It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a choice of scales of independent variables in the reductive perturbation method. Recently a novel method based on the perturbative renormalization group theory has...

In present study is concerned with the propagation of axisymmetric vibrations in a homogenous isotropic micropolar thermoelastic cubic crystal plate bordered with layers or half spaces of inviscid liquid subjected to stress free boundary conditions in context of Lord and Shulman (L-S) and Green and Lindsay (G-L) theories of thermoelasticity. The secular equations for symmetric and skew-symmetri...

We study incremental wave propagation for what is seemingly the simplest boundary value problem, namely that constitued by the plane interface of a semi-infinite solid. With a view to model loaded elastomers and soft tissues, we focus on incompressible solids, subjected to large homogeneous static deformations. The resulting strain-induced anisotropy complicates matters for the incremental boun...

A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious diiculty in the previous reduction to amplitude equations by eliminating all of the secular terms but also consistent derivation of higher-order correction to amplitude equations. Recently a novel method based on the pert...

A system of equations is derived for the secular motion of a hierarchic triple stellar system. Mean anomalies of the inner binary system and of the outer star orbit are eliminated up to order 9 in the ratio of their Delaunay momenta. Thanks to the use of vectorial elements (angular momenta and Laplace vectors) the equations are non-singular, compact, and independent on the choice of the referen...

Equations describing serial radioactive decay are reviewed along with published descriptions of transient and secular equilibrium. It is shown that terms describing equilibrium are not used in the same way by various authors. Specific definitions are proposed; they suggest that secular equilibrium is a subset of transient equilibrium.

In the present paper is concerned with study of thermoelastic interaction in an infinite KelvinVoigt type viscoelastic, thermally conducting solid bordered with viscous liquid half-spaces/layers of varying temperature. Complex secular equations in closed and isolated mathematical conditions for Rayleigh wave propagation in completely separate terms are derived. The results for coupled and uncou...

The problem of Stoneley waves in a non-homogeneous orthotropic elastic medium under the influence of gravity was studied recently by Abd-Alla and Ahmed [A.M. Abd-Alla, S.M. Ahmed, Stoneley waves and Rayleigh waves in a non-homogeneous orthotropic elastic medium under the influence of gravity, Appl. Math. Comput. 135 (2003) 187-200], who derived the secular equation of the wave in the implicit f...

Master equations are a vital tool to model heat flow through nanoscale thermodynamic systems. Most practical devices made up of interacting sub-system, and often modelled using either local master (LMEs) or global (GMEs). While the limiting cases in which LME GME breaks down well understood, there exists 'grey area' both capture steady-state currents reliably, but predict very different transie...

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...