Perturbation Equations Research Articles

Bounce corrections to gravitational lensing, quasinormal spectral stability, and gray-body factors of Reissner-Nordström black holes

Gravitational lensing in the weak field limit, quasinormal spectra, and gray-body factors are investigated in the Reissner-Nordstr\"om spacetime corrected by bounce parameters. Using the Gauss-Bonnet theorem, we analyze the effects of bounce corrections to the weak gravitational deflection angle and find that the divergence of the deflection angle can be suppressed by a bounce correction in the Reissner-Nordstr\"om spacetime. We also notice that the bounce correction plays the same role as the Morse potential in the deflection angle. Moreover, we derive the perturbation equations with spin-dependent effective potentials and discuss the quasinormal spectral stability. We observe that the quasinormal spectra have the same behavior in large bounce parameters for different multiple numbers and they decrease significantly if the bounce parameter is much bigger than the charge. We further study the transmission probability of particles scattered by the effective potentials and reveal that the bounce correction introduced into the Reissner-Nordstr\"om spacetime increases the gray-body factors of perturbation fields.

Simulating gravitational waves passing through the spacetime of a black hole

We investigate how GWs pass through the spacetime of a Schwarzschild black hole using time-domain numerical simulations. Our work is based on the perturbed $3+1$ Einstein's equations up to the linear order. We show explicitly that our perturbation equations are covariant under infinitesimal coordinate transformations. Then we solve a symmetric second-order hyperbolic wave equation with a spatially varying wave speed. As the wave speed in our wave equation vanishes at the horizon, our formalism can naturally avoid boundary conditions at the horizon. Our formalism also does not contain coordinate singularities and, therefore, does not need regularity conditions. Then, based on our code, we simulate both finite and continuous initially plane-fronted wave trains passing through the Schwarzschild black hole. We find that for the finite wave train, the wave zone of GWs is wildly twisted by the black hole. While for the continuous wave train, unlike geometric optics, GWs cannot be sheltered by the black hole. A strong beam and an interference pattern appear behind the black hole along the optical axis. Moreover, we find that the back-scattering due to the interaction between GWs and the background curvature is strongly dependent on the direction of the propagation of the trailing wavefront relative to the black hole. Finally, for a realistic input waveform generated by binary black holes, we find that the lensed waveform in the merger and ringdown phases is much longer than that of the input waveform due to the effect of back-scattering.

The Effective Fluid Approach for Modified Gravity and Its Applications

In this review, we briefly summarize the so-called effective fluid approach, which is a compact framework that can be used to describe a plethora of different modified gravity models as general relativity (GR) and a dark energy (DE) fluid. This approach, which is complementary to the cosmological effective field theory, has several benefits, as it allows for the easier inclusion of most modified gravity models into the state-of-the-art Boltzmann codes that are typically hard-coded for GR and DE. Furthermore, it can also provide theoretical insights into their behavior since in linear perturbation theory it is easy to derive physically motivated quantities such as the DE anisotropic stress or the DE sound speed. We also present some explicit applications of the effective fluid approach with f(R), Horndeski and scalar–vector–tensor models, namely, how this approach can be used to easily solve the perturbation equations and incorporate the aforementioned modified gravity models into Boltzmann codes so as to obtain cosmological constraints using Monte Carlo analyses.

Kelvin–Helmholtz stability of rotating magnetoplasma with electron inertia

Abstract In this theoretical exploration, the stabilizing or destabilizing impacts of the rotation, electron inertia, and electrical resistivity on the Kelvin–Helmholtz stability in two-superimposed incompressible magnetized plasma fluids incorporating finite ion Larmor radius (FLR) correction and suspended dust particulates are studied. The linearized perturbation equations for the Kelvin–Helmholtz instability problems are determined based on the magnetohydrodynamic (MHD) model. The general dispersion equation is derived by using appropriate boundary conditions. By the numerical estimation, the finite ion Larmor radius does not have any significant role in the Kelvin–Helmholtz instability of the magnetoplasma medium. The graphical estimates reveal the destabilization impact of the resistivity and electron inertia on the Kelvin–Helmholtz hydrodynamic plasma fluid system. In this paper, graphical representations have also analyzed the effect of rotation on the Kelvin–Helmholtz stability growth rate with the variation of electron inertia and resistivity. This current analysis provides pertinent information about the significant involvement of this considered system in space and astrophysical structures.

A symplectic homotopy perturbation method for random structural dynamics response analysis based on Birkhoffian systems

With the enhancement of the engineering structure complexity, numerical computation plays a prominent role in structural dynamics analysis. In theory, general mechanical systems can be transformed into Birkhoffian forms, whose matching symplectic numerical algorithms perform well in accuracy and stability. Besides, the influence of uncertainty cannot be ignored in practical engineering, but the research on uncertainty symplectic algorithms of Birkhoffian systems is still weak. This paper proposes a symplectic homotopy perturbation method (SHPM) for general Birkhoffian equations with random uncertainties. Different from the traditional perturbation method, the proposed method does not depend on small parameters. Based on the homotopy perturbation method, embedded parameters are introduced to establish the matrix and parameter perturbation equations of random Birkhoffian equations, respectively. Then the formulas for calculating the mean value and standard deviation of the response are derived with probability theory. Combined with Birkhoffian symplectic preserving algorithms, a symplectic homotopy perturbation method for the numerical solution of random Birkhoffian equations is proposed. Finally, numerical examples are given to verify the applicability and effectiveness of the proposed method and its superiority compared with the traditional non-symplectic method.

A Hybrid, Runtime Coupled Incompressible CFD-CAA Method for Analysis of Thermoacoustic Instabilities

Abstract Thermoacoustic instabilities in gas turbine engines are of increasing interest for design of future low-emission technology combustors. Numerical methods used to predict thermoacoustic instabilities often employ either fully compressible resource-intense computational fluid dynamics (CFD) simulations, or two-step approaches where source terms extracted from CFD simulations are supplied to subsequent computational aeroacoustics (CAA) simulations. This work demonstrates an analysis of self-excited thermoacoustic instabilities using a hybrid method based on runtime coupling of incompressible CFD and CAA simulations. A prior implementation for the computation of combustion noise through one-way coupling of CFD and CAA solvers has been extended to a two-way coupling that allows acoustics to influence the flow field. The resulting hybrid method couples acoustic and convective physical phenomena by using mean flow field quantities and the thermoacoustic energy source term obtained from the solution of the Navier–Stokes equations in the low Mach number limit as an input for the acoustic perturbation equations (APEs). The fluctuating acoustic quantities pressure and velocity obtained from the solution of the APE are in turn included in the solution of the low Mach number Navier–Stokes equations, influencing the convective dynamics of the flow field. The suitability of the present implementation to capture thermoacoustic feedback is demonstrated through analysis of the well-known self-excited instability observed in a Rijke tube. The results are presented and discussed in comparison with a fully compressible reference solution.

On black holes with scalar hairs

By using the Taylor series and the solution-generating methods, we construct exact black hole solutions with minimally coupled scalar fields. We find that the black hole solutions can have many hairs except for the physical mass. These hairs come from the scalar potential. Different from the mass, there is no symmetry corresponding to these hairs. Thus they are not conserved and one cannot understand them as Noether charges. They arise as coupling constants. Although there are many hairs, the black hole has only one horizon. The scalar potential becomes negative for sufficient large $$\phi $$ (or in the vicinity of black hole singularity). Therefore, the no-scalar-hair theorem does not apply to our solutions since the latter do not obey the dominant energy condition. Although the scalar potential becomes negative for sufficient large $$\phi $$ , the black holes are stable to both odd parity and scalar perturbations. As for even parity perturbations, we find there remains parameter space for the stability of the black holes. Finally, the black hole thermodynamics is developed.

Modeling of the heat conduction process in composite media

In this work we proposed a two-channel model of heat conduction processes in composite media on the basis of the general transfer theory. The obtained system of equations can be reduced to both the generalized Fourier equation and the system of Cattaneo equations describing fast processes. The stability of the processes is considered. A system of equations for perturbations is obtained. The calculation of the perturbations’ spectrum is given depending on the parameters of the model. From this fact it follows that in a linear system the stationary process of heat conduction is stable with respect to any small perturbations. If we take into account nonlinearity even in the simplest cases it leads to the appearance of various instabilities and the excitation of heat waves.

Multifluid cosmology in f(G) gravity

The treatment of (1+3)-covariant perturbation in a multifluid cosmology with the consideration of [Formula: see text] gravity, [Formula: see text] being the Gauss–Bonnet term, is done in this paper. We define a set of covariant and gauge-invariant variables to describe density, velocity and entropy perturbations for both the total matter and component fluids. We then use different techniques such as scalar decomposition, harmonic decomposition, quasi-static approximation together with the redshift transformation to get simplified perturbation equations for analysis. We then discuss a number of interesting applications like the case where the universe is filled with a mixture of radiation and Gauss–Bonnet fluids as well as dust with Gauss–Bonnet fluids for both short- and long-wavelength limits. Considering polynomial [Formula: see text] model, we get numerical solutions of energy density perturbations and show that they decay with increase in redshift. This feature shows that under [Formula: see text] gravity, specifically under the considered [Formula: see text] model, one expects that the formation of the structure in the late Universe is enhanced.

CosmicNet II: emulating extended cosmologies with efficient and accurate neural networks

In modern analysis pipelines, Einstein-Boltzmann Solvers (EBSs) are an invaluable tool for obtaining CMB and matter power spectra. To significantly accelerate the computation of these observables, the CosmicNet strategy is to replace the usual bottleneck of an EBS, which is the integration of a system of differential equations for linear cosmological perturbations, by trained neural networks. This strategy offers several advantages compared to the direct emulation of the final observables, including very small networks that are easy to train in high-dimensional parameter spaces, and which do not depend by construction on primordial spectrum parameters nor observation-related quantities such as selection functions. In this second CosmicNet paper, we present a more efficient set of networks that are already trained for extended cosmologies beyond ΛCDM, with massive neutrinos, extra relativistic degrees of freedom, spatial curvature, and dynamical dark energy. We publicly release a new branch of the class code, called classnet, which automatically uses networks within a region of trusted accuracy. We demonstrate the accuracy and performance of classnet by presenting several parameter inference runs from Planck, BAO and supernovae data, performed with classnet and the cobaya inference package. We have eliminated the perturbation module as a bottleneck of the EBS, with a speedup that is even more remarkable in extended cosmologies, where the usual approach would have been more expensive while the network's performance remains the same. We obtain a speedup factor of order 150 for the emulated perturbation module of class. For the whole code, this translates into an overall speedup factor of order 3 when computing CMB harmonic spectra (now dominated by the highly parallelizable and further optimizable line-of-sight integration), and of order 50 when computing matter power spectra (less than 0.1 seconds even in extended cosmologies).

Close-range leader–follower flight control technology for near-circular low-orbit satellites

Abstract Based on the characteristics of near-circular orbits and close-range leader–follower flights, the relative dynamics equations of the eccentricity/inclination ( e/i ) vector method are introduced herein. Additionally, the constraint terms in the design of the leader–follower flight formation are found to satisfy the conditions of the line-of-sight angle and inter-satellite distance. The control box algorithm is proposed under the flying task’s constraints, such as the line-of-sight angle and distance between the satellites according to the e/i vector and Gauss perturbation equations. The algorithm comprehensively takes into account the relationship between the relative motion variations in the satellite formation in near-circular orbits as well as their relationship with the velocity increment applied to the satellites. The example simulated in this study not only illustrates the existence of a coupling relationship between the flight-following distance and flight-following line-of-sight angle but also verifies the influence of the relative eccentricity of the two satellites on the leader–follower flight stability. The simulation results show that when the control box algorithm was used to maintain the leader–follower flight, this method was simple, intuitive, and may be feasibly introduced as a flight-following control strategy.

Effects of boundary and spatial heterogeneity on nonlocal dispersal equations

This paper is concerned with the positive solutions of some nonlocal dispersal equations. We study the effects of boundary condition and spatial heterogeneity on the asymptotic behavior of positive solutions. By analyzing the perturbation equations, we obtain the asymptotic profiles and limiting behaviors. The results of the paper exhibit how the boundary condition and spatial heterogeneity change the patterns of nonlocal dispersal equations.

Revisiting the quasinormal modes of the Schwarzschild black hole: Numerical analysis

We revisit the problem of calculating the quasinormal modes of spin 0, 1/2, 1, 3/2, 2, and spin 5/2 fields in the asymptotically flat Schwarzschild black hole spacetime. Our aim is to investigate the problem from the numerical point of view, by comparing some numerical methods available in the literature and still not applied for solving the eigenvalue problems arising from the perturbation equations in the Schwarzschild black hole spacetime. We focus on the pseudo-spectral and the asymptotic iteration methods. These numerical methods are tested against the available results in the literature, and confronting the precision between each other. Besides testing the different numerical methods, we calculate higher overtones quasinormal frequencies for all the investigated perturbation fields in comparison with the known results. Additionally, we obtain purely imaginary frequencies for spin 1/2 and 3/2 fields that are in agreement with analytic results reported previously in the literature. The purely imaginary frequencies for the spin 1/2 perturbation field are exactly the same as the frequencies obtained for the spin 3/2 perturbation field. In turn, the quasinormal frequencies for the spin 5/2 perturbation field are calculated for the very first time, and purely imaginary frequencies are found also in this case. We conclude that both methods provide accurate results and they complement each other.

Instability of de-Sitter black hole with massive scalar field coupled to Gauss–Bonnet invariant and the scalarized black holes

The black hole scalarization in a special Einstein-scalar–Gauss–Bonnet (EsGB) gravity has been widely investigated in recent years. Especially, the spontaneous scalarization of scalar-free black hole in de-Sitter (dS) spacetime possesses interesting features due to the existence of cosmological horizon. In this work, firstly, we focus on the massive scalar field perturbation on Schwarzschild dS (SdS) black hole in a special EsGB theory. By analyzing the fundamental QNM frequency and time evolution of the scalar field perturbation, we figure out the unstable/stable regions in (Lambda ,alpha )-plane as well as in (m,alpha )-plane for various perturbation modes, where Lambda , alpha and m denote the cosmological constant, the GB coupling strength and the mass of scalar field, respectively. Then by solving the static perturbation equation, we analyze the bifurcation point at which the SdS black hole supports spherical scalar clouds, and we find that the bifurcation points match well with alpha _c on the border of unstable/stable region. Finally, after addressing that the scalarised solutions could only emerge from the scalar could with node kge 1. we explicitly construct the scalarized hairy solutions for different scalar masses and compare the profile of scalar field to the corresponding scalar clouds.

Derivation of a second-order acoustic wave equation in an air-saturated porous medium from a volume-averaged transport model

For propagation of high-amplitude acoustic waves in a rigid porous frame saturated by air, significant departures from a constant flow resistivity model have been observed. This departure can be modeled as a quadratic modification to the linear Darcy’s drag law, known as Forchheimer’s correction. To study the physical cause and relative significance of this nonlinear correction with respect to convective nonlinearity, a second-order acoustic wave equation is derived from volume-averaged equations of mass, momentum, and entropy conservation. Due to the scale separation between the wavelength and the porous structure, the particle velocity is approximated as the sum of irrotational macroscopic and incompressible microscopic fields. The porosity, tortuosity, and permeability are defined and incorporated into the macroscopic conservation equations. Porous drag terms are also derived in the macroscopic momentum equation for Darcy’s law and Forchheimer’s correction. Conservation equations for fluid parameter perturbations are obtained, and a second-order wave equation is derived. Dimensional analysis, in terms of the acoustic Reynolds number and Darcy number, describes the criteria for significant Forchheimer and convective nonlinearity. A case is obtained for a Westervelt-like equation for approximately progressive plane waves. These results inform modeling of nonlinearities for sound propagation in porous media under practical conditions.

Ambipolar Diffusion in the Lower Solar Atmosphere: Magnetohydrodynamic Simulations of a Sunspot

Magnetohydrodynamic (MHD) simulations of the solar atmosphere are often performed under the assumption that the plasma is fully ionized. However, in the lower solar atmosphere a reduced temperature often results in only the partial ionization of the plasma. The interaction between the decoupled neutral and ionized components of such a partially ionized plasma produces ambipolar diffusion. To investigate the role of ambipolar diffusion in propagating wave characteristics in the photosphere and chromosphere, we employ the Mancha3D numerical code to model magnetoacoustic waves propagating through the atmosphere immediately above the umbra of a sunspot. We solve the nonideal MHD equations for data-driven perturbations to the magnetostatic equilibrium and the effect of ambipolar diffusion is investigated by varying the simulation to include additional terms in the MHD equations that account for this process. Analyzing the energy spectral densities for simulations with/without ambipolar diffusion, we find evidence to suggest that ambipolar diffusion plays a pivotal role in wave characteristics in the weakly ionized low density regions, hence maximizing the local ambipolar diffusion coefficient. As a result, we propose that ambipolar diffusion is an important mechanism that requires careful consideration into whether it should be included in simulations, and whether it should be utilized in the analysis and interpretation of particular observations of the lower solar atmosphere.

Massive neutrino self-interactions and inflation

Certain inflationary models like Natural inflation (NI) and Coleman-Weinberg inflation (CWI) are disfavoured by cosmological data in the standard ΛCDM+r model (where r is the scalar-to-tensor ratio), as these inflationary models predict the regions in the ns -r parameter space that are excluded by the cosmological data at more than 2σ (here ns is the scalar spectral index). The same is true for single field inflationary models with an inflection point that can account for all or majority of dark matter in the form of PBHs (primordial black holes). Cosmological models incorporating strongly self-interacting neutrinos (with a heavy mediator) are, however, known to prefer lower ns values compared to the ΛCDM model. Considering such neutrino self-interactions can, thus, open up the parameter space to accommodate the above inflationary models. In this work, we implement the massive neutrino self-interactions with a heavy mediator in two different ways: flavour-universal (among all three neutrinos), and flavour-specific (involving only one neutrino species). We implement the new interaction in both scalar and tensor perturbation equations of neutrinos. Interestingly, we find that the current cosmological data can support the aforementioned inflationary models at 2σ in the presence of such neutrino self-interactions.

Approximated Risk Probability of having Atherosclerosis, Cardiovascular Disease, and Stroke during the COVID-19 Period Using the Pre-COVID Period’S Dataset as Baseline of Calculations and Higher-Order Perturbation Equations from Quantum Mechanics Based on GH-Method: Math-Physical Medicine (No. 465)

This paper describes the author’s assessment on his risk probability percentage of having atherosclerosis, cardiovascular disease (CVD), and stroke. During the 7-quarters of the COVID-19 period from 2/5/2020 to 11/4/2021, he utilized his earlier 7-quarters data from 5/5/2018 to 2/4/2020 or the “pre-COVID period” and higher-order perturbation theory. The purpose of this study is to predict the present and future period’s CVD/stroke risks based on the previous period’s CVD/stroke risks via an effective approximation method of perturbation theory. In summary, this approximation method of perturbation equation from quantum mechanics offers high prediction accuracies on the present and future period’s (the “COVID period”) risks using the past pre-COVID period’s dataset and waveform as baseline calculations. The three orders of perturbation equations have provided the following high prediction accuracies in comparison against the COVID period’s calculated risks which includes the past 5-quarters of calculated risks and the future 2-quarters speculated risks of the COVID period.

Approximated Health Age Calculation Using Higher-Order Perturbation Equations from Quantum Mechanics and the 90-Days Moving Average Metabolism Index as its Primary Perturbation Factor Based on GH-Method: Math-Physical Medicine (No. 466)

The author became interested in geriatrics in early 2019, especially in regard to longevity. During the period of 2010-2013, he self-studied metabolism, endocrinology, chronic diseases, and food nutrition. In 2014, he applied topology concept and engineering finite element method to develop a mathematical model of metabolism. His collected big data of ~2 million on metabolism, chronic diseases, and lifestyle details allowed him to extend his research work into the area of longevity. In January 2020, he published his first geriatric paper, No. 223, regarding effective health age. Back in July 2010, he developed a simplified APP (application software program) on the iPhone for estimating a patients’ effective health age (Health Age) with or without chronic diseases to compare against the biological real age (Real Age). He then published his findings in paper, No. 292, where the data were utilized from four key medical conditions based on the health examination reports of 4 biomarkers weight, glucose, blood pressure, and lipids; along with the input by the patient of six lifestyle details involving diet, water intake, exercise, sleep, stress, and daily life routines. The APP can instantly calculate and show the metabolism index (MI) score and Health Age on the iPhone. Furthermore, he published two papers, No. 313 and No. 323, regarding the amplification factor used in the equation for effective health age.

Investigation of combustion noise generated by an open lean-premixed H[formula omitted]/air low-swirl flame using the hybrid LES/APE-RF framework

An open lean-premixed hydrogen/air low-swirl (LPHALS) turbulent flame exhibiting a pronounced peak in its combustion noise spectra, is investigated numerically using a hybrid Computational Fluid Dynamics/Computational Aero-Acoustics (CFD/CAA) framework. Under this framework, the reacting flow-field of the flame is computed via Large-Eddy Simulation (LES), while the direct combustion noise it produces is captured by solving the Acoustic Perturbation Equations for Reacting Flows (APE-RF). Flame configuration and simulation conditions correspond to those of an experimental study on an open lean-premixed H2/air flame stabilized using a Low-Swirl Burner (LSB). LES results are validated against experimental data. The CAA simulation is able to predict a pronounced sharp peak in the computed combustion noise spectra, similar to one of the two characteristic peaks observed in the measured combustion noise spectra. Frequency of this spectral peak predicted by the CAA simulation is 840 Hz, which is close to that of the higher frequency secondary spectral peak at 940 Hz measured in the experiment. Upon examining the hybrid LES/APE-RF results, the noise generation mechanism at 840 Hz is found to be the intense local heat release rate fluctuations, caused by strong interaction between the flame and the periodically generated vortical flow structures in the shear layers, downstream of the LSB exit. Additionally, analysis of the spectral content and directivity of the noise generated by different acoustic source terms is performed, in order to investigate their impact on the radiated acoustic field, and hence the characteristics of direct combustion noise produced by the open LPHALS flame.