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Publications (2)0 Total impact

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    David Head
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    ABSTRACT: It is argued that systems whose elements are renewed according to an extremal criterion can generally be expected to exhibit long-term memory. This is verified for the minimal extremally driven model, which is first defined and then solved for all system sizes N>=2 and times t>=0, yielding exact expressions for the persistence R(t) = [1 + t/(N-1)]-1 and the two-time correlation function C(tw + t,tw) = (1-1/N)(N + tw)/(N + tw + t-1). The existence of long-term memory is inferred from the scaling of C(tw + t,tw)~f(t/tw), denoting aging. Finally, we suggest ways of investigating the robustness of this mechanism when competing processes are present.
    Journal of Physics A General Physics 01/2000; 33(42).
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    David Head
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    ABSTRACT: We introduce the strongly-interacting trap model, a version of Bouchaud's trap model for glasses [Bouchaud J-P 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate timeframes but reaches a steady state at finite times. In limit of zero temperature and with a suitably renormalised timescale the model maps onto the Bak-Sneppen model, widely studied in the context of self-organised criticality [Bak P and Sneppen K 1993 {\em Phys. Rev. Lett. {\bf 71}} 4083]. Hence zero temperature is a critical point in all dimensions. These claims are supported by mean field analysis of the stationary solution and numerical simulations of a finite-dimensional lattice model. Comment: 16 pages in IOP format; 6 figures
    Journal of Physics A General Physics 08/1999;