244 research outputs found
Graphical Representations for Ising Systems in External Fields
A graphical representation based on duplication is developed that is suitable
for the study of Ising systems in external fields. Two independent replicas of
the Ising system in the same field are treated as a single four-state
(Ashkin-Teller) model. Bonds in the graphical representation connect the
Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is
characterized by percolation in this representation. The representation leads
immediately to cluster algorithms; some applications along these lines are
discussed.Comment: 13 pages amste
The Advantage of Foraging Myopically
We study the dynamics of a \emph{myopic} forager that randomly wanders on a
lattice in which each site contains one unit of food. Upon encountering a
food-containing site, the forager eats all the food at this site with
probability ; otherwise, the food is left undisturbed. When the forager
eats, it can wander additional steps without food before starving
to death. When the forager does not eat, either by not detecting food on a full
site or by encountering an empty site, the forager goes hungry and comes one
time unit closer to starvation. As the forager wanders, a multiply connected
spatial region where food has been consumed---a desert---is created. The
forager lifetime depends non-monotonically on its degree of myopia , and at
the optimal myopia , the forager lives much longer than a
normal forager that always eats when it encounters food. This optimal lifetime
grows as in one dimension and faster than a
power law in in two and higher dimensions.Comment: 10 pages, 1o figure
Facilitated diffusion of proteins on chromatin
We present a theoretical model of facilitated diffusion of proteins in the
cell nucleus. This model, which takes into account the successive
binding/unbinding events of proteins to DNA, relies on a fractal description of
the chromatin which has been recently evidenced experimentally. Facilitated
diffusion is shown quantitatively to be favorable for a fast localization of a
target locus by a transcription factor, and even to enable the minimization of
the search time by tuning the affinity of the transcription factor with DNA.
This study shows the robustness of the facilitated diffusion mechanism, invoked
so far only for linear conformations of DNA.Comment: 4 pages, 4 figures, accepted versio
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