Related papers: Dynamics of the optical swallowtail catastrophe
We experimentally realize higher-order catastrophic structures in light fields to access the rich class of caustic swallowtail and butterfly beams. These beams present solutions of paraxial diffraction catastrophe integrals that are…
Photochromic diarylethene is known to exhibit reversible photoisomerization under irradiation with ultraviolet (UV) and visible light. Besides reversible optical properties upon light irradiation, a variety of discontinuous morphological…
This paper explores the topologies of caustics observed in instruments that employ charged particles, such as electron and ion microscopes. These geometrical figures are studied here using catastrophe theory. The application of this…
We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure,…
Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the…
The uniaxial elastic-plastic deformation process is considered. Mathematical model of this process was built. According to this model all stable static states form the lattice, which is called the delta-lattice.
We report on a direct quantitative comparison between Thom's general catastrophe theory for systems presenting discontinuous behavior and experimental reality. It is demonstrated that the model provides a striking quantitative description…
It has been recently established that heterogeneous bootstrap percolation and related dynamic facilitation models exhibit a complex hierarchy of continuous and discontinuous transitions depending on lattice connectivity and kinetic…
The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…
The effective Nambu-Goto description of $(2+1)$-dimensional domain walls predicts singular behavior of its worldsheet resulting in swallowtail bifurcations. This phenomenon is intimately related to the formation of cusps, which emerge in…
Caustics are optical phenomena which occur when a family of rays creates an envelope of divergent intensity. Here we show that caustic surfaces also appear when a real or complex field is mapped to its order parameter manifold. We study…
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…
Metallic glasses response to the mechanical stress in a complex and inhomogeneous manner with plastic strain highly localized into nanoscale shear bands. Contrary to the well-defined deformation mechanism in crystalline solids,…
A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
A number of physical processes show some form of bifurcation or periodic splintering of a single distribution into two new ones. Recently, it has been noted that cavity searches for interactions between photons and exotic fields may also…
What are the signatures of the onset of catastrophe? Here we present the rich system physics characterizing the transition from homeostasis to stochasticity driven breakdown in an experimentally motivated minimal model. Recent…