A problem in non-linear Diophantine approximation

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution

Modelling diverse root density dynamics and deep nitrogen uptake — a simple approach

We present a 2-D model for simulation of root density and plant nitrogen (N) uptake for crops grown in agricultural systems, based on a modification of the root density equation originally proposed by Gerwitz and Page in J Appl Ecol 11:773–781, (1974). A root system form parameter was introduced to describe the distribution of root length vertically and horizontally in the soil profile. The form parameter can vary from 0 where root density is evenly distributed through the soil profile, to 8 where practically all roots are found near the surface. The root model has other components describing root features, such as specific root length and plant N uptake kinetics. The same approach is used to distribute root length horizontally, allowing simulation of root growth and plant N uptake in row crops. The rooting depth penetration rate and depth distribution of root density were found to be the most important parameters controlling crop N uptake from deeper soil layers. The validity of the root distribution model was tested with field data for white cabbage, red beet, and leek. The model was able to simulate very different root distributions, but it was not able to simulate increasing root density with depth as seen in the experimental results for white cabbage. The model was able to simulate N depletion in different soil layers in two field studies. One included vegetable crops with very different rooting depths and the other compared effects of spring wheat and winter wheat. In both experiments variation in spring soil N availability and depth distribution was varied by the use of cover crops. This shows the model sensitivity to the form parameter value and the ability of the model to reproduce N depletion in soil layers. This work shows that the relatively simple root model developed, driven by degree days and simulated crop growth, can be used to simulate crop soil N uptake and depletion appropriately in low N input crop production systems, with a requirement of few measured parameters

Magnetic Moment Formation in Quantum Point Contacts

We study the formation of local magnetic moments in quantum point contacts. Using a Hubbard-like model to describe point contacts formed in a two dimensional system, we calculate the magnetic moment using the unrestricted Hartree approximation. We analyze different type of potentials to define the point contact, for a simple square potential we calculate a phase diagram in the parameter space (Coulomb repulsion - gate voltage). We also present an analytical calculation of the susceptibility to give explicit conditions for the occurrence of a local moment, we present a simple scaling argument to analyze how the stability of the magnetic moment depends on the point contact dimensions.Comment: 7 pages, 2 figure

A Coupled Cavity Micro Fluidic Dye Ring Laser

We present a laterally emitting, coupled cavity micro fluidic dye ring laser, suitable for integration into lab-on-a-chip micro systems. The micro-fluidic laser has been successfully designed, fabricated, characterized and modelled. The resonator is formed by a micro-fluidic channel bounded by two isosceles triangle mirrors. The micro-fluidic laser structure is defined using photo lithography in 10 microns thick SU-8 polymer on a glass substrate. The micro fluidic channel is sealed by a glass lid, using PMMA adhesive bonding. The laser is characterized using the laser dye Rhodamine 6G dissolved in ethanol or ethylene glycol as the active gain medium, which is pumped through the micro-fluidic channel and laser resonator. The dye laser is optically pumped normal to the chip plane at 532 nm by a pulsed, frequency doubled Nd:YAG laser and lasing is observed with a threshold pump pulse energy flux of around 55 micro-Joule/square-milimeter. The lasing is multi-mode, and the laser has switchable output coupling into an integrated polymer planar waveguide. Tuning of the lasing wavelength is feasible by changing the dye/solvent properties.Comment: Accepted for Microelectronic Engineerin

Evidence for a single hydrogen molecule connected by an atomic chain

Stable, single-molecule conducting-bridge configurations are typically identified from peak structures in a conductance histogram. In previous work on Pt with H$_2$ at cryogenic temperatures it has been shown that a peak near 1 $G{_0}$ identifies a single molecule Pt-H$_{2}$-Pt bridge. The histogram shows an additional structure with lower conductance that has not been identified. Here, we show that it is likely due to a hydrogen decorated Pt chain in contact with the H$_2$ molecular bridge.Comment: 4 pages, 4 figure

Geoacoustic seafloor exploration with a towed array in a shallow water area of the Strait of Sicily (2)

Acoustic propagation in shallow water is greatly dependent on the geoacoustic properties of the seabottom. This paper exploits this dependence for estimating geoacoustic sediment properties from the bottom acoustic returns of known signals received on a hydrophone line array. There are two major issues in this approach: one is the feasibility of acoustic inversion with a limited aperture line array, the other is related to the knowledge of the geometry of the experimental configuration. To test the feasibility of this approach, a 40-hydrophone4-m spaced towed array together with a low-frequency acoustic source, was operated at a shallow water site in the Strait of Sicily. In order to estimate the array deformation in real time, it has been equipped with a set of nonacoustic positioning sensors (compasses, tiltmeters, pressure gauges). The acoustic data were inverted using two complementary approaches: a genetic algorithm (GA) like approach and a radial basis functions (RBF) inversion scheme. More traditional methods, based on core sampling, seismic survey and geophone data, together with Hamilton’s regression curves, have also been employed on the same tracks, in order to provide a ground truth reference environment. The results of the experiment, can be summarized as follows: 1) the towed array movement is not negligible for the application considered and the use of positioning sensors are essential for a proper acoustic inversion, 2) the inversion with GA and RBF are in good qualitative agreement with the ground truth model, and 3) the GA scheme tends to have better stability properties. On the other hand, repeated inversion of successive field measurements requires much less computational effort with RBF.The authors wish to acknowledge the master and crew of the RN ALLIANCE and the SACLANT Centre Engineering Department for their outstanding respective contributions in the leadership, sea-going operation and equipment preparation before and during the sea trial. The support of E. Dias and E. Coelho from the Hydrographic Institute, Lisbon, on the acquisition of the nonacoustic data and of P. Gershoft, SACLANT Centre, on genetic algorithms setup, are also appreciated. The authors wish also to express their appreciation to the anonymous reviewers, whose comments have greatly helped to reshape the second draft of this paper, and hopefully to improve its readability

Quantum Interaction ϕ44\phi^4_4: the Construction of Quantum Field defined as a Bilinear Form

We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation $\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can be expanded over Wick polynomials of the free $in$-field, and where $:\!\phi^3(t,{\bf x})\!:$ is defined as the normal ordered product with respect to the free $in$-field. The constructed solution is correctly defined as a bilinear form on $D_{\theta}\times D_{\theta}$, where $D_{\theta}$ is a dense linear subspace in the Fock space of the free $in$-field. On $D_{\theta}\times D_{\theta}$ the diagonal Wick symbol of this bilinear form satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe