相关论文: Fractal Patterns in the Parameter Space of Bi-stab…

Using molecular dynamics simulation, we study structural and dynamical heterogeneities at melting in two-dimensional one-component systems with 36000 particles. Between crystal and liquid we find intermediate hexatic states, where the…

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as…

The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…

We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…

We study stability of the Dynamical Fixed Points (DFPs) of the cascading gauge theory at strong coupling in de Sitter space-time. We compute the spectra of the perturbative fluctuations and identify stable/unstable DFPs, characterized by…

For a hyperbolic map f on a saddle type fractal Lambda with self-intersections, the number of f- preimages of a point x in Lambda may depend on x. This makes estimates of the stable dimensions more difficult than for diffeomorphisms or for…

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…

We study several fractal properties of the Weierstrass-type function \[ W(x)=\sum_{n=0} ^\infty \lambda (x) \lambda(\tau x) \cdots \lambda (\tau ^{n-1}x)\, g(\tau ^n x), \] where $\tau :[0,1)\to[0,1)$ is a cookie cutter map with possibly…

We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…

Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…

We examine global dynamics and bifurcations occurring in a truncated model of a stellar mean field dynamo. This model has symmetry-forced invariant subspaces for the dynamics and we find examples of transient type I intermittency and…

We show that the interparticle friction coefficient significantly influences the flow and jamming behavior of granular materials exiting through the orifice of a two-dimensional silo in the presence of another orifice located in its…

The stability and bifurcation behaviour of a wake-induced vibro-impacting oscillator is studied. The effects of a discontinuity on the stability of the structure while it is undergoing phase-locked motions due to the surrounding…

Recently has been investigated that the ground-state wavefunction of the one dimensional quantum spin-1/2 chain models is multifractal in general with non-trivial fractal dimension. We are studying this phenomena for the quantum Ising chain…

For suitable parameters, the classical Duffing oscillator has a known bistability in its stationary states, with low- and high-amplitude branches. As expected from the analogy with a particle in a double-well potential, transitions between…

Interactions between fluids and elastic solids are ubiquitous in application ranging from aeronautical and civil engineering to physiological flows. Here we study the pulsatile flow through a two-dimensional Starling resistor as a simple…

We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter ${\tilde{\nu}}=\nu+1$ which is…

We analyse different types of nonlinear resonances in a weakly damped Duffing oscillator using bifurcation theory techniques. In addition to (i) odd subharmonic resonances found on the primary branch of symmetric periodic solutions with the…

For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For…

While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…