We investigate the formation of wrinkles and bulging in single-layer graphene sheets using an equivalent atomistic continuum nonlinear hyperelastic theory for nanoindentation and nanopressurization. We show that nonlinear geometrical effects play a key role in the development of wrinkles. Without abandoning the classical tension field membrane theory, we develop an enhanced model based upon the...

An original homogenization method was used to analyze the nonlinear elastic properties of epithelial cells probed by magnetic twisting cytometry. In this approach, the apparent rigidity of a cell with nonlinear mechanical properties is deduced from the mechanical response of the entire population of adherent cells. The proposed hyperelastic cell model successfully accounts for the variability i...

In addition to its intrinsic practical importance, nonlinear time delayed feedback control applied to lifting surfaces can result in interesting aeroelastic behaviors. In this paper, nonlinear aeroelastic response to external time-dependent loads and stability boundary for actively controlled lifting surfaces, in an incompressible flow field, are considered. The structural model and the unstead...

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than o...

A nonlinear functional is considered in this short communication for time interval segmentation and noise reduction of signals. An efficient algorithm that exploits the signal geometrical properties is proposed to optimise the nonlinear functional for signal smoothing. Discontinuities separating consecutive time intervals of the original signal are initially detected by measuring the curvature ...

Sound synthesis algorithms which radically depart from acoustical equations, and seek out numerical quirks at audio rate, can still have a part to play in the art-science investigations of computer music. This paper describes a host of ideas in alternative sound synthesis, from dilation equations and nonlinear dynamical equations, through probabilistic sieves, to oscillators based on geometrica...

Random fatigue analysis techniques have concentrated on linear structures that exhibit symmetric stress range probability density functions (PDF). In narrowband response and broadband random response it is assumed that the bending stress range PDF is symmetric and has zero mean stress. Structures that can exhibit geometrical nonlinearity, under large deflections, typically introduce membrane ef...

As an important model in quantum semiconductor devices, the Schrödinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical op...

We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besi...