Reduction and approximation in gyrokinetics

The gyrokinetics formulation of plasmas in strong magnetic fields aims at the elimination of the angle associated with the Larmor rotation of charged particles around the magnetic field lines. In a perturbative treatment or as a time-averaging procedure, gyrokinetics is in general an approximation to the true dynamics. Here we discuss the conditions under which gyrokinetics is either an approximation or an exact operation in the framework of reduction of dynamical systems with symmetryComment: 15 pages late

On a Watson-like Uniqueness Theorem and Gevrey Expansions

We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the formal power series solutions of a wide range of systems of ordinary (even non-linear) analytic differential equations are in fact the Gevrey expansions for the regular solutions. Watson's uniqueness theorem belongs to the foundations of this new theory. This paper contains a discussion of an extension of Watson's uniqueness theorem for classes of functions which admit a Gevrey expansion in angular regions of the complex plane with opening less than or equal to (\frac \pi k,) where (k) is the order of the Gevrey expansion. We present conditions which ensure uniqueness and which suggest an extension of Watson's representation theorem. These results may be applied for solutions of certain classes of differential equations to obtain the best accuracy estimate for the deviation of a solution from a finite sum of the corresponding Gevrey expansion.Comment: 18 pages, 4 figure

Criticality without frustration for quantum spin-1 chains

Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s=1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as log(n)/2 + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.Comment: 11 pages, 2 figures. Version 2: minor changes in the proof of Lemma

Fauna coralina de las plataformas mixtas del Paleógeno de las Baleares

Abstract not availabl

Evaluation of two alternative procedures for measuring airflow resistance of sound absorbing materials

[EN] It is well known that sound absorption and sound transmission properties of open porous materials are highly dependent on their airflow resistance values. Low values of airflow resistance indicate little resistance for air streaming through the porous material and high values are a sign that most of the pores inside the material are closed. The laboratory procedures for measuring airflow resistance have been stan- dardized by several organizations, including ISO and ASTM for both alternate flow and continuous flow. However, practical implementation of these standardized methods could be both complex and expensive. In this work, two indirect alternative measurement procedures were compared against the alternate flow standardized technique. The techniques were tested using three families of eco-friendly sound absorbent materials: recycled polyurethane foams, coconut natural fibres, and recycled polyester fibres. It is found that the values of airflow resistance measured using both alternative methods are very similar. There is also a good correlation between the values obtained through alternative and standardized methods.This project has been made possible thanks to the FONDECYT Project 1110605 and the grant GV/2012/066 Projects I+D for emerging research groups. The authors would like to thank Dr. Luis Godinho from the Department of Civil Engineering of University of Coimbra (Portugal) for his help with the experimental work and the ISO data reported in Table 1 of this paper.Rey Tormos, RMD.; Alba Fernández, J.; Arenas, JP.; Ramis Soriano, J. (2013). Evaluation of two alternative procedures for measuring airflow resistance of sound absorbing materials. Archives of Acoustics. 38(4):547-554. https://doi.org/10.2478/aoa:2013-0064S54755438