Wilson loops stability in the gauge/string correspondence

We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual gravity backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuations for classical string embedding solutions having positive length function derivative $L'(r_0)>0$. Finally we make a brief discussion of 't Hooft loops in non-conformal backgrounds.Comment: 34 pages, 36 figures. Reference added. Final version JHEP accepte

Nonlinear Stability Analysis of the Classical Nested PI Control of Voltage Sourced Inverters

This note provides the first nonlinear analysis of the industry standard "partial decoupling plus nested PI loops" control of voltage sourced inverters. In spite of its enormous popularity, to date only linearization-based tools are available to carry out the analysis, which are unable to deal with large-signal stability and fail to provide estimates of the domain of attraction of the desired equilibrium. Instrumental to establish our result is the representation of the closed-loop dynamics in a suitable Lure-like representation, that is, a forward system in closed-loop with a static nonlinearity. The stability analysis is then done by generating an adequate Popov multiplier. Comparison with respect to linearization is discussed together with numerical results demonstrating non-conservativeness of the proposed conditions

Band structure in classical field theory

Stability and instability bands in classical mechanics are well-studied in connection with systems such as described by the Mathieu equation. We examine whether such band structure can arise in classical field theory in the context of an embedded kink in 1+1 dimensions. The static embedded kink is unstable to perturbations but we show that if the kink is dynamic it can exhibit stability in certain parameter bands. Our results are relevant for estimating the lifetimes of various embedded defects and, in particular, loops of electroweak Z-string.Comment: 6 pages, 4 fig. Reference added, Fig. 3 updated with improved numerical code, minor comments added. Version to be published in Phys. Rev.

Superconducting String Texture

We present a detailed analytical and numerical study of a novel type of static, superconducting, classically stable string texture in a renormalizable topologically trivial massive U(1) gauge model with one charged and one neutral scalar. An upper bound on the mass of the charged scalar as well as on the current that the string can carry are established. A preliminary unsuccesful search for stable solutions corresponding to large superconducting loops is also reported.Comment: RevTex, 14 pages, 8 figure

A robust and low frequency stable time domain PMCHWT equation

The time domain PMCHWT equation models transient scattering by piecewise homogeneous dielectrics. After discretization, it can be solved using the marching-on-in-time algorithm. Unfortunately, the PMCHWT equation suffers from DC instability: it supports constant in time regime solutions. Upon discretization, the corresponding poles of the system response function shift into the unstable region of the complex plane, rendering the MOT algorithm unstable. Furthermore, the discrete system becomes ill-conditioned when a large time step is used. This phenomenon is termed low frequency breakdown. In this contribution, the quasi Helmholtz components of the PMCHWT equation are separated using projector operators. Judicially integrating or differentiating these components of the basis and testing functions leads to an algorithm that (i) does not suffer from unstable modes even in the presence of moderate numerical errors, (ii) remains well-conditioned for large time steps, and (iii) can be applied effectively to both simply and multiply connected geometries

Stability and mode analysis of solar coronal loops using thermodynamic irreversible energy principles

We study the modes and stability of non - isothermal coronal loop models with different intensity values of the equilibrium magnetic field. We use an energy principle obtained via non - equilibrium thermodynamic arguments. The principle is expressed in terms of Hermitian operators and allow to consider together the coupled system of equations: the balance of energy equation and the equation of motion. We determine modes characterized as long - wavelength disturbances that are present in inhomogeneous media. This character of the system introduces additional difficulties for the stability analysis because the inhomogeneous nature of the medium determines the structure of the disturbance, which is no longer sinusoidal. Moreover, another complication is that we obtain a continuous spectrum of stable modes in addition to the discrete one. We obtain a unique unstable mode with a characteristic time that is comparable with the characteristic life-time observed for loops. The feasibility of wave-based and flow-based models is examined.Comment: 29 pages 10 figure

Study of hybrid air vehicles stability using computational fluid dynamics

This paper uses Computational Fluid Dynamics to predict aerodynamic damping of airships or hybrid air vehicles. This class of aircraft is characterised by large lifting bodies combining buoyancy and circulatory lift. Damping is investigated via forced oscillations of the vehicle in pitch and yaw. The employed method is verified using data for lighter than air vehicles. The use of fins and stabilisers was found to be beneficial. The rear part of the body was dominated by separated flow that containedmore frequencies than the forcing frequency imposed on the body. The final design is seen to be dynamically stable across a range of conditions for small pitch angles