Cellular structures in instabilities : An introduction

Dispersion Relation in a Ferrofluid Layer of Any Thickness and Viscosity in a Normal Magnetic Field; Asymptotic Regimes

“…As seen above, a band of wavenumbers of width ε 1/2 near threshold is unstable [13]. This means that the order of magnitude δk 2 is at most ε so we can take s 2 to be of order ε.…”

“…Above the threshold of linear stability, a broad band of wavenumber is theoretically found unstable. It is seen from other instabilities that the mechanisms of wavenumber selection are very complex, including the effects of sidewalls, time-dependent effects in cellular structures, axisymmetric stucture in the case of Eutectic solidification, the nonlinearities of the problem, etc.. [13]. A common choice has been to consider then that one wavenumber k m is selected.…”

Excitation of E1-forbidden atomic transitions with electric, magnetic, or mixed multipolarity in light fields carrying orbital and spin angular momentum [Invited]

“…The interest of scientists to vortex-like dislocations in various media goes back to 1970's [1,2]. For historic and topical reviews we would like to refer the reader to such sources as [3,4].…”

Thermal buckling of functionally graded rectangular plates subjected to partial heating

“…The study associated with a localized buckling is one of important topics in elastic instability problems. The rigorous discussions of localized Table 1 The results of the convergence study for the degree of freedom buckling phenomena are found elsewhere [27] which include an alternative mathematical formulation, but we do not discuss it any further. For the buckling modes, in other words, we can realize a localized buckling mode by making use of many degrees of freedom without the alternative mathematical formulation.…”