8,314 research outputs found
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
Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap
A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional
trap can be described with the lowest Landau-level set of states. In this case,
the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 +
y^2, multiplied by an analytic function P(z) of the single complex variable z=
x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar
description is used for a rapidly rotating anisotropic two-dimensional trap
with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate
wave function psi(x,y) has the form of a complex anisotropic Gaussian with a
phase proportional to xy, multiplied by an analytic function P(zeta), where
zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter
that depends on the trap anisotropy and the rotation frequency. The zeros of
P(zeta) again fix the locations of the vortices. Within the set of lowest
Landau-level states at zero temperature, an anisotropic parabolic density
profile provides an absolute minimum for the energy, with the vortex density
decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur
Darboux transformation and multi-soliton solutions of Two-Boson hierarchy
We study Darboux transformations for the two boson (TB) hierarchy both in the
scalar as well as in the matrix descriptions of the linear equation. While
Darboux transformations have been extensively studied for integrable models
based on within the AKNS framework, this model is based on
. The connection between the scalar and the matrix
descriptions in this case implies that the generic Darboux matrix for the TB
hierarchy has a different structure from that in the models based on
studied thus far. The conventional Darboux transformation is shown to be quite
restricted in this model. We construct a modified Darboux transformation which
has a much richer structure and which also allows for multi-soliton solutions
to be written in terms of Wronskians. Using the modified Darboux
transformations, we explicitly construct one soliton/kink solutions for the
model.Comment:
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
Families of stable and metastable solitons in coupled system of scalar fields
In this paper, we obtain stable and metastable soliton solutions of a coupled
system of two real scalar fields with five five discrete points of vacua. These
solutions have definite topological charges and rest energies and show
classical dynamical stability. From a quantum point of view, however, the
V-type solutions are expected to be unstable and decay to D-type solutions. The
induced decay of a V-type soliton into two D-type ones is calculated
numerically, and shown to be chiral, in the sense that the decay products do
not respect left-right symmetry.Comment: 9 pages and 5 figure
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
A cadaver study comparing spread of dye and nerve involvement after three different quadratus lumborum blocks
Poincare' normal forms and simple compact Lie groups
We classify the possible behaviour of Poincar\'e-Dulac normal forms for
dynamical systems in 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 SUSY Yang-Mills/ 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 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
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