Lagrangian submanifolds and dynamics on Lie affgebroids

We introduce the notion of a symplectic Lie affgebroid and their Lagrangian submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a Lie affgebroid in terms of this type of structures. Several examples are discussed.Comment: 50 pages. Several sections update

A new multisymplectic unified formalism for second-order classical field theories

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincar\'e-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.Comment: 52 pp. Revision of our previous paper. Minor corrections on the statement of some results. A new example is added (Section 6.1). Conclusions and bibliography have been enlarged, and some comments on the higher-order case have been adde

Profits, Markups and Entry: Fiscal Policy in an Open Economy

In this paper we develop a general model of an imperfectly competitive small open economy. There is a traded and non-traded sector, whose outputs are combined in order to produce a single final good that can be either consumed or invested. We make general assumptions about preferences and technology, and analyze the impact of fiscal policy on the economy. We find that the fiscal multiplier is between zero and one, and provide sufficient conditions for it to be increasing in the degree of imperfect competition. We also are able to compare the multiplier under free-entry and with a fixed number of firms and welfare. A simple graphical representation of the model is developed.Imperfect competition, open economy, fiscal policy

Surface Percolation and Growth. An alternative scheme for breaking the diffraction limit in optical patterning

A nanopatterning scheme is presented by which the structure height can be controlled in the tens of nanometers range and the lateral resolution is a factor at least three times better than the point spread function of the writing beam. The method relies on the initiation of the polymerization mediated by a very inefficient energy transfer from a fluorescent dye molecule after single photon absorption. The mechanism has the following distinctive steps: the dye adsorbs on the substrate surface with a higher concentration than in the bulk, upon illumination it triggers the polymerization, then isolated islands develop and merge into a uniform structure (percolation), which subsequently grows until the illumination is interrupted. This percolation mechanism has a threshold that introduces the needed nonlinearity for the fabrication of structures beyond the diffraction limit.Comment: 10 pages, 8 figure