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

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

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

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

Planning the Future of U.S. Particle Physics (Snowmass 2013): Chapter 4: Cosmic Frontier

These reports present the results of the 2013 Community Summer Study of the APS Division of Particles and Fields ("Snowmass 2013") on the future program of particle physics in the U.S. Chapter 4, on the Cosmic Frontier, discusses the program of research relevant to cosmology and the early universe. This area includes the study of dark matter and the search for its particle nature, the study of dark energy and inflation, and cosmic probes of fundamental symmetries.Comment: 61 page

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.

Generation and Structure of Solitary Rossby Vortices in Rotating Fluids

The formation of zonal flows and vortices in the generalized Charney-Hasegawa-Mima equation is studied. We focus on the regime when the size of structures is comparable to or larger than the deformation (Rossby) radius. Numerical simulations show the formation of anticyclonic vortices in unstable shear flows and ring-like vortices with quiescent cores and vorticity concentrated in a ring. Physical mechanisms that lead to these phenomena and their relevance to turbulence in planetary atmospheres are discussed.Comment: 3 pages in REVTeX, 5 postscript figures separately, submitted to Phys. Rev.

Effects of administration of a growth promoting implant during the suckling phase or at weaning on growth, reproduction, and ovarian development in replacement heifers grazing native range

Management strategies utilized during pre-breeding development of replacement heifers can impact fertility and the ovarian reserve. Angus- Hereford crossbred heifers (n = 233) were utilized over a 3-yr period to determine the effects of administration of a growth promoting implant at either branding or weaning on growth, reproduction, and ovarian development. Heifer calves were randomly assigned to one of three treatments: 1) nonimplanted controls (CON; n = 79), 2) implanted at approximately 2 mo of age (average calf age = 58 d) with Synovex-C (BIMP, n = 82), or 3) implanted at approximately 7 mo of age (average calf age = 210 d) with Synovex-C (WIMP; n = 72). In years 2 and 3, a subset of heifers (year 2 n = 16; year 3 n = 14) were unilaterally ovariectomized. Heifers implanted at 2 mo of age were heavier at weaning, yearling (mid-February; average calf age = 332 d), and at the beginning of the breeding season (P \u3c 0.01) compared to CON and WIMP heifers. Average daily gain (ADG) was similar among treatments from weaning to yearling and weaning to the start of the breeding season (P ≥ 0.61); however, WIMP heifers had increased (P = 0.05) ADG from yearling to the start of the breeding season compared to BIMP heifers. Antral follicle count and reproductive tract scores were not influenced by implant treatment (P ≥ 0.18). Response to synchronization of estrus was increased (P = 0.02) in WIMP compared to CON heifers, with BIMP heifers similar to all other treatments. First service conception rates tended to be increased (P = 0.09) in CON heifers compared to WIMP heifers, with BIMP heifers similar to CON and WIMP. Final pregnancy rates were similar (P = 0.54) among treatments. A treatment × yr interaction was detected (P = 0.01) for the number of primordial follicles/section with increased primordial follicles in WIMP heifers in year 3 compared to BIMP and WIMP heifers in year 2 and CON heifers in year 3, as well as in BIMP compared to WIMP heifers in year 2. Utilization of growth promoting implants did not negatively impact postweaning reproductive development or compromise pregnancy rates in beef heifers. Based on these results, administration of a growth promoting Synovex-C implant at 2 mo of age may allow for increased body weight at weaning, without hindering reproductive performance

Semiclassical analysis of Wigner 3j3j-symbol

We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's oscillators. A novel element is the appearance of compact Lagrangian manifolds that are not tori, due to the fact that the observables defining the quantum states are noncommuting. These manifolds can be quantized by generalized Bohr-Sommerfeld rules and yield all the correct quantum numbers. The geometry of the classical angular momentum vectors emerges in a clear manner. Efficient methods for computing amplitude determinants in terms of Poisson brackets are developed and illustrated.Comment: 7 figure file