Constraints on Beta Functions from Duality

We analyze the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. A consistency condition we propose shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the 2-d Ising model, and used towards finding the exact beta function of the $q$-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.Comment: LaTeX, 6 page

The non-centrosymmetric lamellar phase in blends of ABC triblock and ac diblock copolymers

The phase behaviour of blends of ABC triblock and ac diblock copolymers is examined using self-consistent field theory. Several equilibrium lamellar structures are observed, depending on the volume fraction of the diblocks, phi_2, the monomer interactions, and the degrees of polymerization of the copolymers. For segregations just above the order-disorder transition the triblocks and diblocks mix together to form centrosymmetric lamellae. As the segregation is increased the triblocks and diblocks spatially separate either by macrophase-separating, or by forming a non-centrosymmetric (NCS) phase of alternating layers of triblock and diblock (...ABCcaABCca...). The NCS phase is stable over a narrow region near phi_2=0.4. This region is widest near the critical point on the phase coexistence curve and narrows to terminate at a triple point at higher segregation. Above the triple point there is two-phase coexistence between almost pure triblock and diblock phases. The theoretical phase diagram is consistent with experiments.Comment: 9 pages, 8 figures, submitted to Macromolecule

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scales as t^{-(2-p)}. Although the average return time to the origin is infinite for all p, the walk eats, on average, only a finite number of cookies until this first return when p<1/2. For the infinite line, the probability distribution for the 1-excited walk has an unusual anomaly at the origin. The positions of the leftmost and rightmost uneaten cookies can be accurately estimated by probabilistic arguments and their corresponding distributions have power-law singularities near the origin. The 2-excited walk on the infinite line exhibits peculiar features in the regime p>3/4, where the walk is transient, including a mean displacement that grows as t^{nu}, with nu>1/2 dependent on p, and a breakdown of scaling for the probability distribution of the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J. Phys.

Effect of chemical treatment on the mechanical and thermal properties of hemp fibre reinforced thermoset sandwich composites

In this study hemp-thermoset sandwich composites were prepared by using unsaturated polyester resin. To improve fibre matrix adhesion alkalization and acetylation treatment on the fibres were carried out. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were used to investigate the changes of fibres chemical constituents after treatment. Mechanical properties such as flexural strength, flexural modulus and strain at break of untreated and treated fibre composites were studied and compared. The incorporation of the alkalized fibres resulted in composites better flexural properties and 8% treatment showed best results. Thermal stability of the fibre was also enhanced for the treated fibre. In general, thermal and mechanical properties of the treated fibre and its composites were superior to the untreated fibres