A new approach to data storage using localized structures

Abstract

In this paper we describe how to use the bifurcation structure of static localized solutions in one dimension to store information on a medium in such a way that no extrinsic grid is needed to locate the information. We demonstrate that these principles, deduced from the mathematics adapted to describe one-dimensional media, also allow one to store information on two-dimensional media.

Dynamics of Domain Walls in Pattern Formation with Traveling-Wave Forcing

“…Spatiotemporal forcing provides a natural tool for defect control or for displacement of nontrivial locked states. These aspects open new possibilities in the context of the recently proposed mechanisms of information storage and transmission in nonequilibrium media [14], with practical applications for instance in nonlinear optics [15] or reaction-diffusion systems [16].…”

“…While the cases of purely temporal [1][2][3] and spatial forcing [4 -6] have been considered for many years, the spatiotemporal modulation of control parameters has been introduced only recently [7][8][9][10][11][12][13]. Simultaneously, both fundamental questions [14] and interesting applications of pattern control have arisen for possible information processing devices based on nonequilibrium patterns [15,16].In the simplest case of a spatiotemporal forcing, using the form of a traveling wave, one allows for a periodic dependence on both space and time. The consequences of spatial resonance of such a forcing with a Turing-like mode were studied in terms of the frequency, or velocity, !, of the traveling-wave forcing and the deviation q from exact spatial resonance.…”

How much information can one store in a nonequilibrium medium?

“…Nonetheless, it is exactly the ability of many physical systems to switch between two (or more) different stable states which is commonly exploited for information storage. More specifically, as already explained in [7], for a quite general class of systems we can use the bistability between an homogeneous and a cellular state, which is distinguished from the usual bistability between two homogeneous states [14], to ensure the existence of stable localized structures and hence to store information on a medium.…”

“…Even though the "HELLO" in Figure 1-a corresponds to a linearly stable solution, one expects that there be a drift in the presence of any non-zero noise, and Figure 1-c confirms this concern, even if one takes the best possible parameter values. Following the teaching of [7], one can also use solutions bi-asymptotic to a cellular solution to store information. We thus have accordingly again written HELLO in Figure 1-b, also using Equation 1 and the same optimal parameter values used for Figure 1-a (as discussed in [7]; see also below).…”

“…Following the teaching of [7], one can also use solutions bi-asymptotic to a cellular solution to store information. We thus have accordingly again written HELLO in Figure 1-b, also using Equation 1 and the same optimal parameter values used for Figure 1-a (as discussed in [7]; see also below). Figure 1-d, a snapshot after the same time used for Figure 1-c, indicates that now the drift due to noise is, for the least, far less of a problem.…”