Holonomic constraints : an analytical result

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows to compute the forces induced by the constraints and therefore, to integrate the equations of motions of the system. Computing analytically the Lagrange multipliers for a constrained system may be a difficult task that is depending on the complexity of systems. For complex systems, it is most of the time impossible to achieve. In computer simulations, some algorithms using iterative procedures estimate numerically Lagrange multipliers or constraint forces by correcting the unconstrained trajectory. In this work, we provide an analytical computation of the Lagrange multipliers for a set of linear holonomic constraints with an arbitrary number of bonds of constant length. In the appendix of the paper, one would find explicit formulas for Lagrange multipliers for systems having 1, 2, 3, 4 and 5 bonds of constant length, linearly connected.Comment: 13 pages, no figures. To appear in J. Phys. A : Math. The

Yukawa potentials in systems with partial periodic boundary conditions II : Lekner sums for quasi-two dimensional systems

Yukawa potentials may be long ranged when the Debye screening length is large. In computer simulations, such long ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we have provided Ewald sums for quasi-two dimensional systems with Yukawa interaction potentials [M. Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007) and M. Mazars, {\it Mol. Phys.}, Paper I]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two dimensional systems with Yukawa interaction potentials and we give some numerical tests for pratical implementations. The main result of this paper is to outline that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work : Lekner sums should not be used for quasi-two dimensional systems with Yukawa interaction potentials.Comment: 25 pages, 5 figures and 1 tabl

Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system

We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.Comment: AMS-LaTeX, 21 page

Pygomelia with genitalia duplication at Treichville Teaching Hospital: two new cases

Pygomelia is a rare deformity (1/100 000) defined by the presence of one or more supernumerary members in the pelvic region. In this article, we report two new cases, including one that was successfully operated upon in our unit. The first case was characterized by the presence of two additional lower limbs postioned in the hypogastric region and a third vestigial epigastric upper limb associated with visceral deformations. Surgical treatment was successfully accomplished. The clinical examination of the second case objectified the third lower limb at the level of the left buttock with a rudimentary pelvis, a sacrococcygeal teratoma, and a genital duplication. The newborn child died during the investigations. The nosological limits of pygomelia are still poorly specified because it is similar to cases of duplication of the lower limbs and dipygus.Keywords: caudal duplication, dipygus, pygomeli

Macroalgae removal on coral reefs: realised ecosystem functions transcend biogeographic locations

Coral reef ecosystems are at the forefront of biodiversity loss and climate change-mediated transformations. This is expected to have profound consequences for the functioning of these ecosystems. However, assessments of ecosystem function on reefs are often spatially limited, within biogeographic realms, or rely on presumed proxies such as traits. To address these shortcomings and assess the effects of biogeography and fish presence on the critical ecosystem function of macroalgal removal, we used assays of six algal genera across three reef habitats in two biogeographically distinct locations: Little Cayman in the Caribbean and Lizard Island on the Great Barrier Reef (GBR). Patterns of fish feeding and realised ecosystem function were strikingly similar between the two geographic locations, despite a threefold difference in the local diversity of nominally herbivorous fishes, a 2.4-fold difference in the diversity of fishes feeding and differences in the biogeographic history of the two locations. In both regions, a single species dominated the function: a surgeonfish, Naso unicornis, at the GBR location and, surprisingly, a triggerfish, Melichthys niger, at the Caribbean location. Both species, especially M. niger, were relatively rare, compared to other nominally herbivorous fishes, in censuses covering more than 14,000 m(2) at each location. Our study provides novel insights into the critical function of macroalgal removal in hyperdiverse coral reef ecosystems, highlighting: (a) that function can transcend biogeographic, taxonomic and historical constraints; and (b) shortcomings in our assumptions regarding fish presence and realised ecosystem function on coral reefs

Potential Role of Inorganic Polyphosphate in the Cycling of Phosphorus Within the Hypoxic Water Column of Effingham Inlet, British Columbia

[1] The upper basin of Effingham Inlet possesses permanently anoxic bottom waters, with a water column redox transition zone typically occurring at least 40 m above the sediment‐water interface. During our sampling campaign in April and July 2007, this redox transition zone was associated with sharp peaks in a variety of parameters, including soluble reactive phosphorus (SRP) and total particulate phosphorus (TPP). Based on sequential extraction results, TPP maxima exhibited preferential accumulation of an operationally defined class of loosely adsorbed organic phosphorus (P), which may contain a substantial fraction of polyphosphate (poly‐P). This poly‐P may furthermore be involved in the redox‐dependent remobilization of SRP. For example, direct fluorometric analysis of poly‐P content revealed that particulate inorganic poly‐P was present at concentrations ranging from 1 to 9 nM P within and several meters above the TPP maximum. Below the depth of 1% oxygen saturation, however, particulate inorganic poly‐P was undetectable

Modelling Silicate - Nitrate - Ammonium Co-Limitation of Algal Growth and the Importance of Bacterial Remineralisation Based on an Experimental Arctic Coastal Spring Bloom Culture Study

Arctic coastal ecosystems are rapidly changing due to climate warming, which makes modelling their productivity crucially important to better understand future changes. System primary production in these systems is highest during the pronounced spring bloom, typically dominated by diatoms. Eventually the spring blooms terminate due to silicon or nitrogen limitation. Bacteria can play an important role for extending bloom duration and total CO2 fixation through ammonium regeneration. Current ecosystem models often simplify the effects of nutrient co-limitations on algal physiology and cellular ratios and neglect bacterial driven regeneration, leading to an underestimation of primary production. Detailed biochemistry- and cell-based models can represent these dynamics but are difficult to tune in the environment. We performed a cultivation experiment that showed typical spring bloom dynamics, such as extended algal growth via bacteria ammonium remineralisation, and reduced algal growth and inhibited chlorophyll synthesis under silicate limitation, and gradually reduced nitrogen assimilation and chlorophyll synthesis under nitrogen limitation. We developed a simplified dynamic model to represent these processes. The model also highlights the importance of organic matter excretion, and post bloom ammonium accumulation. Overall, model complexity is comparable to other ecosystem models used in the Arctic while improving the representation of nutrient co-limitation related processes. Such model enhancements that now incorporate increased nutrient inputs and higher mineralization rates in a warmer climate will improve future predictions in this vulnerable system

Structure and thermodynamics of a ferrofluid bilayer

We present extensive Monte Carlo simulations for the thermodynamic and structural properties of a planar bilayer of dipolar hard spheres for a wide range of densities, dipole moments and layer separations. Expressions for the stress and pressure tensors of the bilayer system are derived. For all thermodynamic states considered the interlayer energy is shown to be attractive and much smaller than the intralayer contribution to the energy. It vanishes at layer separations of the order of two hard sphere diameters. The normal pressure is negative and decays as a function of layer separation $h$ as $-1/h^5$. Intralayer and interlayer pair distribution functions and angular correlation functions are presented. Despite the weak interlayer energy strong positional and orientational correlations exist between particles in the two layers.Comment: 45 pages, 4 Tables, 9 Figure

Ocular Blood Flow Measured Noninvasively in Zero Gravity

In spaceflight or a reduced-gravity environment, bodily fluids shift to the upper extremities of the body. The pressure inside the eye, or intraocular pressure, changes significantly. A significant number of astronauts report changes in visual acuity during orbital flight. To date this remains of unknown etiology. Could choroidal engorgement be the primary mechanism and a change in the curvature or shape of the cornea or lens be the secondary mechanism for this change in visual acuity? Perfused blood flow in the dense meshwork of capillaries of the choroidal tissue (see the preceding illustration) provides necessary nutrients to the outer layers of the retina (photoreceptors) to keep it healthy and maintain good vision. Unlike the vascular system, the choroid has no baroreceptors to autoregulate fluid shifts, so it can remain engorged, pushing the macula forward and causing a hyperopic (farsighted) shift of the eye. Experiments by researchers at the NASA Glenn Research Center could help answer this question and facilitate planning for long-duration missions. We are investigating the effects of zero gravity on the choroidal blood flow of volunteer subjects. This pilot project plans to determine if choroidal blood flow is autoregulated in a reduced-gravity environment