3.9 Stationary Circuits


3.9 Stationary Circuits

A stationary, or architecture-based, universality is usually achieved by "conventional" techniques: One simply fabricates varieties of traditional computers made of nonstandard materials (tubulin microtubles, glass tubes filled with chemicals, artificially grown silicon-neuron interfaces). Here, we consider three illustrative examples of reaction-diffusion logical gates.

The first example is a mass-transfer or kinetic-based logical gate (Hjelmfelt, Weinberger, and Ross 1991; Hjelmfelt and Ross 1993; Blittersdorf, M ller, and Schneider 1995). Typically, several reactors are connected through peristaltic pumps (figure 3.5a). Concentrations of reagents in a few reactors represent values of input logical variables and other (usually sinks of the reactor network) values of outputs. To construct a particular logical gate, one directly adjusts flow rates between the reactors.

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Figure 3.5: Architecture-based chemical gates. (a) A mass-transfer chemical device for computation of basic logical functions: x, y and z are acidity levels in the reactors; A and B are feeding tubes for supply of reagent A and B solutions with an indicator; α and β are coupling coefficients, and γ is a flow rate. Modified after (Blittersdorf et al 1995) (b) A wave realization of x OR y OR z gate. Waves in output chambers are asynchronous when all three input variables take the value FALSE. If one of the inputs is TRUE, represented by an excitation wave, the output chambers exhibit synchronous waves, that is represent TRUE. (Modified after Steinbock, Kettunen, and Showalter 1996.)

The second example exploits the fine characteristics of wave dynamics in excitable media. There are two types of wave gate (Toth and Showalter 1995; Steinbock, Kettunen, and Showalter 1996). In the gates, Boolean states of inputs and outputs are represented by the presence or absence of a phase wave at a specified location of the tube-based circuit. The first wave gate (Toth and Showalter 1995) employs particulars—namely, a wave-nucleation size critical for successful generation of a wave—of wave interactions in the Belousov-Zhabotinsky reaction. The Belousov-Zhabotinsky logic circuit comprises several very narrow tubes filled with a Belousov-Zhabotinsky medium; the tubes are connected via expansion chambers or junctions where logical functions are implemented. In experimental realizations of and wave gates, the size of wire tubes is selected such that if a single excitation wave reaches an expansion chamber along one tube, it will not generate any excitation in the chamber. Two waves satisfy a critical nucleation radius constraint and thus will generate excitation in the chamber. The second wave gate (shown in figure 3.5b) is based on ideas of geometrically constrained excitable media. Logic operations are determined by the geometry of tubes and chamber connections. The operations are expressed in (a) synchronous occurrences of excitation waves in the output tubes of the Belousov-Zhabotinsky circuit (figure 3.5b).

The third example undermines our "perfect" division of all reaction-diffusion processors into either specialized or universal. We show that an xor gate (z = x XOR y = TRUE if x y) can be implemented in a very simple modification (De Lacy Costello 2002) of the palladium processor discussed in relation to image processing in previous sections. The gate looks like a letter T made of gel (the gel is mixed with palladium chloride). Shoulders of the T are the gate's inputs, and the vertical segment is an output (figure 3.6): presence\absence of the palladium-iodide species indicate TRUE\FALSE values for the input variables. To specify TRUE value for an input, we put a drop of potassium iodide to an appropriate shoulder (figure 3.6b). The potassium iodide diffuses along the gel strip; palladium-iodide species are formed and color the gel. When both shoulders initially contain drops of potassium iodide, a middle part of the vertical segment will remain uncoloured due to the mechanics of diffusive waves interaction (figure 3.6c; see details in Adamatzky and De Lacy Costello 2002a, 2002b). When only one of the shoulders contains potassium iodide, all gel strips become colored (figure 3.6b). When "nothing happens" (or when both shoulders of the gate contain potassium iodide), at least the central part of the vertical strip will be uncolored (figure 3.c6). Thus, assuming colored sites of the gel represent the value true and uncolored the value FALSE, we demonstrate that the T-shaped gel implements the gate XOR.

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Figure 3.6: A palladium-based xor gate (colored zones represent precipitating palladium-iodine species). (a) The gate architecture, this also reflects the situation x = FALSE and y = FALSE. (b) Reaction development in the gate for x = TRUE and y = FALSE. (c) Formation of a bisector (uncolored strip) when two diffusive fronts "collide": this happens when x = TRUE and x = TRUE.




Molecular Computing
Molecular Computing
ISBN: 0262693313
EAN: 2147483647
Year: 2003
Pages: 94

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