ShantanuT01/DACTYL-Pretraining huggingface dataset:
Context. The abundances of the three main isotopes of oxygen are altered in the course of the CNO-cycle. When the first dredge-up mixes the burning products to the surface, the nucleosynthesis processes can be probed by measuring oxygen isotopic ratios. Aims. By measuring 16O/17O and 16O/18O in red giants of known mass we compare the isotope ratios with predictions from stellar and galactic evolution modelling. Methods. Oxygen isotopic ratios were derived from the K-band spectra of six red giants. The sample red giants are open cluster members with known masses of between 1.8 and 4.5 Msun . The abundance determination employs synthetic spectra calculated with the COMARCS code. The effect of uncertainties in the nuclear reaction rates, the mixing length, and of a change in the initial abundance of the oxygen isotopes was determined by a set of nucleosynthesis and mixing models using the FUNS code. Results. The observed 16O/17O ratios are in good agreement with the model results, even if the measured values do not present clear evidence of a variation with the stellar mass. The observed 16O/18O ratios are clearly lower than the predictions from our reference model. Variations in nuclear reaction rates and mixing length parameter both have only a very weak effect on the predicted values. The 12C/13C ratios of the K giants studied implies the absence of extra-mixing in these objects. Conclusions. A comparison with galactic chemical evolution models indicates that the 16O/18O abundance ratio underwent a faster decrease than predicted. To explain the observed ratios, the most likely scenario is a higher initial 18O abundance combined with a lower initial 16 O abundance. Comparing the measured 18 O/17 O ratio with the corresponding value for the ISM points towards an initial enhancement of 17O as well. Limitations imposed by the observations prevent this from being a conclusive result.
A class of free quantum fields defined on the Poincare' group, is described by means of their two-point vacuum expectation values. They are not equivalent to fields defined on the Minkowski spacetime and they are "elementary" in the sense that they describe particles that transform according to irreducible unitary representations of the symmetry group, given by the product of the Poincare' group and of the group SL(2, C) considered as an internal symmetry group. Some of these fields describe particles with positive mass and arbitrary spin and particles with zero mass and arbitrary helicity or with an infinite helicity spectrum. In each case the allowed SL(2, C) internal quantum numbers are specified. The properties of local commutativity and the limit in which one recovers the usual field theories in Minkowski spacetime are discussed. By means of a superposition of elementary fields, one obtains an example of a field that present a broken symmetry with respect to the group Sp(4, R), that survives in the short-distance limit. Finally, the interaction with an accelerated external source is studied and and it is shown that, in some theories, the average number of particles emitted per unit of proper time diverges when the acceleration exceeds a finite critical value.
For a given generalized eta-quotient, we show that linear progressions whose residues fulfill certain quadratic equations do not give rise to a linear congruence modulo any prime. This recovers known results for classical eta-quotients, especially the partition function, but also yields linear incongruences for more general weakly holomorphic modular forms like the Rogers-Ramanujan functions.
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.
We study the integer points on superelliptic and hyperelliptic curves of the form $y^n=f(x)g(x),$ $n\ge 2, {\rm{deg}}{f}+{\rm{deg}}{g}\ge 4.$
The world-sheet quantum conformal invariance can be realized in the presence of the conformal factor $F$, by inclusion of Liouville term. In the background with linear dilaton field, $\Phi(x)=\Phi_0+a_\mu x^\mu$, the field $F$ becomes a new noncommutative variable. Therefore, it is natural to extend space-time with a new coordinate, $F$, in order to unify expressions for noncommutativity parameter $\Theta^{ij}$ of the space-time coordinates $x^i$, with the part $\Theta^i$ connecting noncommutativity between coordinates $x^i$ and $F$. In this way we solve the problems of Dp-brane noncommutativity in a more elegant way. The technical advantage uses the fact that in the extended space-time the action with dilaton field can be rewritten in dilaton free form. We use canonical method and extend its application to the derivation of boundary conditions. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form.
We describe a method for forecasting errors in interferometric measurements of polarization of the cosmic microwave background (CMB) radiation, based on the use of the Fisher matrix calculated from the visibility covariance and relation matrices. In addition to noise and sample variance, the method can account for many kinds of systematic error by calculating an augmented Fisher matrix, including parameters that characterize the instrument along with the cosmological parameters to be estimated. The method is illustrated with examples of gain errors and errors in polarizer orientation. The augmented Fisher matrix approach is applicable to a much wider range of problems beyond CMB interferometry.
We present a medium-dependent quantum optics approach to describe the influence of electron-acoustic phonon coupling on the emission spectra of a strongly coupled quantum-dot cavity system. Using a canonical Hamiltonian for light quantization and a photon Green function formalism, phonons are included to all orders through the dot polarizability function obtained within the independent Boson model. We derive simple user-friendly analytical expressions for the linear quantum light spectrum, including the influence from both exciton and cavity-emission decay channels. In the regime of semiconductor cavity-QED, we study cavity emission for various exciton-cavity detunings and demonstrate rich spectral asymmetries as well as cavity-mode suppression and enhancement effects. Our technique is nonperturbative, and non-Markovian, and can be applied to study photon emission from a wide range of semiconductor quantum dot structures, including waveguides and coupled cavity arrays. We compare our theory directly to recent and apparently puzzling experimental data for a single site-controlled quantum dot in a photonic crystal cavity and show good agreement as a function of cavity-dot detuning and as a function of temperature.
We have obtained the exact expression of the diffusion propagator in the time-dependent anharmonic potential $V(x,t)={1/2}a(t)x^2+b\ln x$. The underlying Euclidean metric of the problem allows us to obtain analytical solutions for a whole family of the elastic parameter a(t), exploiting the relation between the path integral representation of the short time propagator and the modified Bessel functions. We have also analyzed the conditions for the appearance of a non-zero flow of particles through the infinite barrier located at the origin (b<0).
We consider the genealogy of a sample of individuals taken from a spatially structured population when the variance of the offspring distribution is relatively large. The space is structured into discrete sites of a graph G. If the population size at each site is large, spatial coalescents with multiple mergers, so called spatial Lambda-coalescents, for which ancestral lines migrate in space and coalesce according to some Lambda-coalescent mechanism, are shown to be appropriate approximations to the genealogy of a sample of individuals.   We then consider as the graph G the two dimensional torus with side length 2L+1 and show that as L tends to infinity, and time is rescaled appropriately, the partition structure of spatial Lambda-coalescents of individuals sampled far enough apart converges to the partition structure of a non-spatial Kingman coalescent. From a biological point of view this means that in certain circumstances both the spatial structure as well as larger variances of the underlying offspring distribution are harder to detect from the sample. However, supplemental simulations show that for moderately large L the different structure is still evident.
An analysis is presented of the optical polarimetric and multicolour photometric ($BVRJ$) behaviour of the blazar PKS 2155$-$304 during an outburst in 2010. This flare develops over roughly 117 days, with a flux doubling time $\tau \sim 11$ days that increases from blue to red wavelengths. The polarization angle is initially aligned with the jet axis but rotates by roughly $90^\circ$ as the flare grows. Two distinct states are evident at low and high fluxes. Below 18 mJy, the polarization angle takes on a wide range of values, without any clear relation to the flux. In contrast, there is a positive correlation between the polarization angle and flux above 18 mJy. The polarization degree does not display a clear correlation with the flux. We find that the photopolarimetric behaviour for the high flux state can be attributed to a variable component with a steady power-law spectral energy distribution and high optical polarization degree (13.3%). These properties are interpreted within the shock-in-jet model, which shows that the observed variability can be explained by a shock that is seen nearly edge-on. Some parameters derived for the relativistic jet within the shock-in-jet model are: $B=0.06$ G for the magnetic field, $\delta=22.3$ for the Doppler factor and $\Phi=2.6^\circ$ for the viewing angle.
This is a note associated with my paper "From Quantum Dynamics to the Canonical Distribution: A Rigorous Derivation in Special Models" (cond-mat/9707253). Here I describe all the technical details which are not discussed in the main paper.
Spin wave excitations were measured in the ferromagnetic phase of Nd$_{1/2}$Sr$_{1/2}$MnO$_{3}$ by neutron scattering. This compound is located in proximity to the A-type antiferromagnetic state, and it shows a clear anisotropy and anomalous softening of the spin wave excitations. The softening in the ferromagnetic phase is induced by the orbital ordering.
We formulate a general and exact method of partial wave decomposition (PWD) of any nucleon-nucleon (NN) potential and any three-nucleon (3N) force. The approach allows one to efficiently use symbolic algebra software to generate the interaction dependent part of the program code calculating the interaction. We demonstrate the feasibility of this approach for the one-boson exchange BonnB potential, a recent nucleon-nucleon chiral force and the chiral two-pion-exchange three-nucleon force. In all cases very good agreement between the new and the traditional PWD is found. The automated PWD offered by the new approach is of the utmost importance in view of future applications of numerous chiral N3LO contributions to the 3N force in three nucleon calculations.
Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.
In this study the charged Higgs signal through triple or double Higgs production in a general two Higgs doublet model (2HDM) is investigated. The main production process is $e^+e^- \rightarrow H^+H^-H^0$ followed by the charged Higgs decay to a pair of $\tau \nu$ and the neutral Higgs decay to $b\bar{b}$. The alternative process $H^+W^-H^0$ is also included as a source of charged Higgs signal in the analysis having comparable cross-section. The focus is on a future $e^+e^-$ linear collider operating at $\sqrt{s}=1.5$ TeV. The final state under consideration ($\tau^+ \tau^- b \bar{b} E^{\textnormal{miss}}_{T}$) is suitable for electroweak background rejection using the $b-$tagging tools. It is shown that although the signal cross section is small, with a reasonable background suppression, high signal significance values are achievable at an integrated luminosity $500 fb^{-1}$ depending on the charged Higgs mass, $\tan\beta~$ and the CP-odd neutral Higgs mass. Finally results are quoted in terms of the signal significance for charged Higgs in the mass range $170<m_{H^{\pm}}<400$ GeV.
Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the triangular lattice, where the typical distance between the nearest exceptional sites is proportional to an integer parameter $n$. Thus, the corresponding curvature is asymptotically proportional to $- n^{-2}_{~}$. Spontaneous magnetization and specific heat are calculated by means of the corner transfer matrix renormalization group method. For all the finite $n$ cases, we observe the mean-field-like phase transition. It is confirmed that the entanglement entropy at the transition temperature is linear in $(c / 6) \ln n$, where $c = 1 / 2$ is the central charge of the Ising model. The fact agrees with the presence of the typical length scale $n$ being proportional to the curvature radius.
As the title ``Generalized regularity and solution concepts for differential equations'' suggests, the main topic of my thesis is the investigation of generalized solution concepts for differential equations, in particular first order hyperbolic partial differential equations with real-valued, non-smooth coefficients and their characteristic system of ordinary differential equations.   In Colombeau theory there have been developed existence results that yield solutions for ordinary and partial differential equations beyond the scope of classical approaches. Nevertheless this comes at the price of sacrificing regularity (in general a Colombeau solution may even lack a distributional shadow). It is prevailing in the Colombeau setting that the question of mere existence of solutions is much easier to answer than to determine their regularity properties (i.e. if a distributional shadow exists and how regular it is). In order order to address these regularity question and encouraged by the fact that the solution of a (homogeneous) first order partial differential equation can be written as a pullback of the initial condition by the characteristic backward flow, a main topic of my thesis deals with the microlocal analysis of pullbacks of c-bounded Colombeau generalized functions.   Another topic is the comparsion of Colombeau techniques for solving ordinary and partial differential equations to other generalized solution concepts, which has led to a joint article with G\"unther H\"ormann. A useful tool for this purpose is the concept of a generalized graph, which has been developed in the thesis.
Recent numerical relativity simulations within the Einstein--Maxwell--(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordstr\"om black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of the superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these $\textit{unstable}$ solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner-Nordstr\"om BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn.
We present a study of the radio emission from a massive runaway star. The star forms a bow shock that is clearly observed in the infrared. We have performed VLA observations under the assumption that the reverse shock in the stellar wind might accelerate charged particles up to relativistic energies. Non-thermal radio emission of synchrotron origin has been detected, confirming the hypothesis. We have then modeled the system and we predict a spectral energy distribution that extends up to gamma-rays. Under some simplifying assumptions, we find that the intensity at high energies is too low to be detected by current instruments, but the future Cherenkov Telescope Array might detect the source.
We study the parity of rank of $2$-${\rm Selmer}$ groups associated to $\pi/3$ and $2\pi/3$-congruent numbers. Our second result gives some positive densities about $\pi/3$ and $2\pi/3$ non-congruent numbers which can support the even part of Goldfeld's conjecture. We give some necessary conditions such that $n$ is non $\pi/3$-congruent number for elliptic curves $E_n$ whose Shafarevich-Tate group is non-trivial. In the last section, we show that for $n=pq\equiv 5(resp. \ 11)\pmod{24}$, the density of non $\pi/3$($resp.$ $2\pi/3$)-congruent numbers is at least 75\%, where $p,q$ are primes.
Let K be an algebraically closed valued field, and let f:X--->Y be a universally open morphism of K-schemes of finite type. We show that the induced map on K-rational points is open for the topologies deduced from the absolute value of K.   ------   Soit K un corps valu\'e alg\'ebriquement clos, et soit f:X--->Y un morphisme universellement ouvert de K-sch\'emas de type fini. On montre que l'application de X(K) dans Y(K) induite par f est ouverte pour les topologies d\'eduites de la valeur absolue sur K.
The spin of a number of black holes (BHs) in X-ray binaries (XBs) has been predicted (and, in at least three cases, confirmed by observations) by using a binary stellar evolution model with Case-C mass transfer . The rotational energy of such BHs is sufficient to power up (long) gamma-ray bursts and hypernovae (GRBs/HNe) and still leave a Kerr BH behind. However, strong magnetic fields (B fields) and/or dynamo effects in the interior of a BH-progenitor star may be capable of rapidly depleting the angular momentum from the stellar core, hence, preventing the formation of a collapsar. Thus, even if binaries can produce Kerr BHs, most of their rotation is acquired from accreting the stellar mantle, with a long delay between the formation of the BH and its spin up. Hence, not being good sources of GRBs.   We study the necessary conditions to produce GRBs by the progenitors of such BHs. Tidal-synchronization and Alfv\'en timescales are compared for B fields of different intensities threading trough He stars. We search for a B-field range which allows tidal spin up all the way into stellar core but prevents its slow down during differential rotation phases. Energetics for producing a strong B field during core collapse, which allows for GRB central engines, are also estimated. An observationally-reasonable choice of parameters is found.
In the first part of this article we show for some examples of surfaces of general type in toric 3-folds how to construct minimal and canonical models by toric methods explicitly. The examples we study turn out to be surfaces of general type, namely so called Kanev surfaces and Todorov surfaces. We show how properties of our examples of surfaces could be derived directly from properties of some polytopes and we compute the singularities of their canonical models.
Spin-dependent parton distributions in the polarized virtual photon are investigated in QCD up to the next-to-leading order (NLO). In the case $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NLO, but they are factorization-scheme-dependent. Parton distributions are analyzed in four different factorization schemes and their scheme dependence are discussed. Particular attentions are paid to the axial anomaly effect on the first moments of quark parton distributions, and also to the large-$x$ behaviors of the parton distributions. Gluon distribution in the virtual photon is found to be factorization-scheme independent up to the NLO.
We implement a one-loop analysis of the $\rho$ parameter in the Left Right Twin Higgs model, including the logarithmically enhanced contributions from both fermion and scalar loops. Numerical results show that the one-loop contributions are dominant over the tree level corrections in most regions of parameter space. The experimentally allowed values of $\rho$-parameter divide the allowed parameter space into two regions; less than $670 {\rm GeV}$ and larger than $1100 {\rm GeV}$ roughly, for symmetry breaking scale $f$. Our numerical analysis significantly reduces the parameter space which are favorably accessible to the LHC.
In this paper we prove an estimate for the total variation distance, in the framework of the Breuer-Major theorem, using the Malliavin-Stein method, assuming the underlying function $g$ to be once weakly differentiable with $g$ and $g'$ having finite moments of order four with respect to the standard Gaussian density. This result is proved by a combination of Gebelein's inequality and some novel estimates involving Malliavin operators.
Recently Lau-Jeyaseeli-Shiu-Arumugam introduced the concept of the "Sudoku colourings" of graphs -- partial $\chi(G)$-colourings of $G$ that have a unique extension to a proper $\chi(G)$-colouring of all the vertices. They introduced the Sudoku number of a graph as the minimal number of coloured vertices in a Sudoku colouring. They conjectured that a connected graph has Sudoku number $n-1$ if, and only if, it is complete. In this note we prove that this is true.
This paper is a review of the recent progresses on the branching brownian motion seen from its left-most particule. We describe in particular the recent works by Arguin-Bovier-Kistler and A\"id\'ekon-Berestycki-Brunet-Shi. This is the text in french of a Bourbaki seminar given in March 2013.
The corrected capacity of a quantum channel is defined as the best one-shot capacity that can be obtained by measuring the environment and using the result to correct the output of the channel. It is shown that (i) all qubit channels have corrected capacity log 2, (ii) a product of N qubit channels has corrected capacity N log 2, and (iii) all channels have corrected capacity at least log 2. The question is posed of finding the channel with smallest corrected capacity in any dimension d.