Related papers: Causal Dynamics of Discrete Surfaces
We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy…
In this paper, we get the time evolution equations of the curvature and torsion of the evolving spacelike curves in the Minkowski space. Also, we give inextensible evolutions of timelike ruled surfaces that are produced by the timelike…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
We study iterations of two classical constructions, the evolutes and involutes of plane curves, and we describe the limiting behavior of both constructions on a class of smooth curves with singularities given by their support functions.…
We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, and contract to points after…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
Discrete autonomous dynamical systems in dimension 1 can exhibit chaotic behavior, whereas the corresponding continuous evolution equations rule it out, and cannot even possess a nontrivial periodic solution. Therefore the passage from…
The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local…
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 study the evolution of behavioral rules in environments with multiple contexts. Agents copy rules used by better-performing peers in the same context and apply them across contexts. Multiple contexts turn discrete-time imitation dynamics…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the…
Nature's many varied complex systems (including galaxies, stars, planets, life, and society) are islands of order within the increasingly disordered universe. All organized systems are subject to physical, biological or cultural evolution,…
How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing…
Causal Graph Dynamics extend Cellular Automata to arbitrary, bounded-degree, time-varying graphs. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of physics-like symmetries:…
We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces.…
This paper establishes the existence of observable footprints that reveal the "causal dispositions" of the object categories appearing in collections of images. We achieve this goal in two steps. First, we take a learning approach to…
The effect of rigid surfaces on the dynamics of thin liquid films which are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution…
The origin of macroscopic complexity is traced in a wide range of systems (imunology, ecology, finance, marketing, etc) to the discrete and auto-catalytic (i.e. multiplicative) character of their elementary components. Even in the simplest…
We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is…