Search

The transformation introduced by Giusti-Suzor and Fano and extended by Lecomte and Ueda for the study of resonance structures in the multichannel quantum defect theory (MQDT) is used to reformulate MQDT into the forms having one-to-one correspondence with those in Fano's configuration mixing (CM) theory of resonance for the photofragmentation processes involving one closed and many open channels. The reformulation thus allows MQDT to have the full power of the CM theory, still keeping its own strengths such as the fundamental description of resonance phenomena without an assumption of the presence of a discrete state as in CM., Comment: 7 pages

Eigenphase shifts and eigentime delays near a resonance for a system of one discrete state and two continua are shown to be functionals of the Beutler- Fano formulas using appropriate dimensionless energy units and line profile indices. Parameters responsible for the avoided crossing of eigenphase shifts and eigentime delays are identified. Similarly, parameters responsible for the eigentime delays due to a frame change are identified. With the help of new parameters, an analogy with the spin model is pursued for the S matrix and time delay matrix. The time delay matrix is shown to comprise three terms, one due to resonance, one due to a avoided crossing interaction, and one due to a frame change. It is found that the squared sum of time delays due to the avoided crossing interaction and frame change is unity., Comment: 17 pages, 3 figures, RevTeX

Recently, we showed that eigenphase shifts and eigentime delays near a resonance for a system of one discrete state and two continua are functionals of the Beutler-Fano formula using appropriate dimensionless energy units and line profile indices and identified parameters responsible for the avoided crossing of eigenphase shifts and eigentime delays and also identified parameters responsible for the eigentime delays due to a change in frame transformation. In this paper, the geometrical realization of the Beutler-Fano formulas is considered in the three-dimensional Liouville space spanned by the Pauli matrices, where dynamic operators are vectors. Vectors corresponding to the background scattering matrix, the S matrix, and the time delay matrix Q form a spherical triangle whose vertex and edge angles are parameters pertaining to the frame transformations among eigenchannels of those matrices and eigenphase shifts of the scattering matrices and the phase shift due to a resonance scattering. The cotangent laws of the spherical triangle yield Beutler-Fano resonance formulas appearing in eigenphase shifts and time delays. Duality holding for the spherical triangle explains the symmetry observed in the relations among parameters and provides a systematic way of defining conjugate dynamic parameters. The spherical triangle also shows the rule of combining the channel-channel couplings in the background scattering with the resonant interaction to give the avoided crossing interactions in the curves of eigenphase shifts as functions of eneryg. The theory developed in the previous and present papers is applied to the vibrational predissociation of triatomic van der Waals molecules., Comment: 26 pages, 7 figures, RevTeX, will be submitted to Phys. Rev. A, Major conceptual changes

Often, late-year, flood-producing storms in the Mediterranean Alps region arise from baroclinic disturbances developing on westerly longwaves, with the incipient storm circulations appearing well west of the flood zone. Regardless of the genesis locations and before the storms begin their flow interactions with the orography of the Mediterranean Alps, a process which can produce intense long-lived rainfall over the mountainous terrain of Italy and France, most of their moisture is drawn from warm Mediterranean waters while important elements of their thermodynamic structure are derived from airmass properties originating in north Africa and the Mediterranean basin itself. In fact, because of strong thermodynamic contrasts between the baroclinic zone producing the incipient disturbance and high potential temperature air from the south advecting into and wrapping around the storm center, a Mediterranean storm whose origins are from an evolving shortwave baroclinic perturbation, can become a quasi-warm core hybrid in term of its energetics composition, a process somewhat akin to the development of polar lows. This process begs the question of whether there are similarities between the autumn-winter season flood producing storms of the Mediterranean Alps and warm core tropical cyclones which become altered dynamically and thermodynamically by landfall over steep orographic terrain. This study investigates, from a comparison and contrast perspective, how the similarities and differences between the two types of storms manifest themselves over their respective life cycles. Before the orographically-induced precipitation-release stage in which both types of storm have evolved to the same hydrometeorlogical conclusion, the two storm categories are transforming from entirely distinctive origins, i.e., the classic eastward traveling, baroclinic mid-latitude cyclone forming in western Europe, and the classic eastward-traveling, warm core tropical cyclone developing in the western Pacific. The analyses use high resolution, nonhydrostatic model simulations, satellite data, and various types of ground data to conduct the study. The flood events of Piemonte- 2000 in northern Italy and Typhoon Rusa-2002 in South Korea are selected to focus the analysis on well documented meteorological events.