Whitham modulation theory for the Zakharov-Kuznetsov equation and transverse instability of its periodic traveling wave solutions

We derive the Whitham modulation equations for the Zakharov-Kuznetsov equation via a multiple scales expansion and averaging two conservation laws over one oscillation period of its periodic traveling wave solutions. We then use the Whitham modulation equations to study the transverse stability of the periodic traveling wave solutions. We find that all such solutions are linearly unstable, and we obtain an explicit expression for the growth rate of the most unstable wave numbers. We validate these predictions by linearizing the equation around its periodic solutions and solving the resulting eigenvalue problem numerically. Finally, we calculate the growth rate of the solitary waves analytically. The predictions of Whitham modulation theory are in excellent agreement with both of these approaches.Comment: 15 pages, 2 figure

Modeling of Subwavelength Gratings: Near-Field Behavior

Subwavelength gratings, with period shorter than the incident wavelength, have garnered significant attention in the fields of photonics, optoelectronics, and image sensor technology. In this research, we delve into the scattering characteristics of these gratings by employing the 2-dimensional point dipole approximation. Additionally, we propose a version of perturbation theory that relies on Fourier decomposition to obtain analytical expressions for the near-field behavior. We validate our models using numerical techniques such as boundary and finite element analysis. Notably, we explore how parameters like the grating period and slit width affect field enhancements. We demonstrate that our models produce qualitatively accurate results even for narrow slits.Comment: 16 pages, 9 figures, bibliography 29 source

FOREWORD

Foreword to the thematic issue entitled:TRIBOLOGY IN AEROSPACE APPLICATIONS – DAMPING, WEAR AND STRUCTURAL DYNAMICS IN AEROSPACE SYSTEM

Quantifying the impact of tissue metabolism on solute transport in feto-placental microvascular networks

The primary exchange units in the human placenta are terminal villi, in which fetal capillary networks are surrounded by a thin layer of villous tissue, separating fetal from maternal blood. To understand how the complex spatial structure of villi influences their function, we use an image-based theoretical model to study the effect of tissue metabolism on the transport of solutes from maternal blood into the fetal circulation. For solute that is taken up under first-order kinetics, we show that the transition between flow-limited and diffusion-limited transport depends on two new dimensionless parameters defined in terms of key geometric quantities, with strong solute uptake promoting flow-limited transport conditions. We present a simple algebraic approximation for solute uptake rate as a function of flow conditions, metabolic rate and villous geometry. For oxygen, accounting for nonlinear kinetics using physiological parameter values, our model predicts that villous metabolism does not significantly impact oxygen transfer to fetal blood, although the partitioning of fluxes between the villous tissue and the capillary network depends strongly on the flow regim

The microstructure of aluminum-magnesium alloy friction stir weld

Friction stir weld joint of aluminum/magnesium alloy has been structurally characterized after tensile testing. A butt-weld flaw which a surface of joining between two sheets has been revealed. This defect dictates the specificity of sample's fracture in a tensile test