It is known that the pitchfork bifurcation of Kelvin-Helmholtz instability occurring at minimum gradient Richardson number Ri(m) similar or equal to 1/4 in viscous stratified shear flows can be subcritical or supercritical depending on the value of the Pra ...
In many applications, such as textiles, fibreglass, paper and several kinds of biological fibrous tissues, the main load-bearing constituents at the micro-scale are arranged as a fibre network. In these materials, rupture is usually driven by micro-mechani ...
In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...
A specific family of spanwise-localised invariant solutions of plane Couette flow exhibits homoclinic snaking, a process by which spatially localised invariant solutions of a nonlinear partial differential equation smoothly grow additional structure at the ...
This paper deals with a singular, nonlinear Sturm-Liouville problem of the form {A(x)u'(x)}'+ lambda u (x) = f (x, u(x), u'(x)) on (0,1) where A is positive on (0,1] but decays quadratically to zero as x approaches zero. This is the lowest level of degener ...
The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a red ...
Following earlier work on some special cases [17,11] and on the analogous problem in higher dimensions [10,20], we make a more thorough investigation of the bifurcation points for a nonlinear boundary value problem of the form -{A(x)u' (x)}'.= f (lambda, x ...
The problem of swinging up an inverted pendulum on a cart and controlling it around the upright position has traditionally been treated as two separate problems. This paper proposes a control strategy that is globally asymptotically stable under actuator s ...
When laminar shear flows in large wall-bounded domains transition to turbulence, the flow exhibits spatio-temporally chaotic dynamics. Despite its chaotic dynamics, the flow may self-organize into characteristic spatially periodic patterns of unknown origi ...
We study experimentally and theoretically the electromagnetic field in amplitude and phase behind ball-lenses across a wide range of diameters, ranging from a millimeter scale down to a micrometer. Based on the observation, we study the transition between ...
