Linear Perturbation Research Articles

Generic spherically symmetric thin-shell wormholes with equilibrium throat at the innermost photonsphere are unstable

In this research, we prove analytically that a generic spherically symmetric thin-shell wormhole (TSW) with its throat located at the innermost photonsphere of the bulk asymptotically flat black hole and supported by a generic surface barotropic perfect fluid is unstable against a radial linear perturbation. This is the generalization of the instability of the Schwarzschild TSW (STSW) with the throat’s radius located at a0=3M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0}=3M$$\\end{document} that was revealed by Poisson and Visser in their seminal work (Poisson and Visser in Phys Rev D 52, 7318, 1995). where they studied the mechanical stability of STSW. Our proof provides a link between the instability of the null circular geodesics on the innermost photonsphere of a generic static spherically symmetric asymptotically black hole and the TSW constructed in the same bulk with a0=rc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0}=r_{c}$$\\end{document} where a0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ a_{0} $$\\end{document} and rc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{c}$$\\end{document} are the radius of the TSW and the innermost photonsphere, respectively. For asymptotically flat spherically symmetric black holes possessing more than one photonspheres, the number of the photonspheres is odd and at least one photonsphere is stable which implies the corresponding TSW with its throat identical with the stable photonsphere is also stable.

The role of density breaks in driving spiral structure in disc galaxies

ABSTRACT It is well established that stellar discs are destabilized by sharp features in their phase space, driving recurrent spiral modes. We explore the extent to which surface-density breaks in disc galaxies – which represent sharp changes in the gradient of the disc density – drive new spiral modes. We employ linear perturbation theory to investigate how disc breaks alter the eigenmode spectrum of an otherwise pure exponential disc. We find that the presence of a density break gives rise to a set of new, vigorously growing, modes. For a given multiplicity, these edge modes occur in pairs, with closely separated resonances between each pair. The growth rate of edge modes decreases when the break is weakened or moved outward to lower-density regions of the disc. Both down- and up-bending profiles excite edge modes, whose origin can be best understood via the gravitational torques they exert on the underlying disc. When the profile is down-bending (Type II) the faster growing mode is the inner one while in the up-bending (Type III) case the outer mode is faster growing. In both cases, the faster growing mode has a corotation almost coincident with the break. We show that the torques of the edge modes tend to smoothen the break.

Probing pole-skipping through scalar Gauss-Bonnet coupling

The holographic phenomena of pole-skipping have been studied in the presence of scalar-Gauss-Bonnet interaction in a four-dimensional Anti-de Sitter-Schwarzchild black hole background. In this paper, we initiated a novel study on understanding the response of those pole-skipping points under the application of external sources. The source is identified with the holographic dual operator of the bulk scalar field with its non-normalizable solutions. We analyze in detail the dynamics of pole-skipping points in both sound and shear channels, considering linear perturbation in bulk. In the perturbative regime, characteristic parameters for chaos, namely Lyapunov exponent and butterfly velocity, remain unchanged. However, the momentum values of the pole-skipping points in various modes are found to be affected by the scalar source. Further, the diffusion coefficient has been observed to evolve non-trivially under the application of external sources.

Estimating Baryon Density through the CAMB and Assessing its Reliability

The Cosmic Microwave Background Radiation and its anisotropies allow us to analyze many properties and phenomena of the early universe. One such important property is the Baryon Density(Ω_b), a cosmological constant for the density of Baryons in the universe in comparison to its critical density. Baryon Density affects the interactions of matter in the early universe and therefore the analysis of CMB Anisotropies to study how matter interacts allows for the estimation of the Baryon Density in the Early Universe. Understanding Ω_b, is crucial as it reveals information about the composition of the universe, such as the amount of dark matter and dark energy, the early formation of celestial bodies and matter-antimatter asymmetry. This paper aimed to test the reliability of CAMB, a simulation algorithm for CMB anisotropies, by estimating Ω_b h^2. The CAMB mainly utilizes a combination of field equations, the Friedmann-Lemaître-Robertson-Walker metric, Fluid Equations, the Boltzmann Equation and Linear Perturbation theory in order to compute the CMB power spectra. We estimated the value of Ω_b h^2, maintaining other cosmological parameters constant and changing Ω_b h^2 from 0.01 to 0.03 in increments of 0.000625. The peaks, troughs, positions, damping scale and amplitudes of the resultant TT and TE power spectra were compared with data from the Planck Satellite. We use chi-square minimization and find the best fit value and uncertainty forΩ_b h^2 to be 0.02325 ± 0.00015. The estimated value of the baryon density from our study was compared to existing estimates to evaluate the reliability of CAMB as a simulation and source of information for further CMB Anisotropy related research, where it was confirmed to be accurate. However, further developments using wider sets of data was acknowledged with deep learning being a potential step forward.

About the onset of the Hopf bifurcation for convective flows in horizontal annuli

Experimental and numerical results cannot yet settle whether, between horizontal coaxial cylinders, if the curvature is large, the first transition for convection is an exchange of stability or rather an Hopf bifurcation. We directly show that if the curvature tends to infinity, no periodic linear perturbation exists when the Rayleigh number is equal to the critical one for nonlinear stability.

Robust and accurate Roe-type Riemann solver with compact stencil: Rotated-RoeM scheme

In this study, we aim to develop a robust and accurate Riemann solver to resolve strong shock waves with compact stencil information by applying the rotated hybrid concept to the RoeM scheme. The original RoeM scheme offers good robustness from the perspective of avoiding shock instability, also called the carbuncle phenomenon, in hypersonic flows by introducing Mach-number-based functions. These functions rely on multi-dimensional shock discontinuity sensing terms to capture grid-aligned shock waves, thus necessitating sharing of values of cells adjacent to each vertex. Consequently, constructing a data structure that can handle such a wide stencil is necessary, particularly for implementations on unstructured grids. Moreover, communication of this stencil information on parallel computation can increase computational costs.To overcome these complexities, the rotated hybrid concept is applied to the RoeM scheme, to replace the multi-dimensional terms while still resolving the grid-aligned shock instability. In addition, a Mach-number-based weighting function is introduced to distinguish between the flow around the boundary layer and the onset of shock instability. The damping characteristic of the proposed scheme is compared to that of the original RoeM scheme by conducting a linear perturbation analysis. The findings reveal that the proposed scheme effectively controls spurious oscillations across strong shock waves. Numerous test cases are presented to demonstrate the robustness and accuracy of the proposed approach. Notably, the proposed scheme successfully resolves thermal boundary layers and accurately predicts the heat transfer rate around stagnation points in hypersonic flows.

Structural instability and linear allocation control in generalized models of substance use disorder

Substance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, including opioid use disorder developed through prescription use and alcoholism developed primarily due to genetic factors or stress, depression, and other psychological factors. In this paper we will demonstrate that even a simple infectious disease model is structurally unstable with respect to a linear perturbation in the infection term — precisely the sort of term necessary to model SUD development in isolation. This implies that models of SUD which exclusively treat problematic substance use as an infectious disease will have misleading dynamics whenever a non-trivial rate of isolated SUD development exists in actuality. As we will show, linearly perturbed SUD models do not have a use disorder-free equilibrium. To investigate management strategies, we implement optimal control techniques with the goal of minimizing the number of SUD cases over time.

The effective field theory approach to the strong coupling issue in f(T) gravity with a non-minimally coupled scalar field

The Hamiltonian analysis for f(T) gravity implies the existence of at least one scalar-type degree of freedom (DoF). However, this scalar DoF of f(T) gravity does not manifest in linear perturbations around a cosmological background, which indicates an underlying strong coupling problem. In this work we expand the scope by introducing an extra scalar field non-minimally coupled to f(T) gravity, aiming to address or alleviate the aforementioned strong coupling problem. Employing the effective field theory (EFT) approach, we provide a class of torsional EFT forms up to second order operators, avoiding the Ostrogradsky ghost. To illustrate this phenomenon, we study a simple model and perform a detailed analysis of its linear scalar perturbations. The results demonstrate that the coupling terms in this toy model are necessary to avoid the initial degenerate situation. The complete avoidance of new constraints requires more coupling terms. Once this vanishing scalar DoF starts propagating in cosmological background at linear level, this phenomenon will demand a revisit of the strong coupling issue that arises in f(T) gravity, particularly in the presence of matter coupling.

Combined effect mechanism of linear loading and disturbance with different amplitudes on sandstone

To comprehend the stress state and response characteristics of materials under complex conditions, researchers have decomposed stress states into fundamental paths and investigated diverse path combinations. To ensure comparability, four identical samples were carefully selected from a pool of 100 samples using ultrasonic tests based on the wave speed and waveform characteristics. These samples underwent specially designed stress paths to analyze the combined effects of linear loading and perturbation. Our result analysis centred on the perturbation amplitude and stress levels during composite action, revealing intricate relationships between the stress levels, strain, and nonlinear/linear energy evolution under complex stress paths. Simultaneously, 3D surface fractures were precisely reconstructed using the YOLOv5 and FAST feature point detection algorithms, elucidating the evolving patterns of the fractures. As a result of our study, the rotation trend of the main fracture was validated by integrating mechanics and P-wave reflection rules. Notably, our experimental results closely aligned with the theoretical predictions, showing the reliability of our study. These findings can significantly contribute to guiding safety protocols in the field of underground engineering.

Can we distinguish dark energy from vacuum-decaying models?

In this paper, we study the distinguishability of dark energy and vacuum decay models. We start showing formally that dark energy fluids and dynamic vacuum are kinematically equivalent. Consequently, cosmological probes, such as the distances of type Ia supernovae (SNe Ia), cosmic microwave background (CMB) distance priors, baryon acoustic oscillations (BAO) distilled parameters and cosmic chronometers, are unable to allow us to distinguish such models from each other. Then, we show that, at least in principle, these models are dynamically distinguishable. So, dynamical probes, such as the evolution of linear matter perturbations, can be used to distinguish between dark energy models and dynamic vacuum models. To exemplify the kinematic equivalence between dark energy models and vacuum decay models, we study two simple models: the wCDM, commonly associated with dark energy, and the Wang–Meng model, often associated with dynamic vacuum. We test these two models with 22 measurements of [Formula: see text]. First, we consider both as dark energy then we consider both as vacuum decay. We show that, although compatible with each other, when seen as dynamical vacuum both models are tightly close to the [Formula: see text]CDM model.

Temporal evolution of cosmological density perturbations of the Bose–Einstein condensate dark matter

Dark matter is assumed to be composed of scalar boson particles that form Bose–Einstein condensate during the cosmic evolution of the Universe when the temperature of the dark matter is below the critical temperature Tcr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cr}$$\\end{document}. At around a redshift z∼1200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z\\sim 1200$$\\end{document}, the normal dark matter converted to Bose–Einstein condensate dark matter through a first-order phase transition and continued to complete the condensation process for nearly 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^6$$\\end{document} years, until then, both phases coexist. In this manuscript, considering Bose–Einstein condensate dark matter as a Gross–Pitaevskii–Poisson system, we study the time evolution of density contrast of Bose–Einstein condensate dark matter using cosmological linear perturbation theory following previous works on the subject. The evolution equation contains quantum pressure due to Heisenberg’s uncertainty principle and self-interaction pressure terms. We solve the temporal density contrast equation of Bose–Einstein condensate dark matter analytically for both the Thomas-Fermi limit and the non-interacting case where the expansion rule follows similarly to that of the Einstein–de Sitter Universe. In addition, we also numerically analyze the temporal nature of the evolution of density contrast of Bose–Einstein condensate dark matter for the complete equation without applying any approximation. We find that the Bose–Einstein condensate model of dark matter could modify the temporal nature of density contrast evolution due to the presence of self-interaction and quantum pressure terms, which shows significant differences with respect to the conventional standard cold dark matter, and successfully solves the small-scale problems in the context of cosmological structure formation.

Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes

We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.

Braneworld sum rules and positive tension branes in a massive gravity

By taking advantage of the braneworld sum rules, we explore the feasibility of constructing a flat 3-brane scenario consisting solely of positive tension branes in a 5D extension of the Lorentz-violating massive gravity. It is found that the theory supports three distinct brane configurations, one of which is exactly what we expected, consisting solely of two positive tension branes. The cosmological problem of Randall-Sundrum-1 model and the gauge hierarchy problem can be solved in this model simultaneously. Furthermore, the analysis of linear perturbations reveals that the tensor, vector and scalar modes are all massive and share the same mass spectrum, except that the ground state of vector mode is absent. Moreover, the tensor and vector modes are robust, but the scalar mode is ghost-like. Interestingly, even though the Kaluza-Klein gravitons have an extremely small mass splitting scale, an estimation of the effective gravitational potential and production of these gravitons on the brane indicates that the phenomenology of the present model is equivalent to that of the 6D ADD model.

Symmetry breaking of 3-dimensional AdS in holographic semiclassical gravity

We show that 3-dimensional AdS spacetime can be semiclassically unstable due to strongly interacting quantum field effects. In our previous paper, we have pointed out the possibility of such an instability of AdS3 by inspecting linear perturbations of the (covering space of) static BTZ black hole with AdS4 gravity dual in the context of holographic semiclassical problems. In the present paper, we further study this issue from thermodynamic viewpoint by constructing asymptotically AdS3 semiclassical solutions and computing free energies of the solutions. We find two asymptotically AdS3 solutions to the semiclassical Einstein equations with non-vanishing source term: the one whose free energy is smaller than that of the BTZ with vanishing source term and the other whose free energy is smaller than that of the global AdS3 with no horizon (thus manifestly zero-temperature background). The instability found in this paper implies the breakdown of the maximal symmetries of AdS3, and its origin is different from the well-known semiclassical linear instability since our holographic semiclassical Einstein equations in 3-dimensions do not involve higher order derivative terms.

Eigenvalue characterization of some structured matrix pencils under linear perturbation

We study the effect of linear perturbations on three families of matrix pencils. The matrix pairs of the first two families are Hermitian/skew-Hermitian with special $3\times 3$ block cases appeared in continuous-time control, and the matrix pairs of the third family are special $3\times 3$ non-Hermitian block matrices appeared in discrete-time control. For the first family of matrix pencils and more general cases of the second family of matrix pencils, based on the properties of the involved matrices, we obtain some upper or lower bounds on the set of eigenvalues of linearly perturbed matrix pencils which are on the imaginary axis. Studying a special $3\times 3$ block matrix pencil, which is associated with continuous-time control, leads us to some linear perturbation that do not preserve (properly) the structure of the matrices. This, in turn, leads to a numerical technique for finding the nearest Hermitian/skew-Hermitian matrix pencil which can satisfy conditions such that, for some nonzero real perturbation parameter, some or all of its eigenvalues lie on the imaginary axis. We also study the linearly perturbed matrix pencils, associated with discrete-time control, using an one-to-one equivalence between the matrix pencil of continuous-time problem and the matrix pencil of discrete-time problem.

Deformations of the Kerr-(A)dS near horizon geometry

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński (2013 Gen. Rel. Grav. 45 987–1004) to eliminate all but a finite number of Fourier modes of linear perturbations. In the second part, we give an argument using analyticity to prove that there are no odd Fourier modes.

Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems

Abstract We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessment of different types of dynamical stability. By comparing numerical results on Erdós-Rényi and Husimi graphs with sign-antisymmetric interactions or mixed sign patterns, we propose a sufficient criterion, called strong local sign stability, for stability not to be affected by system size, as traditionally implied by the complexity-stability trade-off in conventional models of random matrices. The criterion requires sign-antisymmetric or unidirectional interactions and a local structure of the graph such that the number of cycles of finite length do not increase with the system size. Note that the last requirement is stronger than the classical local tree-like condition, which we associate to the less stringent definition of local sign stability, also defined in the paper.
In addition, for strong local sign stable graphs which show stability to linear perturbations irrespectively of system size, we observe that the leading eigenvalue can undergo a transition from being real to acquiring a nonnull imaginary part, which implies a dynamical transition from nonoscillatory to oscillatory linear response to perturbations. Lastly, we ascertain the discontinuous nature of this transition.

Effect of conformational sampling on redox properties using linear response and free energy perturbation

Effect of conformational sampling on redox properties using linear response and free energy perturbation

Self-consistent interaction of linear gravitational and electromagnetic waves in non-magnetized plasma

This paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave properties are derived from first principles for inhomogeneous plasma, without assuming any symmetries of the background metric. First, we derive the effective (“oscillation-center”) Hamiltonian that governs the average dynamics of plasma particles in a prescribed quasimonochromatic wave that involves metric perturbations and EM fields simultaneously. Then, using this Hamiltonian, we derive the backreaction of plasma particles on the wave itself and obtain gauge-invariant equations that describe the resulting self-consistent gravito-electromagnetic (GEM) waves in a plasma. The transverse tensor modes of gravitational waves are found to have no interaction with the plasma and the EM modes in the geometrical-optics limit. However, for longitudinal GEM modes with large values of the refraction index, the interplay between gravitational and EM interactions in plasma can have a strong effect. In particular, the dispersion relation of the Jeans mode is significantly affected by electrostatic interactions. As a spin-off, our calculation also provides an alternative resolution of the so-called Jeans swindle.

Constraining the growth rate on linear scales by combining SKAO and DESI surveys

In the pursuit of understanding the large-scale structure of the Universe, the synergy between complementary cosmological surveys has proven to be a powerful tool. Using multiple tracers of the large-scale structure can significantly improve the constraints on cosmological parameters. We explore the potential of combining the Square Kilometre Array Observatory (SKAO) and the Dark Energy Spectroscopic Instrument (DESI) spectroscopic surveys to enhance precision on the growth rate of cosmic structures. We employ a multi-tracer Fisher analysis to estimate precision on the growth rate when using pairs of mock surveys that are based on SKAO and DESI specifications. The pairs are at both low and high redshifts. For SKA-MID, we use the HI galaxy and the HI intensity mapping samples. In order to avoid the complexities and uncertainties at small scales, we confine the analysis to scales where linear perturbations are reliable. The consequent loss of signal in each individual survey is mitigated by the gains from the multi-tracer. After marginalising over cosmological and nuisance parameters, we find a significant improvement in the precision on the growth rate.