Showing papers in "Physica D: Nonlinear Phenomena in 1984"

TL;DR: Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.

TL;DR: In this article, the authors survey Rayleigh-Taylor instability, describing the phenomenology that occurs at a Taylor unstable interface, and reviewing attempts to understand these phenomena quantitatively, and present a survey of the literature on Rayleigh Taylor instability.

TL;DR: In this article, two-dimensional hydrodynamic codes are used to simulate the growth of perturbations at an interface between two fluids of different density due to Rayleigh-Taylor instability.

TL;DR: In this article, the authors developed a theory of transport in Hamiltonian systems in the context of iteration of area-preserving maps, where invariant closed curves present complete barriers to transport, but in regions without such curves there are invariant Cantor sets named cantori, which appear to form partial barriers.

TL;DR: In this article, it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic, and that such attractors are persistent under perturbations which preserve the original system type.

TL;DR: It is drawn that although the capacity for universal construction is a sufficient condition for self-reproduction, it is not a necessary condition, and a simple self- reproducing structure is exhibited which satisfies these new criteria.

TL;DR: A novel experimental technique using solid fuel rocket motors has been developed at AWRE Foulness to study the growth of Rayleigh-Taylor instabilities in fluids as mentioned in this paper, which achieves near constant acceleration up to 750 m s-2 over distances of 1.25 m.

TL;DR: In this article, the Kramers-Moyal type equations for correlation functions between points on the attractor were proposed, where the drift terms are the Lyapunov exponents, the diffusion terms depend on the above fluctuations.

TL;DR: In this paper, the space, time, and intrinsic symmetries and corresponding conservation laws of reversible cellular automata are studied, with an emphasis on the conservation of information obeyed by reversible automata.

TL;DR: Reversible cellular automata as mentioned in this paper are computer models that embody discrete analogues of the classical-physics notions of space, time, locality, and microscopic reversibility, and they are offered as a step towards models of computation that are closer to fundamental physics.

TL;DR: The problem of encoding the state-variables and evolution laws of a physical system into this new setting, and of giving suitable correspondence rules for interpreting the model's behavior, is discussed.

TL;DR: In this paper, a comparison theorem for stability criteria which was postulated by Langer is proved in the framework of the natural boundary conditions, and the full set of equilibrium solutions is specified.

TL;DR: In this article, the authors studied kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing and showed that kinks lose the memory of their initial velocity and propagate preferentially at well-defined velocities which correspond to quasi-steady states.

TL;DR: An overview is given of special numerical methods for tracking discontinuous fronts and interfaces that include surface tracking methods based on connected marker points along the interface, volume tracking methods that track the volume occupied by the solution regions bounded by the interfaces, and moving-mesh methods where the underlying mesh is aligned and moved with the interface.

TL;DR: The structure of chaos border in phase space and its impact on the correlation and other statistical properties of the chaotic motion are considered in this article, where it is conjectured that such a structure is described by a chaotic renormalization group.

TL;DR: Emergent, highly ordered dynamical behavior in random automata rich in a specific class of “canalizing” Boolean functions due to the crystallization of powerful subautomata called forcing structures is discussed.

TL;DR: In this paper, a generalised Calogero-Moser many-body system is introduced and solved by the method of Olshanetsky and Perelomov, and the hierarchy of flows commuting with this system is obtained from a hierarchy of linear systems possessing SL( N ) symmetry.

TL;DR: It is shown that some of the apparent self-organization of cellular automata is an artifact of the synchronization of the clocks.

TL;DR: In this paper, a theory for the statics and slow dynamics of convective rolls encountered in large aspect ratio Rayleigh-Benard boxes is developed, which includes the notion of Busse stability balloon, reduces near critical values of the stress parameter to the Newell-Whitehead-Segel equations, and contains the Pomeau-Manneville phase equation.

TL;DR: In this article, the process of pattern selection between rolls and hexagons in Rayleigh-Benard convection with reflectional symmetry in the horizontal midplane is described, and all possible local bifurcation diagrams (assuming certain non-degeneracy conditions) are found using only group theory.

TL;DR: In this paper, the authors describe the behavior of the escape rate near the disappearance of a KAM trajectory, which is related to the action-generating function of a two-dimensional area-preserving map.

TL;DR: It is shown that cellular automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group, and therefore their statistical and dynamical behavior can be told exactly by using Fourier analysis and ergodic theory.

TL;DR: In this article, the weakly nonlinear, resonant response of a damped, spherical pendulum (length l, damping ratio δ, natural frequency ω 0 ) to the planar displacement e l cos ω t (e ⪡ 1) of its point of suspension is examined in a four-dimensional phase space in which the coordinates are slowly varying amplitudes of a sinusoidal motion.

TL;DR: In this paper, the Lagrangian density for the regularized long-wave equation (also known as the BBM equation) is presented using the trial function technique, ordinary differential equations that describe the time dependence of the position of the peaks, amplitudes, and widths for the collision of two solitary waves are obtained.

TL;DR: In this article, for each irreducible representation of SO(3) and O(3), the existence of solutions corresponding to a number of different planforms was shown.

TL;DR: CAM can show the evolution of cellular automata on a color monitor with an update rate, dynamic range, and spatial resolution comparable to those of a Super-8 movie, thus permitting intensive interactive experimentation.

TL;DR: In this article, a general scheme for the theoretical treatment of self-synchronization of many-body oscillators with variable amplitudes, close to harmonic ones with small nonlinearity and dissipative interactions, in the presence of external noises and a native frequency distribution is presented.

TL;DR: In this article, a 3-dimensional (3-D) array of switching elements with densities of 10 15 to 10 18 elements per cc is presented. But the authors do not consider the use of soliton propagation in cellular automata.

TL;DR: A simple system of four ordinary differential equations exhibiting chaotic behavior is introduced in this paper, where points on the attractor where two variables simultaneously assume prechosen values are located by a numerical integration procedure in which suitable antecedent conditions are obtained by successive approximations.

TL;DR: It is shown that some of the deterministic one-dimensional cellular automata studied recently by Wolfram exhibit a kind of spontaneous symmetry breaking, by mapping the automata onto dynamical systems defined by iterations of the unit square.