The momentum map for nonholonomic field theories with symmetry

In this note, we introduce a suitable generalization of the momentum map for nonholonomic field theories and prove a covariant form of the nonholonomic momentum equation. We show that these covariant objects coincide with their counterparts in mechanics by making the transition to the Cauchy formalism

The motion of solid bodies in potential flow with circulation: a geometric outlook

The motion of a circular body in 2D potential flow is studied using symplectic reduction. The equations of motion are obtained starting front a kinetic-energy type system on a space of embeddings and reducing by the particle relabelling symmetry group and the special Euclidian group. In the process, we give a geometric interpretation for the Kutta-Joukowski lift force in terms of the curvature of a connection on the original phase space

Multi-Dirac Structures and Hamilton-Pontryagin Principles for Lagrange-Dirac Field Theories

The purpose of this paper is to define the concept of multi-Dirac structures and to describe their role in the description of classical field theories. We begin by outlining a variational principle for field theories, referred to as the Hamilton-Pontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then discuss the role of multi-Dirac structures in field theory by showing that the implicit field equations obtained from the Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac structures. Furthermore, we show that any multi-Dirac structure naturally gives rise to a multi-Poisson bracket. We treat the case of field theories with nonholonomic constraints, showing that the integrability of the constraints is equivalent to the integrability of the underlying multi-Dirac structure. We finish with a number of illustrative examples, including time-dependent mechanics, nonlinear scalar fields and the electromagnetic field.Comment: 50 pages, v2: correction to prop. 6.1, typographical change

Alcohol outlets near schools in a midsize Romanian city : prevalence and characteristics

Objective: alcohol availability is one of the strongest predictors of adolescent alcohol use, and subsequent harm. Alcohol outlets near schools are an important indicator of three types of availability related to adolescent alcohol use; physical (number), economic (price), and legal (compliance with age limits).\ud \ud Method: two teams with trained students (16 and 17 years old) visited all 37 schools in a 200,000 inhabitant Romanian city (Pitesti). On the spot all alcohol outlets were visited and data was collected on outlet characteristics and visitors. Also, by conducting mystery shopping purchase attempts by the researchers, compliance on the age limits for alcohol sales was tested.\ud \ud Results: a total of 40 outlets were found within a 250 meter distance around 23 schools. Alcohol turns out to be cheap, and commercial alcohol brand signs are dominantly visible. With respect to compliance with the 18-year-old Romanian age limit for alcohol sales, only eight (20%) outlets refused to sell alcohol to under aged decoy customers.\ud \ud Conclusion: adolescent alcohol availability is high on the physical, economic and legal aspect. Pitesti is the first city in\ud Romania where an international alcohol prevention project has started to reduce alcohol related consequences. This project\ud involves all relevant stakeholders, and the first new legislation on this subject had been implemented