Notes on implementation of Coulomb friction in coupled dynamical simulations

A coupled dynamical system is defined as an assembly of rigid/flexible bodies that may be coupled by kinematic connections. The interfaces between bodies are modeled using hinges having 0 to 6 degrees of freedom. The equations of motion are presented for a mechanical system of n flexible bodies in a topological tree configuration. The Lagrange form of the D'Alembert principle was employed to derive the equations. The equations of motion are augmented by the kinematic constraint equations. This augmentation is accomplished via the method of singular value decomposition

Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) = \zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal Societ

Effects of age on strength and morphology of toe flexor muscles

Study Design: Cross-sectional. 27 Objective: To compare the strength and size of the toe flexor muscles of older adults relative 28 to their younger counterparts. 29 Background: Age related muscle atrophy is common in lower limb muscles and we therefore 30 speculated that foot muscles also diminish with age. However, there is a paucity of literature 31 characterizing foot muscle strength and morphology, and any relationship between these two, 32 in older people. 33 Methods: Seventeen young adults with a normal foot type were matched by gender and BMI 34 to 17 older adults with a normal foot type, from an available sample of 41 young (18-50 35 years) and 44 older (60+ years) adults. Among the matched groups (n=34), muscle thickness 36 and cross-sectional area (CSA) for five intrinsic and two extrinsic toe flexor muscles were 37 obtained using ultrasound. Toe strength was assessed using a pressure platform. Differences 38 in toe flexor strength and muscle size between the young and older matched groups were 39 determined using ANCOVA (controlling for height). Correlations between strength and size 40 of the toe flexor muscles of the pooled group (n=34) were also calculated. 41 Results: Toe strength and the thickness and CSA of most foot muscles and were significantly 42 reduced in the older adults (P<0.05). Hallux and toe flexor strength were strongly correlated 43 with the size of the intrinsic muscles toe flexor muscles. 44 Conclusion: The smaller foot muscles appear to be affected by sarcopenia in older adults. 45 This could contribute to reduced toe flexion force production and affect the ability of older 46 people to walk safely. Interventions aimed at reversing foot muscle atrophy in older people 47 require further investigation

Biases in Cometary Catalogues and Planet X

Two sets of investigators -- Murray (1999) and Matese, Whitman & Whitmire (1999) -- have recently claimed evidence for an undiscovered Solar System planet from possible great circle alignments in the aphelia directions of the long period comets. However, comet discoveries are bedevilled by selection effects. These include anomalies caused by the excess of observers in the northern as against the southern hemisphere, seasonal and diurnal biases, directional effects which make it harder to discover comets in certain regions of the sky, as well as sociological biases. The stream proposed by Murray is shown on an equal area Hammer-Aitoff projection. The addition of newer data weakens the case for the alignment. There is also evidence that the subsample in the stream is affected by seasonal and north-south biases. The stream proposed by Matese et al. is most obvious in the sample of dynamically new comets, and especially in those whose orbits are best known. The most recent data continues to maintain the overpopulation in this great circle. This pattern in the data occurs about once in a thousand times by chance. Numerical integrations are used to demonstrate that a planet by itself can reduce the perihelia of comets in its orbital plane to sufficiently small values so that they could be discovered from the Earth. There is a need for a sample of long period comets that is free from unknown or hard-to-model selection effects. Such will be provided by the European Space Agency satellite GAIA.Comment: 16 pages, 14 figures, MNRAS in pres

Characterising the Gravitational Instability in Cooling Accretion Discs

We perform numerical analyses of the structure induced by gravitational instabilities in cooling gaseous accretion discs. For low enough cooling rates a quasi-steady configuration is reached, with the instability saturating at a finite amplitude in a marginally stable disc. We find that the saturation amplitude scales with the inverse square root of the cooling parameter beta = t_cool / t_dyn, which indicates that the heating rate induced by the instability is proportional to the energy density of the induced density waves. We find that at saturation the energy dissipated per dynamical time by weak shocks due is of the order of 20 per cent of the wave energy. From Fourier analysis of the disc structure we find that while the azimuthal wavenumber is roughly constant with radius, the mean radial wavenumber increases with radius, with the dominant mode corresponding to the locally most unstable wavelength. We demonstrate that the density waves excited in relatively low mass discs are always close to co-rotation, deviating from it by approximately 10 per cent. This can be understood in terms of the flow Doppler-shifted phase Mach number -- the pattern speed self-adjusts so that the flow into spiral arms is always sonic. This has profound effects on the degree to which transport through self-gravity can be modelled as a viscous process. Our results thus provide (a) a detailed description of how the self-regulation mechanism is established for low cooling rates, (b) a clarification of the conditions required for describing the transport induced by self-gravity through an effective viscosity, (c) an estimate of the maximum amplitude of the density perturbation before fragmentation occurs, and (d) a simple recipe to estimate the density perturbation in different thermal regimes.Comment: 16 pages, 22 figures. Accepted for publication in MNRAS 11 November 200

Human sarcopenia reveals an increase in SOCS-3 and myostatin and a reduced efficiency of Akt phosphorylation

Age-related skeletal muscle sarcopenia is linked with increases in falls, fractures, and death and therefore has important socioeconomic consequences. The molecular mechanisms controlling age-related muscle loss in humans are not well understood, but are likely to involve multiple signaling pathways. This study investigated the regulation of several genes and proteins involved in the activation of key signaling pathways promoting muscle hypertrophy, including GH/STAT5, IGF-1/Akt/GSK-3&beta;/4E-BP1, and muscle atrophy, including TNF&alpha;/SOCS-3 and Akt/FKHR/atrogene, in muscle biopsies from 13 young (20 &plusmn; 0.2 years) and 16 older (70 &plusmn; 0.3 years) males. In the older males compared to the young subjects, muscle fiber cross-sectional area was reduced by 40&ndash;45% in the type II muscle fibers. TNF&alpha; and SOCS-3 were increased by 2.8 and 1.5 fold, respectively. Growth hormone receptor protein (GHR) and IGF-1 mRNA were decreased by 45%. Total Akt, but not phosphorylated Akt, was increased by 2.5 fold, which corresponded to a 30% reduction in the efficiency of Akt phosphorylation in the older subjects. Phosphorylated and total GSK-3&beta; were increased by 1.5 and 1.8 fold, respectively, while 4E-BP1 levels were not changed. Nuclear FKHR and FKHRL1 were decreased by 73 and 50%, respectively, with no changes in their atrophy target genes, atrogin-1 and MuRF1. Myostatin mRNA and protein levels were significantly elevated by 2 and 1.4 fold. Human sarcopenia may be linked to a reduction in the activity or sensitivity of anabolic signaling proteins such as GHR, IGF-1, and Akt. TNF&alpha;, SOCS-3, and myostatin are potential candidates influencing this anabolic perturbation.<br /