Related papers: Hexagonal eutectic solidification patterns operati…
The dynamics of a flexible filament sedimenting in a viscous fluid are explored analytically and numerically. Compared to the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a…
We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is coupled to an external…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
The solidification behavior of a eutectic AlCu specimen is investigated via in situ scanning transmission electron microscope (STEM) experiments. Solidification conditions are varied by imposing various cooling conditions via a…
The formation of regular patterns is a common feature of many solidification processes involving cast materials. We describe here how regular patterns can be obtained in porous alumina and hydroxyapatite (HAP) by controlling the freezing of…
The goal of quantitative elastography is to identify biomechanical parameters from interior displacement data, which are provided by other modalities, such as ultrasound or magnetic resonance imaging. In this paper, we analyze the stability…
We study polynomial stability to the one-dimensional system in the linear isothermal theory of swelling porous elastic soils with an internal fractional damping. We establish an optimal decay result by frequency domain method
In this work, we investigate the elastic properties of deflated vesicles and their shape dynamics in uniaxial extensional flow. By analysing the Helfrich bending energy and viscous flow stresses in the limit of highly elongated shapes, we…
The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our intention is to extend the periodic unfolding method to the…
This paper presents a new generalized Mackey-Glass model with a non-linear harvesting term and mixed delays. The main purpose of this work is to study the existence and the exponential stability of the pseudo almost periodic solution for…
Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…
In aggregation-fragmentation processes, a steady state is usually reached in the long time limit. This indicates the existence of a fixed point in the underlying system of ordinary differential equations. The next simplest possibility is an…
Transition metal oxide heterostructures and interfaces host a variety of exciting quantum phases and can be grown with atomic-scale precision by utilising the intensity oscillations of $in$ $situ$ reflection high-energy electron diffraction…
Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of…
Metals are important structural materials for transport and the built environment. Low carbon steels can fail through strain localisation due to the role of interstitial solute atoms (such as carbon and nitrogen) interacting with mobile…
We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 \mu m-thick samples, and in the planar configuration (director…
We show that, in a two-dimensional (2d) ideal fluid (also applies to a column of quasi-2d non-neutral plasma in an axial magnetic field), large elliptical vortices in a finite disk are stable. The stability is established by comparison…
The presented investigation is motivated by the need to uncover connections between underlying rotor fluid-structure interactions and vortex dynamics to fatigue performance and characterization of flexible rotor blades, their hub, and their…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
We prove that the stability problem of a vertical uniform rotation of a heavy top is completely solved by using the linearization method and the conserved quantities of the differential system which describe the rotation of the heavy top.