148 research outputs found
Exact solutions for a class of integrable Henon-Heiles-type systems
We study the exact solutions of a class of integrable Henon-Heiles-type
systems (according to the analysis of Bountis et al. (1982)). These solutions
are expressed in terms of two-dimensional Kleinian functions. Special periodic
solutions are expressed in terms of the well-known Weierstrass function. We
extend some of our results to a generalized Henon-Heiles-type system with n+1
degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy
Mechanical similarity as a generalization of scale symmetry
In this paper we study the symmetry known as mechanical similarity (LMS) and
present for any monomial potential. We analyze it in the framework of the
Koopman-von Neumann formulation of classical mechanics and prove that in this
framework the LMS can be given a canonical implementation. We also show that
the LMS is a generalization of the scale symmetry which is present only for the
inverse square potential. Finally we study the main obstructions which one
encounters in implementing the LMS at the quantum mechanical level.Comment: 9 pages, Latex, a new section adde
Breakdown of Lindstedt Expansion for Chaotic Maps
In a previous paper of one of us [Europhys. Lett. 59 (2002), 330--336] the
validity of Greene's method for determining the critical constant of the
standard map (SM) was questioned on the basis of some numerical findings. Here
we come back to that analysis and we provide an interpretation of the numerical
results by showing that no contradiction is found with respect to Greene's
method. We show that the previous results based on the expansion in Lindstedt
series do correspond to the transition value but for a different map: the
semi-standard map (SSM). Moreover, we study the expansion obtained from the SM
and SSM by suppressing the small divisors. The first case turns out to be
related to Kepler's equation after a proper transformation of variables. In
both cases we give an analytical solution for the radius of convergence, that
represents the singularity in the complex plane closest to the origin. Also
here, the radius of convergence of the SM's analogue turns out to be lower than
the one of the SSM. However, despite the absence of small denominators these
two radii are lower than the ones of the true maps for golden mean winding
numbers. Finally, the analyticity domain and, in particular, the critical
constant for the two maps without small divisors are studied analytically and
numerically. The analyticity domain appears to be an perfect circle for the SSM
analogue, while it is stretched along the real axis for the SM analogue
yielding a critical constant that is larger than its radius of convergence.Comment: 12 pages, 3 figure
Symbolic dynamics for the -centre problem at negative energies
We consider the planar -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 centres in two non-empty sets
Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
Strategies intended to resolve the problem of time in quantum gravity by
means of emergent or hidden timefunctions are considered in the arena of
relational particle toy models. In situations with `heavy' and `light' degrees
of freedom, two notions of emergent semiclassical WKB time emerge; these are
furthermore equivalent to two notions of emergent classical
`Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach,
in a geometric phase formalism, extended to include linear constraints, and
with particular care to make explicit those approximations and assumptions
used. I propose a new iterative scheme for this in the cosmologically-motivated
case with one heavy degree of freedom. I find that the usual semiclassical
quantum cosmology emergence of time comes hand in hand with the emergence of
other qualitatively significant terms, including back-reactions on the heavy
subsystem and second time derivatives. I illustrate my analysis by taking it
further for relational particle models with linearly-coupled harmonic
oscillator potentials. As these examples are exactly soluble by means outside
the semiclassical approach, they are additionally useful for testing the
justifiability of some of the approximations and assumptions habitually made in
the semiclassical approach to quantum cosmology. Finally, I contrast the
emergent semiclassical timefunction with its hidden dilational Euler time
counterpart.Comment: References Update
Spatio-temporal genetic tagging of a cosmopolitan planktivorous shark provides insight to gene flow, temporal variation and site-specific re-encounters
Migratory movements in response to seasonal resources often influence population structure and dynamics. Yet in mobile marine predators, population genetic consequences of such repetitious behaviour remain inaccessible without comprehensive sampling strategies. Temporal genetic sampling of seasonally recurring aggregations of planktivorous basking sharks, Cetorhinus maximus, in the Northeast Atlantic (NEA) affords an opportunity to resolve individual re-encounters at key sites with population connectivity and patterns of relatedness. Genetic tagging (19 microsatellites) revealed 18% of re-sampled individuals in the NEA demonstrated inter/multi-annual site-specific re-encounters. High genetic connectivity and migration between aggregation sites indicate the Irish Sea as an important movement corridor, with a contemporary effective population estimate (Ne) of 382 (CIâ=â241â830). We contrast the prevailing view of high gene flow across oceanic regions with evidence of population structure within the NEA, with early-season sharks off southwest Ireland possibly representing genetically distinct migrants. Finally, we found basking sharks surfacing together in the NEA are on average more related than expected by chance, suggesting a genetic consequence of, or a potential mechanism maintaining, site-specific re-encounters. Long-term temporal genetic monitoring is paramount in determining future viability of cosmopolitan marine species, identifying genetic units for conservation management, and for understanding aggregation structure and dynamics
Atomic-scale structure of dislocations revealed by scanning tunneling microscopy and molecular dynamics
Critical Perspective: Named Reactions Discovered and Developed by Women
Named organic reactions. As chemists, weâre all familiar with them: who can forget the DielsâAlder reaction? But how much do we know about the people behind the names? For example, can you identify a reaction named for a woman? How about a reaction discovered or developed by a woman but named for her male adviser? Our attempts to answer these simple questions started us on the journey that led to this Account.
We introduce you to four reactions named for women and nine reactions discovered or developed by women. Using information obtained from the literature and, whenever possible, through interviews with the chemists themselves, their associates, and their advisers, we paint a more detailed picture of these remarkable women and their outstanding accomplishments.
Some of the women you meet in this Account include Irma Goldberg, the only woman unambiguously recognized with her own named reaction. Gertrude Maud Robinson, the wife of Robert Robinson, who collaborated with him on several projects including the PilotyâRobinson pyrrole synthesis. Elizabeth Hardy, the Bryn Mawr graduate student who discovered the Cope rearrangement. Dorothee Felix, a critical member of Albert Eschenmoserâs research lab for over forty years who helped develop both the EschenmoserâClaisen rearrangement and the EschenmoserâTanabe fragmentation. Jennifer Loebach, the University of Illinois undergraduate who was part of the team in Eric Jacobsenâs lab that discovered the JacobsenâKatsuki epoxidation. Keiko Noda, a graduate student in Tsutomu Katsukiâs lab who also played a key role in the development of the JacobsenâKatsuki epoxidation. Lydia McKinstry, a postdoc in Andrew Myersâs lab who helped develop the Myers asymmetric alkylation. Rosa Lockwood, a graduate student at Boston College whose sole publication is the discovery of the Nicholas reaction. Kaori Ando, a successful professor in Japan who helped develop the Roush asymmetric alkylation as a postdoc at MIT. Bianka Tchoubar, a critically important member of the organic chemistry community in France who developed the TiffeneauâDemjanov rearrangement.
The accomplishments of the women in this Account illustrate the key roles women have played in the discovery and development of reactions used daily by organic chemists around the world. These pioneering chemists represent the vanguard of women in the field, and we are confident that many more of the growing number of current and future female organic chemists will be recognized with their own named reactions
Four-body co-circular central configurations
We classify the set of central configurations lying on a common circle in the Newtonian
four-body problem. Using mutual distances as coordinates, we show that the set of four-body
co-circular central configurations with positive masses is a two-dimensional surface, a graph
over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid,
are investigated extensively. We also prove that a co-circular central configuration requires a
specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to
the general four-body case, we show that if any two masses of a four-body co-circular central
configuration are equal, then the configuration has a line of symmetry.Peer ReviewedPostprint (authorâs final draft
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