Related papers: Dynamics of the optical swallowtail catastrophe
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
Recent developments in theory and phenomenology relevant to deep inelastic lepton scattering are reviewed, concentrating on the following topics: Predicted behaviour of non-singlet and polarized structure functions at small $x$; Theoretical…
Spatial characteristics of diffracted beams produced by the "fork" holograms from incident circular Lauerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the…
Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…
Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
Caustics are singularities that occur naturally in optical, hydrodynamic and quantum waves, giving rise to high amplitude patterns that can be described using catastrophe theory. In this paper we study caustics in a statistical field theory…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed.…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
The concept of (auto)catalytic systems has become a cornerstone in understanding evolutionary processes in various fields. The common ground is the observation that for the production of new species/goods/ideas/elements etc. the…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallowtail loops…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…
The routine transformation of a liquid, as it is cooled rapidly, resulting in glass formation, is remarkably complex. A theoretical explanation of the dynamics associated with this process has remained one of the major unsolved problems in…
Supercooled first order phase transitions are typical of theories where conformal symmetry is predominantly spontaneously broken. In these theories the fate of the flat scalar direction is highly sensitive to the size and the scaling…