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

CPT Violation Implies Violation of Lorentz Invariance

An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.Comment: Minor changes in the published versio

Hamiltonian Formalism for Space-time Non-commutative Theories

Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to the evolution time. The Hamiltonian path integral quantization is considered and the Feynman rules in the Lagrangian formalism are derived. The case of non-commutative \phi^3 theory is considered as an example.Comment: 6 pages, A new section is added with other comments and references. To appear in PR

Perturbative Hamiltonian constraints for higher order theories

We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan scalar field. We also compare the results, both at the classical and quantum level, with the ones corresponding to a direct perturbative construction applied to the exact higher order theory. This comparison highligths the soundness of the present formalism.Comment: 26 pages, 4 figures; review section shortened and appendices change

Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.

Luminous, pc-scale CO 6-5 emission in the obscured nucleus of NGC1377

High resolution submm observations are important in probing the morphology, column density and dynamics of obscured active galactic nuclei (AGNs). With high resolution (0.06 x 0.05) ALMA 690 GHz observations we have found bright (TB >80 K) and compact (FWHM 10x7 pc) CO 6-5 line emission in the nucleus of the extremely radio-quiet galaxy NGC1377. The integrated CO 6-5 intensity is aligned with the previously discovered jet/outflow of NGC1377 and is tracing the dense (n>1e4 cm-3), hot gas at the base of the outflow. The velocity structure is complex and shifts across the jet/outflow are discussed in terms of jet-rotation or separate, overlapping kinematical components. High velocity gas (deltaV +-145 km/s) is detected inside r<2-3 pc and we suggest that it is emerging from an inclined rotating disk or torus of position angle PA=140+-20 deg with a dynamical mass of approx 3e6 Msun. This mass is consistent with that of a supermassive black hole (SMBH), as inferred from the M-sigma relation. The gas mass of the proposed disk/torus constitutes <3% of the nuclear dynamical mass. In contrast to the intense CO 6-5 line emission, we do not detect dust continuum with an upper limit of S(690GHz)<2mJy. The corresponding, 5 pc, H2 column density is estimated to N(H2)<3e23 cm-2, which is inconsistent with a Compton Thick (CT) source. We discuss the possibility that CT obscuration may be occuring on small (subparsec) or larger scales. From SED fitting we suggest that half of the IR emission of NGC1377 is nuclear and the rest (mostly the far-infrared (FIR)) is more extended. The extreme radio quietness, and the lack of emission from other star formation tracers, raise questions on the origin of the FIR emission. We discuss the possibility that it is arising from the dissipation of shocks in the molecular jet/outflow or from irradiation by the nuclear source along the poles.Comment: 7 pages, 5 figures, submitted to Astronomy and Astrophysic