Far-field Approximations to the Derivatives of the Green's Function for the Ffowcs Williams and Hawkings Equation

The surface correction to the quadrupole source term of the Ffowcs Williams and Hawkings integral in the frequency domain suffers from the computation of high-order derivatives of the Green's function. The far-field approximations to the derivatives of the Green's function have been used without derivation and verification in the previous work. In this work, we provide the detailed derivations of the far-field approximations to the derivatives of the Green's function. The binomial expansions for the derivatives of the Green's function and the far-field condition are employed during the derivations to circumvent the difficulties in computing the high-order derivatives. The approximations to the derivatives of the Green's function are systemically verified by using the benchmark two dimensional convecting vortex and the co-rotating vortex pair. In addition, we provide the derivations of the approximations to the multiple integrals of the Green's function by using the far-field approximations to the derivatives.

Numerical Modeling on Crack Propagation Based on a Multi-Grid Bond-Based Dual-Horizon Peridynamics

Peridynamics (PD) is a novel nonlocal theory of continuum mechanics capable of describing crack formation and propagation without defining any fracture rules in advance. In this study, a multi-grid bond-based dual-horizon peridynamics (DH-PD) model is presented, which includes varying horizon sizes and can avoid spurious wave reflections. This model incorporates the volume correction, surface correction, and a technique of nonuniformity discretization to improve calculation accuracy and efficiency. Two benchmark problems are simulated to verify the reliability of the proposed model with the effect of the volume correction and surface correction on the computational accuracy confirmed. Two numerical examples, the fracture of an L-shaped concrete specimen and the mixed damage of a double-edged notched specimen, are simulated and analyzed. The simulation results are compared against experimental data, the numerical solution of a traditional PD model, and the output from a finite element model. The comparisons verify the calculation accuracy of the corrected DH-PD model and its advantages over some other models like the traditional PD model.

Time-lapse detection using raypath interferometry

ABSTRACTThe objective of most seismic time-lapse studies is to detect rock property changes in a subsurface formation caused by fluid withdrawal or injection, often by comparing seismic reflection images of the subsurface before and after the operation. Since rock property changes can affect the amplitudes of seismic reflection events associated with the boundaries of the formation, amplitude anomalies are the usual target of time-lapse experiments. Sometimes, however, particularly in harder, less porous rocks, a seismic amplitude anomaly can be relatively small and difficult to detect. There is a secondary time-lapse effect, however, which may be detectable even in the absence of a significant reflectivity anomaly: the time-delay of reflections from layers beneath a formation whose wave propagation velocity has been altered by pore fluid change. We introduce a near-surface correction technique for land data, which we call joint raypath interferometry, to specifically enhance and detect small time delays between corresponding events on two or more comparable time-lapse seismic images. We demonstrate the technique first on a numerical model, then on an actual time-lapse field survey in which a reflection amplitude anomaly is difficult to detect.

Significance of Ms and Validation of Reference Stress Solutions for Crack Like Flaws: Part 2

This is Part 2 of two papers discussing the significance of two key factors of crack like flaw assessment in the Fitness for Service assessment. While FEM analysis technology has been advancing amazingly in recent years, and FEM based fitness-for-service assessment of a damaged components, such as crack like flaws and local metal loss assessment, has become mainstream in assessments, it is still important to understand the reference stress solution based on a limit load analysis and the role of each factor in the failure mode to control the damaged component safely until the end of its life. In API 579-1/ASME FFS-1[1], Part 9, Assessment of Crack like Flaws, those reference stress solutions were developed based on the limit load analysis using Folias factor Mt and surface correction factor Ms. Folias factor Mt and surface correction factor Ms, are factors that account for the bulging effect around flaws. Those factors enable prediction of a maximum allowable pressure of a damaged cylindrical shell from a simple flat plate model that contain same size of a damaged area. As for Folias factor, Mt, it is well known to express the relationship between the reference stress of a through-wall crack flat plate and a through-wall crack cylinder. The application of Mt is clearly defined in ASME/API 579 FFS-1 part 9C, as well as papers by Folias et al. The the significance of the surface correction factor for surface flaw, Ms, has not been commonly understood well enough in general. Unfortunately, API 579-1/ASME FFS-1 also does not clearly mention its significance and how Ms is to be applied in the stress analysis. At a glance, Ms looks like a similar factor to Mt, and it is tempting to simply apply Ms to primary membrane stress term like Mt, but that is not correct. Eventually, an incorrect application of Ms would lead to an incorrect discussion of a flaw characterization. Often, there is a question about ASME/API 579 FFS-1 Part 9C reference stress solutions, especially for ASME/API 579 FFS-1 eq. 9C.76, from the misunderstanding meaning of the Ms factor. Addressing this issue is important to maintain the integrity of the Fitness-For-Service technology. In this Part 2 of two papers, validation of equations obtained in Part 1 are discussed and proven based on FEM analysis.

Significance of Ms and Validation of Reference Stress Solutions for Crack Like Flaws: Part 1

This is Part 1 of two papers discussing the significance of two key factors of crack like flaw assessment in the Fitness for Service assessment. While FEM analysis technology has been advancing amazingly in recent years, and FEM based fitness-for-service assessment of damaged components, such as crack like flaws and local metal loss assessment, has become mainstream in assessments, it is still important to understand the reference stress solution and the role of each factor in the failure mode to operate the damaged component safely until the end of its life. In API 579-1/ASME FFS-1[1], Part 9, Assessment of Crack like Flaws, those reference stress solutions were developed based on the limit load analysis using Folias factor Mt and surface correction factor Ms. Folias factor Mt and surface correction factor Ms, are factors that account for the bulging effect around flaws. Those factors enable prediction of a maximum allowable pressure of a damaged cylindrical shell from a simple flat plate model that contain same size of defected area. As for Folias factor, Mt, it is well known to express the relationship between the reference stress of a through-wall crack flat plate and a through-wall crack cylinder. The application of Mt is clearly defined in ASME/API 579 FFS-1 part 9C [1], as well as papers by Folias et al. [2][3]. The significance of the surface correction factor for surface flaw, Ms, has not been commonly understood well enough in general. Unfortunately, API 579-1/ASME FFS-1[1] also does not clearly mention its significance and how Ms is to be applied in the stress analysis. Also the detailed discussion of the derivation process of each reference solution was rooted in several papers with different nomenclature and slightly different definition of factors, which can be very confusing. At a glance, surface correction factor, Ms, looks like a similar factor to Mt, and it is tempting to simply apply Ms to primary membrane stress term like Mt, but that is not correct. Eventually, an incorrect application of Ms would lead to an incorrect discussion of a flaw characterization. Often, there is a question about ASME/API 579 FFS-1[1] Part 9C reference stress solutions, especially for ASME/API 579 FFS-1[1] eq.9C.76, from the misunderstanding meaning of the Ms factor. Addressing this issue is important to maintain the understanding and integrity of the Fitness-For-Service technology. In this Part 1 of two papers, authors reviewed and reorganized step by step procedure of each reference stress solutions for flat plates and cylinders. Through this discussion, authors clarified the significance of Mt and Ms that are defined in ASME/API 579 FFS-1[1] Part 9C. In part 2, validation of equations obtained in this paper is discussed based on FEM analysis.

Investigating surface correction relations for RGB stars

ABSTRACT State-of-the-art stellar structure and evolution codes fail to adequately describe turbulent convection. For stars with convective envelopes such as red giants, this leads to an incomplete depiction of the surface layers. As a result, the predicted stellar oscillation frequencies are haunted by systematic errors, the so-called surface effect. Different empirically and theoretically motivated correction relations have been proposed to deal with this issue. In this paper, we compare the performance of these surface correction relations for red giant branch stars. For this purpose, we apply the different surface correction relations in asteroseismic analyses of eclipsing binaries and open clusters. In accordance with previous studies of main-sequence stars, we find that the use of different surface correction relations biases the derived global stellar properties, including stellar age, mass, and distance estimates. We, furthermore, demonstrate that the different relations lead to the same systematic errors for two different open clusters. Our results overall discourage from the use of surface correction relations that rely on reference stars to calibrate free parameters. Due to the demonstrated systematic biasing of the results, the use of appropriate surface correction relations is imperative to any asteroseismic analysis of red giants. Accurate mass, age, and distance estimates for red giants are fundamental when addressing questions that deal with the chemo-dynamical evolution of the Milky Way galaxy. In this way, our results also have implications for fields such as galactic archaeology that draw on findings from stellar physics.

Spatially distributed mass balance of 14 Icelandic glaciers, 1945−2017. Trends and link with climate.

<p>Excluding the three largest ice caps, Icelandic glaciers have, until recently, received limited attention in terms of mass balance observations over the last century. In this study, mass balance estimates from 1945 to 2017 are presented, in decadal time spans, for 14 glaciers (total area 1054 km<sup>2</sup>) subject to different climatic forcing in Iceland. The mass balances are derived from airborne and spaceborne stereo imagery and airborne lidar, and correlated with precipitation and air temperature by a first order equation including a reference-surface correction term. This permits statistical modelling of annual mass balances and to temporally homogenize the mass balances for a region-wide, multidecadal mass balance study. The mean (standard deviation) mass balances of the target glaciers were −0.43 (0.17) m w.e. a<sup>−1</sup> in 1945−1960, 0.01 (0.21) m w.e. a<sup>−1</sup> in 1960−1980, 0.10 (0.23) m w.e. a<sup>−1</sup> in 1980−1994, −0.98 (0.44) m w.e. a<sup>−1</sup> in 1994−2004, −1.23 (0.57) m w.e. a<sup>−1</sup> in 2004−2010 and 0.06 (0.35) m w.e. a<sup>−1</sup> in 2010−2017. The majority of mass loss occured in 1994−2010, accounting for 22.5±1.6 Gt (1.4±0.1 Gt a<sup>−1</sup>). High decadal mass-balance variability is found on glaciers located at the south and west coasts,<br>in contrast to the glaciers located inland, north and northwest. These patterns are likely explained by the proximity to warm (south and west) versus cold (northwest) oceanic currents.</p>