Inward linear perturbation can produce unbounded solutions

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

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Influence of the geometric configuration of accretion flow on the black hole spin dependence of relativistic acoustic geometry

International Journal of Modern Physics D ◽

10.1142/s0218271818500232 ◽

2018 ◽

Vol 27 (03) ◽

pp. 1850023 ◽

Cited By ~ 2

Author(s):

Pratik Tarafdar ◽

Tapas K. Das

Keyword(s):

Black Hole ◽

Kerr Black Hole ◽

Geometric Configuration ◽

Surface Gravity ◽

Linear Perturbation ◽

Flow Profile ◽

White Hole ◽

Accretion Flow ◽

Black Hole Spin ◽

General Relativistic

Linear perturbation of general relativistic accretion of low angular momentum hydrodynamic fluid onto a Kerr black hole leads to the formation of curved acoustic geometry embedded within the background flow. Characteristic features of such sonic geometry depend on the black hole spin. Such dependence can be probed by studying the correlation of the acoustic surface gravity [Formula: see text] with the Kerr parameter [Formula: see text]. The [Formula: see text]–[Formula: see text] relationship further gets influenced by the geometric configuration of the accretion flow structure. In this work, such influence has been studied for multitransonic shocked accretion where linear perturbation of general relativistic flow profile leads to the formation of two analogue black hole-type horizons formed at the sonic points and one analogue white hole-type horizon which is formed at the shock location producing divergent acoustic surface gravity. Dependence of the [Formula: see text]–[Formula: see text] relationship on the geometric configuration has also been studied for monotransonic accretion, over the entire span of the Kerr parameter including retrograde flow. For accreting astrophysical black holes, the present work thus investigates how the salient features of the embedded relativistic sonic geometry may be determined not only by the background spacetime, but also by the flow configuration of the embedding matter.

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The interaction between dark energy and dark matter and its connection to the modified gravity

International Journal of Modern Physics A ◽

10.1142/s0217751x15450128 ◽

2015 ◽

Vol 30 (28n29) ◽

pp. 1545012

Author(s):

Jian-Hua He ◽

Bin Wang

Keyword(s):

Analytic Form ◽

Rate Function ◽

Einstein Frame ◽

Linear Perturbation ◽

Jordan Frame ◽

Expansion Of The Universe ◽

Text Model ◽

Conformal Equivalence ◽

The Universe ◽

Dilation Rate

We review the conformal equivalence in describing the background expansion of the universe by [Formula: see text] gravity both in the Jordan frame and the Einstein frame. In the Jordan frame, we present the general analytic expression for [Formula: see text] models that have the same expansion history as the [Formula: see text]CDM model. This analytic form can provide further insights on how cosmology can be used to test the [Formula: see text] gravity at the largest scales. Moreover we present a systematic and self-consistent way to construct the viable [Formula: see text] model in Jordan frame using the mass dilation rate function from the Einstein frame through the conformal transformation. In addition, we extend our study to the linear perturbation theories and we further exhibit the equivalence of the [Formula: see text] gravity presented in the Jordan frame and Einstein frame in the perturbed space–time. We argue that this equivalence has solid physics root.

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Simple Algebraic Expressions for the Prediction and Control of High-Temperature Annealed Structures by Linear Perturbation Analysis

Mathematical and Computational Applications ◽

10.3390/mca26020043 ◽

2021 ◽

Vol 26 (2) ◽

pp. 43

Author(s):

Constantino Grau Grau Turuelo ◽

Cornelia Breitkopf

Keyword(s):

High Temperature ◽

Surface Diffusion ◽

Perturbation Analysis ◽

Algebraic Model ◽

Structure Design ◽

Linear Perturbation ◽

Prediction And Control ◽

Void Shape ◽

Void Structure ◽

And Control

The prediction and control of the transformation of void structures with high-temperature processing is a critical area in many engineering applications. In this work, focused on the void shape evolution of silicon, a novel algebraic model for the calculation of final equilibrium structures from initial void cylindrical trenches, driven by surface diffusion, is introduced. This algebraic model provides a simple and fast way to calculate expressions to predict the final geometrical characteristics, based on linear perturbation analysis. The obtained results are similar to most compared literature data, especially, to those in which a final transformation is reached. Additionally, the model can be applied in any materials affected by the surface diffusion. With such a model, the calculation of void structure design points is greatly simplified not only in the semiconductors field but in other engineering fields where surface diffusion phenomenon is studied.

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Finite Element Analysis of Thermoelastic Contact Stability

Journal of Applied Mechanics ◽

10.1115/1.2901578 ◽

1994 ◽

Vol 61 (4) ◽

pp. 919-922 ◽

Cited By ~ 12

Author(s):

Taein Yeo ◽

J. R. Barber

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Steady State ◽

Eigenvalue Problem ◽

Linear Perturbation ◽

Dimensional System ◽

The Finite Element Method ◽

One Dimensional ◽

Thermoelastic Contact ◽

Element Method

When heat is conducted across an interface between two dissimilar materials, theimoelastic distortion affects the contact pressure distribution. The existence of a pressure-sensitive thermal contact resistance at the interface can cause such systems to be unstable in the steady-state. Stability analysis for thermoelastic contact has been conducted by linear perturbation methods for one-dimensional and simple two-dimensional geometries, but analytical solutions become very complicated for finite geometries. A method is therefore proposed in which the finite element method is used to reduce the stability problem to an eigenvalue problem. The linearity of the underlying perturbation problem enables us to conclude that solutions can be obtained in separated-variable form with exponential variation in time. This factor can therefore be removed from the governing equations and the finite element method is used to obtain a time-independent set of homogeneous equations in which the exponential growth rate appears as a linear parameter. We therefore obtain a linear eigenvalue problem and stability of the system requires that all the resulting eigenvalues should have negative real part. The method is discussed in application to the simple one-dimensional system of two contacting rods. The results show good agreement with previous analytical investigations and give additional information about the migration of eigenvalues in the complex plane as the steady-state heat flux is varied.

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Three-dimensional forced-damped dynamical systems with rich dynamics: Bifurcations, chaos and unbounded solutions

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2015.09.001 ◽

2015 ◽

Vol 311-312 ◽

pp. 25-36 ◽

Cited By ~ 5

Author(s):

Tomoyuki Miyaji ◽

Hisashi Okamoto ◽

Alex D.D. Craik

Keyword(s):

Dynamical Systems ◽

Three Dimensional ◽

Unbounded Solutions

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Resistive MHD modes in hollow cathodes external plasma

Plasma Sources Science and Technology ◽

10.1088/1361-6595/ac43c4 ◽

2021 ◽

Author(s):

Giulia Becatti ◽

Francesco Burgalassi ◽

Fabrizio Paganucci ◽

Matteo Zuin ◽

Dan M Goebel

Keyword(s):

Magnetic Field ◽

Hollow Cathode ◽

Electric Propulsion ◽

Axial Magnetic Field ◽

Mhd Equations ◽

Linear Perturbation ◽

Plasma Parameters ◽

Hollow Cathodes ◽

Plume Region ◽

Helical Mode

Abstract A significant number of plasma instabilities occur in the region just outside of hollow cathodes, depending on the injected gas flow, the current level and the application of an external magnetic field. In particular, the presence of an axial magnetic field induces a helical mode, affecting all the plasma parameters and the total current transported by the plasma. To explore the onset and behavior of this helical mode, the fluctuations in the plasma parameters in the current-carrying plume outside of a hollow cathode discharge have been investigated. The hollow cathode was operated at a current of 25 A, and at variable levels of propellant flow rate and applied magnetic fields. Electromagnetic probes were used to measure the electromagnetic fluctuations, and correlation analysis between each of the probe signals provided spatial-temporal characterization of the generated waves. Time-averaged plasma parameters, such as plasma potential and ion energy distribution function, were also collected in the near-cathode plume region by means of scanning emissive probe and retarding potential analyzer. The results show that the helical mode exists in the cathode plume at sufficiently high applied magnetic field, and is characterized by the presence of a finite electromagnetic component in the axial direction, detectable at discharge currents $\geq$ 25 A. A theoretical analysis of this mode reveals that one possible explanation is consistent with the hypotheses of resistive magnetohydrodynamics, which predicts the presence of helical modes in the forms of resistive kink. The analysis has been carried out by linear perturbation of the resistive MHD equations, from which it is possible to obtain the dispersion relation of the mode and find the $k-\omega$ unstable branch associated with the instability. These findings provided the basis for more detailed investigation of resistive MHD modes and their effect in the plume of hollow cathodes developed for electric propulsion application.

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Linear perturbation response of self-similar ablative flows relevant to inertial confinement fusion

Journal of Fluid Mechanics ◽

10.1017/s0022112008002279 ◽

2008 ◽

Vol 609 ◽

pp. 1-48 ◽

Cited By ~ 12

Author(s):

J.-M. CLARISSE ◽

C. BOUDESOCQUE-DUBOIS ◽

S. GAUTHIER

Keyword(s):

Inertial Confinement Fusion ◽

Similarity Solutions ◽

Linear Perturbation ◽

Inertial Confinement ◽

Mean Flow ◽

Direct Laser ◽

Confinement Fusion ◽

Self Similar ◽

The Mean ◽

Compressibility Effects

A family of exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction is proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Dynamical multi-domain Chebyshev spectral methods are employed for computing both the similarity solution and its time-dependent linear perturbations. This approach has been exploited to analyse the linear stability properties of two self-similar ablative configurations subjected to direct laser illumination asymmetries. Linear perturbation temporal and reduced responses are analysed, evidencing a maximum instability for illumination asymmetries of zero transverse wavenumber as well as three distinct regimes of ablation-front distortion evolution, and emphasizing the importance of the mean flow unsteadiness, compressibility and stratification.

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