Related papers: Novel exact solutions of the Duffing equation: sta…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
We numerically investigate the athermal creep deformation of amorphous materials having a wide range of stability. The imposed shear stress serves as the control parameter, allowing us to examine the time-dependent transient response…
The universal generalising approach for non-isothermal behaviour of different alloys has been provided together with the novel deformation modelling. Strong correlation between the model approach and experimental results is shown that…
We apply the well-established theoretical method developed for geometrical nonlinearities of micro/nano-mechanical clamped beams to circular drums. The calculation is performed under the same hypotheses, the extra difficulty being to…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
We resolve issues that have plagued reliable prediction of relative phase stability for solid-solutions and compounds. Due to its commercially important phase diagram, we showcase Al-Li system because historically density-functional theory…
The vastness of the space of possible multicomponent metal alloys is hoped to provide improved structural materials but also challenges traditional, low-throughput materials design efforts. Computational screening could narrow this search…
We explore stability and instability of rapidly oscillating solutions $x(t)$ for the hard spring delayed Duffing oscillator $$x''(t)+ ax(t)+bx(t-T)+x^3(t)=0.$$ Fix $T>0$. We target periodic solutions $x_n(t)$ of small minimal periods…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
The Duffing oscillator describes the dynamics of a mass suspended on a spring with position-dependent stiffness. The mass is assumed to experience a linear damping and a time-dependent external forcing. The model has been instrumental in…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
Determining the melting curves of materials up to high pressures has long been a challenge experimentally and theoretically. A large class of materials, including most metals, has been shown to exhibit hidden scale invariance, an…
Amorphization during severe plastic deformation has been observed in various crystalline materials, yet its underlying mechanisms remain poorly understood. This study introduces a novel phase-field model at the mesoscale, integrating…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…
In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…
We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is…
Recently, it was demonstrated that electrochemical doping fronts in organic semiconductors ex- hibit a new fundamental instability growing from multidimensional perturbations [Phys. Rev. Lett. 107, 016103 (2011)]. In the instability…
The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase…
In disordered materials under mechanical stress, the produced deformation can deviate from the affine one already in the elastic regime. The nonaffine contribution was observed and characterized in numerical simulations for various systems.…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…