions of projected $\mathbb{P}^2 \times \mathbb{P}^2$ for $n=7$.   We compute the degree of $X_\omega$ as the $n$-th Fine number and study the Hilbert scheme of these congruences proving that the choice of $\omega$ bijectively corresponds to $X_\omega$ except when $n=5$. The fundamental locus of the congruence is also studied together with its singular locus: these varieties include the Coble cubic for $n=8$ and the Peskine variety for $n=9$.   The residual congruence $Y$ of $X_\omega$ with respect to a general linear congruence containing $X_\omega$ is analysed in terms of the quadrics containing the linear span of $X_\omega$. We prove that $Y$ is Cohen-Macaulay but non-Gorenstein in codimension $4$. We also examine the fundamental locus $G$ of $Y$ of which we determine the singularities and the irreducible components.
In the current study, we explore digital homology and cohomology modules, and investigate their fundamental properties on pointed digital images. We also examine pointed digital Hopf spaces and base point preserving digital Hopf functions between the pointed digital Hopf spaces with suitable digital multiplications, and explore the digital primitive homology and cohomology classes, the digital Pontryagin algebras and coalgebras on the digital Hopf spaces as digital images.
The "s-f model", also known as the ferromagnetic Kondo lattice, contains a description of band electrons coupled to localized spins which is an appropriate description of the magnetic part of the low-energy physics of Gd metal. Here the model is used to estimate the lifetime broadening of the minority spin component of the surface electron band in ferromagnetic gadolinium metal at temperatures below the Curie temperature. The low temperature result 0.10 eV agrees nicely with a measurement by Fedorov et al.
Let $F(x, y)$ be a binary form with integer coefficients, degree $n\geq 3$ and irreducible over the rationals. Suppose that only $s + 1$ of the $n + 1$ coefficients of $F$ are nonzero. We show that the Thue inequality $|F(x,y)|\leq m$ has $\ll sm^{2/n}$ solutions provided that the absolute value of the discriminant $D(F)$ of $F$ is large enough. We also give a new upper bound for the number of solutions of $|F(x,y)|\leq m$, with no restriction on the discriminant of $F$ that depends mainly on $s$ and $m$, and slightly on $n$. Our bound becomes independent of $m$ when $m<|D(F)|^{2/(5(n-1))}$, and also independent of $n$ if $|D(F)|$ is large enough.
We prove that the quivers with potentials associated to triangulations of surfaces with marked points, and possibly empty boundary, are non-degenerate, provided the underlying surface with marked points is not a closed sphere with exactly 5 punctures. This is done by explicitly defining the QPs that correspond to tagged triangulations and proving that whenever two tagged triangulations are related by a flip, their associated QPs are related by the corresponding QP-mutation. As a byproduct, for (arbitrarily punctured) surfaces with non-empty boundary we obtain a proof of the non-degeneracy of the associated QPs which is independent from the one given by the author in the first paper of the series.   The main tool used to prove the aforementioned compatibility between flips and QP-mutations is what we have called \emph{Popping Theorem}, which, roughly speaking, says that an apparent lack of symmetry in the potentials arising from ideal triangulations with self-folded triangles can be fixed by a suitable right-equivalence.
In this paper we report on the optical properties of site controlled InGaAs dots with GaAs barriers grown in pyramidal recesses by metalorganic vapour phase epitaxy. The inhomogeneous broadening of excitonic emission from an ensemble of quantum dots is found to be unusually narrow, with a standard deviation of 1.19 meV, and spectral purity of emission lines from individual dots is found to be very high (18-30 ueV), in contrast with other site-controlled systems.
It is shown that a transition from a multidimensional cosmological model with one internal space of the dimension d_1 to the effective tree-level bosonic string corresponds to an infinite number of the internal dimensions: d_1 -> infinity.
The origin of high velocity stars observed in the halo of our Galaxy is still unclear. In this work we test the hypothesis, raised by results of recent high precision $N$-body simulations, of strong acceleration of stars belonging to a massive globular cluster orbitally decayed in the central region of the host galaxy where it suffers of a close interaction with a super massive black hole, which, for these test cases, we assumed $10^8$ M$_\odot$ in mass.
The extended Dynamical Mean Field Equations (EDMFT) are analyzed using semiclassical methods for a model describing an interacting fermi-bose system. We compare the semiclassical approach with the exact QMC (Quantum Montecarlo) method. We found the transition to an ordered state to be of the first order for any dimension below four.
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical formula is derived using saddle point methods for short times, it works well even for intermediate times. Our formula goes beyond conventional "short time heat kernel expansions" in that it is nonperturbative in the spatial coordinate, a feature that is ideal for studying large deviations. Our work suggests a new and efficient algorithm for numerical integration of the diffusion equation on a sphere. We perform Monte Carlo simulations to compare the numerical efficiency of the new algorithm with the older Gaussian one.
In this article we consider several probabilistic processes defining random grapha. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each of the probabilistic processes, we prove that the probability for the random graph to be a tree has an extremely simple expression, which is independent of most parameters of the problem. This raises many open questions.
Long gamma-ray bursts (GRBs) are considered to be originated from core collapse of massive stars. It is believed that the afterglow property is determined by the density of the material in the surrounding interstellar medium. Therefore, the circumburst density can be used to distinguish between an interstellar wind $n(R) \propto R^{\rm -k}$, and a constant density medium (ISM), $n(R) = const$. Previous studies with different afterglow samples, show that the circumburst medium of GRBs is neither simply supported by an interstellar wind, nor completely favored by an ISM. In this work, our new sample is consisted of 39 GRBs with smoothly onset bump-like features in early X-ray afterglows, in which 20 GRBs have the redshift measurements. By using a smooth broken power law function to fit the bumps of X-ray light curves, we derive the full width at half-maximum (FWHM) as the feature width ($\omega$), as well as the rise and decay time scales of the bumps ($T_{\rm r}$ and $T_{\rm d}$). The correlations between the timescales of X-ray bumps are similar to those found previously in the optical afterglows. Based on the fireball forward shock (FS) model of the thin shell case, we obtain the distribution of the electron spectral index $p$, and further constrain the medium density distribution index $k$. The new inferred $k$ is found to be concentrated at 1.0, with a range from 0.2 to 1.8. This finding is consistent with previous studies. The conclusion of our detailed investigation for X-ray afterglows suggests that the ambient medium of the selected GRBs is not homogeneous, i.e., neither ISM nor the typical interstellar wind.
Hybrid organic-inorganic perovskites (HOIPs) have emerged to the forefront of optoelectronic materials advancement in the past few years. Due to the nature of organic compounds within the perovskite structure, its optoelectronic properties are affected by complex interaction and correlation effects between the organic and inorganic ions. Using spectroscopic ellipsometry, we observe two broad plasmonic excitation from the calculated loss function (LF) -Im[\varepislon^{-1} (\omega)], peak A' and B' at 3.28 eV and 4.26 eV, respectively.The presence of these two asymmetric peaks in the spectroscopic ellipsometry (SE) spectra indicates the existence of unconventional plasmons at room temperature. This is inferred due to the absence of the zero-crossing in the real part of dielectric function \varepsilon_1 (\omega). Through combined Near-Edge X-ray Absorption Fine Structure (NEXAFS) and Resonant Photoemission Spectroscopies (ResPES), we observe resonance enhancement peak close to 15 eV in the C K-edge region that unravels a charge transfer event due to the opening of an extra autoionization channel. Additionally, photoluminescence (PL) spectrum confirms the presence of broadband emission originating from the self-trapped emission excitons at 2.38 eV due to the soft 2D-HOIPs crystal structure. We believe that these phenomena directly impact the correlation strength in 2D-HOIPs. Our results have confirmed the existence of unconventional plasmons of 2D-HOIPs at room temperature. Such studies in the emission and plasmonic behavior of perovskites will pave the way for the efficient light emitting devices or lasers with minimal integrations of the materials.
A simple approximation to shell model is proposed in which the low energy excitation spectra corresponds to the identical nucleons occupying the same single particle states where they preferred to form pairs for the ground states. We call this approximation as nonzero angular momentum pairing shell model. It not only reduces the dimensionality of the shell model but also matches the number of low energy levels in experimental spectra for few cases where exact shell model predicts many more states. The special focus has been done to consider the realistic interaction derived from free nucleon-nucleon scattering data to cope with the experimental spectra. The proposed approximation to shell model has been applied to calculate the energy spectra of O18 and Ni58 nuclei where only two neutrons occupy the valence states outside the core. When compared with the experimental data, the results are found to be encouraging. It is expected that results will be more pronounced if the even-even nuclei with higher number of valence nucleons are considered.
Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering in the first queue is a zero mean ergodic process. We prove that the departure process from the n-th queue converges in distribution to a Brownian motion as n goes to infinity. In particular this implies that the Brownian motion is an attractive invariant measure for the Brownian queueing operator. Our proof exploits the relationship between the Brownian queues in tandem and the last-passage Brownian percolation model, developing a coupling technique in the second setting. The result is also interpreted in the related context of Brownian particles acting under one sided reflection.
A paradigm for a global algebraic number theory of the reals is formulated with the purpose of providing a unified setting for algebraic and transcendental number theory. This is achieved through the study of subgroups of nonstandard models of Dedekind domains called diophantine approximation groups. The arithmetic of diophantine approximation groups is defined in a way which extends the ideal-theoretic arithmetic of algebraic number theory, using the structure of an approximate ideal: a bi-filtration by subgroups along which partial products may be performed.
We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let $X_n$ be a Hermitian random matrix of size $n\times n$ that can be split into independent blocks of the size at most $d_n=o(n^2)$. We prove that under some mild conditions on the distribution of the entries of $X_n$, the empirical spectral measure of $X_n$ concentrates around its mean.   The main theorem is a strengthening of a recent result by Kemp and Zimmerman, where the size of blocks grows as $o(\log n)$. As an application, we are able to upgrade the results of Schenker and Schulz on the convergence in expectation to the semicircle law of a class of random matrices with dependent entries to weak convergence in probability. Other applications include patterned random matrices, e.g. matrices of Toeplitz, Hankel or circulant type and matrices with heavy tailed entries in the domain of attraction of the Gaussian distribution.