Clebsch (String) Parameterization of 3-Vectors and Their Actions

We discuss some properties of the intrinsically nonlinear Clebsch decomposition of a vector field into three scalars in d=3. In particular, we note and account for the incompleteness of this parameterization when attempting to use it in variational principles involving Maxwell and Chern-Simons actions. Similarities with string decomposition of metrics and their actions are also pointed out.Comment: 4 pages, LaTeX; email correspondence to [email protected]

Soundness of a concurrent collector for actors (extended version)

ORCA is a garbage collection protocol for actor-based programs. Multiple actors may mutate the heap while the collector is running without any dedicated synchronisation. ORCA is applicable to any actor language whose type system prevents data races and which supports causal message delivery. We present a model of ORCA which is parametric to the host language and its type system. We describe the interplay between the host language and the collector. We give invariants preserved by ORCA, and prove its soundness and completeness

Variational formulation of ideal fluid flows according to gauge principle

On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized by symmetries of translation and rotation. The rotational transformations are regarded as gauge transformations as well as the translational ones. In addition to the Lagrangians representing the translation symmetry, a structure of rotation symmetry is equipped with a Lagrangian $\Lambda_A$ including the vorticity and a vector potential bilinearly. Euler's equation of motion is derived from variations according to the action principle. In addition, the equations of continuity and entropy are derived from the variations. Equations of conserved currents are deduced as the Noether theorem in the space of Lagrangian coordinate \ba. Without $\Lambda_A$, the action principle results in the Clebsch solution with vanishing helicity. The Lagrangian $\Lambda_A$ yields non-vanishing vorticity and provides a source term of non-vanishing helicity. The vorticity equation is derived as an equation of the gauge field, and the $\Lambda_A$ characterizes topology of the field. The present formulation is comprehensive and provides a consistent basis for a unique transformation between the Lagrangian \ba space and the Eulerian \bx space. In contrast, with translation symmetry alone, there is an arbitrariness in the ransformation between these spaces.Comment: 34 pages, Fluid Dynamics Research (2008), accepted on 1st Dec. 200

Possíveis genes Rps em linhagens de soja da Embrapa Trigo.

A podridão radicular de fitóftora, causada por Phytophthora sojae, pode causar redução de rendimento de grãos de soja de até 100% em cultivares altamente suscetíveis. A principal forma de controle da doença é o uso de cultivares com genes de resistência dominantes (Rps). O objetivo deste trabalho foi determinar possíveis genes Rps presentes em linhagens de soja desenvolvidas pela Embrapa Trigo. A caracterização da efetividade de genes Rps foi realizada pela técnica de inoculação do hipocótilo em plântulas das seguintes diferenciais: PI 547677 (Rps1a), PI 547842 (Rps1b), PI 547834 (Rps1c), PI 103091 (Rps1d), Williams 82 (Rps1k), PI 547838 (Rps2), PI 547862 (Rps3a), PI 591509 (Rps3b), L92-7857 (Rps3c), L85-2352 (Rps4), PI 547876 (Rps5), PI 591511 (Rps6), Harosoy (Rps7) e PI 399073 (Rps8). Considerou-se efetivo o gene da diferencial que apresentou até 30% de plantas mortas, e inefetivo, a diferencial com mortalidade de plantas acima de 70%. As linhagens desenvolvidas no programa de melhoramento genético de soja da Embrapa Trigo e testadas com o isolado Ps 2.4/07 podem possuir um ou mais dos seguintes genes dominantes de resistência à PRF: Rps1a, Rps1b, Rps1c, Rps1k, Rps3a e Rps8. Embora ainda considerados efetivos, os altos índices de mortalidade expressos pelo isolado Ps 2.4/07 a Rps1b e Rps3a não qualificariam estes genes para uso em manejo da PRF

Orca: GC and type system co-design for actor languages

ORCA is a concurrent and parallel garbage collector for actor programs, which does not require any stop-the-world steps, or synchronisation mechanisms, and which has been designed to support zero-copy message passing and sharing of mutable data. \ORCA is part of the runtime of the actor-based language Pony. Pony's runtime was co-designed with the Pony language. This co-design allowed us to exploit certain language properties in order to optimise performance of garbage collection. Namely, ORCA relies on the absence of race conditions in order to avoid read/write barriers, and it leverages actor message passing for synchronisation among actors. This paper describes Pony, its type system, and the ORCA garbage collection algorithm. An evaluation of the performance of ORCA suggests that it is fast and scalable for idiomatic workloads

Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems under study include the shallow water equation and Dym type equation. The classes of solutions are described in terms of theta-functions and their singular limits by using new parameterizations. A qualitative description of real valued solutions is provided

Closed geodesics and billiards on quadrics related to elliptic KdV solutions

We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards. Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero systemComment: 23 pages, Latex, 1 figure Postscrip