相关论文: Complex patterns and tip effect evolution

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…

The web of relations linking technological innovation can be fairly described in terms of patent citations. The resulting patent citation network provides a picture of the large-scale organization of innovations and its time evolution. Here…

The concept of evolution patterns is introduced for Collatz sequences and it is shown that any finite evolution pattern is implemented in some particular Collatz sequence.

The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…

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…

To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…

The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…

We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is…

The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…

Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous…

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

From the striped coats of zebras to the ripples in windblown sand, the natural world abounds with locally banded patterns. Such patterns have been of great interest throughout history, and, in the last twenty years, scientists in a wide…

Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…

Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…

Although different learning systems are coordinated to afford complex behavior, little is known about how this occurs. This article describes a theoretical framework that specifies how complex behaviors that might be thought to require…

Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression…

Spiral wave, whose rotation center can be regarded as a point defect, widely exists in various two dimensional excitable systems. In this paper, by making use of \emph{Duan's topological current theory}, we obtain the charge density of…

A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organisation (more than the parts) what largely conditions most higher-level properties, which are not…

In this article we focus on evolving information systems. First a delimitation of the concept of evolution is provided, resulting in a first attempt to a general theory for such evolutions. The theory makes a distinction between the…

In this paper, we have formulated a phase-field model based on the grand-potential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns…