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Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the…
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being…
In this work, we show that a recently proposed method for experimental nonlinear modal analysis based on the extended periodic motion concept is well suited to extract modal properties for strongly nonlinear systems (i.e. in the presence of…
The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
Nonlinear interactions between phonon modes govern the behavior of vibrationally highly excited solids and molecules. Here, we demonstrate theoretically that optical cavities can be used to control the redistribution of energy from a highly…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…
Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…
A pure frequency domain method for the computation of periodic solutions of nonlinear ordinary differential equations (ODEs) is proposed in this study. The method is particularly suitable for the analysis of systems that feature distinct…
In this work we explore how nonlinear modes described by a dispersive wave equation (in our example, the nonlinear Schrodinger equation) and localized in a few wells of a periodic potential can act analogously to a chain of coupled…
Bead spring models for polymers in solution are nonlinear if either the finite extensibility of the polymer, excluded volume effects or hydrodynamic interactions between polymer segments are taken into account. For such models we use a…
A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of…
The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the 'add-drop filter', which comprises an optical microcavity and…
The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the…
The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate…
A new technique is introduced to reconstruct a nonlinear stochastic model of the cardiorespiratory interaction. Its inferential framework uses a set of polynomial basis functions representing the nonlinear force governing the system…
We demonstrate a variety of nonlinear phenomena at extremely low powers in cryogenic acoustic cavities fabricated from quartz material, which have not undergone any electrodiffusion processes. Nonlinear phenomena observed include lineshape…