Perturbation Modes Research Articles

A brief review on the interaction between resonant magnetic perturbation and tearing mode in J-TEXT

A brief review on the interaction between resonant magnetic perturbation and tearing mode in J-TEXT

Prandtl number effects on the hydrodynamic stability of compressible boundary layers: flow–thermodynamics interactions

Hydrodynamic stability of compressible boundary layers is strongly influenced by the Mach number ( $M$ ), Prandtl number ( $Pr$ ) and thermal wall boundary condition. These effects manifest on the flow stability via the flow–thermodynamics interactions. Comprehensive understanding of stability flow physics is of fundamental interest and important for developing predictive tools and closure models for integrated transition-to-turbulence computations. The flow–thermodynamics interactions are examined using linear analysis and direct numerical simulations in the following parameter regime: $0.5 \leq M \leq 8$ ; and $0.5 \leq Pr \leq 1.3$ . For the adiabatic wall boundary condition, increasing Prandtl number has a destabilizing effect. In this work, we characterize the behaviour of production, pressure–strain correlation and pressure dilatation as functions of the Mach and Prandtl numbers. First and second instability modes exhibit similar stability trends but the underlying flow physics is shown to be diametrically opposite. The Prandtl number influence on instability is explicated in terms of the base flow profile with respect to the different perturbation mode shapes.

Internal structure and its connection with thermodynamics and dynamics in black holes

In general, a finite metric function at the center of a black hole describes a non-singular spacetime but an infinite metric at the center gives a singular spacetime, where the former is associated with convergent Ricci and Kretschmann scalars together with complete radial geodesics, while the latter is related to divergent Ricci and Kretschmann scalars together with incomplete radial geodesics. For the charged black hole in the four-dimensional Einstein-Gauss-Bonnet theory, we find that its metric function is finite at its center in one region of parameters but complex in the other region of parameters. The finite case describes a strange spacetime which presents the Ricci and Kretschmann scalars of a singular spacetime and the radial geodesics of a non-singular spacetime, while the complex case gives rise to the similar situation. We verify that the cosmic censorship conjecture is maintained for the black hole model. Further, we investigate the second-order phase transition, quasinormal modes of perturbation of a test scalar field in the eikonal limit, and shadow radius for the black hole and find that the thermodynamic and dynamic properties depend on the metrics. In this way, we connect the internal structure with the thermodynamics and dynamics for this black hole. Moreover, we compare such a black hole of modified gravity with the Reissner-Nordström black hole of Einstein's general relativity in these thermodynamic and dynamic properties.

Extremely Low-Profile Periodic 2-D Leaky-Wave Antenna: An Optimal Solution for Antenna-Frontend Integration

We investigate and present a very low-profile, high-efficiency, and high-gain 2-D leaky-wave antenna (2DLWA) implemented on a high permittivity substrate operating in the millimeter-wave range, paving the way for the seamless integration of a high-gain and high-efficiency antenna with a frontend. In contrast to the typical air-filled 2DLWA, where a perturbation of the first higher-order mode (TE1/TM1) results in highly directed broadside radiation, in the proposed antenna, the propagation and leakage of a quasi-TEM (Q-TEM) mode results in an extremely low-profile ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.065\lambda _{0}$ </tex-math></inline-formula> ), high-gain (~15 dBi) antenna. In this scenario, the transverse resonance condition for a Q-TEM mode is established by employing a capacitive partially reflective surface (PRS) in a thin ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.065\lambda _{0}$ </tex-math></inline-formula> ) substrate with a relative permittivity of 10.2. The proposed periodic 2DLWA, unlike the conventional uniform/quasi-uniform air-filled counterparts, radiates based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {n}=-\mathbf {1}$ </tex-math></inline-formula> space harmonic operation. Due to a strong mutual interaction between the PRS and ground plane, conventional design and analysis approaches are no longer relevant in this low-profile architecture. Instead, we employ the Floquet modal expansion theory to create an equivalent circuit model (ECM) for the PRS that takes into account the contributions and mutual interactions of the Floquet harmonics as well as the ground plane effect. By employing reflecting boundaries realized with edge truncation (air trenches) in a high permittivity substrate, we show that the aperture efficiency is enhanced by 15% compared to conventional counterpart.

Sound from extra dimensions: Quasinormal modes of a thick brane

In this work, we investigate the quasinormal modes of a thick brane system. Considering the transverse-traceless tensor perturbation of the brane metric, we obtain the Schr\"odinger-like equation of the Kaluza-Klein modes of the tensor perturbation. Then we use the Wentzel-Kramers-Brillouin approximation and the asymptotic iteration method to solve this Schr\"odinger-like equation. We also study the numeric evolution of an initial wave packet against the thick brane. The results show that there is a set of discrete quasinormal modes in the thick brane model. These quasinormal modes appear as the decaying massive gravitons for a brane observer. They are characteristic modes of the thick brane and can reflect the structure of the thick brane.

Quasinormal oscillations and late-time tail of massless scalar perturbations of a magnetized black hole in Rastall gravity* *Supported by the National Natural Science Foundation of China (NNSFC) (11805166, 11925503, 12175076). We also gratefully acknowledge the financial support from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro

In this study, we investigate the quasinormal mode and late-time tail of charged massless scalar perturbations of a black hole in generalized Rastall gravity. The black hole metric in question is spherically symmetric, accompanied by a power-Maxwell field surrounded by a quintessence fluid. We show that the massless scalar field, when dressed up with the magnetic field, acquires an effective mass, which significantly affects the properties of the resultant quasinormal oscillations and late-time tails. Specifically, the quasinormal frequencies become distorted and might even be unstable for particular spacetime configurations. Additionally, the exponent of the usual power-law tail is modified according to the modification in the structure of the branch cut of the retarded Green's function. In particular, as the effective mass is generated dynamically owing to the presence of the magnetic field, we may consider a process through which the field is gradually removed from the spacetime configuration. In this context, while the quasinormal oscillations converge to the case of massless perturbations, we argue that the properties of resultant late-time tails do not fall back to their massless counterpart. The relevant characteristics are investigated using numerical and analytic approaches.

The nature of cosmological metric perturbations in presence of gravitational particle production

The present paper tries to answer the question: Can a de Sitter phase in presence of radiation be a competitor of the standard inflationary paradigm for the early universe? This kind of a de Sitter phase can exist in cosmological models where gravitational particle production takes place. To address the issue the metric perturbations in the de Sitter phase in presence of radiation must be known. The evolution of metric perturbations are explicitly calculated in the paper. It is seen that the evolution of scalar and vector perturbations are considerably different from standard inflationary models. These differences arise due to the particle production mechanism. The scalar perturbation power spectrum grows exponentially at small length scales. However, one cannot uniquely specify the scale at which this exponential growth starts because of the dependence of the power spectrum on the initial perturbation value. The time slice on which the initial perturbation starts is arbitrary. The arbitrariness of the initial time slice is related to the problem of setting the initial condition on the perturbations in the present model. The paper briefly opines on vector and tensor perturbations in the de Sitter space filled with radiation. It is seen that quantization of the perturbation modes in the present model is considerably difficult. One has to modify the present model to provide a consistent scheme of quantization of the perturbation modes.

Transition mechanisms in a boundary layer controlled by rotating wall-normal cylindrical roughness elements

The transition to turbulence induced by counter-rotating wall-normal rotating cylindrical roughness pairs immersed within a laminar boundary layer on a flat plate is investigated with direct numerical simulations, dynamic mode decomposition (DMD) and perturbation kinetic energy (PKE) analysis. As long as the cylinder stub is rotating, the wake contains a steady dominating inner vortex (DIV) surrounded by a secondary inner vortex. Its circumferential velocity accelerates the fluid on one side of the cylinder and decelerates it on the other side. With low rotation speed, the perturbation is initiated by a combination of elliptical and centrifugal instabilities in the near wake. At medium rotation speeds, Taylor–Couette-like streamwise vortices are generated on the decelerated side, resulting in a protruding reverse-flow zone. Results from DMD analysis and corresponding PKE analysis reveal the unstable nature of the deceleration region and the wake. At the largest rotation speed investigated, the onset of perturbations is directly located on the decelerated side of the cylinder stubs, where a deceleration mechanism feeds the instability. In the near wake, the mechanism gradually changes to a pure centrifugal instability when the rotation speed increases. In the far wake, both elliptical and centrifugal instabilities fade away, and the streaky flow featuring a vigorous DIV is then only subject to inviscid inflectional instability.

Quasinormal modes of NUT-charged black branes in the AdS/CFT correspondence

We study the scalar, electromagnetic and gravitational perturbations of planar AdS4 black holes with NUT charge. In the context of the AdS/CFT correspondence, these solutions describe a thermal quantum field theory embedded in a Gödel-type Universe with closed time-like curves. For a given temperature and NUT charge, two different planar Taub–NUT solutions exist, but we show that only the one with a positive specific heat contributes to the Euclidean saddle point in the path integral. By using the Newman–Penrose formalism, we then derive the master equations satisfied by scalar, electromagnetic and gravitational perturbations in this background, and show that the corresponding equations are separable. Interestingly, the solutions pile up in the form of Landau levels, and hence are characterized by a single quantum number q. We determine the appropriate boundary conditions satisfied by the master variables and using these we compute the quasinormal modes of scalar and gravitational perturbations. On the other hand, electromagnetic perturbations depend on a free parameter whose determination is problematic. We find that all the scalar and gravitational QNM frequencies lie in the lower half of the complex plane, indicating that these Taub–NUT spacetimes are stable. We discuss the implications of these results in the light of the AdS/CFT correspondence.

Naked singularity in 4D Einstein-Gauss-Bonnet novel gravity: Echoes and instability

We study the stability of an asymptotically flat, static, spherically symmetric naked singularity spacetime in the novel four-dimensional Einstein-Gauss-Bonnet (EGB) gravity. The four-dimensional EGB black hole for large enough values of the coupling parameter leads to such a naked singularity. The stability and the response of the spacetime are studied against the perturbations by test scalar, electromagnetic and Dirac fields, and the time evolution of these perturbations was observed numerically. Implementing a null Dirichlet boundary condition near the singularity, we observed that for $l=1$ modes of scalar, electromagnetic perturbation, and $l=0$, 1 modes of Dirac perturbation, the time-domain profiles give rise to distinct echoes. However, as the coupling constant increases, the echoes align, and the quasinormal mode structure of the 4D-EGB naked singularity-spacetime becomes prominent. For higher values of the multipole number, the spacetime becomes unstable, thereby restricting the parameter space for the coupling parameter.

Analysis of limited coverage effects on areal density measurements in inertial confinement fusion implosions

Accurate diagnosis of areal density (ρR) is critical for the inference of performance metrics in inertial confinement fusion implosions. One potential source of error in this diagnosis is the existence of low mode perturbations in the imploding target, which lead to asymmetries in the inference of the ρR from different lines of sight. Here, the error accrued as a result of limited coverage of the sphere due to a finite number of detectors is quantified, and the development of a forward scatter measurement from the OMEGA neutron time-of-flight detectors is motivated. A method by which the 1D-equivalent 4π-averaged ⟨ρR⟩ can be reconstructed, if accurate mode information can be diagnosed by other means, is validated.

Stability of KdV solitons with respect to transverse perturbations: Absolute and convective instabilities

We study the stability of one-dimensional solitons propagating in an anisotropic medium. We derived the Kadomtsev-Petviashvili equation for nonlinear waves propagating in an anisotropic medium. By a proper variable substitution this equation reduces either to the KPI or to the KPII equation. In the former case solitons are unstable with respect to the normal modes of transverse perturbations, and in the latter they are stable. We only consider the case when the solitons are unstable. We formulated the linear stability problem. Using the Laplace–Fourier transform, we found the solution describing the evolution of an initial perturbation. Then, using Briggs’ method we studied the absolute and convective instabilities. We found that a soliton is convectively unstable unless it propagates at an angle smaller then critical with respect to a critical direction defined by the condition that the group velocity is parallel to the phase velocity. The critical angle is proportional to the ratio of the dispersion length to the soliton width, which is a small parameter. The coefficient of proportionality is expressed in terms of the phase speed and its second derivative with respect to the angle between the propagation direction and the critical direction. As an example we consider the stability of solitons propagating in Hall plasmas.

Exact nonsingular black holes and thermodynamics

We show that regular black holes given by Culetu [14] can be obtained by coupling Einstein's gravity with the nonlinear electrodynamics source. The non-singular black hole has a mass function m(r)=Me−k/r, k is the deviation parameter, and it interpolates between the Schwarzschild black hole (k=0) and the Reissner-Nordstrom black hole (r≫k). Interestingly, there exists a critical mass parameter M=Mc, which corresponds to an extremal black hole when Cauchy and event horizons coincide. For M>Mc, it describes a nonextremal black hole with two horizons and no black hole for M<Mc. The Hawking temperature of the nonsingular black hole is maximum, where the specific heat diverges and changes its sign at the value of mass Mc2>Mc1, and the second-order phase transition occurs at that point. The smaller nonsingular black holes are always stable due to positive heat capacity and negative free energy. A discussion on the quasinormal modes of scalar field perturbations on nonsingular black holes background is included.

Stability of steady frictional sliding at an interface between two elastic layers

Instabilities in dynamic antiplane frictional sliding on a planar interface between two elastic layers with dissimilar elastic properties are studied. At the interface, a rate- and state-dependent friction law with a positive instantaneous dependency on slip velocity and velocity weakening behaviour in the steady state is assumed to be in effect. The linearized response of the sliding of the two elastic layers to a Fourier mode perturbation along the interface is studied. A key aspect of the problem is that interfacial waves exist for the problem in both freely slipping and bonded contact. The growth rate of slip instabilities and their phase velocities are obtained numerically. The stability of both rapid and slow slip is analyzed. The results show that one mechanism for instabilities is the destabilization due to friction of interfacial waves in freely slipping contact and in bonded contact. The effect of layer thickness on the stability results is also studied.

Analysis of gravitational waves from inflation model with minimal, non-minimal, and non-minimal derivative coupling of scalar field from Horndeski theory

Inflation theory provides solutions for problems in cosmology, such as horizon problem and flatness problem. The study of Gravitational waves production in cosmic inflation era not prove the general inflation theory, but also to differentiate in detail among specific models. In this research, we use inflation model with minimal, non-minimal, and non-minimal derivative coupling of scalar field without potential from Horndeski Theory. From this model, we calculate scalar and tensor perturbation equations and then obtain its equation of gravitational waves, spectral index for each perturbation mode and tensor-to-scalar ratio. Spectral index and tensor-to-scalar ratio nearly scale-invariant and agree with observational data for some Ho, ζ, and ξ. Gravitational waves remain constant during inflation and start oscillates when its modes enter the horizon. Energy of this gravitational waves is scale-invariant for modes that re-enter horizon during radiation dominated era and rises toward lower frequencies.

Instabilities of a Nonstationary Model of a Self-Gravitating Disk. V. New Annular Perturbation Modes

Instabilities of a Nonstationary Model of a Self-Gravitating Disk. V. New Annular Perturbation Modes

Discovering sparse control strategies in neural activity.

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology. Though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity and could eventually help characterize collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations-ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms-to neural states and their impact on collective neural activity. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, "pivotal" neurons that account for most of the system's sensitivity, suggesting a sparse mechanism of collective control.

Bounce Universe with Finite-Time Singularity

This work explains how the presence of a Type-IV singularity (a mild singularity) can influence the dynamics of a bouncing universe. In particular, we examine the bounce cosmology that appears with a Type-IV singularity in the context of a ghost-free Gauss–Bonnet theory of gravity. Depending on the time of occurrence of the Type-IV singularity, three different cases may arise—when the singularity occurs before the bounce, after the bounce, or at the instant of the bounce. However, in all of these cases, we find that in the case when the singularity “globally” affects the spacetime, the scalar power spectrum becomes red-tilted, and the tensor-to-scalar ratio is too large to be consistent with the observational data. Based on these findings, we investigate a different bouncing scenario which also appears with a Type-IV singularity, and wherein the singularity affects the spacetime “locally” around the time when it occurs. As a result, and unlike the previous scenario, the perturbation modes in the second bouncing scenario are likely to be generated far away from the bounce in the deep contracting phase. This finally results in the simultaneous compatibility of the observable quantities with the Planck data and ensures the viability of the bounce model where the Type-IV singularity has local effects on the spacetime around the time of the singularity.

Quasinormal modes and late-time falloff of Finslerian black holes with cosmological constant

Quasinormal modes of scalar and electromagnetic field perturbations in Finslerian Reissner-Nordstr\"om black holes with a cosmological constant are investigated in this paper. We analyze the fundamental frequencies and dynamical evolution of quasinormal modes using the WKB approximation and finite difference method, respectively. Both approaches show that the periods of oscillation of quasinormal modes increase with higher Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ if the multipole quantum number $l\ensuremath{\ge}2$. Using the Prony method, we show that the results obtained from the finite difference method are consistent with the results obtained from the WKB approximation. Quasinormal modes of Finslerian black holes possess spectrum splitting, which reflects the fact that the spherical symmetry of the Finslerian black holes is broken. The effects of the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ on the late-time tails of scalar and electromagnetic field perturbations are shown. The late-time tails of the Finslerian Reissner-Nordstr\"om black holes possess a power-law falloff. The power-law index has a discontinuous jump, while the Finslerian parameter ${\ensuremath{\epsilon}}^{2}$ varies from 0 to nonzero. Such a fact reflects the fact that asymptotic-infinity behaviors of the Finslerian Reissner-Nordstr\"om black holes are different from their counterparts in general relativity.

Schwarzschild quasi-normal modes of non-minimally coupled vector fields

We study perturbations of massive and massless vector fields on a Schwarzschild black-hole background, including a non-minimal coupling between the vector field and the curvature. The coupling is given by the Horndeski vector-tensor operator, which we show to be unique, also when the field is massive, provided that the vector has a vanishing background value.We determine the quasi-normal mode spectrum of the vector field, focusing on the fundamental mode of monopolar and dipolar perturbations of both even and odd parity, as a function of the mass of the field and the coupling constant controlling the non-minimal interaction. In the massless case, we also provide results for the first two overtones, showing in particular that the isospectrality between even and odd modes is broken by the non-minimal gravitational coupling.We also consider solutions to the mode equations corresponding to quasi-bound states and static configurations. Our results for quasi-bound states provide strong evidence for the stability of the spectrum, indicating the impossibility of a vectorization mechanism within our set-up. For static solutions, we analytically and numerically derive results for the electromagnetic susceptibilities (the spin-1 analogs of the tidal Love numbers), which we show to be non-zero in the presence of the non-minimal coupling.