Regularized Renormalization Group Reduction of Symplectic Map

By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the symplectic symmetry and fails to describe a long-time behaviour. In order to preserve the symplectic symmetry, we present a regularization procedure, which gives a regularized symplectic RG map describing an approximate long-time behaviour succesfully

Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX

Photon Mass Bound Destroyed by Vortices

The Particle Data Group gives an upper bound on the photon mass $m < 2 \times 10^{-16}$eV from a laboratory experiment and lists, but does not adopt, an astronomical bound $m < 3 \times 10^{-27}$eV, both of which are based on the plausible assumption of large galactic vector-potential. We argue that the interpretations of these experiments should be changed, which alters significantly the bounds on $m$. If $m$ arises from a Higgs effect, both limits are invalid because the Proca vector-potential of the galactic magnetic field may be neutralized by vortices giving a large-scale magnetic field that is effectively Maxwellian. In this regime, experiments sensitive to the Proca potential do not yield a useful bound on $m$. As a by-product, the non-zero photon mass from Higgs effect predicts generation of a primordial magnetic field in the early universe. If, on the other hand, the galactic magnetic field is in the Proca regime, the very existence of the observed large-scale magnetic field gives $m^{-1}\gtrsim 1$kpc, or $m\lesssim 10^{-26}$eV.Comment: 9 pages, discussion of primordial magnetic field adde

Failure processes of cemented granular materials

The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here, we use a discrete element model (DEM) simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular media with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure and compaction banding or anti-cracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow and foam

Basaltic Clasts in Y-86032 Feldspathic Lunar Meteorite: Ancient Volcanism far from the Procellarum Kreep Terrane

Lunar meteorite, Y-86032 is a fragmental or regolith breccia enriched in Al2O3 (28-31 wt%) and having very low concentrations of REEs and Th, U [e.g., 1]. Nyquist et al. [2] suggested that Y- 86032 contains a variety of lithologies not represented by the Apollo samples. They found clasts with old Ar-Ar ages and an ancient Sm-Nd age, and negative Nd indicating a direct link to the primordial magma ocean. Importantly, the final lithification of the Y-86032 breccia was likely >3.8-4.1 Ga ago. Therefore, any lithic components in the breccia formed prior to 3.8 Ga, and lithic components in breccia clasts in the parent breccia formed even earlier. Here we report textures and mineralogy of basaltic and gabbroic clasts in Y- 86032 to better understand the nature of ancient lunar volcanism far from the Procellarum KREEP Terrain (PKT) [3] and the central nearside

Comparisons of Mineralogy Between Cumulate Eucrites and Lunar Meteorites Possibly from the Farside Anorsothitic Crust

Anorthosites composed of nearly pure anorthite (PAN) at many locations in the farside highlands have been observed by the Kaguya multiband imager and spectral profiler [1]. Mineralogical studies of lunar meteorites of the Dhofar 489 group [2,3] and Yamato (Y-) 86032 [4], all possibly from the farside highlands, showed some aspects of the farside crust. Nyquist et al. [5] performed Sm-Nd and Ar-Ar studies of pristine ferroan anorthosites (FANs) of the returned Apollo samples and of Dhofar 908 and 489, and discussed implications for lunar crustal history. Nyquist et al. [6] reported initial results of a combined mineralogical/chronological study of the Yamato (Y-) 980318 cumulate eucrite with a conventional Sm-Nd age of 4567 24 Ma and suggested that all eucrites, including cumulate eucrites, crystallized from parental magmas within a short interval following differentiation of their parent body, and most eucrites participated in an event or events in the time interval ~4400- 4560 Ma in which many isotopic systems were partially reset. During the foregoing studies, we recognized that variations in mineralogy and chronology of lunar anorthosites are more complex than those of the crustal materials of the HED parent body. In this study, we compared the mineralogies and reflectance spectra of the cumulate eucrites, Y-980433 and 980318, to those of the Dhofar 307 lunar meteorite of the Dhofar 489 group [2]. Here we consider information from these samples to gain a better understanding of the feldspathic farside highlands and the Vesta-like body