585 research outputs found
Equation of state of low--density neutron matter and the pairing gap
We report results of the equation of state of neutron matter in the
low--density regime, where the Fermi wave vector ranges from . Neutron matter in this regime is superfluid because of
the strong and attractive interaction in the channel. The properties of
this superfluid matter are calculated starting from a realistic Hamiltonian
that contains modern two-- and three--body interactions. The ground state
energy and the superfluid energy gap are calculated using the Auxiliary
Field Diffusion Monte Carlo method. We study the structure of the ground state
by looking at pair distribution functions as well as the Cooper-pair wave
function used in the calculations.Comment: 12 pages, 7 figure
Inherited crustal deformation along the East Gondwana margin revealed by seismic anisotropy tomography
Acknowledgments We thank Mallory Young for providing phase velocity measurements in mainland Australia and Tasmania. Robert Musgrave is thanked for making available his tilt-filtered magnetic intensity map. In the short term, data may be made available by contacting the authors (S.P. or N.R.). A new database of passive seismic data recorded in Australia is planned as part of a national geophysics data facility for easy access download. Details on the status of this database may be obtained from the authors (S.P., N.R., or A.M.R.). There are no restrictions on access for noncommercial use. Commercial users should seek written permission from the authors (S.P. or N.R.). Ross Cayley publishes with the permission of the Director of the Geological Survey of Victoria.Peer reviewedPublisher PD
Hyperdeterminants as integrable discrete systems
We give the basic definitions and some theoretical results about
hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability
(understood as 4d-consistency) of a nonlinear difference equation defined by
the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis:
the difference equations defined by hyperdeterminants of any size are
integrable.
We show that this hypothesis already fails in the case of the
2x2x2x2-hyperdeterminant.Comment: Standard LaTeX, 11 pages. v2: corrected a small misprint in the
abstrac
Evidence of micro-continent entrainment during crustal accretion
Peer reviewedPublisher PD
The frequency map for billiards inside ellipsoids
The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely
integrable. Its phase space is a symplectic manifold of dimension , which
is mostly foliated with Liouville tori of dimension . The motion on each
Liouville torus becomes just a parallel translation with some frequency
that varies with the torus. Besides, any billiard trajectory inside
is tangent to caustics , so the
caustic parameters are integrals of the
billiard map. The frequency map is a key tool to
understand the structure of periodic billiard trajectories. In principle, it is
well-defined only for nonsingular values of the caustic parameters. We present
four conjectures, fully supported by numerical experiments. The last one gives
rise to some lower bounds on the periods. These bounds only depend on the type
of the caustics. We describe the geometric meaning, domain, and range of
. The map can be continuously extended to singular values of
the caustic parameters, although it becomes "exponentially sharp" at some of
them. Finally, we study triaxial ellipsoids of \Rset^3. We compute
numerically the bifurcation curves in the parameter space on which the
Liouville tori with a fixed frequency disappear. We determine which ellipsoids
have more periodic trajectories. We check that the previous lower bounds on the
periods are optimal, by displaying periodic trajectories with periods four,
five, and six whose caustics have the right types. We also give some new
insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure
The falling chain of Hopkins, Tait, Steele and Cayley
A uniform, flexible and frictionless chain falling link by link from a heap
by the edge of a table falls with an acceleration if the motion is
nonconservative, but if the motion is conservative, being the
acceleration due to gravity. Unable to construct such a falling chain, we use
instead higher-dimensional versions of it. A home camcorder is used to measure
the fall of a three-dimensional version called an -slider. After
frictional effects are corrected for, its vertical falling acceleration is
found to be . This result agrees with the theoretical
value of for an ideal energy-conserving -slider.Comment: 17 pages, 5 figure
The partially alternating ternary sum in an associative dialgebra
The alternating ternary sum in an associative algebra, , gives rise to the partially alternating ternary sum in an
associative dialgebra with products and by making the
argument the center of each term: . We use computer algebra to determine the polynomial identities in
degree satisfied by this new trilinear operation. In degrees 3 and 5 we
obtain and ; these identities define a new variety of partially alternating ternary
algebras. We show that there is a 49-dimensional space of multilinear
identities in degree 7, and we find equivalent nonlinear identities. We use the
representation theory of the symmetric group to show that there are no new
identities in degree 9.Comment: 14 page
Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition
We show that a type of linear superposition principle works for several
nonlinear differential equations. Using this approach, we find periodic
solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear
Schrodinger (NLS) equation, the model, the sine-Gordon
equation and the Boussinesq equation by making appropriate linear
superpositions of known periodic solutions. This unusual procedure for
generating solutions is successful as a consequence of some powerful, recently
discovered, cyclic identities satisfied by the Jacobi elliptic functions.Comment: 19 pages, 4 figure
On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice
A new type of correlated disorder is shown to be responsible for the
appearance of extended electronic states in one-dimensional aperiodic systems
like the Thue-Morse lattice. Our analysis leads to an understanding of the
underlying reason for the extended states in this system, for which only
numerical evidence is available in the literature so far. The present work also
sheds light on the restrictive conditions under which the extended states are
supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in
Physical Review Letter
Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants
We classify 2-center extremal black hole charge configurations through
duality-invariant homogeneous polynomials, which are the generalization of the
unique invariant quartic polynomial for single-center black holes based on
homogeneous symmetric cubic special Kaehler geometries. A crucial role is
played by an horizontal SL(p,R) symmetry group, which classifies invariants for
p-center black holes. For p = 2, a (spin 2) quintet of quartic invariants
emerge. We provide the minimal set of independent invariants for the rank-3 N =
2, d = 4 stu model, and for its lower-rank descendants, namely the rank-2 st^2
and rank-1 t^3 models; these models respectively exhibit seven, six and five
independent invariants. We also derive the polynomial relations among these and
other duality invariants. In particular, the symplectic product of two charge
vectors is not independent from the quartic quintet in the t^3 model, but
rather it satisfies a degree-16 relation, corresponding to a quartic equation
for the square of the symplectic product itself.Comment: 1+31 pages; v2: amendments in Sec. 9, App. C added, other minor
refinements, Refs. added; v3: Ref. added, typos fixed. To appear on
J.Math.Phy
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