154 research outputs found

    Effective theories of scattering with an attractive inverse-square potential and the three-body problem

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    A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalisation of the three-body interactions, with the renormalisation-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces.Comment: 19 pages (RevTeX), 2 figure

    Rossby wave dynamics of the North Pacific extra-tropical response to El Niño: importance of the basic state in coupled GCMs

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    The extra-tropical response to El Nino in a "low" horizontal resolution coupled climate model, typical of the Intergovernmental Panel on Climate Change fourth assessment report simulations, is shown to have serious systematic errors. A high resolution configuration of the same model has a much improved response that is similar to observations. The errors in the low resolution model are traced to an incorrect representation of the atmospheric teleconnection mechanism that controls the extra-tropical sea surface temperatures (SSTs) during El Nino. This is due to an unrealistic atmospheric mean state, which changes the propagation characteristics of Rossby waves. These erroneous upper tropospheric circulation anomalies then induce erroneous surface circulation features over the North Pacific. The associated surface wind speed and direction errors create erroneous surface flux and upwelling anomalies which finally lead to the incorrect extra-tropical SST response to El Nino in the low resolution model. This highlights the sensitivity of the climate response to a single link in a chain of complex climatic processes. The correct representation of these processes in the high resolution model indicates the importance of horizontal resolution in resolving such processes
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