601 research outputs found
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
Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice
It is shown that some special reduction of infinite 1D Toda lattice gives
differential constraints compatible with the Kaup -- Broer system. A family of
the travelling wave solutions of the Kaup -- Broer system and its higher
version is constructed.Comment: LaTeX, uses IOP styl
Dissipative Boussinesq System of Equations in the B\'enard-Marangoni Phenomenon
By using the long-wave approximation, a system of coupled evolution equations
for the bulk velocity and the surface perturbations of a B\'enard-Marangoni
system is obtained. It includes nonlinearity, dispersion and dissipation, and
it can be interpreted as a dissipative generalization of the usual Boussinesq
system of equations. As a particular case, a strictly dissipative version of
the Boussinesq system is obtained. Finnaly, some speculations are made on the
nature of the physical phenomena described by this system of equations.Comment: 15 Pages, REVTEX (Version 3.0), no figure
Bifurcation curves of subharmonic solutions
We revisit a problem considered by Chow and Hale on the existence of
subharmonic solutions for perturbed systems. In the analytic setting, under
more general (weaker) conditions, we prove their results on the existence of
bifurcation curves from the nonexistence to the existence of subharmonic
solutions. In particular our results apply also when one has degeneracy to
first order -- i.e. when the subharmonic Melnikov function vanishes
identically. Moreover we can deal as well with the case in which degeneracy
persists to arbitrarily high orders, in the sense that suitable generalisations
to higher orders of the subharmonic Melnikov function are also identically
zero. In general the bifurcation curves are not analytic, and even when they
are smooth they can form cusps at the origin: we say in this case that the
curves are degenerate as the corresponding tangent lines coincide. The
technique we use is completely different from that of Chow and Hale, and it is
essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure
Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations
We obtain new gauge-invariant forms of two-dimensional integrable systems of
nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the
generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov
system. We show how these forms imply both new and well-known two-dimensional
integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt
equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and
modified Nizhnik-Veselov-Novikov equation. We consider Miura-type
transformations between nonlinear equations in different gauges.Comment: Talk given at the Workshop "Nonlinear Physics: Theory and Experiment.
V", Gallipoli (Lecce, Italy), 12-21 June, 200
Clinical and self-reported markers of reproductive function in female survivors of childhood Hodgkin lymphoma
Purpose: To evaluate the impact of treatment for Hodgkin lymphoma (HL) on clinical reproductive markers and pregnancy outcomes.Methods: This study was embedded within the DCOG LATER-VEVO study; a Dutch, multicenter, retrospective cohort study between 2004 and 2014. Serum anti-Müllerian hormone (AMH), follicle stimulating hormone (FSH), inhibin B, antral follicle count (AFC), and self-reported (first) pregnancy outcomes were evaluated in female childhood HL survivors and controls.Results: 84 HL survivors and 798 controls were included, aged 29.6 and 32.7 years old at time of assessment. Median age at HL diagnosis was 13.4 years. Cyclophosphamide equivalent dose (CED-score) exceeded 6000 mg/m2 in 56 women and 14 survivors received pelvic irradiation.All clinical markers were significantly deteriorated in survivors (odds-ratio for low AMH (< p10) 10.1 [95% CI 4.9; 20.6]; low AFC (< p10) 4.6 [95% CI 2.1; 9.9]; elevated FSH (> 10 IU/l) 15.3 [95% CI 5.7; 41.1], low Inhibin B (< 20 ng/l) 3.6 [95% CI 1.7; 7.7], p < 0.001). Pregnancy outcomes were comparable between survivors and controls (± 80% live birth, ± 20% miscarriage). However, survivors were significantly younger at first pregnancy (27.0 years vs 29.0 years, P = 0.04). Adjusted odds-ratio for time to pregnancy > 12 months was 2.5 [95% CI 1.1; 5.6] in survivors, p = 0.031. Adverse outcomes were specifically present after treatment with procarbazine and higher CED-score.Conclusion: HL survivors appear to have an impaired ovarian reserve. However, chance to achieve pregnancy seems reassuring at a young age. Additional follow-up studies are needed to assess fertile life span and reproductive potential of HL survivors, in particular for current HL treatments that are hypothesized to be less gonadotoxic.</p
Structure and photophysics of indigoids for singlet fission: Cibalackrot
We report an investigation of structure and photophysics of thin layers of cibalackrot, a sturdy dye derived from indigo by double annulation at the central double bond. Evaporated layers contain up to three phases, two crystalline and one amorphous. Relative amounts of all three have been determined by a combination of X-ray diffraction and FT-IR reflectance spectroscopy. Initially, excited singlet state rapidly produces a high yield of a transient intermediate whose spectral properties are compatible with charge-transfer nature. This intermediate more slowly converts to a significant yield of triplet, which, however, does not exceed 100% and may well be produced by intersystem crossing rather than singlet fission. The yields were determined by transient absorption spectroscopy and corrected for effects of partial sample alignment by a simple generally applicable procedure. Formation of excimers was also observed. In order to obtain guidance for improving molecular packing by a minor structural modification, calculations by a simplified frontier orbital method were used to find all local maxima of singlet fission rate as a function of geometry of a molecular pair. The method was tested at 48 maxima by comparison with the ab initio Frenkel-Davydov exciton model. Published under license by AIP Publishing
Panorganismal metabolic response modeling of an experimental Echinostoma caproni infection in the mouse.
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