Related papers: On Oscillations in Cellular Automata
Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form and linear stability of frequency synchronization in…
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…
The quantum dynamics of optomechanical systems was mostly studied for their fluctuations around classical steady states. We present a theoretical approach to determining the system observables of optomechanical systems as genuine quantum…
We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array,…
Previous study of cellular automata and random Boolean networks has shown emergent behavior occurring at the edge of chaos where the randomness (disorder) of internal connections is set to an intermediate critical value. The value at which…
The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an…
We introduce a generalization of the Kuramoto model by explicit consideration of time-dependent parameters. The oscillators' natural frequencies and/or couplings are supposed to be influenced by external, time-dependant fields, with…
A model for 1D traffic flow is developed, which is discrete in space and time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go traffic. Due to…
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…
We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically…
Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously…
Gauge-invariance is a fundamental concept in Physics -- known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at…
We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution $U$. We require that this global evolution $U$ be unitary, in accordance with quantum…
Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…