Perturbation Components Research Articles

High-resolution 3-D imaging of electron density perturbations using ultra-dense GNSS observation networks in Japan: an example of medium-scale traveling ionospheric disturbances

For the first time using computerized ionospheric tomography (CIT) and leveraging ultra-dense slant total electron content (STEC) measurements derived from two ground-based Global Navigation Satellite System (GNSS) receiver networks in Japan, we have reconstructed the 3-D field-aligned structure of nighttime medium-scale traveling ionospheric disturbances (MSTIDs) with high spatiotemporal resolution. The CIT algorithm focuses on electron density perturbation components, allowing for the imaging of disturbances with small amplitudes and scales. Slant TECs used for CIT are setup to consist of two components: the background derived from IRI-2016 model and TEC perturbations obtained by subtracting a 30-min running average from observations. The resolution is set to 0.25º in latitude and longitude, 10 km in altitude, 30 s in time. Simulations were conducted to assess the performance of the CIT algorithm, revealing that this technique has good fidelity by accurately reconstructing more than 80% of the electron density perturbations. The focus is on the nighttime event of July 4, 2022, when data were accessible. The reconstruction results show that the MSTIDs initially form at lower altitudes and subsequently develop to exhibit large amplitudes and scales that extend to higher altitudes, characterized by a well-defined frontal structure with electrodynamic signatures. These results are consistent with theories and snippets of observational evidence regarding electromagnetic-influenced MSTIDs, hence affirming the effectiveness of the developed CIT technique in probing of the variations in the 3-D structure of ionospheric electron density. This is expected to contribute to a compressive understanding of the underlying mechanisms of ionospheric inhomogeneities.Graphical

Dynamics and wave analysis in longitudinal motion of elastic bars or fluids

We look at the bifurcation analysis, chaotic behavior, multistability, and sensitivity analysis of the van der Waals equation, which is used in science and engineering to study the dynamics of various structures. The variant van der Waals equation covers one-dimensional longitudinal isothermal motion in elastic bars or fluids, which is the main focus of this research. The Galilean transformation transfers the given model into a planar dynamical system. The power series methodology produces exact wave solutions. In addition, after accounting for the perturbation component, sensitivity analysis for various initial value problems is used to investigate quasi-periodic, chaotic, and time series behavior. Numerical simulation results show that influencing viscosity and the coefficient of interfacial capillarity influence the dynamical factors of the examined model. We are observing what happens with viscosity and the interface coefficients to the wave solution. In some cases, for different parameter values, we present plots of both one-dimensional and two-dimensional graphical representations of individual solutions.

An operator-splitting numerical scheme for relativistic magnetohydrodynamics

We describe a novel operator-splitting approach to numerical relativistic magnetohydrodynamics designed to expand its applicability to the domain of ultra-high magnetisation. In this approach, the electromagnetic field is split into the force-free component, governed by the equations of force-free degenerate electrodynamics (FFDE), and the perturbation component, governed by the perturbation equations derived from the full system of relativistic magnetohydrodynamics (RMHD). The combined system of the FFDE and perturbation equations is integrated simultaneously, for which various numerical techniques developed for hyperbolic conservation laws can be used. At the end of every time-step of numerical integration, the force-free and the perturbation components of the electromagnetic field are recombined and the result is regarded as the initial value of the force-free component for the next time-step, whereas the initial value of the perturbation component is set to zero. To explore the potential of this approach, we build a 3rd-order WENO code, which was used to carry out 1D and 2D test simulations. Their results show that this operator-splitting approach allows us to bypass the stiffness of RMHD in the ultra-high-magnetisation regime where the perturbation component becomes very small. At the same time, the code performs very well in problems with moderate and low magnetisation too.

Abstract 5846: Inhibiting elements of the proteasome recovery pathway sensitizes glioblastoma to proteasome inhibitors

Abstract Bacground: Glioblastoma (GBM) is the most common primary brain tumor, accounting for 15% of all central nervous system related tumors. Despite the aggressive standard of care treatment including chemotherapy, radiotherapy, and maximally safe surgical resection, patient outcomes are abysmal: with 95% of patients relapsing and a median overall survival of 15 months. Thus, this necessitates the rapid query for personalized therapeutics and agents that can potentiate the clinical effects of currently approved treatments. One such pathway that demonstrates aberrant functioning in cancer and is a targetable mechanism is the ubiquitin-proteosome pathway (UPP). Studies have shown that UPP related proteolysis remains constitutively active in cancer cells leading to the rapid degradation of proteins that regulate tumor suppressor genes and oncogenes. Despite robust preclinical evaluations for the usage of proteosome inhibitors against GBM, most tested proteosome inhibitors failed in phase II and III trials, indicating resistance. Methods: We conducted an unbiased genome wide CRISPR-Cas9 screen in human HAP1 cells treated with the proteosome inhibitor, Bortezomib (BTZ), to identify genes that may lead to a BTZ-resistant phenotype. We identified several genes that when perturbed, sensitized cells to BTZ including N-glycanase-1 (NGLY-1), Nuclear factor Erythroid 2-Like-1 (NFE2L1), and DNA damage inducible 1 homolog 2 (DDI2). Herein we sought to evaluate the effects of perturbing components of the proteosome rescue pathway in our Singh lab patient derived GBM cell lines by utilizing CRISPR/Cas9 knockout technology in vitro and in vivo. Results: The generation of NGLY-1, DDI2, and NFE2L1 KO cell lines demonstrated functional sensitivity to the proteosome inhibitor Marizomib (MZB) as observed through a significant reduction of the IC50 in the KO cell lines compared to a control. Functional evaluation also revealed a reduction in proliferation capacity as well as sphere formation in these genetically modified GBM lines. Ongoing in vivo work will aim to evaluate the mitigation of this resistant pathway in our NSG mouse models orthotopically transplanted with these patient derived KO cell lines. In an ongoing collaborative effort, we are working to identify and functionally assess a novel small molecule NGLY-1 inhibitor to evaluate preclinical sensitivity to MZB in our in vitro and in vivo models. Citation Format: Alisha Anand, Muhammad Vaseem Shaikh, Chirayu Chokshi, Benjamin Brakel, William Maich, Shan Grewal, Chitra Venugopal, Sheila Singh. Inhibiting elements of the proteasome recovery pathway sensitizes glioblastoma to proteasome inhibitors [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 5846.

Cavity tuning and beam commissioning of the radio-frequency quadrupole linac for a transportable neutron source

A transportable, compact, accelerator-based neutron source is under development at Xi’an Jiaotong University. At the heart of the linear accelerator is a radio-frequency quadrupole (RFQ) unit that has been designed to accelerate a proton beam from 30 keV to 2.5 MeV with a peak current of 12 mA and a duty factor of 3%. Recently, the manufacturing of the RFQ cavity has been completed. Cavity tuning, including field unevenness, resonant frequency, and rf coupling coefficient, was carried out after finishing brazing and assembly. The quadrupole perturbative component was controlled within ±2.0%, and the two dipole components were about ±2.5%. The value of the intrinsic Q was 9609, 89% of that of the theoretical simulation. We have completed the installation of the RFQ experimental setup and performed beam commissioning experiments. The output beam current reached 10.6 mA with a transmission efficiency of 93.8%.

Influence of the far non-resonant components of high-n resonant magnetic perturbations on energetic passing ions loss

The influence on the loss of energetic passing ions by the n = 4 resonant magnetic perturbation (RMP) is investigated through numerical simulations (here, n is the toroidal mode number of the RMP field). Dedicated efforts have been made to uncover how the plasma response modifies the loss fractions and underlying mechanisms. The stochastization of the drift surfaces and the particle loss fractions increase significantly under the response field, in which the resonant component is significantly shielded. In order to better understand how the response field contributes a considerable drift island width, the respective effect of each poloidal component mb on the outermost drift island mp/n=9/4 are compared (here, mb and mp are poloidal mode numbers of the RMP components and drift island, respectively). Contrary to the intuition that the components with mb=mp±1 should dominate the sideband resonance, some of the components which fulfill |mp−mb|≫1 have the dominant contributions under the response field. There are mainly two reasons accounting for this phenomenon, i.e. the drift motion of particles and the enhancement of amplitudes of non-resonant high-m components by the plasma response near the edge due to the resonant field amplification (RFA) effect. The former made it possible for particles to resonate with the far non-resonant components, and the latter significantly enhanced the perturbation field experienced by particles. The above results imply that the RFA effect is more critical than the stochastization of magnetic topology in the fast ion losses under RMP.

Velocity Field due to a Vertical Deformation of the Bottom of a Laminar Free-Surface Fluid Flow

This article investigates the velocity field of a free-surface flow subjected to harmonic deformation of the channel bottom, progressing asymptotically from a flat initial state to a maximum amplitude. Assuming a uniform main flow with the primary velocity component transverse to the bed undulation, analytical solutions are obtained for the three velocity components and free surface distortion using the method of perturbations. The perturbation components of the velocity field, streamlines, and surface deformation depend on a dimensionless parameter that reflects the fluid inertia induced by bed deformation relative to viscous resistance. When viscous effects dominate, a monotonic decay of the perturbations from the bed to the free surface is observed. In contrast, when inertia dominates, the perturbations can exhibit an oscillatory behavior and introduce circulation cells in the plane normal to the main flow. The interplay between inertia and viscosity reveals scenarios where surface and bed deformations are either in or out of phase, influencing vertical velocity components. Figures illustrate these phenomena, providing insights into the complex dynamics of free-surface flows with harmonic bed deformation in the direction normal to the main flow, and amplitude growing with time. The results are limited to small deformations of the channel bottom, as imposed by the linearization of the momentum equations. Even so, to the best of the authors’ knowledge, this problem has not been addressed before.

Examining the Applicability of Direct Analytic Method (DAM) to Normal Modes of Poloidal Oscillations Under Symmetric and Asymmetric Boundary Conditions

AbstractA working Direct Analytic Method (DAM) model is envisaged to explain the normal modes of poloidal Alfven waves in the Earth's magnetosphere. The model solves the ideal, cold, magnetohydrodynamic (MHD) equations associated with transverse components of the magnetic perturbations in a dipolar magnetic field. DAM model is used to study the transverse poloidal waves in different regions of magnetosphere characterized by their L‐value and different plasma variability. The plasma density distribution is assumed to be governed by the standard power law, 1/rm, where r is the geocentric distance of any point of interest on the field line and m is the density index. The eigen frequencies and spatial structures are obtained analytically under different ideal ionospheric boundary conditions and the results are compared with the numerical solutions to establish the validity of the model. DAM, being an analytic model, is used to explain the distinctive structural features of transverse poloidal waves which are obtained under different boundary conditions, for different density indices. Furthermore, the application of the analytic model in the computation of eigen frequency as well as plasma density is demonstrated under different observational scenario.

Threshold analysis of an algae-zooplankton model incorporating general interaction rates and nonlinear independent stochastic components

<abstract><p>The stochastic nature of ecological systems is fundamental to their modeling and understanding. In this paper, we introduce a comprehensive algae-zooplankton model that incorporates general interaction rate and second-order independent stochastic components. Our model's perturbation component encompasses both white noise and jump processes, enabling us to account for various sources of variability and capture a wide range of potential fluctuations in the system. By utilizing an auxiliary equation, we establish a global threshold for the stochastic system, distinguishing between scenarios of extinction and ergodicity. This threshold serves as a critical determinant of the system's long-term behavior and sheds light on the delicate balance between population persistence and decline in ecological communities. To elucidate the impact of noise on the dynamics of algae and zooplankton, we present a series of numerical illustrations. Through these simulations, we highlight how noise influences not only the extinction time but also the shape of the stationary distribution. Our findings underscore the significant role of stochasticity in shaping ecological dynamics and emphasize the importance of considering noise effects in ecological modeling and management practices.</p></abstract>

Apathy scores in Parkinson's disease relate to EEG components in an incentivized motor task.

Apathy is one of the most prevalent non-motor symptoms of Parkinson's disease and is characterized by decreased goal-directed behaviour due to a lack of motivation and/or impaired emotional reactivity. Despite its high prevalence, the neurophysiological mechanisms underlying apathy in Parkinson's disease, which may guide neuromodulation interventions, are poorly understood. Here, we investigated the neural oscillatory characteristics of apathy in Parkinson's disease using EEG data recorded during an incentivized motor task. Thirteen Parkinson's disease patients with apathy and 13 Parkinson's disease patients without apathy as well as 12 healthy controls were instructed to squeeze a hand grip device to earn a monetary reward proportional to the grip force they used. Event-related spectral perturbations during the presentation of a reward cue and squeezing were analysed using multiset canonical correlation analysis to detect different orthogonal components of temporally consistent event-related spectral perturbations across trials and participants. The first component, predominantly located over parietal regions, demonstrated suppression of low-beta (12-20 Hz) power (i.e. beta desynchronization) during reward cue presentation that was significantly smaller in Parkinson's disease patients with apathy compared with healthy controls. Unlike traditional event-related spectral perturbation analysis, the beta desynchronization in this component was significantly correlated with clinical apathy scores. Higher monetary rewards resulted in larger beta desynchronization in healthy controls but not Parkinson's disease patients. The second component contained gamma and theta frequencies and demonstrated exaggerated theta (4-8 Hz) power in Parkinson's disease patients with apathy during the reward cue and squeezing compared with healthy controls (HCs), and this was positively correlated with Montreal Cognitive Assessment scores. The third component, over central regions, demonstrated significantly different beta power across groups, with apathetic groups having the lowest beta power. Our results emphasize that altered low-beta and low-theta oscillations are critical for reward processing and motor planning in Parkinson's disease patients with apathy and these may provide a target for non-invasive neuromodulation.

Stationary Bragg reflection of laser light in inhomogeneous absorbing plasmas inside inertial confinement fusion Hohlraums

Laser-produced plasma in inertial confinement fusion (ICF) Hohlraums are marked with density non-uniformity whose length scale can go down to micrometers. This scale is of the order of the laser wavelength. The WKB approximation, which is classically used in radiation-hydrodynamic codes to compute the laser trajectory, cannot correctly take into account such small-scale inhomogeneity of the plasma. Going beyond this approximation, we predict a novel mechanism for the laser reflection. We show that an electromagnetic plane wave with wave number k resonates with the kB=2 k Fourier component of a multimode perturbation of the background density and generates a reflected wave. It is the first time that this reflection is considered for stationary inhomogeneous ICF plasmas, and the energy absorption is taken into account. This mechanism, which is a form of Bragg reflection, can occur away from the critical surface and generate a drift of the location of the laser absorption. Furthermore, this absorption will be periodically modulated with a kB wave number. The stationary Bragg reflection can explain ongoing discrepancies between experimental and numerical data about laser trajectory and absorption in ICF Hohlraums.

On the adiabatic approximation for the laser-dressed atom

The adiabatic approximation is analyzed for non-perturbative interaction of an atomic system with an intense low-frequency laser field. We find that the well-known adiabatic ansatz, which consists in using the DC-based Green’s and wave functions for an atom in the instantaneous AC field to calculate transition matrix elements, exceeds the level of accuracy of the adiabatic approximation and requires further theoretical revision. It is shown that the non-analyticity in the field strength of the DC-based Green’s and wave functions leads to violation of the adiabaticity constrains and the appearance of rapidly oscillating components in the transition matrix elements. We suggest an improved adiabatic approach utilizing the analytical parts in the DC-based Green’s and wave functions. We illustrate our revised adiabatic approach for analysis of atomic polarizability in two-component laser field with an intense infrared and perturbative extreme ultraviolet components within the zero-range potential model.

Impacts of Multiscale Components of Initial Perturbations on Error Growth Characteristics and Ensemble Forecasting Skill

Abstract To compare the roles of two kinds of initial perturbations in a convection-permitting ensemble prediction system (CPEPS) and reveal the effects of the differences in large-scale/small-scale perturbation components on the CPEPS, three initial perturbation schemes are introduced, including a dynamical downscaling (DOWN) scheme originating from a coarse-resolution model, a multiscale ensemble transform Kalman filter (ETKF) scheme, and a filtered ETKF (ETKF_LARGE) scheme. First, the comparisons between the DOWN and ETKF schemes reveal that they behave differently in many ways. Specifically, the ensemble spread and forecast error for precipitation in the DOWN scheme are larger than those in the ETKF; the probabilistic forecasting skill for precipitation in the DOWN scheme is better than that in the ETKF at small neighborhood radii, whereas the advantages of the ETKF begin to appear as the neighborhood radius increases; DOWN possesses better spread–skill relationships than ETKF and has comparable probabilistic forecasting skills for nonprecipitation. Second, the comparisons between DOWN and ETKF_LARGE indicate that the differences in the large-scale initial perturbation components are key to the differences between DOWN and ETKF. Third, the comparisons between ETKF and ETKF_LARGE demonstrate that the small-scale initial perturbations are important since they can increase the precipitation spread in the early times and decrease the forecast errors while simultaneously improving the probabilistic forecasting skill for precipitation. Given the advantages of the DOWN and ETKF schemes and the importance of both large-scale and small-scale initial perturbations, multiscale initial perturbations should be constructed in future research.

A machine learning approach combined with wavelet analysis for automatic detection of Pc5 geomagnetic pulsations observed at geostationary orbits

Pc5 geomagnetic pulsations are ultra-low frequency (ULF) waves whose period lies within 150–600 s. Their detection is crucial for accurate space weather modelling, monitoring, and analysis. Identification of these pulsations using manual approaches is difficult and time-consuming because of the smaller magnitudes and the limited durations within which they occur. To overcome this challenge, we propose a robust Cascade Forward Neural Network (CFNN) model combined with the wavelet technique for automatically detecting Pc5 events from satellite datasets observed at geostationary orbits. The dataset used in this study is the magnetic field vector measurements retrieved from the Geostationary Operational Environmental Satellite-10 (GOES-10) from 2000 to 2009. Pc5 geomagnetic pulsations were extracted from the toroidal component of the field perturbation using a bandpass Butterworth filter. Continuous wavelet transform (CWT) analysis using the mother Morlet wavelet was utilized to validate the integrity of the extracted signal in the time–frequency domain. The extracted Pc5 signal was decomposed into details and approximations using Daubechies wavelet transform to separate the intelligible signal from the incoherent noise that left their trace on the magnetic field time series. The detail signal was subjected to denoising using the heuristic Stein Unbiased Risk Estimate (SURE) approach with soft thresholding to obtain the denoised Pc5 events. The denoised Pc5 events were utilized as the target in the machine learning whereas the inputs were obtained from 5-dimensional space transformation of the toroidal component of the time series. The developed algorithm performed well and demonstrated a detection accuracy of 80 % and a Root Mean Square Error (RMSE) of 0.13 nT indicating a high performance in detecting Pc5 events. For effective validation of the model, Pc5 events detected by our model were correlated with the Kp index and the amplitude of the Pc5 events observed at geostationary orbit. A good correlation was obtained in both cases, making our model a practical and preferred choice for Pc5 pulsation detection in contrast to conventional frequency analysis tools which take much time for signal processing on large data sets.

THE CONTRIBUTION OF THE RELAXATION OF THE HEAT FLOW TO THE CHARACTERISTICS OF THE FUNDAMENTAL HARMONICS OF A NONLINEAR PHOTOACOUSTIC SIGNAL IN CONDENSED MEDIA

Based on the system of nonlinear heat conduction equations, which takes into account the relaxation of the heat flux for the gas layer, the sample, and the substrate, a system of equations is obtained for temperature fluctuations at the fundamental harmonic (FH) of a nonlinear photoacoustic (PA) signal. It is believed that all three layers in the PA-chamber have their own relaxation times, and the irradiated photon flux is modulated according to the harmonic law. The temperature dependence of thermophysical and optical parameters is represented by thermal coefficients. By solving the boundary problem, general expressions were obtained for the oscillatory component of the temperature perturbation in the exhaust gas, and then, according to a well-known scheme, for pressure fluctuations in the gas layer. The obtained expressions are analyzed. The frequency dependence of the amplitude and phase of this signal is numerically calculated for two possible substrates: the substrate is a thermal insulator and the substrate is an ideal conductor. It has been established that the frequency dependence of the PA-signal amplitude for these cases is antiphase. While, this dependence for the phase of the PA-signal is consistent in phases moreover, the values of the maximum and minimum coincide. The only significant difference is that in the region of zero modulation frequencies, the phase of the signal for a substrate made of a thermal insulator is positive, while for a substrate made of an ideal conductor is negative.

A Small-scale Structure Model of a Jet Based on Observations of Microvariability

We developed a multiregion radiation model for the evolution of flux and spectral index with time. In this model, each perturbation component in the jet produces an independent flare. The model can be used to study the decomposition of microvariability, the structural scale of the perturbed components, and the physical parameters of the acceleration processes. Based on the shock acceleration model for a relativistic jet, the influence of the acceleration parameters on multiband flare parameters is calculated. We present the results of multiband optical microvariability of the blazar BL Lacertae observed during 89 nights in the period from 2009 to 2021, and use them as a sample for model fitting. The results show that both the amplitude and duration of flares decomposed from the microvariability light curves conform to a log-normal distribution. The time delays between the optical bands follow a normal distribution and amount to several minutes, which corroborate with both predictions from the theoretical model and the calculation of the discrete correlation function. Using the spectral index evolution and the simultaneous fitting of the multiband variability curves, we obtain the acceleration and radiation parameters to constrain and distinguish the origins of different flares. Based on the flare decomposition, we can effectively reproduce the time-domain evolution trends of the optical variations and energy spectrum, and explain the various redder-when-brighter and bluer-when-brighter behaviors.

Ionospheric Perturbations Due to Large Thunderstorms and the Resulting Mechanical and Acoustic Signatures

Perturbations from thunderstorms can play a notable role in the dynamics of the ionosphere. In this work, ionospheric perturbation effects due to thunderstorms were extracted and studied. Thunderstorm-associated lightning activities and their locations were detected by the World-Wide Lightning Location Network (WWLLN). The mechanical components of ionospheric perturbations due to thunderstorms were extracted from the total electron content (TEC), which was measured at selected thunderstorm locations using the polynomial filtering method. Further analyses were conducted using wavelet analysis and Discrete Fourier Transform (DFT) to study the frequency modes and periodicities of TEC deviation. It was revealed that the highest magnitudes of TEC deviations could reach up to ~2.2 TECUs, with dominant modes of frequency in the range of ~0.2 mHz to ~1.2 mHz, falling within the gravity wave range and the second dominant mode in the acoustic range of >1 mHz to <7.5 mHz. Additionally, a 20–60 min time delay was observed between the sprite events, the other high-energy electrical discharges, and the time of occurrence at the highest peak of acoustic-gravity wave perturbations extracted from TEC deviations. The possible mechanism responsible for this phenomenon is further proposed and discussed.

An extended Bueckner–Rice theory for arbitrary geometric perturbations of cracks

The aim of this paper is to define a new, simple and efficient method of solution of elasticity problems for 3D bodies containing cracks slightly perturbed out of their original plane or surface. This method extends that proposed by Rice (1985, 1989), from a re-formulation of Bueckner (1987)’s 3D weight function theory, for the treatment of coplanar crack perturbations. First, a general formula is derived for the variation of total energy of a cracked elastic body, resulting from some small but otherwise arbitrary geometric perturbation of the embedded crack(s). This formula, which involves integrals over both the front and the surface of the crack, is derived from an expression of deLorenzi (1982) and Destuynder et al. (1983) in the form of a volumic integral, originally limited to purely tangential crack perturbations but duly extended here to arbitrary perturbations having both tangential and normal components. It is then used to derive a general expression of the variation of displacement arising from a general perturbation of the crack(s), anywhere in the cracked body. The reasoning here basically follows the same lines as in the works of Rice (1985, 1989), but for the presence of an additional normal component of the crack perturbation. The possible use of the formalism developed to treat problems of out-of-plane, or out-of-surface perturbations of cracks is finally briefly evoked; the straightforwardness of the new method proposed is hoped to permit future applications to non-coplanar crack problems too complex to be accessible by more conventional methods.

Sensitivity of wave merging and mixing to initial perturbations in Holmboe instabilities

Initial perturbations are commonly used in direct numerical simulations (DNS) to trigger the shear instability of stratified fluids. We investigate the effects of initial perturbations on the evolution of Holmboe instabilities with DNS. In particular, we model the interaction between a primary Holmboe wave and a subharmonic component that has a wavelength double that of the primary wave. We show that the phase difference and the amplitude of the primary and subharmonic components of the initial perturbation control the merging of Holmboe instabilities, which, in turn, influence diapycnal mixing in stratified flows. The amplitude difference has a more significant effect on the merging of Holmboe instabilities compared to the initial phase difference. For a given amplitude of the primary perturbation, a larger subharmonic perturbation results in an earlier merging event. In three-dimensional simulations, this preference of the subharmonic initial perturbation increased the amplitude of Holmboe waves by a factor of two. Although the subharmonic mode grows slower, it grows for longer producing more net mixing.

Gauge invariant perturbations of general spherically symmetric spacetimes

In this paper, the gauge choices in general spherically symmetric spacetimes have been explored. We construct the gauge invariant variables and the master equations for both the Detweiler easy gauge and the Regge-Wheeler gauge, respectively. The particular cases for $l=0,1$ are also been investigated. Our results provide analytical calculations of metric perturbation in general spherically symmetric spacetimes, which can be applied to various cases, including the Effective-One-Body problem. A simple example is presented to show how the metric perturbation components are related to the source perturbation terms.