Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

Modeling the CO2-effects of forest management and wood usage on a regional basis

BACKGROUND: At the 15(th) Conference of Parties of the UN Framework Convention on Climate Change, Copenhagen, 2009, harvested wood products were identified as an additional carbon pool. This modification eliminates inconsistencies in greenhouse gas reporting by recognizing the role of the forest and timber sector in the global carbon cycle. Any additional CO(2)-effects related to wood usage are not considered by this modification. This results in a downward bias when the contribution of the forest and timber sector to climate change mitigation is assessed. The following article analyses the overall contribution to climate protection made by the forest management and wood utilization through CO(2)-emissions reduction using an example from the German state of North Rhine-Westphalia. Based on long term study periods (2011 to 2050 and 2100, respectively). Various alternative scenarios for forest management and wood usage are presented. RESULTS: In the mid- to long-term (2050 and 2100, respectively) the net climate protection function of scenarios with varying levels of wood usage is higher than in scenarios without any wood usage. This is not observed for all scenarios on short and mid term evaluations. The advantages of wood usage are evident although the simulations resulted in high values for forest storage in the C pools. Even the carbon sink effect due to temporal accumulation of deadwood during the period from 2011 to 2100 is outbalanced by the potential of wood usage effects. CONCLUSIONS: A full assessment of the CO(2)-effects of the forest management requires an assessment of the forest supplemented with an assessment of the effects of wood usage. CO(2)-emission reductions through both fuel and material substitution as well as CO(2) sink in wood products need to be considered. An integrated assessment of the climate protection function based on the analysis of the study’s scenarios provides decision parameters for a strategic approach to climate protection with regard to forest management and wood use at regional and national levels. The short-term evaluation of subsystems can be misleading, rendering long-term evaluations (until 2100, or even longer) more effective. This is also consistent with the inherently long-term perspective of forest management decisions and measures

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Exactly solvable model of quantum diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wavenumber contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. On the other hand, an analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling.Comment: Submitted to J. Stat. Phy

Hamiltonian dynamics of the two-dimensional lattice phi^4 model

The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure

Approximating multi-dimensional Hamiltonian flows by billiards

Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ to the original billiard, and provide asymptotic expansion of the smooth Hamiltonian solution in terms of these billiard approximations. The asymptotic expansion includes error estimates in the $C^{r}$ norm and an iteration scheme for improving this approximation. Applying this theory to smooth potentials which limit to the multi-dimensional close to ellipsoidal billiards, we predict when the separatrix splitting persists for various types of potentials

Chaotic eigenfunctions in momentum space

We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are derived. We present a detailed numerical study for the stadium and the cardioid billiard, which shows in several cases that the radially integrated momentum distribution is a good indicator of localized eigenstates, such as scars, or bouncing ball modes. We also find examples, where the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally applications and generalizations are discussed.Comment: 30 pages. The figures are included in low resolution only. For a version with figures in high resolution see http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp99-2.htm

Comparison of target enrichment strategies for ancient pathogen DNA

In ancient DNA research, the degraded nature of the samples generally results in poor yields of highly fragmented DNA; targeted DNA enrichment is thus required to maximize research outcomes. The three commonly used methods ? array-based hybridization capture and in-solution capture using either RNA or DNA baits ? have different characteristics that may influence the capture efficiency, specificity and reproducibility. Here we compare their performance in enriching pathogen DNA of Mycobacterium leprae and Treponema pallidum from 11 ancient and 19 modern samples. We find that in-solution approaches are the most effective method in ancient and modern samples of both pathogens and that RNA baits usually perform better than DNA baits

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.Comment: RevTex, 40 pages, 8 PostScript figures, to be published in Phys. Rev. E (scheduled for November 1996

Treponema Infection Associated With Genital Ulceration in Wild Baboons

The authors describe genital alterations and detailed histologic findings in baboons naturally infected with Treponema pallidum. The disease causes moderate to severe genital ulcerations in a population of olive baboons (Papio hamadryas anubis) at Lake Manyara National Park in Tanzania. In a field survey in 2007, 63 individuals of all age classes, both sexes, and different grades of infection were chemically immobilized and sampled. Histology and molecular biological tests were used to detect and identify the organism responsible: a strain similar to T pallidum ssp pertenue, the cause of yaws in humans. Although treponemal infections are not a new phenomenon in nonhuman primates, the infection described here appears to be strictly associated with the anogenital region and results in tissue alterations matching those found in human syphilis infections (caused by T pallidum ssp pallidum), despite the causative pathogen’s greater genetic similarity to human yaws-causing strains