6,356 research outputs found
Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle
Revisiting canonical integration of the classical solid near a uniform
rotation, canonical action angle coordinates, hyperbolic and elliptic, are
constructed in terms of various power series with coefficients which are
polynomials in a variable depending on the inertia moments. Normal forms
are derived via the analysis of a relative cohomology problem and shown to be
obtainable without the use of ellitptic integrals (unlike the derivation of the
action-angles). Results and conjectures also emerge about the properties of the
above polynomials and the location of their roots. In particular a class of
polynomials with all roots on the unit circle arises.Comment: 26 pages, 1 figur
Partition function of the eight-vertex model with domain wall boundary condition
We derive the recursive relations of the partition function for the
eight-vertex model on an square lattice with domain wall boundary
condition. Solving the recursive relations, we obtain the explicit expression
of the domain wall partition function of the model. In the
trigonometric/rational limit, our results recover the corresponding ones for
the six-vertex model.Comment: Latex file, 20 pages; V2, references adde
On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain
A generalization of Jacobi's elliptic functions is introduced as inversions
of hyperelliptic integrals. We discuss the special properties of these
functions, present addition theorems and give a list of indefinite integrals.
As a physical application we show that periodic kink solutions (kink chains) of
the double sine-Gordon model can be described in a canonical form in terms of
generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table
Particles in a magnetic field and plasma analogies: doubly periodic boundary conditions
The -particle free fermion state for quantum particles in the plane
subject to a perpendicular magnetic field, and with doubly periodic boundary
conditions, is written in a product form. The absolute value of this is used to
formulate an exactly solvable one-component plasma model, and further motivates
the formulation of an exactly solvable two-species Coulomb gas. The large
expansion of the free energy of both these models exhibits the same O(1) term.
On the basis of a relationship to the Gaussian free field, this term is
predicted to be universal for conductive Coulomb systems in doubly periodic
boundary conditions.Comment: 12 page
The eVALuate study: two parallel randomised trials, one comparing laparoscopic with abdominal hysterectomy, the other comparing laparoscopic with vaginal hysterectomy
OBJECTIVE: To compare the effects of laparoscopic hysterectomy
and abdominal hysterectomy in the abdominal trial, and
laparoscopic hysterectomy and vaginal hysterectomy in the
vaginal trial.
DESIGN: Two parallel, multicentre, randomised trials.
Setting 28 UK centres and two South African centres.
Participants 1380 women were recruited; 1346 had surgery;
937 were followed up at one year.
PRIMARY OUTCOME: outcome Rate of major complications.
RESULTS: In the abdominal trial laparoscopic hysterectomy was
associated with a higher rate of major complications than
abdominal hysterectomy (11.1% v 6.2%, P = 0.02; difference
4.9%, 95% confidence interval 0.9% to 9.1%) and the number
needed to treat to harm was 20. Laparoscopic hysterectomy
also took longer to perform (84 minutes v 50 minutes) but was
less painful (visual analogue scale 3.51 v 3.88, P = 0.01) and
resulted in a shorter stay in hospital after the operation (3 days
v 4 days). Six weeks after the operation, laparoscopic
hysterectomy was associated with less pain and better quality of
life than abdominal hysterectomy (SF-12, body image scale, and
sexual activity questionnaires).
In the vaginal trial we found no evidence of a difference in
major complication rates between laparoscopic hysterectomy
and vaginal hysterectomy (9.8% v 9.5%, P = 0.92; difference
0.3%, − 5.2% to 5.8%), and the number needed to treat to harm
was 333.We found no evidence of other differences between
laparoscopic hysterectomy and vaginal hysterectomy except
that laparoscopic hysterectomy took longer to perform (72
minutes v 39 minutes) and was associated with a higher rate of
detecting unexpected pathology (16.4% v 4.8%, P = < 0.01).
However, this trial was underpowered.
CONCLUSIONS: Laparoscopic hysterectomy was associated with a
significantly higher rate of major complications than abdominal
hysterectomy. It also took longer to perform but was associated
with less pain, quicker recovery, and better short term quality of
life. The trial comparing vaginal hysterectomy with laparoscopic
hysterectomy was underpowered and is inconclusive on the rate
of major complications; however, vaginal hysterectomy took less
time
Spacetime Encodings II - Pictures of Integrability
I visually explore the features of geodesic orbits in arbitrary stationary
axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst
potential. Some of the geometric features of integrable and chaotic orbits are
highlighted. The geodesic problem for these SAV spacetimes is rewritten as a
two degree of freedom problem and the connection between current ideas in
dynamical systems and the study of two manifolds sought. The relationship
between the Hamilton-Jacobi equations, canonical transformations, constants of
motion and Killing tensors are commented on. Wherever possible I illustrate the
concepts by means of examples from general relativity. This investigation is
designed to build the readers' intuition about how integrability arises, and to
summarize some of the known facts about two degree of freedom systems. Evidence
is given, in the form of orbit-crossing structure, that geodesics in SAV
spacetimes might admit, a fourth constant of motion that is quartic in momentum
(by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure
A slowly rotating perfect fluid body in an ambient vacuum
A global model of a slowly rotating perfect fluid ball in general relativity
is presented. To second order in the rotation parameter, the junction surface
is an ellipsoidal cylinder. The interior is given by a limiting case of the
Wahlquist solution, and the vacuum region is not asymptotically flat. The
impossibility of joining an asymptotically flat vacuum region has been shown in
a preceding work.Comment: 7 pages, published versio
Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites
We calculate the bulk contribution for the doubly degenerated largest
eigenvalue of the transfer matrix of the eight vertex model with an odd number
of lattice sites N in the disordered regime using the generic equation for
roots proposed by Fabricius and McCoy. We show as expected that in the
thermodynamic limit the result coincides with the one in the N even case.Comment: 11 pages LaTeX New introduction, Method change
Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians,
we analyze three sets of complex potentials with real spectra, recently derived
by a potential algebraic approach based upon the complex Lie algebra sl(2, C).
This extends to the complex domain the well-known relationship between SUSYQM
and potential algebras for Hermitian Hamiltonians, resulting from their common
link with the factorization method and Darboux transformations. In the same
framework, we also generate for the first time a pair of elliptic partner
potentials of Weierstrass type, one of them being real and the other
imaginary and PT symmetric. The latter turns out to be quasiexactly solvable
with one known eigenvalue corresponding to a bound state. When the Weierstrass
function degenerates to a hyperbolic one, the imaginary potential becomes PT
non-symmetric and its known eigenvalue corresponds to an unbound state.Comment: 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int.
J. Mod. Phys.
Dynamic Fano Resonance of Quasienergy Excitons in Superlattices
The dynamic Fano resonance (DFR) between discrete quasienergy excitons and
sidebands of their ionization continua is predicted and investigated in dc- and
ac-driven semiconductor superlattices. This DFR, well controlled by the ac
field, delocalizes the excitons and opens an intrinsic decay channel in
nonlinear four-wave mixing signals.Comment: 4pages, 4figure
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