What is the length of a knot in a polymer?

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 ~ N^t, where N is the ring length and t ~ 0.75 is independent of the knot topology. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show delocalization (t~1).Comment: 9 pages, 5 Postscript figure

A scale-free network hidden in the collapsing polymer

We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent $\gamma = 1/(2-c)$ up to a cut-off degree $d_c \propto L^{2-c}$, where $c$ is the loop exponent for dense polymers ($c=11/8$ in two dimensions) and $L$ is the length of the polymer. Our results exemplify how a scale-free network (SFN) can emerge from standard criticality.Comment: 4 pages, 3 figures, address correcte

Climatic change mitigation: analysis of electrical fans usage impact on dwellers heat stress

Climate change is responsible for a consistent increase in ambient temperatures, leading to social and health problems for individuals residing indoors. The effect should be seriously considered by authorities, especially regarding people's health; high temperatures can be very dangerous for elder people and in general for vulnerable categories. Mitigation approaches are important in case of heat waves that are expected to increase in frequency and intensity due to climatic change effects. One approach for avoiding such a problem is to install cooling systems, but sometimes this isn't a viable solution, for example in case of low-income families which cannot afford the expense for the installation and the bill costs for running such systems. An alternative solution is using electric ventilators and the main objective of this paper is to revise the effect of electric fans and assess if they can be useful for mitigating the heat effect on people inside buildings. The results showed that the number of hours with people exposed to heat strain, in the worst-case scenario, dropped from 168 without a fan to 13 with an active fan, confirming the positive effect of this system

Experimental investigation of fuel-cooled combustor: Cooling efficiency and coke formation

Scramjet is an air-breathing engine designed to propel advanced aircrafts in the atmosphere, suitable, according to various studies, to thrust high-speed hypersonic flights (over Mach 5). The thermal protection of vehicles flying at hypersonic velocities is a critical problem; as at supersonic speeds the incoming air is at too high temperature to be used as a coolant, the fuel becomes the only adequate source of cooling for the vehicle. Regenerative cooling is a well-known cooling technique using the fuel as coolant. As the development of regeneratively cooled engines faces many difficulties, an empirical study of this cooling technology and of its complex dynamics is of high interest. In this context, a remotely controlled fuel-cooled combustor, suitable for the experimental analysis of the pyrolysis-combustion coupling characterizing a fuel-cooled combustion chamber when a hydrocarbon propellant is used, has been designed. Tests are realized under both stationary and transient conditions using ethylene as fuel and air as oxidizer. Two operating parameters, i.e. fuel mass flow rate (between 0.010 and 0.040 g.s-1) and equivalence ratio (between 1.0 and 1.5), have been investigated. It has been observed that fuel mass flow rate increases always result in the raise of the heat flux density passing from the combustion gases to the combustor walls. It has been seen that mass flow rate raises between 16 and 20 % lead to increases in the thermal energy evacuated by the fuel-coolant in the range from 30.4 to 48.5 %, depending on equivalence ratio and pressure. The dependence of the cooling system heat exchange efficiency on the two operating parameters has been demonstrated. The consequences of the coking activity of the fuel have also been investigated. For applied interest, a monitoring method for carbon deposits formation has been developed and validated

Anomalous scaling due to correlations: Limit theorems and self-similar processes

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, justify their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance.Comment: Through text revision. 15 pages, 3 figure

Mean Field Renormalization Group for the Boundary Magnetization of Strip Clusters

We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that this approximation yields not only the exact critical point, but also the exact boundary magnetization of a semi--infinite Ising model, independent of the size of the strips used. Then we develop a new mean field renormalization group strategy based on this approximation and make connections with finite size scaling. Applying our strategy to the quadratic Ising and three--state Potts models we obtain results for the critical exponents which are in excellent agreement with the exact ones. In this way we also clarify some advantages and limitations of the mean field renormalization group approach.Comment: 16 pages (plain TeX) + 8 figures (PostScript, appended), POLFIS-TH.XX/9

Geometry and topology of knotted ring polymers in an array of obstacles

We study knotted polymers in equilibrium with an array of obstacles which models confinement in a gel or immersion in a melt. We find a crossover in both the geometrical and the topological behavior of the polymer. When the polymers' radius of gyration, $R_G$, and that of the region containing the knot, $R_{G,k}$, are small compared to the distance b between the obstacles, the knot is weakly localised and $R_G$ scales as in a good solvent with an amplitude that depends on knot type. In an intermediate regime where $R_G > b > R_{G,k}$, the geometry of the polymer becomes branched. When $R_{G,k}$ exceeds b, the knot delocalises and becomes also branched. In this regime, $R_G$ is independent of knot type. We discuss the implications of this behavior for gel electrophoresis experiments on knotted DNA in weak fields.Comment: 4 pages, 6 figure

Central limit theorem for anomalous scaling due to correlations

We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling and is based on a correspondence with the L\'evy-Gnedenko uncorrelated case. In particular, correlated anomalous diffusion is mapped onto L\'evy diffusion. Under suitable assumptions, the nonstandard multiplicative structure used for constructing the characteristic function of the total sum allows us to determine correlations of partial sums exclusively on the basis of the global anomalous scaling.Comment: The content of this manuscript was presented at the 3rd International Conference "Next Sigma-Phi", Kolymbari - Greece, 13-18 August 200