The string pendulum consists of a mass attached to the end of an inextensible string which is fastened to a support. Applying an external forcing to the pendulum’s support is motivated by understanding the behavior of suspension bridges or of tethered structures during earthquakes. The forced string pendulum can go from taut to slack states and vice versa, and is capable of exhibiting interesti...

The truncated forced non-linear Schrödinger (NLS) model is known to mimic well the forced NLS solutions in the regime at which only one linearly unstable mode exists. Using a novel framework in which a hierarchy of bifurcations is constructed, we analyze this truncated model and provide insights regarding its global structure and the type of instabilities which appear in it. In particular, the ...

Large explosive volcanic eruptions are capable of injecting considerable amounts of particles and sulphur gases (mostly sulphur dioxide) above the tropopause, causing increases in the stratospheric aerosol optical depth that may be even larger than one order of magnitude. The efolding particle lifetime in the stratosphere is much longer than in the troposphere (one year versus a few days) so th...

Abstract Transport of a particle in a spatially periodic harmonic potential under the influence of a slowly time-dependent unbiased periodic external force is studied. The equations of motion are the same as in the problem of a slowly forced nonlinear pendulum. Using methods of the adiabatic perturbation theory we show that for a periodic external force of general kind the system demonstrates d...

We consider randomly forced 2D Navier–Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturbation is non-degenerate, and its law is periodic in time and has a support localised with respect to space and time. Concerning the unperturbed problem, we assume that it is approximately controllable in infinite time by an external force whose support is include...

We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy–Hammel route for the creation of strange nonchaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computerassisted a...

Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such 'non-adiabatic' processes are ubiquitous, but little understood. We identify these processes with a new nonlinear phenomenon-an intricate threshold where a forced system fails to adiabatically follow a changing stable state. In systems with mul...

Forced displacement of oil by polymer flooding in oil reservoir is one of the effective methods of enhanced (tertiary) oil recovery. A classical model of this process within Hele-Shaw approximation involves three-layer fluid in a Hele-Shaw cell having a variable viscosity fluid in the intermediate layer between oil and water. The goal here is to find an optimal viscosity profile of the intermed...

An experimental investigation of nonlinear scale interactions in a forced turbulent boundary layer is presented here. A dynamic wall perturbation mechanism was used to externally force two distinct large-scale synthetic modes with well-defined spatial and temporal wave numbers in a fully turbulent flow. The focus is on characterizing the nonlinear flow response at triadically consistent wave nu...

Transverse vibrations of Timoshenko type beams carrying a concentrated mass have been investigated. Both ends of this mass-beam system have simply supports. Hamilton Principle has been used in order to derive equation of motion . For this coupled differential equations, approximately solutions have been searched by means of Method of Multiple Scales(a perturbation method). These solutions consi...