Related papers: Oscillating Fracture in Rubber
The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state…
Hopf bifurcations are a universal route to self-sustained oscillations in driven systems. Despite the absence of any singular stationary state, we show that time-averaged observables generically exhibit singularities at the onset of…
The transition route and bifurcations of the buoyant flow developing on a heated circular horizontal surface are elaborated using direct numerical simulations and direct stability analysis. A series of bifurcations, as a function of…
A study was made of the instability that arises when acoustic and gravity waves propagate in an inhomogeneous medium which is characterized by oscillatory approach of the reaction coordinates to the steady state. It is shown that loss of…
The rupture of the interface joining two materials under frictional contact controls their macroscopic sliding. Interface rupture dynamics depend markedly on the mechanical properties of the bulk materials that bound the frictional…
We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules…
We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the…
A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural…
Unstable growth of cracks (rough crack surface and crack branching) in dynamic fracture has long been observed in various materials. Until now, there was no universally agreed upon explanation for these instabilities. Here, we demonstrate…
We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
This paper presents a general framework to derive the weakly nonlinear stability near a Hopf bifurcation in a special class of multi-scale reaction-diffusion equations. The main focus is on how the linearity and nonlinearity of the fast…
For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…
The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically.…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
{We study a model of small-amplitude traveling waves arising in a supercritical Hopf-bifurcation, that are coupled to a slowly varying, real field. The field is advected by the waves and, in turn, affects their stability via a coupling to…
Bistability and snap-through instabilities are central to various mechanisms in nature and engineering, enabling rapid movement and large shape changes with minimal energy input. These phenomena are easily demonstrated by bending a piece of…
Convection structures in binary fluid mixtures are investigated for positive Soret coupling in the driving regime where solutal and thermal contributions to the buoyancy forces compete. Bifurcation properties of stable and unstable…
We investigate the question of stability of a solid thin film which experiences external interactions such as van der Waals forces from a contacting surface or forces from an external electric field. Both perfectly elastic and viscoelastic…
In order to investigate the emergence of periodic oscillations of rimming flows, we study analytically the stability of steady states for the model of (Benilov, Kopteva, O'Brien, 2005), which describes the dynamics of a thin fluid film…