An exact equation for the free surface of a fluid in a porous medium

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.

Soliton-cuspon interaction for the Camassa-Holm equation

The interaction of different kinds of solitary waves of the Camassa-Holm equation is investigated. We consider soliton-soliton, soliton-cuspon and cuspon-cuspon interactions. The description of these solutions had previously been shown to be reducible to the solution of an algebraic equation. Here we give explicit examples, numerically solving these algebraic equations and plotting the corresponding solutions. Further, we show that the interaction is elastic and leads to a shift in the position of the solitons or cuspons. We give the analytical expressions for this shift and represent graphically the coupled soliton-cuspon, soliton-soliton and cuspon-cuspon interactions.

Short-wave instabilities in the Benjamin-Bona-Mahoney-Peregrine equation: theory and numerics

In this paper we discuss the nonlinear propagation of waves of short wavelength in dispersive systems. We propose a family of equations that is likely to describe the asymptotic behaviour of a large class of systems. We then restrict our attention to the analysis of the simplest nonlinear short-wave dynamics given by U-0 xi tau, = U-0 - 3(U-0)(2). We integrate numerically this equation for periodic and non-periodic boundary conditions, and we find that short waves may exist only if the amplitude of the initial profile is not too large.

Nonlinear Schrodinger equation with power-law confining potential

Critical limits of a stationary nonlinear three-dimensional Schrodinger equation with confining power-law potentials (similar to r(alpha)) are obtained using spherical symmetry. When the nonlinearity is given by an attractive two-body interaction (negative cubic term), it is shown how the maximum number of particles N-c in the trap increases as alpha decreases. With a negative cubic and positive quintic terms we study a first order phase transition, that occurs if the strength g(3) of the quintic term is less than a critical value g(3c). At the phase transition, the behavior of g(3c) with respect to alpha is given by g(3c)similar to 0.0036+0.0251/alpha+0.0088/alpha(2).

Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painleve VI equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.

Z gamma production and limits on anomalous ZZ gamma and Z gamma gamma couplings in pp collisions at root s=1.96 TeV

We present a study of eey and mu mu gamma events using 1109 (1009) pb-(1) of data in the electron (muon) channel, respectively. These data were collected with the DO detector at the Fermilab Tevatron pp collider at Is = 1.96 TeV. Having observed 453 (515) candidates in the eey (jtAy) final state, we measure the Z gamma production cross section for a photon with transverse energy ET > 7 GeV, separation between the photon and leptons Delta Rey > 0.7, and invariant mass of the di-lepton pair Mee > 30 GeV/(2)(c), to be 4.96 0.30(stat. + syst.) zE 0.30(lumi.) pb, in agreement with the Standard Model prediction of 4.74 0.22 pb. This is the most precise Zy cross section measurement at a hadron collider. We set limits on anomalous trilinear Zyy and ZZy gauge boson couplings of -0.085 < h(30)(y) < 0.084, -0.0053 < h(40)(y) < 0.0054 and -0.083 < h(30)(Z) < 0.082, 30 40 30 -0.0053 < h(40)(Z) < 0.0054 at the 95% C.L. for the form-factor scale A = 1.2 TeV. 40 Published by Elsevier B.V.

Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.

Asymptotic soliton train solutions of the defocusing nonlinear Schrodinger equation

Asymptotic behavior of initially large and smooth pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrodinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp v(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

Measurement of the pp(-)-> W gamma plus X cross section at root s=1.96 TeV and WW gamma anomalous coupling limits

The WW gamma triple gauge boson coupling parameters are studied using p (p) over bar -> l nu gamma + X(l = e, mu) events at root s = 1.96 TeV. The data were collected with the D0 detector from an integrated luminosity of 162 pb(-1) delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p (p) over bar -> W(gamma) + X -> l nu gamma + X with E-T(gamma) > 8 GeV and Delta R-l gamma > 0.7 is 14.8 +/- 1.6(stat) +/- 1.0(syst) +/- 1.0(lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa(gamma) < 0.96 and -0.20 < lambda(gamma) < 0.20.

Production of WZ events in pp(-) collisions at root s=1.96 TeV and limits on anomalous WWZ couplings

We present results from a search for WZ production with subsequent decay to l nu l'(l) over bar'(l and l' = e or mu) using 0.30 fb(-1) of data collected by the D0 experiment between 2002 and 2004 at the Fermilab Tevatron. Three events with WZ decay characteristics are observed. With an estimated background of 0.71 +/- 0.08 events, we measure the WZ production cross section to be 4.5(-2.6)(+3.8) pb, with a 95% C.L. upper limit of 13.3 pb. The 95% C.L. limits for anomalous WWZ couplings are found to be -2.0

Study Z gamma events and limits on anomalous ZZ gamma and Z gamma gamma couplings in pp(-) collisions at root s=1.96 Tev

We present a measurement of the Z gamma production cross section and limits on anomalous ZZ gamma and Z gamma gamma couplings for form-factor scales of Lambda=750 and 1000 GeV. The measurement is based on 138 (152) candidates in the ee gamma (mu mu gamma) final state using 320(290) pb(-1) of p (p) over bar collisions at root s=1.96 TeV. The 95% C.L. limits on real and imaginary parts of individual anomalous couplings are vertical bar h(10,30)(Z)vertical bar < 0.23, vertical bar h(20,40)(Z)vertical bar < 0.020, vertical bar h(10,30)(gamma)vertical bar < 0.23, and vertical bar h(20,40)(gamma)vertical bar < 0.019 for Lambda=1000 GeV.

Limits on anomalous couplings from Higgs boson production at the Tevatron

We estimate the attainable limits on the coefficients of dimension-6 operators from the analysis of Higgs boson phenomenology, in the framework of a SUL(2) x U-Y(1) gauge-invariant effective Lagrangian. Our results, based on the data sample already collected by the collaborations at Fermilab Tevatron, show that the coefficients of Higgs-vector boson couplings can be determined with unprecedented accuracy. Assuming that the coefficients of all blind operators are of the same magnitude, we are also able to impose more restrictive bounds on the anomalous vector-boson triple couplings than the present limit from double gauge boson production at the Tevatron collider.

q-Analog of the gap equation for cuprates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Measurement of the WZ -> lvll cross section and limits on anomalous triple gauge couplings in p(p)over-bar collisions at root s=1.96 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)