Recently solutions to a simple reaction diffusion system have been discovered in which localized structures (spots) make copies of themselves. In this Letter we analyze the one-dimensional analog of this process in which replication occurs until the domain is Glled with a periodic array of spots. Vfe provide a heuristic explanation of why this replication process should occur in a broad class of systems. Time dependent solutions are developed for model systems and their analytic structures investigated.PACS numbers: 82.40.Ck, 87.40.+w Over the past three decades the study of selforganization in far-from-equilibrium systems has become a major field of scientific inquiry. Within this field, the study of chemically reacting and difFusing (RD) systems has attained the status of paradigm. Although there are many reasons for the role that RD systems play, perhaps the most compelling is their obvious relevance for biological systems.Recently, Pearson [1] has observed spot patterns in a RD system that replicate themselves until they occupy the entire domain. This observation was made during a successful attempt to reproduce the labyrinthine patterns observed in [2]. In this Letter, we will look at this model system in one dimension and derive several analytic solutions to the nonlinear partial difFerential equations, including replicating spot structures. The model[3] is given by dt =7' u -uv +A(l -u), -=b V v+uv -Bv. OV 2 2 2 dt Here u(z, t) and v(x, t) are fields representing the concentrations of two chemical species with difFering difFusion coefficients, whose ratio is 62. A and B are parameters describing a feed from an external reservoir with the fixed concentrations u = 1 and v = 0.One of the most interesting structures observed by Pearson in 2D simulations consists of localized regions of high v and low u concentration, "spots, " surrounded by regions where the concentrations are nearer to the kinetics' only fixed point: u = 1, v = 0. The spots replicate: a single spot first divides into two new spots, which then separate until another replication occurs, finally filling the entire domain. Typical asymptotic configurations in these 2D simulations depend on the parameters and consist of either chaotic states in which the spots compete for territory in a continuous process of replication and death or steady states where the spots form a hexagonal pattern.In 1D, an analogous situation is realized for small enough b, although the time asymptotic state is always static in a finite domain. Figure 1 is a space-time plot of v for this case. Related phenomena have been observed by other authors [4]. In particular, Kerner and Osipov have derived numerous results on self-organization processes in active media including an analysis of the static division of one-dimensional pulses as the system size is changed.Recently, replicating spot patterns have been observed experimentally in a RD system [5]. This occurs despite 500 4QQ -~W~~0 ( 5) h o 300 4J
We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a chemoattractant concentration as well as to nutrient and waste fields. The latter serves as a triggering field for emission of chemoattractant. Important elements in the proposed model include the propagation of a front of motile bacteria radially outward form an initial site, a Turing instability of the uniformly dense state and a reduction of motility for cells sufficiently far behind the front. The wide variety of patterns seen in the experiments is explained as being due the variation of the details of the initiation of the chemoattractant emission as well as the transition to a non-motile phase.Comment: 4 pages, REVTeX with 4 postscript figures (uuencoded) Figures 1a and 1b are available from the authors; paper submitted to PRL
In a recent article ͓Phys. Rev. Lett. 72, 2797 ͑1994͔͒ we analyzed the phenomena of self-replicating spots in the Gray-Scott model. In this article we present those results in detail and generalize them to a class of models that derives from our heuristic explanation of spot replication.
The detection of sub-surface defects and structures, by thermal pulse video compatible thermal imagers, ie beginning to complement the slower methods of ultrasonic scanning and in some applications to surpass them.In principal a short pulse of radiation is emitted from a xenon flash tube and is absorbed by the surface of the material under inspection. This energy diffuses as heat through the material and sub -surface features are revealed as variations in surface temperature, either on the far face or near face, by a scanning infrared camera.The promise of thermal pulse thermography lies in its ability to inspect materials for defects and quality with great speed and without physical contact. Other methodsof applying heat are currently being investigated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.