Peeling from a patterned thin elastic film

Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement controlled peeling of a flexible plate from an incision-patterned thin adhesive elastic layer. We find that crack initiation from an incision on the film occurs at a load much higher than that required to propagate it on a smooth adhesive surface; multiple incisions thus cause the crack to propagate intermittently. Microscopically, this mode of crack initiation and propagation in geometrically confined thin adhesive films is related to the nucleation of cavitation bubbles behind the incision which must grow and coalesce before a viable crack propagates. Our theoretical analysis allows us to rationalize these experimental observations qualitatively and quantitatively and suggests a simple design criterion for increasing the interfacial fracture toughness of adhesive films.Comment: 8 pages, To appear in Proceedings of Royal Society London, Ser.

Magnetoelectric Effect and Spontaneous Polarization in HoFe3_3(BO3_3)4_4 and Ho0.5_{0.5}Nd0.5_{0.5}Fe3_3(BO3_3)4_4

The thermodynamic, magnetic, dielectric, and magnetoelectric properties of HoFe$_3$(BO$_3$)$_4$ and Ho$_{0.5}$Nd$_{0.5}$Fe$_3$(BO$_3$)$_4$ are investigated. Both compounds show a second order Ne\'{e}l transition above 30 K and a first order spin reorientation transition below 10 K. HoFe$_3$(BO$_3$)$_4$ develops a spontaneous electrical polarization below the Ne\'{e}l temperature (T$_N$) which is diminished in external magnetic fields. No magnetoelectric effect could be observed in HoFe$_3$(BO$_3$)$_4$. In contrast, the solid solution Ho$_{0.5}$Nd$_{0.5}$Fe$_3$(BO$_3$)$_4$ exhibits both, a spontaneous polarization below T$_N$ and a magnetoelectric effect at higher fields that extends to high temperatures. The superposition of spontaneous polarization, induced by the internal magnetic field in the ordered state, and the magnetoelectric polarizations due to the external field results in a complex behavior of the total polarization measured as a function of temperature and field.Comment: 12 pages, 15 figure

Theoretical analysis of neutron scattering results for quasi-two dimensional ferromagnets

A theoretical study has been carried out to analyse the available results from the inelastic neutron scattering experiment performed on a quasi-two dimensional spin-1/2 ferromagnetic material $K_2CuF_4$. Our formalism is based on a conventional semi-classical like treatment involving a model of an ideal gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg ferromagnet on a square lattice. The results for dynamical structure functions for our model corresponding to spin-1/2, show occurrence of negative values in a large range of energy transfer even encompassing the experimental range, when convoluted with a realistic spectral window function. This result indicates failure of the conventional theoretical framework to be applicable to the experimental situation corresponding to low spin systems. A full quantum formalism seems essential for treating such systems.Comment: 16 pages, 6 figures, 1 Table Submitted for publicatio

Contrasting seed biology of two ornamental palms: Pygmy Date Palm (Phoenix roebelenii O’Brien) and Fishtail Palm (Caryota urens L.)

The Arecaceae family includes palm trees of economic importance both as a source of agricultural produce and asornamental components in landscaping projects. Pygmy date palm (Phoenix roebelenii) and solitary fishtail palm (Caryotaurens) are well known landscaping plants today. Both species have their origin in Southeast Asia and, especially C. urens iswidespread in peninsular India and Sri Lanka. They are multipurpose species with a variety of applications and thus veryheavily utilized. Knowledge of palm seed storage biology will improve their conservation prospects. In present studies, freshseed moisture content in P. roebelenii was recorded to be 30% with germinability of 98%. After desiccation to 8% moisturegerminability was reduced to 90% and the seeds survived cryo-exposure. Fresh seeds of C. urens, with initial moisturecontent of 34% and 95% germinability could be desiccated to lowest level of only 29% moisture content, with complete lossof germinability. Fresh as well as desiccated seeds of this species did not survive cryo-exposure. While the seeds of C. urensstored at room temperature lost their germinability by 110 days, seeds of P. roebelenii could germinate even after 9 monthsof storage. P. roebelenii is proven to exhibit orthodox seed storage behaviour while C. urens is found to exhibit recalcitrantseed storage behaviour. Long-term ex situ cryo-conservation in the form of seed gene banks would be suitable for seedpropagated orthodox palm species and a few germplasm centres may be established for recalcitrant Indian palms in suitablebio-geographic regions as a complimentary ex situ conservation

On Fair Division of Indivisible Items

We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of $e^{1/e} \approx 1.445$