Fluxonic Cellular Automata

We formulate a new concept for computing with quantum cellular automata composed of arrays of nanostructured superconducting devices. The logic states are defined by the position of two trapped flux quanta (vortices) in a 2x2 blind-hole-matrix etched on a mesoscopic superconducting square. Such small computational unit-cells are well within reach of current fabrication technology. In an array of unit-cells, the vortex configuration of one cell influences the penetrating flux lines in the neighboring cell through the screening currents. Alternatively, in conjoined cells, the information transfer can be strengthened by the interactions between the supercurrents in adjacent cells. Here we present the functioning logic gates based on this fluxonic cellular automata (FCA), where the logic operations are verified through theoretical simulations performed in the framework of the time-dependent Ginzburg-Landau theory. The input signals are defined by current loops placed on top of the two diagonal blind holes of the input cell. For given current-polarization, external flux lines are attracted or repelled by the loops, forming the '0' or '1' configuration. The read-out technology may be chosen from a large variety of modern vortex imaging methods, transport and LDOS measurements.Comment: Featured on the cover page of APL, November 2007 issu

The Enlightened Game of Life

We investigate a special class of cellular automata (CA) evolving in a environment filled by an electromagnetic wave. The rules of the Conway's Game of Life are modified to account for the ability to retrieve life-sustenance from the field energy. Light-induced self-structuring and self-healing abilities and various dynamic phases are displayed by the CA. Photo-driven genetic selection and the nonlinear feedback of the CA on the electromagnetic field are included in the model, and there are evidences of self-organized light-localization processes. The evolution of the electromagnetic field is based on the Finite Difference Time Domain (FDTD) approach. Applications are envisaged in evolutionary biology, artificial life, DNA replication, swarming, optical tweezing and field-driven soft-matter.Comment: Revised and enlarged version. Added genetic selection and nonlinear feedback of the CA on the electromagnetic field. 12 pages, 13 figures. To appear in the book Game of Life Cellular Automata (Springer 2010, Andy Adamtzky ed.)

Subshifts with Simple Cellular Automata

A subshift is a set of infinite one- or two-way sequences over a fixed finite set, defined by a set of forbidden patterns. In this thesis, we study subshifts in the topological setting, where the natural morphisms between them are ones defined by a (spatially uniform) local rule. Endomorphisms of subshifts are called cellular automata, and we call the set of cellular automata on a subshift its endomorphism monoid. It is known that the set of all sequences (the full shift) allows cellular automata with complex dynamical and computational properties. We are interested in subshifts that do not support such cellular automata. In particular, we study countable subshifts, minimal subshifts and subshifts with additional universal algebraic structure that cellular automata need to respect, and investigate certain criteria of ‘simplicity’ of the endomorphism monoid, for each of them. In the case of countable subshifts, we concentrate on countable sofic shifts, that is, countable subshifts defined by a finite state automaton. We develop some general tools for studying cellular automata on such subshifts, and show that nilpotency and periodicity of cellular automata are decidable properties, and positive expansivity is impossible. Nevertheless, we also prove various undecidability results, by simulating counter machines with cellular automata. We prove that minimal subshifts generated by primitive Pisot substitutions only support virtually cyclic automorphism groups, and give an example of a Toeplitz subshift whose automorphism group is not finitely generated. In the algebraic setting, we study the centralizers of CA, and group and lattice homomorphic CA. In particular, we obtain results about centralizers of symbol permutations and bipermutive CA, and their connections with group structures.Siirretty Doriast

Regular binary thermal lattice-gases

We analyze the power spectrum of a regular binary thermal lattice gas in two dimensions and derive a Landau-Placzek formula, describing the power spectrum in the low-wavelength, low frequency domain, for both the full mixture and a single component in the binary mixture. The theoretical results are compared with simulations performed on this model and show a perfect agreement. The power spectrums are found to be similar in structure as the ones obtained for the continuous theory, in which the central peak is a complicated superposition of entropy and concentration contributions, due to the coupling of the fluctuations in these quantities. Spectra based on the relative difference between both components have in general additional Brillouin peaks as a consequence of the equipartition failure.Comment: 20 pages including 9 figures in RevTex

An exploration and validation of computer modeling of evolution, natural selection, and evolutionary biology with cellular automata for secondary students.

The Evolutionary Tool Kit, a new software package, is the prototype of a concept simulator providing an environment for students to create microworlds of populations of artificial organisms. Its function is to model processes, concepts and arguments in natural selection and evolutionary biology, using either Mendelian asexual or sexual reproduction, or counterfactual systems such as \u27paint pot\u27 or blending inheritance. In this environment students can explore a conceptual What if? in evolutionary biology, test misconceptions and deepen understanding of inheritance and changes in populations. Populations can be defined either with typological, or with populational thinking, to inquire into the role and necessity of variation in natural selection. The approach is generative not tutorial. The interface is highly graphic with twenty traits set as icons that are moved onto the \u27phenotypes\u27. Activities include investigations of evolutionary theory of aging, reproductive advantage, sexual selection and mimicry. Design of the activities incorporates Howard Gardner\u27s Theory of Multiple Intelligences. Draft of a teacher and student manual are included