Related papers: Regularity and energy transfer for a nonlinear bea…
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable…
While extensive studies have been conducted on purely elastic ribbons, in this paper we explore the influence of magnetisation on the deformation of planar ferromagnetic elastic ribbons. We begin the investigation by deriving the…
Existing smart composite piezoelectric beam models in the literature mostly ignore the electro-magnetic interactions and adopt the linear elasticity theory. However, these interactions substantially change the controllability and…
We study waves in a rod of finite length with a viscoelastic constitutive equation of fractional distributed-order type for the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain case…
In this paper, we investigate the energy decay of the solution to a viscoelastic wave equation with variable exponents logarithmic nonlinearity and weak damping in a bounded domain. We establish an explicit general decay result under mild…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…
We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and…
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case…
The derivative discontinuity is a key concept in electronic structure theory in general and density functional theory in particular. The electronic energy of a quantum system exhibits derivative discontinuities with respect to different…
In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of…
We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic…
Treating the ideal coherent state as a reference state, the effects due to departure from coherence of an initial wave packet propagating through a nonlinear medium, were examined, specifically in the context of non-classical effects such…
A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…
When subjected to electro-mechanical loading, ferroelectrics see their polarization evolve through the nucleation and evolution of domains. Existing mesoscale phase-field models for ferroelectrics are typically based on a gradient-descent…
A full theory for hinged beams and degenerate plates with multiple intermediate piers is developed. The analysis starts with the variational setting and the study of the linear stationary problem in one dimension. Well-posedness results are…
The approach to calculating the effective dielectric and magnetic response in bounded composite materials is developed. The method is essentially based on the renormalisation of the dielectric matrix parameters to account for the surface…
The nonlinear transfer rate of the total energy (transfer rate of kinetic energy + transfer rate due to the work done by the magnetization) for an incompressible turbulent ferrofluid system is studied under the assumption of statistical…
We study the global existence and decay estimates for nonlinear wave equations with the space-time dependent dissipative term in an exterior domain. The linear dissipative effect may vanish in a compact space region. Moreover the nonlinear…
We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the…
In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…