[en] Plutonium Futures--The Science 2006 provided opportunities to examine present knowledge of the chemical and physical properties of plutonium and other actinides in complex media and materials; to discuss the current and emerging science (chemistry, physics, materials science, nuclear science, and environmental effects) of plutonium and actinides relevant to enhancing global nuclear security; and to exchange ideas. This international conference also provided a forum for illustrating and enhancing capabilities and interests, and assessing issues in these areas. U.S. and international scientists, engineers, faculty, and students from universities, national laboratories, and DOE's nuclear complex were encouraged to participate and make technical contributions. The Conference ran from Sunday, July 9th through Thursday, July 13th. A popular aspect of the conference was the opening tutorial session on Sunday afternoon intended for students and scientists new to the area of plutonium research. The tutorial was well attended by novices and veterans alike, and featured such diverse topics as; plutonium metallurgy, plutonium in the environment, and international arms control and nonproliferation. Two plenary lectures began each morning and each afternoon session and highlighted the breakout sessions on coordination/organometallic chemistry, solid-state physics, environmental chemistry, materials science, separations and reprocessing, advanced fuels and waste forms, phase transformations, solution and gas-phase chemistry, compounds and complexes, electronic structure and physical properties, and more. Chemistry Highlights--Among the many chemistry highlights presented in this proceedings are the overview of concepts and philosophies on inert nuclear fuel matrices and concerns about the ever-increasing amounts of minor actinides and plutonium generated in the fuel cycle. The various ideas involve multiple reduction schemes for these materials, suggesting fuels for 'burning' or 'cradle-to-grave' accountability for various reactor types. Related work is presented on identification of the unique reaction mechanisms and identification of the intermediate products, including Pu(III), at the end of the PUREX process. In the important area of nuclear forensics, actual scenarios of nuclear materials confiscation and the successes of applying forensics protocols to determine attribution and possible intention are provided. In the area of reactor incidents, there is no other place on Earth like the Chernobyl Site Object Shelter and radioactive aerosol particle characterization studies reflect an important effort described herein. An additional report from another unique environmental site presents results on radionuclide monitoring, fate, and transport in the ecosystem of the Yenisei River in the Krasoyarsk region. In the area of nuclear waste disposal, a study of the ion irradiation damage to pyrochlore compounds with varying amounts of host elements and actinide dopants is presented. Papers on both the aqueous and nonaqueous chemistry of plutonium and other actinides are presented including anhydrous coordination chemistry and redox behavior in the presence of humic materials and the their sorption on common minerals in the environment. Also published herein are reports on the field of anhydrous coordination chemistry of the transuranic elements where there is scarce information. Solid-State and Materials Highlights--Plutonium solid-state and materials research is represented in these proceedings by a wealth of leading edge discovery class research. The breadth of this research is reflected in the topics covered: solid-state; materials science; superconductivity; phase changes, phonons, and entropy; electronic structure and physical properties; surface science and corrosion; and radiation effects, defects, impurities, and property changes. Indeed the scientific challenge and excitement of plutonium can best be highlighted by quoting the tutorial prospectus of Drs. Sarrao and Schwartz. 'Plutonium has long been recognized as a complex and scientifically rich metal. The challenge of Pu derives from the fact that its 5f electrons are neither fully localized nor fully itinerant. The resulting low energy scales lead to competing interactions and important entropic and lattice considerations as well. As a consequence, plutonium is on the verge of magnetic order and can be stabilized in a variety of crystal structures. The past several years have seen a renaissance in plutonium materials research. Despite significant progress and important breakthroughs, metallic plutonium remains a mystery at the frontier of materials research'. As we hope you will discover, much progress is being made that is reflected in these proceedings. More importantly however, is that the papers herein also inspire new experiments and theoretical approaches that we trust will not go unnoticed by the reader

[en] Systematic electron diffraction and electron microscopy studies have been used to identify the mechanisms of deformation in cross-linked polyethylene single crystals. The crystals were cross-linked by exposing them to γ-rays. A marked difference between the operative deformation mechanisms in unirradiated and irradiated single crystals was observed, including the observation that stress-induced martensitic transformations are far more predominant in the cross-linked crystals. All of the observed differences in deformation behaviour have been explained satisfactorily in terms of the limited extensibility of cross-linked fold loops. (author)

[en] An account is given about further improvements of the SAS4A-Ref. 94.R0 version of the HCDA code. They concern in particular the DEFORM fuel rod deformation module. For a validation of the new code version, various CABRI experiments have been calculated, especially tests with high burnup fuel rods. Progress was shown to be achieved, but the precise timing and location of the observed fuel failures is still hard to calculate. The work was performed in close cooperation with partners in France, Britain, and Japan. An important application concerns the CAPRA project of a reactor for actinide burning. Its behavior under ULOF conditions was analyzed using the improved SAS4A Ref. 94 R0 code. The core design turned out to tend toward a long-term coolable configuration even more so than the EFR core design would do in an ULOF. (orig.)

[en] The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in “natural form”, the kinetic energy has geometric origins and, in the flat and constant curvature cases, the large isometry group plays a vital role. We explain how to use the corresponding first integrals to build separable and super-integrable systems. We also show how to use the automorphisms of the symmetry algebra to help build the Poisson relations of the corresponding non–Abelian Poisson algebra. Finally, we take both the classical and quantum Zernike system, recently discussed by Pogosyan et al., and show how the algebraic structure of its super-integrability can be understood in this framework.

[en] We discuss the role of commuting operators for quantum superintegrable systems, showing how they are used to build eigenfunctions. These ideas are illustrated in the context of resonant harmonic oscillators, the Krall–Sheffer operators, with polynomial eigenfunctions, and the Calogero–Moser system with additional harmonic potential. The construction is purely algebraic, avoiding the use of separation of variables and differential equation theory. (paper)

[en] We consider a class of multidimensional maps which naturally generalize the QRT map of the plane. Our 2n-dimensional maps are volume preserving and have n rational invariants, but we do not generally have a symplectic form. However, many specializations and reductions are integrable, some of which we present. Included in these are some new four-dimensional generalizations of the McMillan map

[en] One of the remarkable properties of cluster algebras is that any cluster, obtained from a sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the initial cluster (known as the ‘Laurent phenomenon’). There are many nonlinear recurrences which exhibit the Laurent phenomenon and thus unexpectedly generate integer sequences. The mutation of a typical quiver will not generate a recurrence, but rather an erratic sequence of exchange relations. How do we ‘design’ a quiver which gives rise to a given recurrence? A key role is played by the concept of ‘periodic cluster mutation’, introduced in 2009. Each recurrence corresponds to a finite dimensional map. In the context of cluster mutations, these are called ‘cluster maps’. What properties do cluster maps have? Are they integrable in some standard sense?In this review I describe how integrable maps arise in the context of cluster mutations. I first explain the concept of ‘periodic cluster mutation’, giving some classification results. I then give a review of what is meant by an integrable map and apply this to cluster maps. Two classes of integrable maps are related to interesting monodromy problems, which generate interesting Poisson algebras of functions, used to prove complete integrability and a linearization. A connection to the Hirota–Miwa equation is explained. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (review)

[en] The Eisenhart lift is a variant of geometrization of classical mechanics with d degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on (d+2)-dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of 2-dimensional mechanics on curved background is studied. The corresponding 4-dimensional metric is governed by two scalar functions which are just the conformal factor and the potential of the original dynamical system. We derive a conformal symmetry and a corresponding quadratic integral, associated with the Eisenhart lift. The energy–momentum tensor is constructed which, along with the metric, provides a solution to the Einstein equations. Uplifts of 2-dimensional superintegrable models are discussed with a particular emphasis on the issue of hidden symmetries. It is shown that for the 2-dimensional Darboux–Koenigs metrics, only type I can result in Eisenhart lifts which satisfy the weak energy condition. However, some physically viable metrics with hidden symmetries are presented.

[en] We recently introduced a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). We discuss differential–difference equations which then we interpret as symmetries of the discrete systems. In particular, we present nonlocal symmetries which are associated with the 2D Toda lattice. (paper)

[en] We introduce a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs, with $N\times <!--\; ??\; -->N$ matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated integrable lattice systems. We present two potential forms and completely classify the generic case. Many well known examples belong to our scheme for N  =  2, so many of our systems may be regarded as generalisations of these. Even at N  =  3, several new integrable systems arise. A decomposable case gives rise to interesting coupled systems of lower dimensional equations. Many of our equations are mutually compatible, so can be used together to form ‘coloured’ lattices. (paper)