1,803 research outputs found
Convergent Analytic Solutions for Homoclinic Orbits in Reversible and Non-reversible Systems
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
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
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
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.
Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
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
Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations
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 -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
Pattern formation driven by cross--diffusion in a 2D domain
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
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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