Dynamics of spinning test particles in Kerr spacetime

We investigate the dynamics of relativistic spinning test particles in the spacetime of a rotating black hole using the Papapetrou equations. We use the method of Lyapunov exponents to determine whether the orbits exhibit sensitive dependence on initial conditions, a signature of chaos. In the case of maximally spinning equal-mass binaries (a limiting case that violates the test-particle approximation) we find unambiguous positive Lyapunov exponents that come in pairs ± lambda, a characteristic of Hamiltonian dynamical systems. We find no evidence for nonvanishing Lyapunov exponents for physically realistic spin parameters, which suggests that chaos may not manifest itself in the gravitational radiation of extreme mass-ratio binary black-hole inspirals (as detectable, for example, by LISA, the Laser Interferometer Space Antenna)

The universal family of semi-stable p-adic Galois representations

Let $K$ be a finite field extension of $Q_p$ and let $G_K$ be its absolute Galois group. We construct the universal family of filtered $(\phi,N)$-modules, or (more generally) the universal family of $(\phi,N)$-modules with a Hodge-Pink lattice, and study its geometric properties. Building on this, we construct the universal family of semi-stable $G_K$-representations in $Q_p$-algebras. All these universal families are parametrized by moduli spaces which are Artin stacks in schemes or in adic spaces locally of finite type over $Q_p$ in the sense of Huber. This has conjectural applications to the $p$-adic local Langlands program.Comment: final version, to appear in AN

Uniformizable families of tt-motives

Abelian $t$-modules and the dual notion of $t$-motives were introduced by Anderson as a generalization of Drinfeld modules. For such Anderson defined and studied the important concept of uniformizability. It is an interesting question, and the main objective of the present article to see how uniformizability behaves in families. Since uniformizability is an analytic notion, we have to work with families over a rigid analytic base. We provide many basic results, and in fact a large part of this article concentrates on laying foundations for studying the above question. Building on these, we obtain a generalization of a uniformizability criterion of Anderson and, among other things, we establish that the locus of uniformizability is Berkovich open.Comment: 40 pages, v2: Section 7 rewritten; to appear in Trans. Amer. Math. So

The Potential Use of Organically Grown Dye Plants in the Organic Textile Industry: Experiences and Results on Cultivation and Yields of Dyers Chamomile (Anthemis tinctoria L.), Dyers Knotweed (Polygonum tinctorium Ait.) and Weld (Reseda luteola L.)

The organic cultivation of dye plants for the certified natural textiles industry is an emerging and promising sector of organic farming. In 1999 a field trial was done with different provenances of Dyer’s Chamomile (Anthemis tinctoria L.), Dyer’s Knotweed Polygonum tinctorium Ait.), and Weld (Reseda luteola L.) on two organic farms in Lower Austria. Yields, dyestuff content, and quality parameters were analyzed. Dry matter yields of Weld ranged between 0.7 and 2.7 t ha-1, of Dyer’s Chamomile (flower heads) between 1.1 and 1.8 t ha-1. Significant differences were found between seed Weld provenances as well as between those of Dyer’s Chamomile. The total leaf dry matter of Dyer’s Knotweed (2 cuts) ranged at both sites on average 3.1 t ha-1. Seed provenances did not show differences. The total flavonoid content of Weld ranged between 1.53 and 4.00%, of Dyer’s Chamomile between 0.84 and 1.5%. The content of indican in Dyer’s Knotweed ranged between 0.50 and 1.45% of leaf dry matter, the calculated theoretical content of indigo ranged between 0.22 and 0.64% of leaf dry matter. The general use fastness properties differ according to species and provenance. Both high and low values were achieved. The data on the cultivation of dye plants in organic farming show promising results. Research should address improvement in yields and quality, development of dyestuff extracts, and optimization of dyeing methods. Research on dye plants needs a systemic look at the whole chain including producers, processors, trade, and consumers

Local Shtukas and Divisible Local Anderson Modules

We develop the analog of crystalline Dieudonn\'e theory for p-divisible groups in the arithmetic of function fields. In our theory p-divisible groups are replaced by divisible local Anderson modules, and Dieudonn\'e modules are replaced by local shtukas. We show that the categories of divisible local Anderson modules and of effective local shtukas are anti-equivalent over arbitrary base schemes. We also clarify their relation with formal Lie groups and with global objects like Drinfeld modules, Anderson's abelian t-modules and t-motives, and Drinfeld shtukas. Moreover, we discuss the existence of a Verschiebung map and apply it to deformations of local shtukas and divisible local Anderson modules. As a tool we use Faltings's and Abrashkin's theory of strict modules, which we review to some extent.Comment: 45 pages, v4: Final version. Appears in Canadian Journal of Mathematics. The present arXiv version contains a few more details and proofs; see page 1 botto