Saturn manufacturing technology for welding methods and techniques

Evaluation of various power supplies for gas tungsten arc welding of aluminu

A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Vanishing Twist near Focus-Focus Points

We show that near a focus-focus point in a Liouville integrable Hamiltonian system with two degrees of freedom lines of locally constant rotation number in the image of the energy-momentum map are spirals determined by the eigenvalue of the equilibrium. From this representation of the rotation number we derive that the twist condition for the isoenergetic KAM condition vanishes on a curve in the image of the energy-momentum map that is transversal to the line of constant energy. In contrast to this we also show that the frequency map is non-degenerate for every point in a neighborhood of a focus-focus point.Comment: 13 page

Adiabatically coupled systems and fractional monodromy

We present a 1-parameter family of systems with fractional monodromy and adiabatic separation of motion. We relate the presence of monodromy to a redistribution of states both in the quantum and semi-quantum spectrum. We show how the fractional monodromy arises from the non diagonal action of the dynamical symmetry of the system and manifests itself as a generic property of an important subclass of adiabatically coupled systems

Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case irrespective of the value, $I$, of the generating Hamiltonian which is a constant of motion. For $I < 0$ we find numerous closed orbits with two unstable eigenvalues strongly indicating that there cannot exist two additional first integrals apart from the Hamiltonian and thus that the system, at least for this case, is very likely not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys.

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

Evolutionary Roots of Property Rights; The Natural and Cultural Nature of Human Cooperation

Debates about the role of natural and cultural selection in the development of prosocial, antisocial and socially neutral mechanisms and behavior raise questions that touch property rights, cooperation, and conflict. For example, some researchers suggest that cooperation and prosociality evolved by natural selection (Hamilton 1964, Trivers 1971, Axelrod and Hamilton 1981, De Waal 2013, 2014), while others claim that natural selection is insufficient for the evolution of cooperation, which required in addition cultural selection (Sterelny 2013, Bowles and Gintis 2003, Seabright 2013, Norenzayan 2013). Some scholars focus on the complexity and hierarchical nature of the evolution of cooperation as involving different tools associated with lower and the higher levels of competition (Nowak 2006, Okasha 2006); others suggest that humans genetically inherited heuristics that favor prosocial behavior such as generosity, forgiveness or altruistic punishment (Ridley 1996, Bowles and Gintis 2004, Rolls 2005). We argue these mechanisms are not genetically inherited; rather, they are features inherited through cultural selection. To support this view we invoke inclusive fitness theory, which states that individuals tend to maximize their inclusive fitness, rather than maximizing group fitness. We further reject the older notion of natural group selection - as well as more recent versions (West, Mouden, Gardner 2011) – which hold that natural selection favors cooperators within a group (Wynne-Edwards 1962). For Wynne-Edwards, group selection leads to group adaptations; the survival of individuals therefore depends on the survival of the group and a sharing of resources. Individuals who do not cooperate, who are selfish, face extinction due to rapid and over-exploitation of resources

From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillators with a homogeneous-{\it cubic} polynomial potential and with a homogeneous-{\it quartic} polynomial potentials admit the same BG-normalization up to degree-4 then both oscillators satisfy the Bertrand-Darboux integrability condition.Comment: 23 pages, LaTeX (iop.sty), typos and Appendix adde