ShantanuT01/DACTYL-Pretraining huggingface dataset:
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here the aim is therefore to generalize this efficient numerical approach in order to obtain an approximation of both the exit time and position for either a general linear diffusion or a growth diffusion. The efficiency of the method is described with particular care through theoretical results and numerical examples.
The density profile of a cool core of intracluster gas is investigated for a cluster of galaxies that is initially in the virial equilibrium state, and then undergoes radiative cooling. The initial gas profile is derived under the assumption that the gas is hydrostatic within the dark-matter potential presented by the NFW or King model, and has a polytropic profile. The contribution of masses of gas and galaxies to the potential in the calculation is ignored compared to the dark matter. The temperature and density profiles of gas in its quasi-hydrostatic cooling phase, which is expected to last for ~Gyr, is then calculated for different initial gas profiles. It is found that in the quasi-hydrostatic cooling phase, while the temperature decreases to about 1/3, the density increases by a factor of 4-6 at the cluster center in comparison with their initial polytropic values, though the profiles over the core depend on the dark-matter potential. Hence, the core radius in the quasi-hydrostatic cooling gas appears to be smaller than that in the initial polytropic gas. We compared the density profile of the cool core with observations to find that, while the initial density is around the upper bounds of large-core (>100 kpc) clusters, most likely relaxed, but the cooling is not yet significant, the central density under quasi-hydrostatic cooling falls between the mid- and high-values of small (<100 kpc)- or cool-core clusters. It is also found for the quasi-hydrostatic cooling gas that the entropy profile roughly agrees with the best-fit model to the ACCEPT sample with a low central entropy; also, the pressure gradient in the inner core is close to that of the REXCESS sample. X-ray surface brightness calculated for the quasi-hydrostatic cooling gas is well represented by the conventional double beta-model, giving a physical basis for applying the double beta-model to cool-core clusters.
Here we present detailed analysis of the distinct X-ray emission features present within the Eastern radio lobe of the Pictor A galaxy, around the jet termination region, utilising the data obtained from the Chandra X-ray Observatory. Various emission features have been selected for the study based on their enhanced X-ray surface brightness, including five sources that appear point-like, as well as three extended regions, one characterised by a filamentary morphology. For those, we perform a basic spectral analysis within the 0.5-7keV range. We also investigate various correlations between the X-ray emission features and the non-thermal radio emission, utilising the high-resolution radio maps from the Very Large Array at GHz frequencies. The main novel findings following from our analysis, regard the newly recognized bright X-ray filament located upstream of the jet termination region, extending for at least thirty kiloparsec (projected), and inclined with respect to the jet axis. For this feature, we observe a clear anti-correlation between the X-ray surface brightness and the polarized radio intensity, as well as a decrease in the radio rotation measure with respect to the surroundings. We speculate on the nature of the filament, in particular addressing a possibility that it is related to the presence of a hot X-ray emitting thermal gas, only partly mixed with the non-thermal radio/X-ray emitting electrons within the lobe, combined with the reversals in the lobe's net magnetic field.
Spectropolarimetric observations have been used to map stellar magnetic fields, many of which display strong bands of azimuthal fields that are toroidal. A number of explanations have been proposed to explain how such fields might be generated though none are definitive. In this paper, we examine the toroidal fields of a sample of 55 stars with magnetic maps, with masses in the range 0.1-1.5$\,{\rm M}_\odot$. We find that the energy contained in toroidal fields has a power law dependence on the energy contained in poloidal fields. However the power index is not constant across our sample, with stars less and more massive than 0.5$\,{\rm M}_\odot$ having power indices of 0.72$\pm$0.08 and 1.25$\pm$0.06 respectively. There is some evidence that these two power laws correspond to stars in the saturated and unsaturated regimes of the rotation-activity relation. Additionally, our sample shows that strong toroidal fields must be generated axisymmetrically. The latitudes at which these bands appear depend on the stellar rotation period with fast rotators displaying higher latitude bands than slow rotators. The results in this paper present new constraints for future dynamo studies.
The purpose of this paper is twofold. First, we will present recent results on the data processing for LISA, including algorithms for elimination of clock jitter noise and discussion of the generation of the data averages that will eventually need to be telemetered to the ground. Second, we will argue, based partly on these results, that a laser interferometer tracking system (LITS) that employs independent lasers in each spacecraft is preferable for reasons of simplicity to that in which the lasers in two of the spacecraft are locked to the incoming beam from the third.
I discuss the relation between the nuclear response and the Green function describing the propagation of a nucleon in the nuclear medium. Within this formalism, the widely used expressions in terms of spectral functions can be derived in a consistent and rigorous fashion. The results of recent applications to the study of the inclusive electron-nucleus cross section in the impulse approximation regime are brielfy analyzed.
In principle the geometry of the universe can be investigated by measuring the angular size of known objects as a function of distance. Thus the distribution of angular sizes provides a critical test of the stable and static model of the universe described by Crawford (1991,1993) that has a simple and explicit relationship between the angular size of an object and its redshift. The result is that the agreement with observations of galactic diameters and the size of double radio sources with the static model is much better than the standard (Big Bang) theory without evolution. However there is still a small discrepancy at large redshifts that could be due to selection effects.
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between physical and mathematical aspects, particularly regarding the role of probability theory. The focus is on the equilibrium case, which is currently better understood, serving also as a prelude for a further discussion of non-equilibrium statistical mechanics.
We consider a generalisation to quasilinear systems of the matched microstructure model. The proof of well posedness in a strong Sobolev setting is based on an approach via maximal regularity.
We discuss the physics capabilities of basic types of future atmospheric detectors being considered at present, with their strengths and limitations, and compare them with those of long baseline (LBL) experiments. We also argue that recent studies signal the importance of synergistically combining complementary features of both these classes of experiments in order to accrue maximum benefit towards furthering our goal of building a complete picture of neutrino properties and parameters.
We promote the Immirzi parameter to be a minimally coupled scalar field and we analyzed the Hamiltonian constraints in the framework of Loop Quantum Gravity without the time gauge. Proper SU(2) connections can be defined and a term containing derivatives of the field $\beta$ enters into their definition. Furthermore, boost degrees of freedom are non-dynamical, while the super-momentum constraints coincide with the scalar field case. Hence, the kinematical Hilbert space can be defined as for gravity in presence of a minimally coupled scalar field. Then, we analyzed the dynamical implications of this scenario and we outlined how a the dynamical relaxation to a non-vanishing vacuum expectation value is predicted.
We present results of morphological and spectroscopic study of hot gas in some early-type galaxies based on the analysis of high resolution X-ray images acquired from the archive of Chandra space mission. Distribution of the hot gas in target galaxies after eliminating contribution from the discrete sources (LMXBs) displays varied morphologies, ranging from very compact nuclear emission to very extensive emission, larger than even optical images of the host galaxies. The surface brightness profile of the hot gas in program galaxies is well described by a single beta model, while spectrum of the diffuse emission is best fitted by a combined soft MEKAL model and a hard power law model. We use these results to derive temperature and abundance profiles of the hot gas in host galaxies. The deprojection of the diffuse emission shows a temperature gradient in some of the galaxies.   We also report on the 2-D distribution of the discrete sources (LMXBs) in host galaxies and compare it with their optical morphologies. The X-ray spectrum of the resolved sources is well-fit by a hard power law model with X-ray luminosities (0.3 to 10 keV) in the range from 5$\times$ 10$^{37}$ to 2.5$\times$ 10$^{39}$ erg s$^{-1}$. X-ray luminosity function (XLF) of the LMXBs shows a break near the luminosity comparable to the Eddington luminosity for a 1.4 M$_\odot$ neutron star.
Critical exponent $\eta$ (Fisher exponent) in $O(N)$-symmetric $\varphi^4$-model was calculated using renormalization group approach in the space of fixed dimension $D=2$ up to 6~loops. The calculation of the renormalization constants was performed with the use of $R'$-operation and specific values for diagrams were calculated in Feynman representation using sector decomposition method. Presented approach allows easy automation and generalization for the case of complex symmetries. Also a summation of the perturbation series was obtained by Borel transformation with conformal mapping. The contribution of the 6-th term of the series led to the increase of the Fisher exponent in $O(1)$ model up to $8\%$.
We present a study of a sample of LMC red giants exhibiting Long Secondary Periods (LSPs). We use radial velocities obtained from VLT spectral observations and MACHO and OGLE light curves to examine properties of the stars and to evaluate models for the cause of LSPs. This sample is much larger than the combined previous studies of Hinkle et al. (2002) and Wood, Olivier & Kawaler (2004). Binary and pulsation models have enjoyed much support in recent years. Assuming stellar pulsation, we calculate from the velocity curves that the typical fractional radius change over an LSP cycle is greater than 30 per cent. This should lead to large changes in Teff that are not observed. Also, the small light amplitude of these stars seems inconsistent with the radius amplitude. We conclude that pulsation is not a likely explanation for the LSPs. The main alternative, physical movement of the star -- binary motion -- also has severe problems. If the velocity variations are due to binary motion, the distribution of the angle of periastron in our large sample of stars has a probability of 1.4e-3 that it comes from randomly aligned binary orbits. In addition, we calculate a typical companion mass of 0.09 Msun. Less than 1 per cent of low mass main sequence stars have companions near this mass (0.06 to 0.12 Msun) whereas ~25 to 50 per cent of low mass red giants end up with LSPs. We are unable to find a suitable model for the LSPs and conclude by listing their known properties.
In this work, we investigate the spectrum of singularities of random stable trees with parameter $\gamma\in(1,2)$. We consider for that purpose the scaling exponents derived from two natural measures on stable trees: the local time $\ell^a$ and the mass measure $\textbf{m}$, providing as well a purely geometrical interpretation of the latter exponent. We first characterise the uniform component of the multifractal spectrum which exists at every level $a>0$ of stable trees and corresponds to large masses with scaling index $h\in[\tfrac{1+\gamma}{\gamma},\tfrac{\gamma}{\gamma-1}]$ for the mass measure (or equivalently $h\in [\tfrac{1}{\gamma},\tfrac{1}{\gamma-1}]$ for the local time). In addition, we investigate the distribution of vertices appearing at random levels with exceptionally large masses of index $h\in[0,\tfrac{1+\gamma}{\gamma})$. Finally, we discuss more precisely the order of the largest mass existing on any subset $\mathcal{T}(F)$ of a stable tree, characterising the former with the packing dimension of the set $F$.
Let $\Omega$ be a smooth, convex, unbounded domain of $\R^N$. Denote by $\mu_1(\Omega)$ the first nontrivial Neumann eigenvalue of the Hermite operator in $\Omega$; we prove that $\mu_1(\Omega) \ge 1$. The result is sharp since equality sign is achieved when $\Omega$ is a $N$-dimensional strip. Our estimate can be equivalently viewed as an optimal Poincar\'e-Wirtinger inequality for functions belonging to the weighted Sobolev space $H^1(\Omega,d\gamma_N)$, where $\gamma_N$ is the $N$-dimensional Gaussian measure.
We prove a central limit theorem with aassumptions which are many weak than classical conditions
We present, and analyze thoroughly, a highly symmetric and efficient scheme for the determination of a single-qubit state, such as the polarization properties of photons emitted by a single-photon source. In our scheme there are only four measured probabilities, just enough for the determination of the three parameters that specify the qubit state, whereas the standard procedure would measure six probabilities.
Over the past two decades, the research of (Ga,Mn)As has led to a deeper understanding of relativistic spin-dependent phenomena in magnetic systems. It has also led to discoveries of new effects and demonstrations of unprecedented functionalities of experimental spintronic devices with general applicability to a wide range of materials. In this article we review the basic material properties that make (Ga,Mn)As a favorable test-bed system for spintronics research and discuss contributions of (Ga,Mn)As studies in the general context of the spin-dependent phenomena and device concepts. Special focus is on the spin-orbit coupling induced effects and the reviewed topics include the interaction of spin with electrical current, light, and heat.
We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, P_c(G), with very high accuracy. The RG flow of P(G) yields a value of the critical exponent nu that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as R_L and R_H is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD) which is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with nu=2.37\pm 0.02. Away from the transition it changes towards the Poisson distribution. We next investigate the plateau-to-insulator transition. For a fully quantum coherent situation, we find a quantized Hall insulator with R_H ~ h/e^2 up to R_L ~ 20 h/e^2 when interpreting the results in terms of the most probable value of the distribution P(R_H). Upon further increasing R_L, the Hall insulator with diverging R_H ~ R_L^kappa is seen. This crossover depends on the precise nature of the averaging of P(R_L) and P(R_H). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition modeled by a power law correlation in the random potential. Similar to the classical percolation, we observe an enhancement of nu with decreasing correlation range. These results exemplify the surprising fact that a small RG unit, containing five nodes, accurately captures most of the correlations responsible for the QH transition.
A method is presented to obtain the canonical-form solutions of the HFB equation for atomic nuclei with zero-range interactions like the Skyrme force. It is appropriate to describe pairing correlations in the continuum in coordinate-space representations. An improved gradient method is used for faster convergences under constraint of orthogonality between orbitals. To prevent high-lying orbitals to shrink into a spatial point, a repulsive momentum dependent force is introduced, which turns out to unveil the nature of high-lying canonical-basis orbitals. The asymptotic properties at large radius and the relation with quasiparticle states are discussed for the obtained canonical basis.
The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated as a quantum field, so no classical metrical or causal structure is present on spacetime. We describe an approach -- much in the spirit of ideas proposed by Misner, Kuchar and others -- to defining states and local observables in quantum gravity which exploits the analogy between the Hamiltonian formulation of general relativity and that of a relativistic particle. In the case ofminisuperspace models, a concrete theory is obtained which appears to be mathematically and physically viable, although it contains some radical features with regard to the presence of an "arrow of time". The viability of this approach in the case ofinfinitely many degrees of freedom rests on a number of fairlywell defined issues, which, however, remain unresolved. As a byproduct of our analysis, the theory of a relativistic particle in curved spacetime is developed.
Measurements of [CI], (J=2-1) 13CO and (J=4-3) 12CO emission from quiescent, starburst and active galaxy centers reveal a distinct pattern characterized by relatively strong [CI] emission. The [CI] to 13CO emission ratio increases with central [CI] luminosity. It is lowest in quiescent and mild starburst centers and highest for strong starburst centers and active nuclei. Neutral C abundances are close to, or even exceed, CO abundances. The emission is characteristic of warm and dense gas rather than either hot tenuous or cold very dense gas. The relative intensities of CO, [CI], [CII] and far-infrared emission suggest that the dominant excitation mechanism in galaxy centers may be different from that in Photon-Dominated Regions (PDRs).
We consider the initial value problem for the Dirac-Klein-Gordon equations in two space dimensions. Global regularity for $C^\infty$ data was proved by Gr\"unrock and Pecher. Here we consider analytic data, proving that if the initial radius of analyticity is $\sigma_0 > 0$, then for later times $t > 0$ the radius of analyticity obeys a lower bound $\sigma(t) \ge \sigma_0 \exp(-At)$. This provides information about the possible dynamics of the complex singularities of the holomorphic extension of the solution at time $t$. The proof relies on an analytic version of Bourgain's Fourier restriction norm method, multilinear space-time estimates of null form type and an approximate conservation of charge.
Some characterizations of mixed renewal processes in terms of exchangeability and of different types of disintegrations are given. As a consequence, an existence result for mixed renewal processes, providing also a new construction for them, is obtained. As an application, some concrete examples of constructing such processes are presented and the corresponding disintegrating measures are explicitly computed.
Form factors in planar N=4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in arXiv:2009.11297. This expansion is based on a decomposition of the dual periodic Wilson loop into elementary building blocks: the known pentagon transitions and a new object that we call form factor transition, which encodes the information about the local operator. In this paper, we compute the two-particle form factor transitions for the chiral part of the stress-tensor supermultiplet at Born level; they yield the leading contribution to the OPE. To achieve this, we explicitly construct the Gubser-Klebanov-Polyakov two-particle singlet states. The resulting transitions are then used to test the OPE against known perturbative data and to make higher-loop predictions.
The Metal-Insulator transition (MIT) in VO2 is characterized by the complex interplay among lattice, electronic and orbital degrees of freedom. In this contribution we investigated the strain-modulation of the orbital hierarchy and the influence over macroscopic properties of the metallic phase of VO2 such as Fermi Level (FL) population and metallicity, i.e., the material ability to screen an electric field, by means of temperature-dependent X-ray Absorption Near Edge Structure (XANES) and Resonant Photoemission spectroscopy (ResPES). We demonstrate that the MIT in strained VO2 is of the Filling Control type, hence it is generated by electron correlation effects. In addition, we show that the MIT in Nanostructured (NS) disordered VO2, where the structural phase transition is quenched, is driven by electron correlation. Therefore a fine tuning of the correlation could lead to a precise control and tuning of the transition features.
OGLE-2014-BLG-0962 (OB140962) is a stellar binary microlensing event that was well-covered by observations from the Spitzer satellite as well as ground-based surveys. Modelling yields a unique physical solution: a mid-M+M-dwarf binary with $M_{\rm prim} = 0.20 \pm 0.01 M_\odot$ and $M_{\rm sec} = 0.16 \pm 0.01 M_\odot$, with projected separation of $2.0 \pm 0.3$ AU. The lens is only $D_{\rm LS} = 0.41 \pm 0.06$ kpc in front of the source, making OB140962 a bulge lens and the most distant Spitzer binary lens to date. In contrast, because the Einstein radius ($\theta_{\rm E} = 0.143 \pm 0.007$ mas) is unusually small, a standard Bayesian analysis, conducted in the absence of parallax information, would predict a brown dwarf binary. We test the accuracy of Bayesian analysis over a set of Spitzer lenses, finding overall good agreement throughout the sample. We also illustrate the methodology for probing the Galactic distribution of planets by comparing the cumulative distance distribution of the Spitzer 2-body lenses to that of the Spitzer single lenses.
The non-Markovian effects in the spin dynamics in diluted magnetic semiconductors found in quantum kinetic calculations can be reproduced very well by a much simpler effective single electron theory, if a finite memory is accounted for. The resulting integro-differential equation can be solved by a differential transform method, yielding the Taylor series of the solution. From the comparison of both theories it can be concluded that the non-Markovian effects are due to the spectral proximity of the excited electrons to the band edge.
We geometrically describe a canonical sequence of modular blowups of the relative Picard stack of the Artin stack of pre-stable genus two curves. The final blowup stack locally diagonalizes certain tautological derived objects. This implies a resolution of the primary component of the moduli space of genus two stable maps to projective space and meanwhile makes the whole moduli space admit only normal crossing singularities. Our approach should extend to higher genera.