The nature and the universal properties of DNA thermal denaturation are investigated by Monte Carlo simulations. For suitable lattice models we determine the exponent c describing the decay of the probability distribution of denaturated loops of length l, P approximately l(-c). If excluded volume effects are fully taken into account, c = 2.10(4) is consistent with a first order transition. The stiffness of the double stranded chain has the effect of sharpening the transition, if it is continuous, but not of changing its order and the value of the exponent c, which is also robust with respect to inclusion of specific base-pair sequence heterogeneities.

Abstract. We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that l ∼ N t , where N is the ring length and t ≃ 0.75 is independent of the knot type. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show knot delocalization (t ≃ 1).Submitted to: J. Phys. A: Math. Gen.

An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches dissipating at the border influence the statistics very sensibly. Only once they are excluded from the sample, the conditional toppling distribution for given area simplifies enough to show also a well defined, multifractal scaling. The resulting picture brings to light unsuspected, novel physics in the model. PACS numbers: 64.60. Lx, 64.60.Ak, 05.40.+j, 05.65.+b Finite size scaling (FSS) [1] is a widely adopted framework for the description of finite, large systems near criticality. In the last decade, after the work of Bak et al.[2], much attention has been devoted to a class of models in which criticality is spontaneously generated by the dynamics itself, without the necessity of tuning parameters. This self-organized criticality (SOC) has been advocated as a paradigm for a wide range of phenomena, from earthquakes to interface depinning, economics and biological evolution [3]. The prototype model of SOC is the two dimensional (2D) Bak, Tang, and Wiesenfeld sandpile (BTW) [2,4], which represents a system driven by a slow external influx, dissipated at the borders through a local, nonlinear mechanism.In spite of its apparent simplicity and relative analytical tractability [4][5][6][7], the 2D BTW resisted, so far, all theoretical attempts to fully and exactly characterize its scaling [6]. These attempts were essentially all based on the FSS ansatz. Numerical approaches, also based on FSS [8], led to rather scattered and sometimes contradictory numerical results [9][10][11], which hardly concile with existing theoretical conjectures. Thus, with its intriguing intractability, BTW scaling remains a formidable challenge for nonequilibrium statistical mechanics [12] and it is very important to check if FSS works in this context.In this Letter we apply a new strategy of data collection and interpretation, in order to determine to what extent the FSS ansatz can be applied, or rather has to be modified, for a correct description of the 2D BTW. Our results are striking and largely unexpected: while compelling evidence is obtained that the probability distribution functions (pdf) of some quantities obey FSS, for other magnitudes, whose fractal dimensions can widely fluctuate within the the nonlinear dynamics, this is definitely not the case. Following our protocol of analysis, we demonstrate that the well known difficulties in the description of the BTW are due to unexpected, very nonstandard features of its dynamical behavior. In the BTW, relations between different key quantities do not reduce to standard power laws, as in FSS, and are substantially influenced by the infrared cutoff given by the size of the system. The peculiar fluctuations characterizing intermittent dissipation at the cutoff scale, provide a dynamical mechanism for unusual deviations from finite size, and even mul...