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On the quasi-static approximation in the initial boundary value problem of linearised elastodynamics
Continuous data dependence estimates are employed to rigorously derive conditions that validate the quasi-static approximation for the initial...
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Spectral Theory, Stability and Continuation
In the framework of nonautonomous difference equations, we review tools to describe stability and hyperbolicity based on their linearisation, namely...
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Spectral Theory, Stability and Continuation
We review concepts to describe stability and hyperbolicity of nonautonomous ordinary differential equations based on their linearisation, namely...
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A New Evans Function for Quasi-Periodic Solutions of the Linearised Sine-Gordon Equation
We construct a new Evans function for quasi-periodic solutions to the linearisation of the sine-Gordon equation about a periodic travelling wave....
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Stability of Hydroelastic Waves in Deep Water
Two-dimensional periodic travelling hydroelastic waves on water of infinite depth are investigated. A bifurcation branch is tracked that delineates a...
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Introduction to Stability Theory with Applications to Mechanics
In this chapter we introduce the basics in the theory of Lyapunov stability, which was first formulated at the end of the nineteenth century.
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The nonlinear stability of plane parallel shear flows with respect to tilted perturbations
The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods. Tilted perturbation refers...
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Active Flux Methods for Hyperbolic Systems Using the Method of Bicharacteristics
The Active Flux method is a third order accurate finite volume method for hyperbolic conservation laws, which is based on the use of point values as...
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Stability of a two-dimensional biomorphoelastic model for post-burn contraction
We consider the stability analysis of a two-dimensional model for post-burn contraction. The model is based on morphoelasticity for permanent...
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Stability Issues of Entropy-Stable and/or Split-form High-order Schemes
The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with...
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On hierarchical competition through reduction of individual growth
We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the...
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Stability bounds of a delay visco-elastic rheological model with substrate friction
Cells and tissues exhibit sustained oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these...
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Stability of Heteroclinic Cycles: A New Approach Based on a Replicator Equation
This paper analyses the stability of cycles within a heteroclinic network formed by six cycles lying in a three-dimensional manifold, for a...
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Semilinear formulation of a hyperbolic system of partial differential equations
In this paper, we solve the Cauchy problem for a hyperbolic system of first-order PDEs defined on a certain Banach space X . The system has a special...
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Spectral and Energy–Lyapunov stability of streamwise Couette–Poiseuille and spanwise Poiseuille base flows
When a fluid fills an infinite layer between two rigid plates in relative motion, and it is simultaneously subject to a gradient of pressure not...
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Global Stability Analysis and DNS of a Swept Airfoil Section in Subsonic Flow
Direct numerical simulations are run for a NACA0012 airfoil at Mach 0.4 and Reynolds number 50,000. The flow fields are characterised by transitional...
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Linear Landau Dam** for a Two Species Vlasov-Poisson System for Electrons and Ions
This paper concerns the linear Landau dam** for the two species Vlasov-Poisson system for ions and electrons near Penrose stable equilibria. The...
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Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System
In this paper, we systematically study two-species reaction-diffusion-advection system with linear cross-diffusion and cross-advection. Firstly, we...
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BiGlobal Stability Analysis of Swept-Wing Boundary Layers with Forward and Backward Facing Steps
The temporal stability characteristics of generic, swept-wing boundary-layer flows of practical engineering significance with a smooth, isolated...