Vector Area Theorem mapping in crystals and polarization stability of SIT-solitons

The stability of polarization, areas, and number of self-induced transparency (SIT)-solitons at the output from the LaF_3:Pr^{3+} crystal is theoretically studied versus the polarization direction and the area of the input linearly polarized laser pulse. For this purpose the Vector Area Theorem is rederived and two-dimensional Vector Area Theorem map is obtained. The map is governed by the crystal symmetry and takes into account directions of the dipole matrix element vectors of the different site subgroups of optically excited ions. The Vector Area Theorem mapping of the time evolution of the laser pulse allows one to highlight soliton polarization properties.Comment: 3 pages, 3 figures; v2: minor corrected labels in Fig. 3 and its cuptur

Validity of a pictorial perceived exertion scale for effort estimation and effort production during stepping exercise in adolescent children

This is the author's PDF version of an article published in European Physical Education Review ©2002. The definitive version is available at http://epe.sagepub.com.Recent developments in the study of paediatric effort perception have continued to emphasise the importance of child-specific rating scales. The purpose of this study was to examine the validity of an illustrated 1 – 10 perceived exertion scale; the Pictorial Children’s Effort Rating Table (PCERT). 4 class groups comprising 104 children; 27 boys and 29 girls, aged 12.1±0.3 years and 26 boys, 22 girls, aged 15.3±0.2 years were selected from two schools and participated in the initial development of the PCERT. Subsequently, 48 of these children, 12 boys and 12 girls from each age group were randomly selected to participate in the PCERT validation study. Exercise trials were divided into 2 phases and took place 7 to 10 days apart. During phase 1, children completed 5 x 3-minute incremental stepping exercise bouts interspersed with 2-minute recovery periods. Heart rate (HR) and ratings of exertion were recorded during the final 15 s of each exercise bout. In phase 2 the children were asked to regulate their exercising effort during 4 x 4-minute bouts of stepping so that it matched randomly prescribed PCERT levels (3, 5, 7 and 9). Analysis of data from Phase 1 yielded significant (P<0.01) relationships between perceived and objective (HR) effort measures for girls. In addition, the main effects of exercise intensity on perceived exertion and HR were significant (P<0.01); perceived exertion increased as exercise intensity increased and this was reflected in simultaneous significant rises in HR. During phase 2, HR and estimated power output (POapprox) produced at each of the four prescribed effort levels were significantly different (P<0.01). The children in this study were able to discriminate between 4 different exercise intensities and regulate their exercise intensity according to 4 prescribed levels of perceived exertion. In seeking to contribute towards children’s recommended physical activity levels and helping them understand how to self-regulate their activity, the application of the PCERT within the context of physical education is a desirable direction for future research

Boundary Conditions in Stepwise Sine-Gordon Equation and Multi-Soliton Solutions

We study the stepwise sine-Gordon equation, in which the system parameter is different for positive and negative values of the scalar field. By applying appropriate boundary conditions, we derive relations between the soliton velocities before and after collisions. We investigate the possibility of formation of heavy soliton pairs from light ones and vise versa. The concept of soliton gun is introduced for the first time; a light pair is produced moving with high velocity, after the annihilation of a bound, heavy pair. We also apply boundary conditions to static, periodic and quasi-periodic solutions.Comment: 14 pages, 8 figure

Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio

On the Singularities of the Magnon S-matrix

We investigate the analytic structure of the magnon S-matrix in the spin-chain description of planar ${\cal N}=4$ SUSY Yang-Mills/$AdS_{5}\times S^{5}$ strings. Semiclassical analysis suggests that the exact S-matrix must have a large family of poles near the real axis in momentum space. In this article we show that these are double poles corresponding to the exchange of pairs of BPS magnons. Their locations in the complex plane are uniquely fixed by the known dispersion relation for the BPS particles. The locations precisely agree with the recent conjecture for the $S$ matrix by Beisert, Hernandez, Lopez, Eden and Staudacher (hep-th/0609044 and hep-th/0610251). These poles do not signal the presence of new bound states. In fact, a certain non-BPS localized classical solution, which was thought to give rise to new bound states, can actually decay into a pair of BPS magnons.Comment: 40 pages, 14 figures; typos corrected, references adde

Massive particles in acoustic space-times emergent inertia and passive gravity

I show that massive-particle dynamics can be simulated by a weak, spherical, external perturbation on a potential flow in an ideal fluid. The effective Lagrangian is of the form mc^2L(U^2/c^2), where U is the velocity of the particle relative to the fluid and c the speed of sound. This can serve as a model for emergent relativistic inertia a la Mach's principle with m playing the role of inertial mass, and also of analog gravity where it is also the passive gravitational mass. m depends on the particle type and intrinsic structure, while L is universal: For D dimensional particles L is proportional to the hypergeometric function F(1,1/2;D/2;U^2/c^2). Particles fall in the same way in the analog gravitational field independent of their internal structure, thus satisfying the weak equivalence principle. For D less or equal 5 they all have a relativistic limit with the acquired energy and momentum diverging as U approaches c. For D less or equal 7 the null geodesics of the standard acoustic metric solve our equation of motion. Interestingly, for D=4 the dynamics is very nearly Lorentzian. The particles can be said to follow the geodesics of a generalized acoustic metric of a Finslerian type that shares the null geodesics with the standard acoustic metric. In vortex geometries, the ergosphere is automatically the static limit. As in the real world, in ``black hole'' geometries circular orbits do not exist below a certain radius that occurs outside the horizon. There is a natural definition of antiparticles; and I describe a mock particle vacuum in whose context one can discuss, e.g., particle Hawking radiation near event horizons.Comment: 15 page: version published in Physical Review

Draft genome sequences of gammaproteobacterial methanotrophs isolated from lake washington sediment.

The genomes of Methylosarcina lacus LW14(T) (=ATCC BAA-1047(T) = JCM 13284(T)), Methylobacter sp. strain 21/22, Methylobacter sp. strain 31/32, Methylomonas sp. strain LW13, Methylomonas sp. strain MK1, and Methylomonas sp. strain 11b were sequenced and are reported here. All the strains are obligately methanotrophic bacteria isolated from the sediment of Lake Washington

Spatiotemporally Localized Multidimensional Solitons in Self-Induced Transparency Media

"Light bullets" are multi-dimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced-transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multi-dimensional generalization of the one-dimensional Sine-Gordon soliton.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let