Scaling and non-scaling of muscle activity, kinematics, and dynamics in sit-ups with different degrees of difficulty

The purpose of this study was to investigate how the CNS adjusts motor patterns for variants of a complex axial movement-the situp. Adjustments were induced by changing the support surface contact and mass distribution of the body. Healthy adults performed straight-legged sit-ups, 3 s in duration, with support added to or removed from the lumbar trunk, or with mass added to the head or to the legs. Each of these interventions either increased or decreased the difficulty of the task. The study addressed the extent to which changes in sit-up difficulty are compensated by scaling of muscle activity, kinematics, and dynamics versus the extent to which they are compensated by changing discretely the motor pattern. The analysis of muscle activity, kinematics, and dynamics focused on the first 30-40% of the sit-up-the trunk flexion phase-since this is the most critical part of the movement. Our results demonstrate that, in some respects, sit-up kinematics and dynamics scaled with difficulty, but in other respects, they did not. Muscle activity also scaled, in many respects, but in more difficult sit-ups, abdominal flexor activity decreased instead of increased. Non-scaling changes in these parameters suggest that complex movements, such as the sit-up, may require discrete changes in motor pattern in order to deal with large loads, which challenge the available leverage. (C) 2005 Elsevier Ltd. All rights reserved.

Shift, scaling and derivative properties for the discrete cosine transform

A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse discrete transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.

Quantum dynamics of three coupled atomic Bose-Einstein condensates

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.

Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants

We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular lattices, using high-temperature series expansions. We consider a model with two exchange constants J1 and J2 on a lattice that interpolates between the limits of a square lattice (J1=0), a triangular lattice (J2=J1), and decoupled linear chains (J2=0). In all cases, the susceptibility, which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature Tp. Scaling the exchange constants to get the same peak temperature shows that the susceptibilities for the square lattice and linear chain limits have similar magnitudes near the peak. Maximum deviation arises near the triangular-lattice limit, where frustration leads to much smaller susceptibility and with a flatter temperature dependence. We compare our results to the inorganic materials Cs2CuCl4 and Cs2CuBr4 and to a number of organic molecular crystals. We find that the former (Cs2CuCl4 and Cs2CuBr4) are weakly frustrated and their exchange parameters determined through the temperature dependence of the susceptibility are in agreement with neutron-scattering measurements. In contrast, the organic materials considered are strongly frustrated with exchange parameters near the isotropic triangular-lattice limit.

Substructure and Dynamics of the Fornax Cluster

We present the first dynamical analysis of a galaxy cluster to include a large fraction of dwarf galaxies. Our sample of 108 Fornax Cluster members measured with the UK Schmidt Telescope FLAIR-II spectrograph contains 55 dwarf galaxies (15.5 > b(j) > 18.0 or -16 > M-B > -13.5). H alpha emission shows that of the dwarfs are star forming, twice the fraction implied by morphological classifications. The total sample has a mean velocity of 1493 +/- 36 kms s(-1) and a velocity dispersion of 374 +/- 26 km s(-1). The dwarf galaxies form a distinct population: their velocity dispersion (429 +/- 41 km s(-1)) is larger than that of the giants () at the 98% confidence level. This suggests that the dwarf population is dominated by infalling objects whereas the giants are virialized. The Fornax system has two components, the main Fornax Cluster centered on NGC 1399 with cz = 1478 km s(-1) and sigma (cz) = 370 km s(-1) and a subcluster centered 3 degrees to the southwest including NGC 1316 with cz = 1583 km s(-1) and sigma (cz) = 377 km s(-1). This partition is preferred over a single cluster at the 99% confidence level. The subcluster, a site of intense star formation, is bound to Fornax and probably infalling toward the cluster core for the first time. We discuss the implications of this substructure for distance estimates of the Fornax Cluster. We determine the cluster mass profile using the method of Diaferio, which does not assume a virialized sample. The mass within a projected radius of 1.4 Mpc is (7 +/- 2) x 10(13) M-., and the mass-to-light ratio is 300 +/- 100 M-./L-.. The mass is consistent with values derived from the projected mass virial estimator and X-ray measurements at smaller radii.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

A power system control scheme based on security visualisation in parameter space

Power system real time security assessment is one of the fundamental modules of the electricity markets. Typically, when a contingency occurs, it is required that security assessment and enhancement module shall be ready for action within about 20 minutes’ time to meet the real time requirement. The recent California black out again highlighted the importance of system security. This paper proposed an approach for power system security assessment and enhancement based on the information provided from the pre-defined system parameter space. The proposed scheme opens up an efficient way for real time security assessment and enhancement in a competitive electricity market for single contingency case

Comparison of BR and QR Eigenvalue Algorithms for Power System Small Signal Stability Analysis

The BR algorithm is a novel and efficient method to find all eigenvalues of upper Hessenberg matrices and has never been applied to eigenanalysis for power system small signal stability. This paper analyzes differences between the BR and the QR algorithms with performance comparison in terms of CPU time based on stopping criteria and storage requirement. The BR algorithm utilizes accelerating strategies to improve its performance when computing eigenvalues of narrowly banded, nearly tridiagonal upper Hessenberg matrices. These strategies significantly reduce the computation time at a reasonable level of precision. Compared with the QR algorithm, the BR algorithm requires fewer iteration steps and less storage space without depriving of appropriate precision in solving eigenvalue problems of large-scale power systems. Numerical examples demonstrate the efficiency of the BR algorithm in pursuing eigenanalysis tasks of 39-, 68-, 115-, 300-, and 600-bus systems. Experiment results suggest that the BR algorithm is a more efficient algorithm for large-scale power system small signal stability eigenanalysis.

Dynamic Similarity and Scale Effects Affecting Air Bubble Entrainment in Hydraulic Jumps

In an open channel, the transition from super- to sub-critical flow is a flow singularity (the hydraulic jump) characterised by a sharp rise in free-surface elevation, strong turbulence and air entrainment in the roller. A key feature of the hydraulic jump flow is the strong free-surface aeration and air-water flow turbulence. In the present study, similar experiments were conducted with identical inflow Froude numbers Fr1 using a geometric scaling ratio of 2:1. The results of the Froude-similar experiments showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding some lesser aeration of the jump roller. The dimensionless bubble count rates were significantly lower in the smaller channel, especially in the mixing layer. The bubble chord time distributions were quantitatively close in both channels, and they were not scaled according to a Froude similitude. Simply the hydraulic jump remains a fascinating two-phase flow motion that is still poorly understood.