Asymptotic shape of the region visited by an Eulerian Walker

We study an Eulerian walker on a square lattice, starting from an initially randomly oriented background using Monte Carlo simulations. We present evidence that, that, for large number of steps $N$, the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as $N^{1/3}$, for large $N$, and the width of the boundary region grows as $N^{\alpha / 3}$, with $\alpha = 0.40 \pm .05$. If we introduce stochasticity in the evolution rules, the mean square displacement of the walker, $\sim N^{2\nu}$, shows a crossover from the Eulerian ($\nu = 1/3$) to a simple random walk ($\nu=1/2$) behaviour.Comment: 7 pages, 11 figures, minor revision

Randomly forced DNA

We study the effect of random forces on a double stranded DNA in unzipping the two strands, analogous to the problem of an adsorbed polymer under a random force. The ground state develops bubbles of various lengths as the random force fluctuation is increased. The unzipping phase diagram is shown to be drastically different from the pure case.Comment: 4 figures, Published Versio

Scalable ultra-sensitive detection of heterogeneity via coupled bistable dynamics

We demonstrate how the collective response of $N$ globally coupled bistable elements can strongly reflect the presence of very few non-identical elements in a large array of otherwise identical elements. Counter-intuitively, when there are a small number of elements with natural stable state different from the bulk of the elements, {\em all} the elements of the system evolve to the stable state of the minority due to strong coupling. The critical fraction of distinct elements needed to produce this swing shows a sharp transition with increasing $N$, scaling as $1/\sqrt{N}$. Furthermore, one can find a global bias that allows robust {\em one bit} sensitivity to heterogeneity. Importantly, the time needed to reach the attracting state does not increase with the system size. We indicate the relevance of this ultra-sensitive generic phenomenon for massively parallelized search applications.Comment: 4 Pages, 4 Figure

Hysteresis and nonequilibrium work theorem for DNA unzipping

We study by using Monte Carlo simulations the hysteresis in unzipping and rezipping of a double stranded DNA (dsDNA) by pulling its strands in opposite directions in the fixed force ensemble. The force is increased, at a constant rate from an initial value $g_0$ to some maximum value $g_m$ that lies above the phase boundary and then decreased back again to $g_{0}$. We observed hysteresis during a complete cycle of unzipping and rezipping. We obtained probability distributions of work performed over a cycle of unzipping and rezipping for various pulling rates. The mean of the distribution is found to be close (the difference being within 10%, except for very fast pulling) to the area of the hysteresis loop. We extract the equilibrium force versus separation isotherm by using the work theorem on repeated non-equilibrium force measurements. Our method is capable of reproducing the equilibrium and the non-equilibrium force-separation isotherms for the spontaneous rezipping of dsDNA.Comment: 8 figures, Final version to appear in Physical Review

Manipulating a single adsorbed DNA for a critical endpoint

We show the existence of a critical endpoint in the phase diagram of unzipping of an adsorbed double-stranded (ds) polymer like DNA. The competition of base pairing, adsorption and stretching by an external force leads to the critical end point. From exact results, the location of the critical end point is determined and its classical nature established.Comment: 6 pages, 5 figures, Published versio

Complete Phase Diagram of DNA Unzipping: Eye, Y-fork and triple point

We study the unzipping of double stranded DNA (dsDNA) by applying a pulling force at a fraction $s$ $(0 \le s \le 1)$ from the anchored end. From exact analytical and numerical results, the complete phase diagram is presented. The phase diagram shows a strong ensemble dependence for various values of $s$. In addition, we show the existence of an ``eye'' phase and a triple point.Comment: 4 pages, 4 figures; revised version: misprints corrected. References corrected/added. To appear in Physical Review Letter

Unzipping DNA by force: thermodynamics and finite size behaviour

We discuss the thermodynamic behaviour near the force induced unzipping transition of a double stranded DNA in two different ensembles. The Y-fork is identified as the coexisting phases in the fixed distance ensemble. From finite size scaling of thermodynamic quantities like the extensibility, the length of the unzipped segment of a Y-fork, the phase diagram can be recovered. We suggest that such procedures could be used to obtain the thermodynamic phase diagram from experiments on finite length DNA.Comment: 10 pages, accepted for publication in special issue of Journal of Physics: Condensed Matte