17,592 research outputs found
Action-gradient-minimizing pseudo-orbits and almost-invariant tori
Transport in near-integrable, but partially chaotic,
degree-of-freedom Hamiltonian systems is blocked by invariant tori and is
reduced at \emph{almost}-invariant tori, both associated with the invariant
tori of a neighboring integrable system. "Almost invariant" tori with rational
rotation number can be defined using continuous families of periodic
\emph{pseudo-orbits} to foliate the surfaces, while irrational-rotation-number
tori can be defined by nesting with sequences of such rational tori. Three
definitions of "pseudo-orbit," \emph{action-gradient--minimizing} (AGMin),
\emph{quadratic-flux-minimizing} (QFMin) and \emph{ghost} orbits, based on
variants of Hamilton's Principle, use different strategies to extremize the
action as closely as possible. Equivalent Lagrangian (configuration-space
action) and Hamiltonian (phase-space action) formulations, and a new approach
to visualizing action-minimizing and minimax orbits based on AGMin
pseudo-orbits, are presented.Comment: Accepted for publication in a special issue of Communications in
Nonlinear Science and Numerical Simulation (CNSNS) entitled "The mathematical
structure of fluids and plasmas : a volume dedicated to the 60th birthday of
Phil Morrison
Infinitesimal rigidity in normed planes
We prove that a graph has an infinitesimally rigid placement in a
non-Euclidean normed plane if and only if it contains a -tight spanning
subgraph. The method uses an inductive construction based on generalised
Henneberg moves and the geometric properties of the normed plane. As a key
step, rigid placements are constructed for the complete graph by
considering smoothness and strict convexity properties of the unit ball.Comment: 26 page
Are ghost surfaces quadratic-flux-minimizing?
Two candidates for "almost-invariant" toroidal surfaces passing through
magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost
surfaces, use families of periodic pseudo-orbits (i.e. paths for which the
action is not exactly extremal). QFMin pseudo-orbits, which are
coordinate-dependent, are field lines obtained from a modified magnetic field,
and ghost-surface pseudo-orbits are obtained by displacing closed field lines
in the direction of steepest descent of magnetic action, . A generalized Hamiltonian definition of ghost
surfaces is given and specialized to the usual Lagrangian definition. A
modified Hamilton's Principle is introduced that allows the use of Lagrangian
integration for calculation of the QFMin pseudo-orbits. Numerical calculations
show QFMin and Lagrangian ghost surfaces give very similar results for a
chaotic magnetic field perturbed from an integrable case, and this is explained
using a perturbative construction of an auxiliary poloidal angle for which
QFMin and Lagrangian ghost surfaces are the same up to second order. While
presented in the context of 3-dimensional magnetic field line systems, the
concepts are applicable to defining almost-invariant tori in other
degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.Comment: 8 pages, 3 figures. Revised version includes post-publication
corrections in text, as described in Appendix C Erratu
{\Gamma}-species and the enumeration of k-trees
We study the class of graphs known as k-trees through the lens of Joyal's
theory of combinatorial species (and an equivariant extension known as
'-species' which incorporates data about 'structural' group actions).
This culminates in a system of recursive functional equations giving the
generating function for unlabeled k-trees which allows for fast, efficient
computation of their numbers. Enumerations up to k = 10 and n = 30 (for a
k-tree with (n+k-1) vertices) are included in tables, and Sage code for the
general computation is included in an appendix.Comment: 26 pages; includes Python cod
The Screened Field of a Test Particle
The screened field (forward field and wake) of a test particle moving at
constant velocity through an unmagnetized collisionless plasma is calculated
analytically and numerically. This paper is based on unpublished material from
my MSc thesis, supervised by the late Dr K. C. Hines.Comment: 27 pp, 14 fig Publ "In Celeb Of KC Hines,"
www.worldscibooks.com/physics/7604.html. Based on Chs 2 & 3 of
"Particle-field interactions in a plasma," RL Dewar, MSc Thesis, U Melbourne
'67. v2: and interchanged after Eq. (4.1); v3: typos
corrected pp 3, 4, 5, 19, in partic. repl. by & putting
hat on k in arg. of \Phi in Eq.(2.5). See also arXiv 1107.520
Review of the New Communities Program: Toward Effective Implementation of Neighborhood Plans
Evaluates the progress of the New Communities Program, an initiative to revitalize sixteen Chicago neighborhoods, and recommends extending the MacArthur Foundation's financial support through another five-year grant
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