1,780 research outputs found

    Convergent Analytic Solutions for Homoclinic Orbits in Reversible and Non-reversible Systems

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    In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many important nonlinear PDEs or PDE systems, for which these analytical solutions would correspond to regular or localized pulses of the PDE. As such, the homoclinic solutions derived here are clearly topical, and they are shown to match closely to earlier results obtained by homoclinic numerical shooting. In addition, the results for the non-reversible case go beyond those that have been typically considered in analyses conducted within bifurcation-theoretic settings. We also comment on generalizing the treatment here to parameter regimes where solutions homoclinic to exponentially small periodic orbits are known to exist, as well as another possible extension placing the solutions derived here within the framework of a comprehensive categorization of ALL possible traveling-wave solutions, both smooth and non-smooth, for our governing ODE.Comment: arXiv admin note: text overlap with arXiv:math-ph/060606

    B -> X_s gamma in supersymmetry: large contributions beyond the leading order

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    We discuss possible large contributions to B -> X_s gamma, which can occur at the next-to-leading order in supersymmetric models. They can originate from terms enhanced by tan(beta) factors, when the ratio between the two Higgs vacuum expectation values is large, or by logarithm of M_{susy}/M_W, when the supersymmetric particles are considerably heavier than the W boson. We give compact formulae which include all potentially large higher-order contributions. We find that tan(beta) terms at the next-to-leading order do not only appear from the Hall-Rattazzi-Sarid effect (the modified relation between the bottom mass and Yukawa coupling), but also from an analogous effect in the top-quark Yukawa coupling. Finally, we show how next-to-leading order corrections, in the large tan(beta) region, can significantly reduce the limit on the charged-Higgs mass, even if supersymmetric particles are very heavy.Comment: 18 pages, 5 figs, extended discussion of light stop case, notational improvement

    The Top Priority: Precision Electroweak Physics from Low to High Energy

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    Overall, the Standard Model describes electroweak precision data rather well. There are however a few areas of tension (charged current universality, NuTeV, (g-2)_\mu, b quark asymmetries), which I review emphasizing recent theoretical and experimental progress. I also discuss what precision data tell us about the Higgs boson and new physics scenarios. In this context, the role of a precise measurement of the top mass is crucial.Comment: 12 pages; invited talk at 21st International Symposium on Lepton and Photon Interactions at High Energies (LP 03), Batavia, Illinois, 11-16 Aug 200

    QCD Corrections to Radiative B Decays in the MSSM with Minimal Flavor Violation

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    We compute the complete supersymmetric QCD corrections to the Wilson coefficients of the magnetic and chromomagnetic operators, relevant in the calculation of b -> s gamma decays, in the MSSM with Minimal Flavor Violation. We investigate the numerical impact of the new results for different choices of the MSSM parameters and of the scale where the quark and squark mass matrices are assumed to be aligned. We find that the corrections can be important when the superpartners are relatively light, and that they depend sizeably on the scale of alignment. Finally, we discuss how our calculation can be employed when the scale of alignment is far from the weak scale.Comment: 16 pages, 5 figures; v2: version to appear in Phys. Lett.

    Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations

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    In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon and cuspon solutions. One of the considered GCH equations supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. The second equation does not support singular traveling waves and the last one supports four-segmented, non-smooth MM-wave solutions. Moreover, smooth traveling waves of the three GCH equations are considered. Here, we use a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of their traveling-wave equations, corresponding to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding GCH equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. We also show the traveling wave nature of these pulse and front solutions to the GCH NLPDEs

    Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion

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    In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; %favors the mechanism of pattern formation with respect to the classical linear diffusion case; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we compute the complex Ginzburg-Landau equation in the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal modulation of the phase and amplitude of the homogeneous oscillatory solution.Comment: Accepted for publication in Acta Applicandae Mathematica

    Pattern formation driven by cross--diffusion in a 2D domain

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    In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, hexagonal patterns

    Indication for Light Sneutrinos and Gauginos from Precision Electroweak Data

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    The present Standard Model fit of precision data has a low confidence level, and is characterized by a few inconsistencies. We look for supersymmetric effects that could improve the agreement among the electroweak precision measurements and with the direct lower bound on the Higgs mass. We find that this is the case particularly if the 3.6 sigma discrepancy between sin^2 theta_eff from leptonic and hadronic asymmetries is finally settled more on the side of the leptonic ones. After the inclusion of all experimental constraints, our analysis selects light sneutrinos, with masses in the range 55-80 GeV, and charged sleptons with masses just above their experimental limit, possibly with additional effects from light gauginos. The phenomenological implications of this scenario are discussed.Comment: 17 pages LaTex, 9 figures, uses epsfi
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