ShantanuT01/DACTYL-Pretraining huggingface dataset:
In a multitype branching process, it is assumed that immigrants arrive according to a nonhomogeneous Poisson or a generalized Polya process (both processes are formulated as a nonhomogeneous birth process with an appropriate choice of transition intensities). We show that the renormalized numbers of objects of the various types alive at time $t$ for supercritical, critical, and subcritical cases jointly converge in distribution under those two different arrival processes. Furthermore, some transient moment analysis when there are only two types of particles is provided. AMS 2000 subject classifications: Primary 60J80, 60J85; secondary 60K10, 60K25, 90B15.
We derive the screen factor for the radiation flux from an optically thick plasma of electron-positron pairs and photons, created by vacuum polarization process around a black hole endowed with electromagnetic structure.
Disk scale length and central surface brightness for a sample of about 29955 bright disk galaxies from the Sloan Digital Sky Survey have been analysed. Cross correlation of the SDSS sample with the LEDA catalogue allowed us to investigate the variation of the scale lengths for different types of disk/spiral galaxies and present distributions and typical trends of scale lengths all the SDSS bands with linear relations that indicate the relation that connect scale lengths in one passband to another. We use the volume corrected results in the r-band and revisit the relation between these parameters and the galaxy morphology. The derived scale lengths presented here are representative for a typical galaxy mass of 10^10.8 solarmasses, and the RMS dispersion is larger for more massive galaxies. We analyse the scale-length-central disk brightness plane and further investigate the Freeman Law and confirm that it indeed defines an upper limit for disk central surface brightness in bright disks (r<17.0), and that disks in late type spirals (T > 6) have fainter central surface brightness. Our results are based on a sample of galaxies in the local universe (z< 0.3) that is two orders of magnitudes larger than any sample previously studied, and deliver statistically significant results that provide a comprehensive test bed for future theoretical studies and numerical simulations of galaxy formation and evolution.
The interplay between long-range and local Coulomb repulsion in strongly interacting electron systems is explored through a two-dimensional Hubbard-Wigner model. An unconventional metallic state is found in which collective low-energy excitations characteristic of the Wigner crystal induce a flow of electrical current despite the absence of one-electron spectral weight at the Fermi surface. Photoemission experiments on certain quarter-filled layered molecular crystals should observe a gap in the excitation spectrum whereas optical spectroscopy should find a finite Drude weight indicating metallic behavior.
A periodically modulated N-state model whose dynamics is governed by a time-convoluted generalized master equation is theoretically analyzed. It is shown that this non-Markovian master equation can be converted to a Markovian master equation having a larger transition matrix, which affords easier analysis. The behavior of this model is investigated by focusing on the cycle-averaged pumping current. In the adiabatic limit, the geometrical current is calculated analytically, and compared to numerical results which are available for a wide range of modulation frequencies.
Recently, it has been demonstrated that the chemical composition of jets in heavy ion collisions is significantly altered compared to jets in the vacuum. This signal can be used to probe the medium formed in nuclear collisions. In this study we investigate the possibility that fast light quarks and gluons can convert to heavy quarks when passing through a quark gluon plasma. We study the rate of light to heavy jet conversions in a consistent Fokker-Planck framework and investigate their impact on the production of high-$p_T$ charm and bottom quarks at RHIC and LHC.
Using VLT/FLAMES optical IFU observations, we present a detailed study of UM 448, a nearby Blue Compact Galaxy (BCG) previously reported to have an anomalously high N/O abundance ratio. NTT/SuSI2 images reveal a morphology suggestive of a merger of two systems of contrasting colour, whilst our H-alpha emission maps resolve UM 448 into three separate regions that do not coincide with the stellar continuum peaks. UM 448 exhibits complex emission line profiles, with lines consisting of a narrow, central component, an underlying broad component and a third, narrow blue-shifted component. Radial velocity maps show signs of solid body rotation across UM 448, with a projected rotation axis that correlates with the continuum morphology of the galaxy. A spatially-resolved, chemodynamical analysis is presented. Whilst the eastern tail of UM 448 has electron temperatures (Te) that are typical of BCGs, we find a region within the main body of the galaxy where the narrow and broad [O III] 4363 line components trace temperatures differing by 5000K and oxygen abundances differing by 0.4 dex. We measure spatially resolved and integrated ionic and elemental abundances for O, N, S and Ne throughout UM 448, and find they do not agree, possibly due the flux-weighting of Te from the integrated spectrum. This has significant implications for abundances derived from long-slit and integrated spectra of star-forming galaxies in the nearby and distant universe. A region of enhanced N/O ratio is indeed found, extended over a ~0.6 kpc^2 region within the main body of the galaxy. Contrary to previous studies, however, we do not find evidence for a large Wolf-Rayet population, and conclude that WR stars alone cannot be responsible for producing the observed N/O excess. Instead, the location and disturbed morphology of the N-enriched region suggests that interaction-induced inflow of metal-poor gas may be responsible.
We present Spitzer IRAC images, along with representative 5.27 to 38.5 micron IRS spectra of the Cassiopeia A supernova remnant. We find that various IRAC channels are each most sensitive to a different spectral and physical component. Channel 1 (3.6 micron) matches radio synchrotron images. Where Channel 1 is strong with respect to the other channels, the longer-wavelength spectra show a broad continuum gently peaking around 26 micron, with weak or no lines. We suggest that this is due to un-enriched progenitor circumstellar dust behind the outer shock, processed by shock photons and electrons. Where Channel 4 (8 micron) is bright relative to the other IRAC channels, the long-wavelength spectra show a strong, 2-3 micron-wide peak at 21 micron, likely due to silicates and proto-silicates, as well as strong ionic lines of [Ar II], [Ar III], [S IV] and [Ne II]. In these locations, the dust and ionic emission originate from the explosion's O-burning layers. The regions where Channels 2 (4.5 micron) and 3 (5.6 micron) are strongest relative to Channel 4 show a spectrum that rises gradually to 21 micron, and then flattens or rises more slowly to longer wavelengths, along with higher ratios of [Ne II] to [Ar II]. Dust and ionic emission in these locations arise primarily from the C- and Ne- burning layers. These findings are consistent with asymmetries in the explosion producing variations in the velocity structure in different directions, but preserving the nucleosynthetic layers. At each location, the dust and ionic lines in the mid-infrared, and the hotter and more highly ionized optical and X-ray emission are then dominated by the layer currently encountering the reverse shock in that direction.
Optimal observables are known to lead to minimal statistical errors on parameters for a given normalised event distribution of a physics reaction. Thereby all statistical correlations are taken into account. Therefore, on the one hand they are a useful tool to extract values on a set of parameters from measured data. On the other hand one can calculate the minimal constraints on these parameters achievable by any data-analysis method for the specific reaction. In case the final states can be reconstructed without ambiguities optimal observables have a particularly simple form. We give explicit formulae for the optimal observables for generic reactions in case of ambiguities in the reconstruction of the final state and for general parameterisation of the final-state phase space.
We present a new implementation of radiation hydrodynamics (RHD) in the adaptive mesh refinement (AMR) code RAMSES. The multi-group radiative transfer (RT) is performed on the AMR grid with a first-order Godunov method using the M1 closure for the Eddington tensor, and is coupled to the hydrodynamics via non-equilibrium thermochemistry of hydrogen and helium. This moment-based approach has the large advantage that the computational cost is independent of the number of radiative sources - it can even deal with continuous regions of emission such as bound-free emission from gas. As it is built directly into RAMSES, the RT takes natural advantage of the refinement and parallelization strategies already in place. Since we use an explicit advection solver for the radiative transport, the time step is restricted by the speed of light - a severe limitation that can be alleviated using the so--called "reduced speed of light" approximation. We propose a rigorous framework to assess the validity of this approximation in various conditions encountered in cosmology and galaxy formation. We finally perform with our newly developed code a complete suite of RHD tests, comparing our results to other RHD codes. The tests demonstrate that our code performs very well and is ideally suited for exploring the effect of radiation on current scenarios of structure and galaxy formation.
The population of field OB stars are an important component of a galaxy's stellar content, representing 20-30% of the massive stars. To study this population, we have undertaken the Runaways and Isolated O Type Star Spectroscopic Survey of the SMC (RIOTS4). RIOTS4 surveys a spatially complete sample of >350 field OB stars in the Small Magellanic Cloud and will serve as a key probe of runaways, binaries, and the stellar IMF in the field massive star population. Here, we focus on the field IMF, which provides an empirical probe of the star-forming process and is a fundamental property of a stellar population. Together with photometry from the OGLE survey, RIOTS4 will yield a definitive stellar IMF for the SMC field massive star population. We present preliminary results that suggests the field IMF is much steeper, Gamma = 2.9, than the canonical stellar IMF of Gamma = 1.35. Despite the steep slope, we see no evidence of a stellar upper mass limit, up to our highest mass star of 65 solar masses.
We introduce the multiplicative coalescent with linear deletion, a continuous-time Markov process describing the evolution of a collection of blocks. Any two blocks of sizes $x$ and $y$ merge at rate $xy$, and any block of size $x$ is deleted with rate $\lambda x$ (where $\lambda\geq 0$ is a fixed parameter). This process arises for example in connection with a variety of random-graph models which exhibit self-organised criticality. We focus on results describing states of the process in terms of collections of excursion lengths of random functions. For the case $\lambda=0$ (the coalescent without deletion) we revisit and generalise previous works by authors including Aldous, Limic, Armendariz, Uribe Bravo, and Broutin and Marckert, in which the coalescence is related to a "tilt" of a random function, which increases with time; for $\lambda>0$ we find a novel representation in which this tilt is complemented by a "shift" mechanism which produces the deletion of blocks. We describe and illustrate other representations which, like the tilt-and-shift representation, are "rigid", in the sense that the coalescent process is constructed as a projection of some process which has all of its randomness in its initial state. We explain some applications of these constructions to models including mean-field forest-fire and frozen-percolation processes.
The modern form of the Moments Method applied to the calculation of the nuclear shell-model level density is explained and examples of the method at work are given. The calculated level density practically exactly coincides with the result of full diagonalization when the latter is feasible. The method provides the pure level density for given spin and parity with spurious center-of-mass excitations subtracted. The presence and interplay of all correlations leads to the results different from those obtained by the mean-field combinatorics.
The classical Theorem of Mumford states that a topologically regular complex algebraic surface in $\mathbb{C}^3$ with an isolated singular point is smooth. We proof that any Lipschitz regular complex algebraic set is smooth. No restriction on the dimension is needed. No restriction of singularity to be isolated is needed.
I review in these lectures our present understanding of the origin and evolution of the universe, making emphasis on the most recent observations of the acceleration of the universe, the precise measurements of the microwave background anisotropies, and the formation of structure like galaxies and clusters of galaxies from tiny primodial fluctuations generated during inflation.
We study two families of cyclotomic graphs and perfect codes in them. They are Cayley graphs on the additive group of $\mathbb{Z}[\zeta_m]/A$, with connection sets $\{\pm (\zeta_m^i + A): 0 \le i \le m-1\}$ and $\{\pm (\zeta_m^i + A): 0 \le i \le \phi(m) - 1\}$, respectively, where $\zeta_m$ ($m \ge 2$) is an $m$th primitive root of unity, $A$ a nonzero ideal of $\mathbb{Z}[\zeta_m]$, and $\phi$ Euler's totient function. We call them the $m$th cyclotomic graph and the second kind $m$th cyclotomic graph, and denote them by $G_{m}(A)$ and $G^*_{m}(A)$, respectively. We give a necessary and sufficient condition for $D/A$ to be a perfect $t$-code in $G^*_{m}(A)$ and a necessary condition for $D/A$ to be such a code in $G_{m}(A)$, where $t \ge 1$ is an integer and $D$ an ideal of $\mathbb{Z}[\zeta_m]$ containing $A$. In the case when $m = 3, 4$, $G_m((\alpha))$ is known as an Eisenstein-Jacobi and Gaussian networks, respectively, and we obtain necessary conditions for $(\beta)/(\alpha)$ to be a perfect $t$-code in $G_m((\alpha))$, where $0 \ne \alpha, \beta \in \mathbb{Z}[\zeta_m]$ with $\beta$ dividing $\alpha$. In the literature such conditions are known to be sufficient when $m=4$ and $m=3$ under an additional condition. We give a classification of all first kind Frobenius circulants of valency $2p$ and prove that they are all $p$th cyclotomic graphs, where $p$ is an odd prime. Such graphs belong to a large family of Cayley graphs that are efficient for routing and gossiping.
We electrically measure intrinsic silicon quantum dots with electrostatically defined tunnel barriers. The presence of both p-type and n-type ohmic contacts enables the accumulation of either electrons or holes. Thus we are able to study both transport regimes within the same device. We investigate the effect of the tunnel barriers and the electrostatically defined quantum dots. There is greater localisation of charge states under the tunnel barriers in the case of hole conduction leading to higher charge noise in the p-regime.
We investigate the dynamics of supermassive black holes (SMBHs) in galactic cores by means of a semi-analytic model based on the Langevin equation, including dynamical friction and stochastic noise accounting for the gravitational interactions with stars. The model is validated against direct $N$-body simulations of intermediate-mass black holes in stellar clusters where a realistic number of particles is accessible. For the galactic case, we find that the SMBH experiences a Brownian-like motion with a typical displacement from the geometric center of the Galaxy of a few parsecs, for system parameters compatible with M87. \keywords{stellar dynamics, black hole physics, methods: n-body simulations, methods: statistical.
We present a refinement of the widely accepted spin-wave spectrum that Kalinikos and Slavin computed for magnetic films with an in-plane magnetization (1986). The spin wave spectrum that follows from the diagonal approximation in this theory becomes inaccurate for relatively thick films, as has already been noted by Kreisel et al. (2009). Rather than solving an integrodifferential equation which follows from the magnetostatic Green's function, as done by Kalinikos and Slavin, we impose the exchange and magnetostatic boundary conditions on bulk spin-wave solutions. This boundary problem has an accurate analytical solution which is quantitatively different from the commonly used diagonal theory for magnetic films.
In this paper, firstly, we give the some fundamental properties of Van Der Laan numbers. After, we define the circulant matrices C(Z) which entries is third order linear recurrent sequence. In addition, we compute eigenvalues, spectral norm and determinant of this matrix. Consequently, by using properties of this sequence, we obtain the eigenvalues, norms and determinants of circulant matrices with Cordonnier, Perrin and Van Der Laan numbers.
We present an elaborate and systematic study of the conductance properties of a zigzag bilayer graphene nanoribbon modeled by a Kane-Mele (KM) Hamiltonian. The interplay of the Rashba and the intrinsic spin-orbit couplings with the edge states, electronic band structures, charge and spin transport are explored in details. We have analytically derived the conditions for the edge states for a bilayer KM nanoribbon and show how these modes decay for lattice sites inside the bulk. It is particularly interesting to note that for a finite-size ribbon an even number of zigzag ribbon hosts a finite energy gap at the Dirac points, while the odd ones do not. This asymmetry is present both in presence and absence of a bias voltage that may exist between the layers. The interlayer Rashba spin-orbit coupling, along with the intralayer intrinsic spin-orbit and intralayer Rashba spin-orbit couplings seem to destroy the quantum spin Hall (QSH) phase where the QSH phase is identified by the presence of a conductance plateau (of magnitude 4e/h) in the vicinity of zero Fermi energy. The plateau is sensitive to the values of the spin-orbit coupling parameters. Further, the spin polarized conductance data reveal that a bilayer KM ribbon is found to be more efficient for spintronic applications compared to a monolayer graphene. Finally, a quick check with experiments is done via computing the effective mass of electrons.
We study the spatiotemporal Bloch states of a high-frequency driven two-component Bose-Einstein condensate (BEC) with spin-orbit coupling (SOC) in an optical lattice. By adopting the rotating-wave approximation (RWA) and applying an exact trial-solution to the corresponding quasistationary system, we establish a different method for tuning SOC via external field such that the existence conditions of the exact particular solutions are fitted. Several novel features related to the exact states are demonstrated, such as SOC leads to spin-motion entanglement for the spatiotemporal Bloch states, SOC increases the population imbalance of the two-component BEC and SOC can be applied to manipulate the stable atomic flow which is conducive to control quantum transport of the BEC for different application purposes.
We propose a Hamiltonian for a nonrelativistic spin 1/2 \QTR{it}{free} particle (e.g. an electron) and find that it contains information of its internal degrees of freedom in the rest coordinate system. We comment on the dynamical symmetry associated with the electron \QTR{it}{Zitterbewegung}.
With a basic knowledge of cohomology theory, the background necessary to understand Hodge theory and polarization, Deligne's Mixed Hodge Structure on cohomology of complex algebraic varieties is described.
The bosonic atoms used in present day experiments on Bose-Einstein condensation are made up of fermionic electrons and nucleons. In this Letter we demonstrate how the Pauli exclusion principle for these constituents puts an upper limit on the Bose-Einstein-condensed fraction. Detailed numerical results are presented for hydrogen atoms in a cubic volume and for excitons in semiconductors and semiconductor bilayer systems. The resulting condensate depletion scales differently from what one expects for bosons with a repulsive hard-core interaction. At high densities, Pauli exclusion results in significantly more condensate depletion. These results also shed a new light on the low condensed fraction in liquid helium II.
This paper is devoted to superlensing using hyperbolic metamaterials: the possibility to image an arbitrary object using hyperbolic metamaterials without imposing any conditions on size of the object and the wave length. To this end, two types of schemes are suggested and their analysis are given. The superlensing devices proposed are independent of the object. It is worth noting that the study of hyperbolic metamaterials is challenging due to the change type of modelling equations, elliptic in some regions, hyperbolic in some others.
We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy method due to Kuelbs, Li, and Linde as well as on classical results about the entropy of classes of analytic functions. They also involve Tsirelson's upper bound for small deviations and shed some light on the limits of sharpness for that estimate.
The physical interpretation of the spectral line polarization produced by the joint action of the Hanle and Zeeman effects offers a unique opportunity to obtain empirical information about hidden aspects of solar and stellar magnetism. To this end, it is important to achieve a complete understanding of the sensitivity of the emergent spectral line polarization to the presence of a magnetic field. Here we present a detailed theoretical investigation on the role of resonance scattering and magnetic fields on the polarization signals of the Ba II D1 and D2 lines of the Fraunhofer spectrum, respectively at 4934 \AA\ and 4554 \AA. We adopt a three-level model of Ba II, and we take into account the hyperfine structure that is shown by the $^{135}$Ba and $^{137}$Ba isotopes. Despite of their relatively small abundance (18%), the contribution coming from these two isotopes is indeed fundamental for the interpretation of the polarization signals observed in these lines. We consider an optically thin slab model, through which we can investigate in a rigorous way the essential physical mechanisms involved (resonance polarization, Zeeman, Paschen-Back and Hanle effects), avoiding complications due to radiative transfer effects. We assume the slab to be illuminated from below by the photospheric solar continuum radiation field, and we investigate the radiation scattered at 90 degrees, both in the absence and in the presence of magnetic fields, deterministic and microturbulent. We show in particular the existence of a differential magnetic sensitivity of the three-peak Q/I profile that is observed in the D2 line in quiet regions close to the solar limb, which is of great interest for magnetic field diagnostics.