Pseudoknots in a Homopolymer

After a discussion of the definition and number of pseudoknots, we reconsider the self-attracting homopolymer paying particular attention to the scaling of the number of pseudoknots at different temperature regimes in two and three dimensions. Although the total number of pseudoknots is extensive at all temperatures, we find that the number of pseudoknots forming between the two halves of the chain diverges logarithmically at (in both dimensions) and below (in 2d only) the theta-temparature. We later introduce a simple model that is sensitive to pseudoknot formation during collapse. The resulting phase diagram involves swollen, branched and collapsed homopolymer phases with transitions between each pair.Comment: submitted to PR

Boundary Spatiotemporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium

In a semi-infinite geometry, a 1D, M-component model of biological evolution realizes microscopically an inhomogeneous branching process for $M \to \infty$. This implies in particular a size distribution exponent $\tau'=7/4$ for avalanches starting at a free end of the evolutionary chain. A bulk--like behavior with $\tau'=3/2$ is restored if `conservative' boundary conditions strictly fix to its critical, bulk value the average number of species directly involved in an evolutionary avalanche by the mutating species located at the chain end. A two-site correlation function exponent ${\tau_R}'=4$ is also calculated exactly in the `dissipative' case, when one of the points is at the border. These results, together with accurate numerical determinations of the time recurrence exponent $\tau_{first}'$, show also that, no matter whether dissipation is present or not, boundary avalanches have the same space and time fractal dimensions as in the bulk, and their distribution exponents obey the basic scaling laws holding there.Comment: 5 pages, 3 eps figure

Strong gravitational field light deflection in binary systems containing a collapsed star

Large light deflection angles are produced in the strong gravitational field regions around neutron stars and black holes. In the case of binary systems, part of the photons emitted from the companion star towards the collapsed object are expected to be deflected in the direction of the earth. Based on a semi-classical approach we calculate the characteristic time delays and frequency shifts of these photons as a function of the binary orbital phase. The intensity of the strongly deflected light rays is reduced by many orders of magnitude, therefore making the observations of this phenomenon extremely difficult. Relativistic binary systems containing a radio pulsar and a collapsed object are the best available candidates for the detection of the strongly deflected photons. Based on the accurate knowledge of their orbital parameters, these systems allow to predict accurately the delays of the pulses along the highly deflected path, such that the sensitivity to very weak signals can be substantially improved through coherent summation over long time intervals. We discuss in detail the cases of PSR 1913+16 and PSR 1534+12 and find that the system geometry is far more promising for the latter. The observation of the highly deflected photons can provide a test of general relativity in an unprecedented strong field regime as well as a tight constraint on the radius of the collapsed object.Comment: 7 pages, uuencoded, gzip'ed, postscript file with figures included. Accepted for pubblication in MNRA

Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as the square root of N in both phases.Comment: 7 pages, 11 figures, revte

Ranking knots of random, globular polymer rings

An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and suggests that the total number of different knots realized grows exponentially with the chain length. Relative frequencies of specific knots converge to definite values because the free energy per monomer, and its leading finite size corrections, do not depend on the ring topology, while a subleading correction only depends on the crossing number of the knots.Comment: 4 pages, 5 figure