The isotropy lattice of a lifted action

We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group $G$ on $TM$ and $T^*M$ based only on the knowledge of $G$ and its action on $M$. Some applications to symplectic geometry are also shown.Comment: minor modification

Particles adsorbed at various non-aqueous liquid-liquid interfaces

Particles adsorbed at liquid interfaces are commonly used to stabilise water-oil Pickering emulsions and water-air foams. The fundamental understanding of the physics of particles adsorbed at water-air and water-oil interfaces is improving significantly due to novel techniques that enable the measurement of the contact angle of individual particles at a given interface. The case of non-aqueous interfaces and emulsions is less studied in the literature. Non-aqueous liquid-liquid interfaces in which water is replaced by other polar solvents have properties similar to those of water-oil interfaces. Nanocomposites of non-aqueous immiscible polymer blends containing inorganic particles at the interface are of great interest industrially and consequently more work has been devoted to them. By contrast, the behaviour of particles adsorbed at oil-oil interfaces in which both oils are immiscible and of low dielectric constant (ε < 3) is scarcely studied. Hydrophobic particles are required to stabilise these oil-oil emulsions due to their irreversible adsorption, high interfacial activity and elastic shell behaviour

Symmetry and quaternionic integrable systems

Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so called hyperhamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperhamiltonian systems, i.e. quaternionic oscillators; and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperhamiltonian systems.Comment: 26 page

Hamiltonian Relative Equilibria with Continuous Isotropy

In symmetric Hamiltonian systems, relative equilibria usually arise in continuous families. The geometry of these families in the setting of free actions of the symmetry group is well-understood. Here we consider the question for non-free actions. Some results are already known in this direction, and we use the so called bundle equations to provide a systematic treatment of this question which both consolidates the known results, extending the scope of the results to deal with non-compact symmetry groups, as well as producing new results. Specifically we address questions about the stability, persistence and bifurcations of these relative equilibria

On the construction of partial difference schemes II: discrete variables and Schwarzian lattices

In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing an arbitrary partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut--Schwarz--Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut--Schwarz--Young theorem. A discussion on the numerical results is also presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.Comment: 14 pages, 4 figure

The Effects of a Sudden CO2 reduction in Spain

Spanish emissions of carbon dioxide have grown by more than 40% in 2004 with respect to 1990. This is not compatible with the EU allocation of Kyoto-mandated CO2 reduction, even taking into account that Spanish emissions are allowed to rise by 15% in 2010. The reasons for this situation stem from a combination of economic growth and an inefficient energy domain, coupled with a total absence of climate change policies. In this paper, we use a static general equilibrium model to assess the effects of a sudden and intense (ie, with a limited time to carry out significant abatement) CO2 reduction by the Spanish economy. Our results show that the costs of immediate and medium-size reductions are not significant in the short run and could lead to the attaining of the EU agreed emissions level for Spain. However, delaying such action means that the degree of Spanish CO2 emission reduction is much higher and that economic costs are far more important.Climate, energy, market