Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1204.5345

Time-dependent wave selection for information processing in excitable media

William M. Stevens·Andrew Adamatzky·Ishrat Jahan·Ben de Lacy Costello
View original source ↗Read source document ↗Export metadata ↓

Abstract

We demonstrate an improved technique for implementing logic circuits in light-sensitive chemical excitable media. The technique makes use of the constant-speed propagation of waves along defined channels in an excitable medium based on the Belousov-Zhabotinsky reaction, along with the mutual annihilation of colliding waves. What distinguishes this work from previous work in this area is that regions where channels meet at a junction can periodically alternate between permitting the propagation of waves and blocking them. These valve-like areas are used to select waves based on the length of time that it takes waves to propagate from one valve to another. In an experimental implementation, the channels which make up the circuit layout are projected by a digital projector connected to a computer. Excitable channels are projected as dark areas, unexcitable regions as light areas. Valves alternate between dark and light: every valve has the same period and phase, with a 50% duty cycle. This scheme can be used to make logic gates based on combinations of OR and AND-NOT operations, with few geometrical constraints. Because there are few geometrical constraints, compact circuits can be implemented. Experimental results from an implementation of a 4-bit input, 2-bit output integer square root circuit are given. This is the most complex logic circuit that has been implemented in BZ excitable media to date.

Explore related subjects

nlin.PScs.CL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

William M. Stevens, Andrew Adamatzky, Ishrat Jahan, Ben de Lacy Costello. 2012-04-24. Time-dependent wave selection for information processing in excitable media. https://doi.org/10.1103/physreve.85.066129

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Rolls and Snaking in a Swift-Hohenberg Equation with Non-smooth Nonlinearity

We study rolls and homoclinic snaking in a variation of the one-dimensional Swift-Hohenberg equation, whose standard forms are prototypical order-parameter models for pattern formation in the sciences. Motivated by classes of differential equation models that involve continuous non-smooth low order nonlinear terms, we replace the standard quadratic-cubic nonlinearity by $ν|u|^α-u^3$, $α\in [1,2]$ with $ν> 0$. In the vicinity of zero, for $α<2$ this nonlinearity falls outside the scope of classical Taylor expansion and bifurcation analysis. Our partially analytical and partially numerical results highlight that the non-smooth term modifies the criticality of pattern-forming bifurcations and alters the associated branches of solutions. In particular, $α\in(1,2)$ implies subcriticality of roll bifurcations for any $ν>0$. At $α=1$ differentiability is lost, which has a strong impact on the bifurcations of sign-changing rolls including the disappearance of homoclinic snaking. Homoclinic snaking thus emerges non-smoothly as $α$ increases from $α=1$, and persists when retaining an additional, e.g., quadratic term.

nlin.PS↗
arXiv2026

Vegetation Pattern Formation with an Energy-Mismatch Variational Closure

We study a vegetation-water model motivated by a canopy energy mismatch. Vegetation follows the gradient of a score that rewards biomass and penalizes the squared mismatch, while water obeys a quasi-steady balance. For a fixed interaction kernel, the linear growth rate about positive uniform vegetation splits into a fixed-water term and a water-feedback term. The fixed-water term is real, even in wavenumber, and equal to a constant minus a squared modulus, including when the kernel is asymmetric. All linear phase propagation enters through water feedback. A second-order expansion of the kernel gives a fourth-order vegetation equation, for which we derive finite-wavenumber growth criteria and corrections from state-dependent spatial coefficients. The short-wave damping and fastest-growing scales of this truncated model require separate justification as approximations to a specified kernel. A numerical dispersion example illustrates the growth and phase velocity of its linear modes. The model creates biomass on bare ground throughout the rainfall range illustrated here, including zero rainfall. At some smooth nonnegative states, the vegetation growth rate is negative where biomass vanishes. These features limit its ecological interpretation.

nlin.PS↗
arXiv2026

Two-Parameter Family of Nonlinear Dirac Equations With Scalar-Scalar plus Vector-Vector Interactions

We obtain exact solutions of the nonlinear Dirac equation in $1+1$ dimensions of the form $ψ(x,t) = e^{-iωt} ψ(x)$ for scalar-scalar (SS) plus vector-vector (VV) interaction with interaction Lagrangian given by $$L_{I} = \frac{g^2}{κ+1}[(\barψ ψ)^{κ+1} +\frac{1}{p} (\barψ γ_μψ\barψ γ^μ ψ)^{κ+1}]$$ where $p > 0$ but arbitrary otherwise. We look for solutions with $0 < ω< m$ where $ω, m$ are frequency and mass, respectively. We find solutions for all values of $ω$ in this range. We compute the charge $Q$ and the energy $E$ for each of the solitary wave solutions and explore the region in the ($p, κ$) parameter space in which solitary wave bound states exist (i.e., for which $E/Q < m$). We show that for all the cases while both $E$ and $Q$ depend on the coupling constant $g$, their ratio $E/Q$ is independent of $g$. We further find that in case $pκ\le 1$, the charge density for all the solitary waves have only single hump while for $p κ> 1$ there is a transition from double to single hump and we determine it as a function of $ω/m$. We notice that for all $p$ there is a transition at $κ=2$ in the behavior of $E/Q$ as a function of $ω$ which we speculate is related to the onset of instability of the solutions at $κ=2$. We obtain the nonrelativistic reduction of the two-parameter family to a non-relativistic modified nonlinear Schrödinger equation (NLSE) and discuss the stability of the single hump olitary waves in the domain of validity of the modified NLSE.

nlin.PS↗