An invariant in shock clustering and Burgers turbulence

1-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from the perspective of integrable systems. Other relevant physical notions such as energy dissipation and spectrum are also discussed.Comment: 11 pages, no figures; v2: corrections mad

A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow

A boundary element implementation of the regularised Stokeslet method of Cortez is applied to cilia and flagella-driven flows in biology. Previously-published approaches implicitly combine the force discretisation and the numerical quadrature used to evaluate boundary integrals. By contrast, a boundary element method can be implemented by discretising the force using basis functions, and calculating integrals using accurate numerical or analytic integration. This substantially weakens the coupling of the mesh size for the force and the regularisation parameter, and greatly reduces the number of degrees of freedom required. When modelling a cilium or flagellum as a one-dimensional filament, the regularisation parameter can be considered a proxy for the body radius, as opposed to being a parameter used to minimise numerical errors. Modelling a patch of cilia, it is found that: (1) For a fixed number of cilia, reducing cilia spacing reduces transport. (2) For fixed patch dimension, increasing cilia number increases the transport, up to a plateau at $9\times 9$ cilia. Modelling a choanoflagellate cell it is found that the presence of a lorica structure significantly affects transport and flow outside the lorica, but does not significantly alter the force experienced by the flagellum.Comment: 20 pages, 7 figures, postprin

P-equilibrium fertilization in an intensive dairy farming system: effects on soil-P status, crop yield and P leaching

In the coming decade, European dairy farms are obliged to realize a balance between phosphor (P) inputs to their farmland (in inorganic fertilizers and manure) and outputs (in crop products), the so-called P-equilibrium fertilization. The objective of the present study is to analyze the long-term effects of P-equilibrium fertilization on soil-P status (total soil-P and available soil-P), crop yield and P leaching on dry sandy soil, using data from experimental dairy farm ‘De Marke’, where P-equilibrium fertilization has been applied since 1989. For grassland, P availability is expressed in P-Al and for arable land in Pw. Total and available P status were monitored in the upper topsoil (layer 0–0.2 m). Total soil-P was also monitored in the lower topsoil (layer 0.2–0.4 m) and in the subsoil (0.4–0.6 m). From 1989 to 2006, Pw and P-Al (means of all farmland) decreased by 26 and 25%, respectively. In the same period, mean total-P content of the farmland decreased by 16%. There was a large variation in initial P status (1989) of the various plots. The rate of decline in all soil-P indicators was positively correlated to their initial values. In plots with the lowest initial values, P status did not change, while in plots with high initial values it tended to stabilize at lower levels. At equilibrium-P fertilization, Pw is estimated to stabilize at 20. This is lower than the recommended P status of Dutch soils used for maize cropping. P-Al is estimated to stabilize at 30–40, which corresponds to the current recommendations for grassland. The data show that at P-equilibrium fertilization, soil available-P status is higher in a maize-ley rotation than in permanent grassland. The decline in total P and available P did not affect crop yield, nor did it affect the P concentration in groundwater, but at ‘De Marke’, P emission to groundwater is generally low. The results obtained suggest that P-equilibrium fertilization can be compatible with efficient crop productio

Urban landscape survey in Italy and the Mediterranean

Field survey has been making a major contribution to our understanding of the rural landscapes of the Mediterranean for nearly forty years. During that time the techniques used to map ancient settlement patterns have grown in sophistication from being a process of simply identifying sites in the landscape, to one which provided nuanced understandings of their layouts, chronologies and contexts. This has led to a revolution in how archaeologists approach urban sites, with survey techniques being used increasingly often to generate a plan of a town site prior to excavation as a way of ensuring that the excavation can be used to address site-specific questions in a way that had not been possible before. Most recently, research has begun to reveal the advantages of integrating a range of different non-destructive techniques on urban sites. In combination with exciting new computer-based means of data visualization, all of this work means that it is now possible to virtually reconstruct a buried town within a relatively short space of time, as opposed to the old and destructive excavation-centered approach that could take generations. Unsurprisingly these advances are starting to make a very important understanding to urbanism in general and the Roman Empire in particular. Urban Landscape Survey in Italy and the Mediterranean builds upon all these new developments and is one of the first publications to focus exclusively upon the contribution of survey techniques to our understanding of ancient towns. It addresses methodology led enquiry into the nature of urban settlements primarily in Italy, but also in Greece, Turkey, Croatia, Portugal and Spain. The twenty-two papers from leading specialists in the field focus on two underlying themes. The first deals with the characterization of urban sites and draws upon a wide range of case studies. These range from key protohistoric centres in central and south Italy, to towns that epitomise the contradictions of cultural change under Rome, such as Paestum, Aquinum and Sagalassos, to Roman centres such as Teano, Suasa and Ammaia. The second theme is inter-urban relationships, looking in particular at wider urbanized landscapes in Italy. The fascinating selection of recent and on-going projects presented here significantly moves the limits of our current knowledge about ancient towns

Direct determination of the gauge coupling derivatives for the energy density in lattice QCD

By matching Wilson loop ratios on anisotropic lattices we measure the coefficients \cs and \ct, which are required for the calculation of the energy density. The results are compared to that of an indirect method of determination. We find similar behaviour, the differences are attributed to different discretization errors.Comment: Talk presented at LATTICE97(finite temperature), 3 pages, 5 Postscript figure

Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry

We describe a boundary-element method used to model the hydrodynamics of a bacterium propelled by a single helical flagellum. Using this model, we optimize the power efficiency of swimming with respect to cell body and flagellum geometrical parameters, and find that optima for swimming in unbounded fluid and near a no-slip plane boundary are nearly indistinguishable. We also consider the novel optimization objective of torque efficiency and find a very different optimal shape. Excluding effects such as Brownian motion and electrostatic interactions, it is demonstrated that hydrodynamic forces may trap the bacterium in a stable, circular orbit near the boundary, leading to the empirically observable surface accumulation of bacteria. Furthermore, the details and even the existence of this stable orbit depend on geometrical parameters of the bacterium, as described in this article. These results shed some light on the phenomenon of surface accumulation of micro-organisms and offer hydrodynamic explanations as to why some bacteria may accumulate more readily than others based on morphology

Pif1 Helicase Lengthens Some Okazaki Fragment Flaps Necessitating Dna2 Nuclease/Helicase Action in the Two-nuclease Processing Pathway

We have developed a system to reconstitute all of the proposed steps of Okazaki fragment processing using purified yeast proteins and model substrates. DNA polymerase δ was shown to extend an upstream fragment to displace a downstream fragment into a flap. In most cases, the flap was removed by flap endonuclease 1 (FEN1), in a reaction required to remove initiator RNA in vivo. The nick left after flap removal could be sealed by DNA ligase I to complete fragment joining. An alternative pathway involving FEN1 and the nuclease/helicase Dna2 has been proposed for flaps that become long enough to bind replication protein A (RPA). RPA binding can inhibit FEN1, but Dna2 can shorten RPA-bound flaps so that RPA dissociates. Recent reconstitution results indicated that Pif1 helicase, a known component of fragment processing, accelerated flap displacement, allowing the inhibitory action of RPA. In results presented here, Pif1 promoted DNA polymerase δ to displace strands that achieve a length to bind RPA, but also to be Dna2 substrates. Significantly, RPA binding to long flaps inhibited the formation of the final ligation products in the reconstituted system without Dna2. However, Dna2 reversed that inhibition to restore efficient ligation. These results suggest that the two-nuclease pathway is employed in cells to process long flap intermediates promoted by Pif1

Clocked Atom Delivery to a Photonic Crystal Waveguide

Experiments and numerical simulations are described that develop quantitative understanding of atomic motion near the surfaces of nanoscopic photonic crystal waveguides (PCWs). Ultracold atoms are delivered from a moving optical lattice into the PCW. Synchronous with the moving lattice, transmission spectra for a guided-mode probe field are recorded as functions of lattice transport time and frequency detuning of the probe beam. By way of measurements such as these, we have been able to validate quantitatively our numerical simulations, which are based upon detailed understanding of atomic trajectories that pass around and through nanoscopic regions of the PCW under the influence of optical and surface forces. The resolution for mapping atomic motion is roughly 50 nm in space and 100 ns in time. By introducing auxiliary guided mode (GM) fields that provide spatially varying AC-Stark shifts, we have, to some degree, begun to control atomic trajectories, such as to enhance the flux into to the central vacuum gap of the PCW at predetermined times and with known AC-Stark shifts. Applications of these capabilities include enabling high fractional filling of optical trap sites within PCWs, calibration of optical fields within PCWs, and utilization of the time-dependent, optically dense atomic medium for novel nonlinear optical experiments

Hall drift of axisymmetric magnetic fields in solid neutron-star matter

Hall drift, i. e., transport of magnetic flux by the moving electrons giving rise to the electrical current, may be the dominant effect causing the evolution of the magnetic field in the solid crust of neutron stars. It is a nonlinear process that, despite a number of efforts, is still not fully understood. We use the Hall induction equation in axial symmetry to obtain some general properties of nonevolving fields, as well as analyzing the evolution of purely toroidal fields, their poloidal perturbations, and current-free, purely poloidal fields. We also analyze energy conservation in Hall instabilities and write down a variational principle for Hall equilibria. We show that the evolution of any toroidal magnetic field can be described by Burgers' equation, as previously found in plane-parallel geometry. It leads to sharp current sheets that dissipate on the Hall time scale, yielding a stationary field configuration that depends on a single, suitably defined coordinate. This field, however, is unstable to poloidal perturbations, which grow as their field lines are stretched by the background electron flow, as in instabilities earlier found numerically. On the other hand, current-free poloidal configurations are stable and could represent a long-lived crustal field supported by currents in the fluid stellar core.Comment: 8 pages, 5 figure panels; new version with very small correction; accepted by Astronomy & Astrophysic