599 research outputs found

    New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case

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    We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.Comment: Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comments and few references. (24 pages and 7 figures

    From nonassociativity to solutions of the KP hierarchy

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    A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with A' a matrix algebra, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 200

    Once-daily intrapleural urokinase treatment of complicated parapneumonic effusion in pediatric patients

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    In this paper, we describe our experience in the treatment of childhood empyema using urokinase. Patients' ages ranged from 2 to 12 years. Urokinase (dosage: 3,100 IU/kg/day) was diluted in normal saline to produce 1000 IU/ml (maximum dosage 100,000 IU in 100 ml of normal saline). After 2 hours, the clamped catheters were released and connected to water-seal suction at a negative pressure of 10 cm H2O. Pleural irrigations were continued once a day until thoracostomy tube output decreased to less than 10 ml/day (urokinase treatment mean duration: 11.5 days). The complete resolution of the chest effusion was assessed on chest ultrasound scan and radiographs. None of the patients experienced any side effects due to urokinase. It would now seem reasonable to advocate small chest tube thoracostomy and intrapleural urokinase as first-line treatment of pleural empyema in children, with surgery indicated as a secondaryintervention

    The theory of optical dispersive shock waves in photorefractive media

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    The theory of optical dispersive shocks generated in propagation of light beams through photorefractive media is developed. Full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of sharp step-like initial discontinuity in a beam with one-dimensional strip-like geometry. This approach is confirmed by numerical simulations which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.Comment: 26 page

    Noise-induced perturbations of dispersion-managed solitons

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    We study noise-induced perturbations of dispersion-managed solitons by developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte-Carlo simulations and reconstruct the probability density functions of the solution parameters under the effect of noise.Comment: 12 pages, 6 figure
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