Triply-Periodic Smectics

Twist-grain-boundary phases in smectics are the geometrical analogs of the Abrikosov flux lattice in superconductors. At large twist angles, the nonlinear elasticity is important in evaluating their energetics. We analytically construct the height function of a pi/2 twist-grain-boundary phase in smectic-A liquid crystals, known as Schnerk's first surface. This construction, utilizing elliptic functions, allows us to compute the energy of the structure analytically. By identifying a set of heretofore unknown defects along the pitch axis of the structure, we study the necessary topological structure of grain boundaries at other angles, concluding that there exist a set of privileged angles and that the \pi/2 and \pi/3 grain boundary structures are particularly simple.Comment: 13 pages, 7 figure

Pore formation in fluctuating membranes

We study the nucleation of a single pore in a fluctuating lipid membrane, specifically taking into account the membrane fluctuations, as well as the shape fluctuations of the pore. For large enough pores, the nucleation free energy is well-described by shifts in the effective membrane surface tension and the pore line tension. Using our framework, we derive the stability criteria for the various pore formation regimes. In addition to the well-known large-tension regime from the classical nucleation theory of pores, we also find a low-tension regime in which the effective line and surface tensions can change sign from their bare values. The latter scenario takes place at sufficiently high temperatures, where the opening of a stable pore of finite size is entropically favorable.Comment: 9 pages, 3 figure

The shape and mechanics of curved fold origami structures

We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single fold prescribes the shape of the entire origami structure. To better explore these structures, we derive continuum equations, valid in the limit of vanishing spacing between folds, to describe the smooth surface intersecting all the mountain folds. We find that this surface has negative Gaussian curvature with magnitude equal to the square of the fold's torsion. A series of open folds with constant fold angle generate a helicoid

Location and R&D Alliances in the European ICT Industry

This paper shows empirically that in an intra-industry oligopolistic scenario the location of a firm’s innovative activities plays an important role in determining its partner selection in R&D alliances. Such a role is mainly attributed to a strategic use of R&D alliances as a means to limit knowledge flows and protect competences, rather than to promote knowledge flows. By drawing on a novel dataset matching alliances and patent data for the European ICT industry, the econometric analysis shows that partners’ prior co-location (at both national and sub-national regional level), previous ties and technological overlap matter in the choice of partner, while common nationality has a negative impact on alliance formation.Alliances, strategy, efficiency, R&D location

New insights on the role of location advantages in international innovation

This paper takes a closer look at the role of location advantages in the spatial distribution of MNE R&D activity. In doing so, we have returned to first principles by revisiting our understanding of L and O advantages and their interaction. We revisit the meaning of L advantages, and offer a succinct differentiation of L advantages. We emphasise the importance of institutions, and flesh out the concept of collocation L advantages, which play an important role at the industry and firm levels of analysis. Just because a country possesses certain L advantages when viewed at a macro-level, does not imply that these are available to all industries or all firms in that location without differential cost. When these are linked to the distinction between location-bound and non location-bound O advantages, and we distinguish between MNEs and subsidiaries it allows for a clearer understanding of the MNE's spatially distributed activities. These are discussed here in the context of R&D, which - in addition to the usual uncertainties faced by firms - must deal with the uncertainties associated with innovation. Although prior literature has sometimes framed the centralisation/decentralisation, spatial separation/collocation debates as a paradox facing firms, when viewed within the context of the cognitive limits to resources, the complexities of institutions, and the slow pace of the evolving specialisation of locations, these are in actuality trade-offs firms must make.FDI, foreign investment, direct investment, multinationals, transnational corporations, MNEs, eclectic paradigm, collocation, locational advantage, country specific advantages

Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order

Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers becomes highly nontrivial. We discuss various topological and geometrical aspects of these materials and present recent progress on finding some exact layer configurations. We also exhibit connections to the study of certain embedded minimal surfaces and briefly summarize some important open problems.Comment: 16 page

Mechanics of large folds in thin interfacial films

A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how to incorporate film weight, self-adhesion and energy dissipation.Comment: 5 pages, 3 figure