Convergence Results for the Double-Diffusion Perturbation Equations

We study the structural stability for the double-diffusion perturbation equations. Using the a priori bounds, the convergence results on the reaction boundary coefficients k1, k2 and the Lewis coefficient Le could be obtained with the aid of some Poincare´ inequalities. The results showed that the structural stability is valid for the the double-diffusion perturbation equations with reaction boundary conditions. Our results can be seen as a version of symmetry in inequality for studying the structural stability.

1 + 3 covariant perturbations in power-law f(R) gravity

We applied the 1+3 covariant approach around the Friedmann–Lemaître–Robertson–Walker (FLRW) background, together with the equivalence between f(R) gravity and scalar-tensor theory to study cosmological perturbations. We defined the gradient variables in the 1 + 3 covariant approach which we used to derive a set of evolution equations. Harmonic decomposition was applied to partial differential equations to obtain ordinary differential equations used to analyse the behavior of the perturbation quantities. We focused on dust dominated area and the perturbation equations were applied to background solution of $$\alpha R+\beta R^{n}$$ α R + β R n model, n being a positive constant. The transformation of the perturbation equations into redshift dependence was done. After numerical solutions, it was found that the evolution of energy-density perturbations in a dust-dominated universe for different values of n decays with increasing redshift.

On perturbation theory and critical exponents for self-similar systems

Gravitational critical collapse in the Einstein-axion-dilaton system is known to lead to continuous self-similar solutions characterized by the Choptuik critical exponent $$\gamma $$ γ . We complete the existing literature on the subject by computing the linear perturbation equations in the case where the axion-dilaton system assumes a parabolic form. Next, we solve the perturbation equations in a newly discovered self-similar solution in the hyperbolic case, which allows us to extract the Choptuik exponent. Our main result is that this exponent depends not only on the dimensions of spacetime but also the particular ansatz and the critical solutions that one started with.

Prediction of flow-control devices' noise with modified acoustic perturbation equations

Fluid-dynamic noise emissions produced by flow-control devices inside ducts are a concerning issue for valve manufacturers and pipeline management. This work proposes a modified formulation of Acoustic Perturbation Equations (APE) that is applicable to industrial frameworks where the interest is addressed to noise prediction according to international standards. This formulation is derived from a literature APE system removing two terms allowing for a computational time reduction of about 20%. The physical contribution of the removed terms is discussed according to the literature. The modified APE are applied to the prediction of the noise emitted by an orifice. The reliability of the new APE system is evaluated by comparing the Sound Pressure Level (SPL) and the acoustic pressure with the ones returned by LES and literature APE. The new formulation agrees with the other methods far from the orifice: moving over nine diameters downstream of the trailing edge, the SPL is in accordance with the other models. Since international standards characterize control devices with the noise measured 1 m downstream of them, the modified APE formulation provides reliable and faster noise prediction for those devices with outlet diameter, d, such that 9d < 1 m.

Linear and Nonlinear Aeroelastic Analysis of a High Aspect Ratio Wing

In this study, analysis and results of linear and nonlinear aeroelastic of a cantilever beam subjected to the airflow as a model of a high aspect ratio wing are presented. A third-order nonlinear beam model is used as structural model to take into account the effects of geometric structural nonlinearities. In order to model aerodynamic loads, Wagner state-space model has been used. Galerkin method is implemented to solve dynamic perturbation equations about a nonlinear static equilibrium state. The small perturbation flutter boundary is determined by these perturbation equations. The effect of geometric structural nonlinearity of the beam model on the flutter behavior is significant. As it is observed the system’s response to upper speed of flutter goes to limit cycle oscillations and also the oscillations lose periodicity and become chaotic.