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The idea of the modal expansion in electromagnetics is derived from the research on electromagnetic resonators, which play an essential role in developments in nanophotonics. All of the electromagnetic resonators share a common property:…

We exploit the techniques of dynamical systems to study the cosmological evolution of cosmic fundamental strings and effective strings arising from branes wrapped on internal cycles. We also include the whole potential of the volume modulus…

We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…

There is a large interest to decrease the size of mechanical oscillators since this can lead to miniaturization of timing and frequency referencing devices, but also because of the potential of small mechanical oscillators as extremely…

We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…

We examine the existence of nonlinear modes and their temporal dynamics, in arrays of split-ring resonators, using a fractional extension of the Laplacian in the evolution equation. We find a closed-form expression for the dispersion…

In this paper, I aim to study free oscillations of a system of oscillators in more than one dimensions in the absence of damping. The basic approach lies in decoupling the motion in the individual perpendicular directions. Once the…

The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved…

Nonlinear dynamics of a two-side electro-statically actuated capacitive micro-beam is studied. The piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to…

A new nonlinear equation governing asymptotic dynamics of ripples is derived by using a short wave perturbative expansion on a generalized version of the Green-Naghdi system. It admits peakon solutions with amplitude, velocity and width in…

Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong…

Optomechanical resonators suffer from the dissipation of mechanical energy through the necessary anchors enabling the suspension of the structure. Here we show that such structural loss in an optomechnaical oscillator can be almost…

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes…

We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…

We consider a beam-string-beam transmission problem, where two structurally damped or undamped beams are coupled with a frictionally damped string by transmission conditions. We show that for this type of structure, the dissipation produced…

This work is devoted to analysis of the nonlinear dynamics of interrelated thermal and electromagnetic perturbations in a superconductor caused by dissipative effects involved in the viscous motion of the magnetic flux. The structure and…

We investigate the behaviour of two non-linearly coupled flexural modes of a doubly-clamped suspended beam (nanomechanical resonator). One of the modes is externally driven. We demonstrate that classically, the behavior of the non-driven…

We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…

Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their…

Coupling a microscopic mechanical resonator to a nano-scale quantum system enables control of the mechanical resonator via the quantum system, and vice versa. The coupling is usually achieved through functionalization of the mechanical…