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How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and outof-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.
We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent alpha are considered for the WTD psi(t) similar to 1/t(1+alpha). We treat continuous-time random walks (CTRWs) with 0 < alpha < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < alpha < 2 and alpha > 2. We demonstrate that in the presence of a drift CTRWs with alpha < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < alpha < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with alpha > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < alpha < 2 and alpha > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with alpha > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent alpha.
A numerical framework is developed to study the hysteresis of elastic properties of porous ceramics as a function of temperature. The developed numerical model is capable of employing experimentally measured crystallographic orientation distribution and coefficient of thermal expansion values. For realistic modeling of the microstructure, Voronoi polygons are used to generate polycrystalline grains. Some grains are considered as voids, to simulate the material porosity. To model intercrystalline cracking, cohesive elements are inserted along grain boundaries. Crack healing (recovery of the initial properties) upon closure is taken into account with special cohesive elements implemented in the commercial code ABAQUS. The numerical model can be used to estimate fracture properties governing the cohesive behavior through inverse analysis procedure. The model is applied to a porous cordierite ceramic. The obtained fracture properties are further used to successfully simulate general non-linear macroscopic stress-strain curves of cordierite, thereby validating the model.
We demonstrate a tilted pulse-front transient grating (TG) technique that allows to optimally utilize time resolution as well as TG line density while probing under grazing incidence as typically done in extreme ultraviolet (EUV) or soft x-ray (SXR) experiments. Our optical setup adapts the pulse front tilt of the two pulses that create the TG to the grazing incident pulse. We demonstrate the technique using all 800 nm femtosecond laser pulses for TG generation on a vanadium dioxide film. We probe that grating via diffraction of a third 800 nm pulse. The time resolution of 90 fs is an improvement by a factor of 30 compared to our previous experiments on the same system. The scheme paves the way for EUV and SXR probing of optically induced TGs on any material.
This study examines the relationship between the magnetic mesostructure with the microstructure of low carbon steel tungsten inert gas welds. Optical microscopy revealed variation in the microstructure of the parent material, in the heat affected and fusion zones, correlating with distinctive changes in the local magnetic stray fields measured with high spatial resolution giant magneto resistance sensors. In the vicinity of the heat affected zone high residual stresses were found using neutron diffraction. Notably, the gradients of von Mises stress and triaxial magnetic stray field modulus follow the same tendency transverse to the weld. In contrast, micro-X-ray fluorescence characterization indicated that local changes in element composition had no independent effect on magnetic stray fields.
We present very-high-resolution 1D MHD simulations of the late-stage supernova remnants (SNRs). In the post-adiabatic stage, the magnetic field has an important and significant dynamical effect on the shock dynamics, the flow structure, and hence the acceleration and emission of cosmic rays. We find that the tangential component of the magnetic field provides pressure support that to a fair degree prevents the collapse of the radiative shell and thus limits the total compression ratio of the partially or fully radiative forward shock. A consequence is that the spectra of cosmic rays would not be as hard as in hydrodynamic simulations. We also investigated the effect on the flow profiles of the magnetic-field inclination and a large-scale gradient in the gas density and/or the magnetic field. A positive density gradient shortens the evolutionary stages, whereas a shock obliquity lowers the shock compression. The compression of the tangential component of the magnetic field leads to its dominance in the downstream region of post-adiabatic shocks for a wide range of orientation of the upstream field, which may explain why one preferentially observes tangential radio polarization in old SNRs. As most cosmic rays are produced at late stages of SNR evolution, the post-adiabatic phase and the influence of the magnetic field during it are most important for modeling the cosmic-ray acceleration at old SNRs and the gamma-ray emission from late-stage SNRs interacting with clouds.
Spectroscopic observations play essential roles in astrophysics. They are crucial for determining physical parameters in our Universe, providing information about the chemistry of various astronomical environments. The proper execution of the spectroscopic analysis requires accounting for all the physical effects that are compatible to the signal-to-noise ratio. We find in this paper the influence on spectroscopy from the atomic/ground state alignment owing to anisotropic radiation and modulated by interstellar magnetic field, has significant impact on the study of interstellar gas. In different observational scenarios, we comprehensively demonstrate how atomic alignment influences the spectral analysis and provide the expressions for correcting the effect. The variations are even more pronounced for multiplets and line ratios. We show the variation of the deduced physical parameters caused by the atomic alignment effect, including alpha-to-iron ratio ([X/Fe]) and ionization fraction. Synthetic observations are performed to illustrate the visibility of such effect with current facilities. A study of Photodissociation regions in rho Ophiuchi cloud is presented to demonstrate how to account for atomic alignment in practice. Our work has shown that due to its potential impact, atomic alignment has to be included in an accurate spectroscopic analysis of the interstellar gas with current observational capability.
Highly ionized metals as probes of the circumburst gas in the natal regions of gamma-ray bursts
(2018)
We present here a survey of high-ionization absorption lines in the afterglow spectra of long-duration gamma-ray bursts (GRBs) obtained with the VLT/X-shooter spectrograph. Our main goal is to investigate the circumburst medium in the natal regions of GRBs. Our primary focus is on the N vλλ 1238, 1242 line transitions, but we also discuss other high-ionization lines such as O vi, C iv, and Si iv. We find no correlation between the column density of N v and the neutral gas properties such as metallicity, H i column density, and dust depletion; however, the relative velocity of N v, typically a blueshift with respect to the neutral gas, is found to be correlated with the column density of H i. This may be explained if the N v gas is part of an H ii region hosting the GRB, where the region’s expansion is confined by dense, neutral gas in the GRB’s host galaxy. We find tentative evidence (at 2σ significance) that the X-ray derived column density, NH, X, may be correlated with the column density of N v, which would indicate that both measurements are sensitive to the column density of the gas located in the vicinity of the GRB. We investigate the scenario where N v (and also O vi) is produced by recombination after the corresponding atoms have been stripped entirely of their electrons by the initial prompt emission, in contrast to previous models where highly ionized gas is produced by photoionization from the GRB afterglow.
Based on our new NuSTAR X-ray telescope data, we rule out any cyclotron line up to 60 keV in the spectra of the high-mass X-ray binary 4U2206+54. In particular, we do not find any evidence of the previously claimed line around 30 keV, independently of the source flux, along the spin pulse. The spin period has increased significantly, since the last observation, up to 5750 +/- 10 s, confirming the rapid spin-down rate (nu)over dot = -1.8 x 10(-14) Hz s(-1). This behaviour might be explained by the presence of a strongly magnetized neutron star (B-s > several times 10(13) G) accreting from the slow wind of its main-sequence O9.5 companion.
Improving network inference
(2018)
Background: A reliable inference of networks from data is of key interest in the Neurosciences. Several methods have been suggested in the literature to reliably determine links in a network. To decide about the presence of links, these techniques rely on statistical inference, typically controlling the number of false positives, paying little attention to false negatives. New method: In this paper, by means of a comprehensive simulation study, we analyse the influence of false positive and false negative conclusions about the presence or absence of links in a network on the network topology. We show that different values to balance false positive and false negative conclusions about links should be used in order to reliably estimate network characteristics. We propose to run careful simulation studies prior to making potentially erroneous conclusion about the network topology. Results: Our analysis shows that optimal values to balance false positive and false negative conclusions about links depend on the network topology and characteristic of interest. Comparison with existing methods: Existing methods rely on a choice of the rate for false positive conclusions. They aim to be sure about individual links rather than the entire network. The rate of false negative conclusions is typically not investigated. Conclusions: Our investigation shows that the balance of false positive and false negative conclusions about links in a network has to be tuned for any network topology that is to be estimated. Moreover, within the same network topology, the results are qualitatively the same for each network characteristic, but the actual values leading to reliable estimates of the characteristics are different.