ShantanuT01/DACTYL-Pretraining huggingface dataset:
Kassapoglou recently proposed a model for fatigue of composite materials which seems to suggest that fatigue SN curve can be entirely predicted on the basis of the statistical distribution of static strengths. The original abstract writes "Expressions for the cycles to failure as a function of R ratio are derived. These expressions do not require any curve fitting and do not involve any experimentally determined parameters. The fatigue predictions do not require any fatigue tests for calibration". These surprisingly ambitious claims and attractive results deserve careful scrutiny. We contend that the results seem to be due to a number of approximations and incorrect derivations, and one particular misleading assumption, which make the model not conform to a fatigue testing in a given specimen with resulting SN curve distribution. The quantitative agreement of some predictions (the scatter of distribution of fatigue lives being close to the mode value found in typical composites of aeronautical interest in the large Navy database) should not motivate any enthusiasm. It is believed that a proper statistical treatment of the fatigue process should not make wear-out constants disappear, and hence the SN curves would depend on them, and not just on scatter of static data. These serious concerns explain the large discrepancies found by 3 independent studies which tried to apply Kassapoglou's model to composite fatigue data, and to other well known results.
A combinatorial approach is used to study the critical behavior of a $q$-state Potts model with a round-the-face interaction. Using this approach it is shown that the model exhibits a first order transition for $q>3$. A second order transition is numerically detected for $q=2$. Based on these findings, it is deduced that for some two-dimensional ferromagnetic Potts models with completely local interaction, there is a changeover in the transition order at a critical integer $q_c\leq 3$. This stands in contrast to the standard two-spin interaction Potts model where the maximal integer value for which the transition is continuous is $q_c=4$. A lower bound on the first order critical temperature is additionally derived.
We prove strong theorems for the local time at infinity of a nearest neighbor transient random walk. First, laws of the iterated logarithm are given for the large values of the local time. Then we investigate the length of intervals over which the walk runs through (always from left to right) without ever returning.
I briefly review the Regge approach to the hadron spectrum and advocate a dynamical emergence of principal quantum number in the known spectrum of light non-strange mesons. Further it is shown how the linear radial trajectories with universal slope can be extended to heavy quarkonia and a qualitative string interpretation is given. After that I discuss a recently proposed non-string model leading to a natural appearance of linear Regge trajectories and explaining many mass relations.
The exact solution of the asymmetric exclusion problem with particles of first and second class is presented. In this model the particles (size 1) of both classes are attached on lattice points and diffuse with equal asymmetric rates, but particles in the first class do not distinguish those in the second class from the holes (empty sites). We generalize and solve exactly this model by considering molecules in the first and second class with sizes $s_1$ and $s_2$ ($s_1,s_2 = 0,1,2,...$), in units of lattice spacing, respectively. The solution is derived by a Bethe ansatz of nested type. We give in this paper a pedagogical and simple presentation of the Bethe ansatz solution of the problem which can easily be followed by a non specialized audience in exactly integrable models.
The space of Hodge cycles of the general Prym variety is proved to be generated by its Neron-Severi group.
Asteroseismology has been proven to be a successful tool to unravel details of the internal structure for different types of stars in various stages of their main sequence and post-main sequence evolution. Recently, we found a relation between the detected pulsation properties in a sample of 34 pre-main sequence (pre-MS) delta Scuti stars and the relative phase in their pre-MS evolution. With this we are able to demonstrate that asteroseismology is similarly powerful if applied to stars in the earliest stages of evolution before the onset of hydrogen core burning.
The nonlinear optical properties and electro-optic effects of some oxygen-octahedric ferroelectrics are studied by the density functional theory (DFT) in the local density approximation (LDA) expressions based on first principle calculations without the scissor approximation. We present calculations of the frequency- dependent complex dielectric function and the second harmonic generation response coefficient \c{hi}(2)(-2{\omega},{\omega},{\omega}) over a large frequency range in tetragonal and rhombohedral phases. The electronic linear electrooptic susceptibility \c{hi}(2) (-{\omega},{\omega},0) is also evaluated below the band gap. These results are based on a series of the LDA calculation using DFT. Results for \c{hi}(2) (-{\omega},{\omega},0) are in agreement with the experiment below the band gap and those for \c{hi}(2)(-2{\omega},{\omega},{\omega}) are compared with the experimental data where available.
We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference term which presents a novel structure, as compared with the standard superposition of coherent states (degenerate case). We prove that, in any dimensions, the structure of the interference term is characterized by a particular quadratic form; in one degree of freedom the phase is hyperbolic. This phase-space structure survives the action of a thermal reservoir. We also discuss certain superpositions of {\em mixed} Gaussian states generated by conditional Gaussian operations or Kerr-type dynamics on thermal states.
We present an overview of precise pulsar timing using data from the Large Area Telescope (LAT) on Fermi. We describe the analysis techniques including a maximum likelihood method for determining pulse times of arrival from unbinned photon data. In addition to determining the spindown behavior of the pulsars and detecting glitches and timing noise, such timing analyses allow the precise determination of the pulsar position, thus enabling detailed multiwavelength follow up.
On the lattice $\widetilde{\mathbb Z}^2_+:={(x,y)\in \mathbb Z \times \mathbb Z_+\colon x+y \text{is even}}$ we consider the following oriented (northwest-northeast) site percolation: the lines $H_i:={(x,y)\in \widetilde {\mathbb Z}^2_+ \colon y=i}$ are first declared to be bad or good with probabilities $\de$ and $1-\de$ respectively, independently of each other. Given the configuration of lines, sites on good lines are open with probability $p_{_G}>p_c$, the critical probability for the standard oriented site percolation on $\mathbb Z_+ \times \mathbb Z_+$, and sites on bad lines are open with probability $p_{_B}$, some small positive number, independently of each other. We show that given any pair $p_{_G}>p_c$ and $p_{_B}>0$, there exists a $\delta (p_{_G}, p_{_B})>0$ small enough, so that for $\delta \le \delta(p_G,p_B)$ there is a strictly positive probability of oriented percolation to infinity from the origin.
A brief review of the energy spectrum of primary cosmic rays above $10^{10}$ eV and the measurement techniques used to investigate the ultra high energy ones is given. This is followed by a discussion of the atmospheric shower profile of the highest energy event observed using the Fly's Eye detector. Finally, cosmic ray simulation tools are discussed and used to investigate the heavy ion interpretation of the highest energy primary. The best way to contribute further to the understanding of this issue is by the collection of new and better data.
Strongly correlated metals close to the Mott transition display unusual transport regimes, together with large spectral weight transfers in optics and photoemission. We briefly review the theoretical understanding of these effects, based on the dynamical mean-field theory, and emphasize the key role played by the two energy scales associated with quasiparticle coherence scale and with the Mott gap. Recent experimental results on two-dimensional organic compounds and transition metal oxides are considered in this perspective. The liquid-gas critical behaviour at the Mott critical endpoint is also discussed. Transport calculations using the numerical renormalization group are presented.
We investigate a possible connection between Galileon gravity and teleparallel gravity. We also propose a new type of second order cosmological lagrangian and study a some of its properties.
The Galton-Watson process belongs to standard teaching in probability. The basic theorem says that survival is only possible when the fecondity exceeds 1. The classical proof is essentially analytic, using generating functions and convexity arguments. We give here a more probabilistic proof, in the spirit of Bezuidenhout and Grimmett.
We report a field-temperature phase diagram and an entropy map for the heavy fermion compound CeAuSb$_2$. CeAuSb$_2$ orders antiferromagnetically below $T_N=6.6$~K, and has two metamagnetic transitions, at 2.8 and 5.6~T. The locations of the critical endpoints of the metamagnetic transitions, which may play a strong role in the putative quantum criticality of CeAuSb$_2$ and related compounds, are identified. The entropy map reveals an apparent entropy balance with Fermi liquid behavior, implying that above the N\'{e}el transition the Ce moments are incorporated into the Fermi liquid. High-field data showing that the magnetic behavior is remarkably anisotropic are also reported.
Blazars are a kind of active galactic nuclei (AGN) in which a relativistic jet is considered to be directed along the line of sight. They are characterized by strong and rapid variability of the flux and high polarization. We performed a monitoring of 41 blazars in the optical and near-infrared regions from 2008 to 2009 using TRISPEC attached to the "Kanata" 1.5-m telescope. In this paper, we report the correlation of the flux, color and polarization using our data, and discuss universal features for blazars, which have not fully been established. Three blazars (3C 454.3, QSO 0454$-$234, and PKS 1510$-$089) tended to be redder when they were brighter, only during their faint states. This color behavior suggests that the contribution of a thermal component is strong in the faint states for those objects. Excluding this "redder-when-brighter" phase, we found that 24 blazars tended to be bluer when they were brighter. This number corresponds to 83% among well-observed objects which we observed for $>10$ nights. Thus, we conclude that the "bluer-when-brighter" trend is a universal feature for blazars. On the other hand, the correlation of the flux and the polarization degree is relatively weak; only 10 objects showed a significant positive correlation. We also investigated the luminosity-dependence of the color and polarization, and found that lower luminosity objects have smaller variation amplitudes both in the flux, color, and polarization degree.
The Kibble-Zurek mechanism describes the saturation of critical scaling upon dynamically approaching a phase transition. This is a consequence of the breaking of adiabaticity due to the scale set by the slow drive. By driving the gap parameter, this can be used to determine the leading critical exponents. But this is just the `tip of the iceberg': Driving more general couplings allows one to activate the entire universal spectrum of critical exponents. Here we establish this phenomenon and its observable phenomenology for the quantum phase transitions in an analytically solvable minimal model and the experimentally relevant transverse XY model. The excitation density is shown to host the sequence of exponents including the subleading ones in the asymptotic scaling behavior by a proper design of the geometry of the driving protocol in the phase diagram. The case of a parallel drive relative to the phase boundary can still lead to the breaking of adiabaticity, and exposes the subleading exponents in the clearest way. Complementarily to disclosing universal information, we extract the restrictions due to the non-universal content of the models onto the extent of the subleading scalings regimes.
The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-\Delta)^{\beta/2} u(t,x) + u(t,x)\dot{W}(t,x), \quad t>0,x \in \bR^d$$ with initial condition bounded above and below, where $\beta \in (0,2]$ and the noise $W$ behaves in time like a fractional Brownian motion of index $H>1/2$, and has a spatial covariance given by the Riesz kernel of index $\alpha \in (0,d)$. As a by-product, we obtain that the necessary and sufficient condition for the existence of the solution is $\alpha<\beta$.
Scalar and tensor cosmological perturbations during an inflationary universe scenario in the context of the a generalized gravity theory are studied. This analyze is carried out considering an ansatz on the variables associated to scalar and tensor perturbation ($z_s$ and $z_t$) in the Jordan frame. In this context, we analyze two different Ansatze for the ratio $z_s/z_t$, and we study in great detail the analytical and exact solutions for the cosmological perturbations together with the corresponding reconstruction of the background variables. Recent observational data from the Planck 2018 results are employed to constrain the parameters of each of the models.
We present a long-term study of the secondary star in the cataclysmic variable AE~Aqr, using Roche tomography to indirectly image starspots on the stellar surface spanning 8~years of observations. The 7 maps show an abundance of spot features at both high and low latitudes. We find that all maps have at least one large high-latitude spot region, and we discuss its complex evolution between maps, as well as its compatibility with current dynamo theories. Furthermore, we see the apparent growth in fractional spot coverage, $f_{\mathrm{s}}$, around $45^{\circ}$~latitude over the duration of observations, with a persistently high $f_{\mathrm{s}}$ near latitudes of $20^{\circ}$. These bands of spots may form as part of a magnetic activity cycle, with magnetic flux tubes emerging at different latitudes, similar to the `butterfly' diagram for the Sun. We discuss the nature of flux tube emergence in close binaries, as well as the activity of AE~Aqr in the context of other stars.
While we have learned much about Ultra-Diffuse Galaxies (UDGs) in groups and clusters, relatively little is known about them in less-dense environments. More isolated UDGs are important for our understanding of UDG formation scenarios because they form via secular mechanisms, allowing us to determine the relative importance of environmentally-driven formation in groups and clusters. We have used the public Kilo-Degree Survey (KiDS) together with the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) to constrain the abundance and properties of UDGs in the field, targeting sources with low surface brightness (24.0$\leq$\bar{\mu}_{e,r}}$\leq$\26.5) and large apparent sizes (3.0\arcsec$\leq$\bar{r}_{e,r}}$\leq$8.0\arcsec). Accounting for several sources of interlopers in our selection based on canonical scaling relations, and using an empirical UDG model based on measurements from the literature, we show that a scenario in which cluster-like red sequence UDGs occupy a significant number of field galaxies is unlikely, with most field UDGs being significantly bluer and showing signs of localised star formation. An immediate conclusion is that UDGs are much more efficiently quenched in high-density environments. We estimate an upper-limit on the total field abundance of UDGs of 8$\pm$3$\times10^{-3}$cMpc$^{-3}$ within our selection range. We also compare the total field abundance of UDGs to a measurement of the abundance of HI-rich UDGs from the literature, suggesting that they occupy at least one-fifth of the overall UDG population. The mass formation efficiency of UDGs implied by this upper-limit is similar to what is measured in groups and clusters.
Let B_1,B_2 be balls in finite-dimensional real vector spaces E_1,E_2, centered around unit length vectors v_1,v_2 and not containing zero. An element in the tensor product space E_1 \otimes E_2 is called B_1 \otimes B_2-separable if it is contained in the convex conic hull of elements of the form w_1 \otimes w_2, where w_1 \in B_1, w_2 \in B_2. We study the cone formed by the separable elements in E_1 \otimes E_2. We determine the largest faces of this cone via a description of the extreme rays of the dual cone, i.e. the cone of the corresponding positive linear maps. We compute the radius of the largest ball centered around v_1 \otimes v_2 that consists of separable elements. As an application we obtain lower bounds on the radius of the largest ball of separable unnormalized states around the identity matrix for a multi-qubit system. These bounds are approximately 12% better than the best previously known. Our results are extendible to the case where B_1,B_2 are solid ellipsoids.
We present the critical theory of a number of zero temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S = 1/2 square lattice antiferromagnet between the Neel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a second order quantum phase transition. The critical theory is not expressed in terms of the order parameters characterizing either state (as would be the case in Landau-Ginzburg-Wilson theory) but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half-filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z_2 spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.
We suggest a novel approach to polynomial processes solely based on a polynomial action operator. With this approach, we can analyse such processes on general state spaces, going far beyond Banach spaces. Moreover, we can be very flexible in the definition of what "polynomial" means. We show that "polynomial process" universally means "affine drift". Simple assumptions on the polynomial action operators lead to stronger characterisations on the polynomial class of processes.   In our framework we do not need to specify polynomials explicitly but can work with a general sequence of graded vector spaces of functions on the state space. Elements of these graded vector spaces form the monomials by introducing a sequence of vector space complements. The basic tool of our analysis is the polynomial action operator, which is a semigroup of operators mapping conditional expected values of monomials acting on the polynomial process to monomials of the same or lower grade. Unlike the classical Euclidean case, the polynomial action operator may not form a finite-dimensional subspace after a finite iteration, a property we call locally finite. We study abstract polynomial processes under both algebraic and topological assumptions on the polynomial actions, and establish an affine drift structure. Moreover, we characterize the covariance structure under similar but slightly stronger conditions. A crucial part in our analysis is the use of the (algebraic or topological) dual of the monomials of grade one, which serves as a linearization of the state space of the polynomial process. Our general framework covers polynomial processes with values in Banach spaces recently studied by Cuchiero and Svaluto-Ferro.
We report the discovery, by the Chandra X-ray Observatory, of X-ray emission from the bipolar planetary nebula Menzel 3. In Chandra CCD imaging, Mz 3 displays hot (3-6x10^6 K) gas within its twin, coaxial bubbles of optical nebulosity, as well as a compact X-ray source at the position of its central star(s). The brightest diffuse X-ray emission lies along the polar axis of the optical nebula, suggesting a jet-like configuration. The observed combination of an X-ray-emitting point source and possible X-ray jet(s) is consistent with models in which accretion disks and, potentially, magnetic fields shape bipolar planetary nebulae via the generation of fast, collimated outflows.
We consider a controlled second order differential equation which is partially observed with an additional fractional noise. we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of the unknown signal drift parameter. When the input depends on the unknow parameter, we will try the one-step estimation procedure using the Newton-Raphson method.
Most of the cosmological information extracted from the CMB has been obtained through the power spectrum, however there is much more to be learnt from the statistical distribution of the temperature random field. We review some recent developments in the study of the Cosmic Microwave Background (CMB) anisotropies and present a description of the novel tools developed to analyse the properties of the CMB anisotropies beyond the power spectrum.
Recently, several authors have criticized time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was the proof, which appeared in various forms, showing that counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with the standard quantum theory. I argue here that the apparent contradiction appears due to inappropriate usage of traditional time asymmetric approach to counterfactuals, and that the contradiction disappears when the problem is analyzed in terms of time-symmetric counterfactuals. I analyze various aspects of time-symmetry of quantum theory and defend the time-symmetrized formalism.