Universal properties of knotted polymer rings

By performing Monte Carlo sampling of $N$-steps self-avoiding polygons embedded on different Bravais lattices we explore the robustness of universality in the entropic, metric and geometrical properties of knotted polymer rings. In particular, by simulating polygons with $N$ up to $10^5$ we furnish a sharp estimate of the asymptotic values of the knot probability ratios and show their independence on the lattice type. This universal feature was previously suggested although with different estimates of the asymptotic values. In addition we show that the scaling behavior of the mean squared radius of gyration of polygons depends on their knot type only through its correction to scaling. Finally, as a measure of the geometrical self-entanglement of the SAPs we consider the standard deviation of the writhe distribution and estimate its power-law behavior in the large $N$ limit. The estimates of the power exponent do depend neither on the lattice nor on the knot type, strongly supporting an extension of the universality property to some features of the geometrical entanglement.Comment: submitted to Phys.Rev.

Lattice Boltzmann simulations of lamellar and droplet phases

Lattice Boltzmann simulations are used to investigate spinodal decomposition in a two-dimensional binary fluid with equilibrium lamellar and droplet phases. We emphasise the importance of hydrodynamic flow to the phase separation kinetics. For mixtures slightly asymmetric in composition the fluid phase separates into bulk and lamellar phases with the lamellae forming distinctive spiral structures to minimise their elastic energy.Comment: 19 pages, 5 figure

Tight and loose shapes in flat entangled dense polymers

We investigate the effects of topological constraints (entanglements) on two dimensional polymer loops in the dense phase, and at the collapse transition (Theta point). Previous studies have shown that in the dilute phase the entangled region becomes tight, and is thus localised on a small portion of the polymer. We find that the entropic force favouring tightness is considerably weaker in dense polymers. While the simple figure-eight structure, created by a single crossing in the polymer loop, localises weakly, the trefoil knot and all other prime knots are loosely spread out over the entire chain. In both the dense and Theta conditions, the uncontracted knot configuration is the most likely shape within a scaling analysis. By contrast, a strongly localised figure-eight is the most likely shape for dilute prime knots. Our findings are compared to recent simulations.Comment: 8 pages, 5 figure

Rheology of distorted nematic liquid crystals

We use lattice Boltzmann simulations of the Beris--Edwards formulation of nematodynamics to probe the response of a nematic liquid crystal with conflicting anchoring at the boundaries under shear and Poiseuille flow. The geometry we focus on is that of the hybrid aligned nematic (HAN) cell, common in devices. In the nematic phase, backflow effects resulting from the elastic distortion in the director field render the velocity profile strongly non-Newtonian and asymmetric. As the transition to the isotropic phase is approached, these effects become progressively weaker. If the fluid is heated just above the transition point, however, another asymmetry appears, in the dynamics of shear band formation.Comment: 7 pages, 4 figures. Accepted for publication in Europhys. Let

Nonthermal hard X-ray excess in the cluster Abell 2256 from two epoch observations

After confirmation of the presence of a nonthermal hard X-ray excess with respect to the thermal emission in the Coma cluster from two independent observations, obtained using the Phoswich Detection System onboard BeppoSAX, we present in this Letter also for Abell 2256 the results of two observations performed with a time interval of about 2.5 yr. In both spectra a nonthermal excess is present at a confidence level of ~3.3sigma and ~3.7sigma, respectively. The combined spectrum obtained by adding up the two spectra allows to measure an excess at the level of ~4.8sigma in the 20-80 keV energy range. The nonthermal X-ray flux is in agreement with the published value of the first observation (Fusco-Femiano et al. 2000) and with that measured by a Rossi X-Ray Timing Explorer observation (Rephaeli & Gruber 2003).Comment: 12 pages, 3 figures, 1 table - ApJL, in pres

Antioxidant and Mineral Composition of Three Wild Leafy Species : A Comparison Between Microgreens and Baby Greens

Wild plants may play an important role in human nutrition and health and, among them, many are the leafy species. We hypothesized that the wild greens could be profitably grown as microgreens and baby greens, specialty products whose market is increasing. We compared three wild leafy species (Sanguisorba minor Scop., Sinapis arvensis L., and Taraxacum officinale Weber ex F. H. Wigg.) harvested at the microgreen and baby green stages. Seedlings were grown hydroponically in a half-strength Hoagland nutrient solution under controlled climatic conditions. At harvest, the yield was assessed, and chlorophylls, carotenoids, anthocyanins, phenolic index, nitrate, and mineral elements were measured in the two types of product. The potential contribution to human mineral intake was calculated, and the possible risk due to the presence of metals potentially detrimental for health was estimated. Results showed that micro/baby greens of the studied wild plants achieved competitive yields and could contribute to the dietary intake of macroelements, microelements, and non-nutrient bioactive compounds. On the other hand, the wild greens showed high amounts of nitrate and traces of some metals potentially detrimental for health, suggesting the need for caution in the use of wild species for producing microgreens and baby leaves

Peculiar scaling of self-avoiding walk contacts

The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N going to infinity they are strictly finite in number but their radius of gyration Rc is power law distributed, ~ Rc^{-\tau}, where \tau>1 is a novel exponent characterizing universal behavior. A continuum of diverging lengths scales is associated to the Rc distribution. A possibly super-universal \tau=2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.Comment: 4 pages, 5 Postscript figures, uses psfig.sty; some sentences clarifie

Topological Constraints at the Theta Point: Closed Loops at Two Loops

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.Comment: 5 pages, RevTeX, typo

Force-induced unfolding of a homopolymer on fractal lattice: exact results vs. mean field predictions

We study the force-induced unfolding of a homopolymer on the three dimensional Sierpinski gasket. The polymer is subject to a contact energy between nearest neighbour sites not consecutive along the chain and to a stretching force. The hierarchical nature of the lattice we consider allows for an exact treatment which yields the phase diagram and the critical behaviour. We show that for this model mean field predictions are not correct, in particular in the exact phase diagram there is {\em not} a low temperature reentrance and we find that the force induced unfolding transition below the theta temperature is second order.Comment: 15 pages, 5 eps figure