The theory of kinks — I. A semi-analytic model of velocity perturbations due to planet-disc interaction

A new technique to detect protoplanets is by observing the kinematics of the surrounding gas. Gravitational perturbations from a planet produce peculiar ‘kinks’ in channel maps of different gas species. In this paper, we show that such kinks can be reproduced using semi-analytic models for the velocity perturbation induced by a planet. In doing so we i) confirm that the observed kinks are consistent with the planet-induced wake; ii) show how to quantify the planet mass from the kink amplitude; in particular, we show that the kink amplitude scales with the square root of the planet mass for channels far from the planet velocity, steepening to linear as the channels approach the planet; iii) show how to extend the theory to include the effect of damping, which may be needed in order to have localized kinks.

Numerical comparison of time-, frequency-, and wavelet-domain methods for coda wave interferometry

Summary Temporal changes in subsurface properties, such as seismic wavespeeds, can be monitored by measuring phase shifts in the coda of two seismic waveforms that share a similar source-receiver path but that are recorded at different times. These nearly identical seismic waveforms are usually obtained either from repeated earthquake waveforms or from repeated ambient noise cross-correlations. The five algorithms that are the most popular to measure phase shifts in the coda waves are the Windowed Cross Correlation (WCC), Trace Stretching (TS), Dynamic Time Warping (DTW), Moving Window Cross Spectrum (MWCS), and Wavelet Cross Spectrum (WCS). The seismic wavespeed perturbation is then obtained from the linear regression of phase shifts with their respective lag times under the assumption that the velocity perturbation is homogeneous between (virtual or active) source and receiver. We categorize these methods into the time domain (WCC, TS, DTW), frequency domain (MWCS), and wavelet domain (WCS). This study complements this suite of algorithms with two additional wavelet-domain methods, which we call Wavelet Transform Stretching (WTS) and Wavelet Transform Dynamic Time Warping (WTDTW), wherein we apply traditional stretching and dynamic time warping techniques to the wavelet transform. This work aims to verify, validate, and test the accuracy and performance of all methods by performing numerical experiments, in which the elastic wavefields are solved for in various 2D heterogeneous halfspace geometries. Through this work, we validate the assumption of a linear increase in phase shifts with respect to phase lags as a valid argument for fully homogeneous and laterally homogeneous velocity changes. Additionally, we investigate the sensitivity of coda waves at various seismic frequencies to the depth of the velocity perturbation. Overall, we conclude that seismic wavefields generated and recorded at the surface lose sensitivity rapidly with increasing depth of the velocity change for all source-receiver offsets. However, measurements made over a spectrum of seismic frequencies exhibit a pattern such that wavelet methods, and especially WTS, provide useful information to infer the depth of the velocity changes.

Source Separation and Medium Change of Contained Chemical Explosions from Coda Wave Interferometry

Differences in the seismic coda of neighboring events can be used to investigate source location offsets and medium change with coda wave interferometry (CWI). We employ CWI to infer the known relative location between two chemical explosions in Phase I of the Source Physics Experiment (SPE). The inferred displacement between the first, SPE-1, and second, SPE-2, chemical explosion is between 6 and 18 m, with an expectation of 9.2 m, where the known separation is close to 9.4 m. We also employ CWI to find any velocity perturbation due to damage from SPE-2, by comparing its coda with the collocated third SPE chemical explosion, SPE-3. We find that damage due to SPE-2 must be confined to a spherical region with radius less than 10 m and velocity perturbation less than 25%.

The Radiation-Dominated Universe in Nonstandard Cosmology

We continue the recent study of our model theory of low-density cosmology without dark matter. We assume a purely radiative spherically symmetric background and treat matter as anisotropic perturbations. Einstein’s equations for the background are solved numerically. We find two irregular singular points, one is the Big Bang and the other a Big Crunch. The radiation temperature continues to decrease for another 0.21 Hubble times and then starts to increase towards infinity. Then we derive the four evolution equations for the anisotropic perturbations. In the Regge- Wheeler gauge there are three metric perturbations and a radial velocity perturbation. The solution of these equations allow a detailed discussion of the cosmic evolution of the model universe under study.

Finite Element Velocity Perturbation Application in Investigating Compressor Dovetail Fretting in Time Domain

In the design of a gas turbine airfoil, avoiding resonance at all conditions is impossible. The airfoil may vibrate fiercely during resonant passages, which then may induce small oscillation motion at the disk attachment. Due to microslip at the contact regions, fretting would occur in conjunction with the reduction of material fatigue properties. This paper presents a finite element analysis using the Velocity Perturbation Method (VPM) in predicting airfoil attachment nonlinear fretting-behavior in the time domain at a resonant frequency of interest. Numerical simulation, showing design fretting fatigue characteristics based on fundamental Ruiz and Smith-Watson-Topper (SWT) criteria, is demonstrated on two models, simplified and representative. The simplified model was used for detail analysis set-up and basic post-processing while the representative model illustrated the difference in nonlinear contact response of an industrial compressor under bending and torsional modes in the time domain. This Finite Element velocity perturbation approach can be used to study the main factors affecting fretting of any two bodies in contact: load, coefficient of friction, contact geometry and impact of different frequencies or modal shapes in the time domain.

Modal Velocity Perturbation Method for Contact Fatigue at Blade Attachment Under Resonant Vibration

In a gas turbine engine, it is often impossible to have rotating components running free of resonance at all operating conditions. As such, blades may be subject to episodes of intense vibration, resulting in fatigue damage at the connection between blade and disk. This paper presents a novel finite element approach allowing to evaluate in the time domain the behavior at the disk fir-tree or dovetail contacts caused by a high response on a resonance. The method can be applied to simple bending or torsion modes as well as to higher modes with complex shapes. The application of a one-time velocity perturbation is an efficient way to initiate an oscillating motion at the frequency of interest. The behavior of the 3D-contact is then studied in the time domain, allowing non-linear behaviors to develop. The basic principle of this approach is described in this work. In the design of turbomachinery blade attachments, this approach can be used to study in the time domain the fretting effect of load, coefficient of friction and sliding distance at different frequency regimes. In conjunction with fretting criteria such as Ruiz and Smith-Watson-Topper, fretting fatigue life can then be predicted.

Magnetic–Internal–Kinetic Energy Interactions in High-Speed Turbulent Magnetohydrodynamic Jets

The goal of this study is to investigate the interactions between turbulent kinetic, internal, and magnetic energies in planar magnetohydrodynamic (MHD) jets at different regimes of Mach and Alfvén Mach numbers. Toward this end, temporal simulations of planar MHD jets are performed, using two types of initial fluctuating velocity field: (i) single velocity perturbation mode with a streamwise wavevector and (ii) random, isotropic perturbations over a band of wavevectors. At low Mach numbers, magnetic tension work results in a reversible exchange of energy between fluctuating velocity and magnetic fields. At high Alfvén Mach numbers, this exchange results in the equipartition of turbulent kinetic and magnetic energies. At higher Mach numbers, dilatational kinetic energy is (reversibly) exchanged with internal and magnetic energies, by means of pressure-dilatation and magnetic-pressure-dilatation, respectively. Therefore, at high Mach and Alfvén Mach numbers, dilatational kinetic energy is seen to be in equipartition with the sum of turbulent internal and magnetic energies. In each of the regimes, the consequent effect of the interactions on the background Kelvin–Helmholtz vortex evolution is also identified.