60 research outputs found
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 β 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
- β¦