Modal Logics with Hard Diamond-free Fragments

We investigate the complexity of modal satisfiability for certain combinations of modal logics. In particular we examine four examples of multimodal logics with dependencies and demonstrate that even if we restrict our inputs to diamond-free formulas (in negation normal form), these logics still have a high complexity. This result illustrates that having D as one or more of the combined logics, as well as the interdependencies among logics can be important sources of complexity even in the absence of diamonds and even when at the same time in our formulas we allow only one propositional variable. We then further investigate and characterize the complexity of the diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers' comments. Accepted at LFCS 201

Vertex Operators in 2K Dimensions

A formula is proposed which expresses free fermion fields in 2K dimensions in terms of the Cartan currents of the free fermion current algebra. This leads, in an obvious manner, to a vertex operator construction of nonabelian free fermion current algebras in arbitrary even dimension. It is conjectured that these ideas may generalize to a wide class of conformal field theories.Comment: Minor change in notation. Change in references

Instabilities in droplets spreading on gels

We report a novel surface-tension driven instability observed for droplets spreading on a compliant substrate. When a droplet is released on the surface of an agar gel, it forms arms/cracks when the ratio of surface tension gradient to gel strength is sufficiently large. We explore a range of gel strengths and droplet surface tensions and find that the onset of the instability and the number of arms depend on the ratio of surface tension to gel strength. However, the arm length grows with an apparently universal law L ~ t^{3/4}

General Solution of the non-abelian Gauss law and non-abelian analogs of the Hodge decomposition

General solution of the non-abelian Gauss law in terms of covariant curls and gradients is presented. Also two non-abelian analogs of the Hodge decomposition in three dimensions are addressed. i) Decomposition of an isotriplet vector field $V_{i}^{a}(x)$ as sum of covariant curl and gradient with respect to an arbitrary background Yang-Mills potential is obtained. ii) A decomposition of the form $V_{i}^{a}=B_{i}^{a}(C)+D_{i}(C) \phi^{a}$ which involves non-abelian magnetic field of a new Yang-Mills potential C is also presented. These results are relevant for duality transformation for non-abelian gauge fields.Comment: 6 pages, no figures, revte

Supergrassmannian and large N limit of quantum field theory with bosons and fermions

We study a large N_{c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.Comment: 24 pages, Latex; v.3 appendix added, typos corrected, to appear in JM

An informed thought experiment exploring the potential for a paradigm shift in aquatic food production

The Neolithic Revolution began c. 10000 years ago and is characterised by the ultimate, near complete transition from hunting and gathering to agricultural food production on land. The Neolithic Revolution is thought to have been catalysed by a combination of local population pressure, cultural diffusion, property rights and climate change. We undertake a thought experiment that examines trends in these key hypothesised catalysts and patters of today to explore whether society could be on a path towards another paradigm shift in food production: away from hunting of wild fish towards a transition to mostly fish farming. We find similar environmental and cultural pressures have driven the rapid rise of aquaculture, during a period that has now been coined the Blue Revolution, providing impetus for such a transition in coming decades to centuries. We also highlight the interacting and often mutually reinforcing impacts of 1)technological and scientific advancement, 2)environmental awareness and collective action and 3)globalisation and trade influencing the trajectory and momentum of the Blue Revolution. We present two qualitative narratives that broadly fall within two future trajectories: 1)a ubiquitous aquaculture transition and 20commercial aquaculture and fisheries coexistence. This scenarios approach aims to encourage logical, forward thinking, and innovative solutions to complex systems dynamics. Scenario-based thought experiments are useful to explore large scale questions, increase the accessibility to a wider readership and ideally catalyse discussion around proactive governance mechanisms. We argue the future is not fixed and society now has greater foresight and capacity to choose the workable balance between fisheries sand aquaculture that supports economic, environmental, cultural and social objectives through combined planning, policies and management