Conservation laws in Skyrme-type models

The zero curvature representation of Zakharov and Shabat has been generalized recently to higher dimensions and has been used to construct non-linear field theories which either are integrable or contain integrable submodels. The Skyrme model, for instance, contains an integrable subsector with infinitely many conserved currents, and the simplest Skyrmion with baryon number one belongs to this subsector. Here we use a related method, based on the geometry of target space, to construct a whole class of theories which are either integrable or contain integrable subsectors (where integrability means the existence of infinitely many conservation laws). These models have three-dimensional target space, like the Skyrme model, and their infinitely many conserved currents turn out to be Noether currents of the volume-preserving diffeomorphisms on target space. Specifically for the Skyrme model, we find both a weak and a strong integrability condition, where the conserved currents form a subset of the algebra of volume-preserving diffeomorphisms in both cases, but this subset is a subalgebra only for the weak integrable submodel.Comment: Latex file, 22 pages. Two (insignificant) errors in Eqs. 104-106 correcte

Investigation of the Nicole model

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP^1 Lagrangian density to the non-integer power 3/2 - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behaviour to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.Comment: Latex, 35 pages, 1 figur

Aroma composition of commercial truffle flavoured oils: does it really smell like truffle?

The present study analyzes the aromatic and odour volatile profiles of truffle flavoured oils commercialized as “black truffle oil”. The aim of this work is twofold: to define the sensory space associated to these products and to explore the possible fraudulent use of artificial flavouring agents not properly identified on the label. For this purpose, 12 commercial truffle flavoured oils available in the Spanish market were submitted to descriptive sensory analysis by a trained panel. The three oils presenting the most interesting profile (in terms of odour nature and/or complexity) were also analyzed by olfactometric analysis, in order to identify the chemical compounds responsible on their aroma. The correlation of sensory and olfactometric data made it possible to understand some of the sensory differences observed among samples, as well as to identify irregularities with respect to the ingredients labelling of some of the studied samples

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.Comment: 23 page

An operator expansion for the elastic limit

A leading twist expansion in terms of bi-local operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other processes. Operators of increasing dimensions contribute to logarithmically enhanced terms which are supressed by corresponding powers of $1-x$. For the longitudinal structure function, in moment ($N$) space, all the logarithmic contributions of order $\ln^k N/N$ are shown to be resummable in terms of the anomalous dimension of the leading operator in the expansion.Comment: 9 pages, 1 figure, uses REVTEX 3.1 and axodra

Non-perturbative quenched propagator beyond the infrared approximation

A new approach to the quenched propagator in QED beyond the IR limit is proposed. The method is based on evolution equations in the proper time.Comment: 13 pages, 1 figure; Misprint on reference correcte

Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.Comment: 64 pages, 8 figure

A clinically oriented computer model for radiofrequency ablation of hepatic tissue with internally cooled wet electrode

Purpose: To improve the computer modelling of radiofrequency ablation (RFA) by internally cooled wet (ICW) electrodes with added clinically oriented features. Methods: An improved RFA computer model by ICW electrode included: (1) a realistic spatial distribution of the infused saline, and (2) different domains to distinguish between healthy tissue, saline-infused tumour, and non-infused tumour, under the assumption that infused saline is retained within the tumour boundary. A realistic saline spatial distribution was obtained from an in vivo pig liver study. The computer results were analysed in terms of impedance evolution and coagulation zone (CZ) size, and were compared to the results of clinical trials conducted on 17 patients with the same ICW electrode. Results: The new features added to the model provided computer results that matched well with the clinical results. No roll-offs occurred during the 4-min ablation. CZ transversal diameter (4.10 ± 0.19 cm) was similar to the computed diameter (4.16 cm). Including the tumour and saline infusion in the model involved (1) a reduction of the initial impedance by 10 − 20 Ω, (2) a delay in roll-off of 20 s and 70 − 100 s, respectively, and (3) 18 − 31% and 22 − 36% larger CZ size, respectively. The saline spatial distribution geometry was also seen to affect roll-off delay and CZ size. Conclusions: Using a three-compartment model and a realistic saline spatial distribution notably improves the match with the outcome of the clinical trials