The design of a Space-borne multispectral canopy LiDAR to estimate global carbon stock and gross primary productivity

Understanding the dynamics of the global carbon cycle is one of the most challenging issues for the scientific community. The ability to measure the magnitude of terrestrial carbon sinks as well as monitoring the short and long term changes is vital for environmental decision making. Forests form a significant part of the terrestrial biosystem and understanding the global carbon cycle, Above Ground Biomass (AGB) and Gross Primary Productivity (GPP) are critical parameters. Current estimates of AGB and GPP are not adequate to support models of the global carbon cycle and more accurate estimates would improve predictions of the future and estimates of the likely behaviour of these sinks. Various vegetation indices have been proposed for the characterisation of forests including canopy height, canopy area, Normalised Difference Vegetation Index (NDVI) and Photochemical Reflectance Index (PRI). Both NDVI and PRI are obtained from a measure of reflectivity at specific wavelengths and have been estimated from passive measurements. The use of multi-spectral LiDAR to measure NDVI and PRI and their vertical distribution within the forest represents a significant improvement over current techniques. This paper describes an approach to the design of an advanced Multi-Spectral Canopy LiDAR, using four wavelengths for measuring the vertical profile of the canopy simultaneously. It is proposed that the instrument be placed on a satellite orbiting the Earth on a sun synchronous polar orbit to provide samples on a rectangular grid at an approximate separation of 1km with a suitable revisit frequency. The systems engineering concept design will be presented

Orthogonal Symmetric Polynomials Associated with the Calogero Model

The Calogero model is a one-dimensional quantum integrable system with inverse-square long-range interactions confined in an external harmonic well. It shares the same algebraic structure with the Sutherland model, which is also a one-dimensional quantum integrable system with inverse-sine-square interactions. Inspired by the Rodrigues formula for the Jack polynomials, which form the orthogonal basis of the Sutherland model, recently found by Lapointe and Vinet, we construct the Rodrigues formula for the Hi-Jack (hidden-Jack) polynomials that form the orthogonal basis of the Calogero model.Comment: 12pages, LaTeX file using citesort.sty and subeqn.sty, to appear in the proceedings of Canada-China Meeting in Mathematical Physics, Tianjin, China, August 19--24, 1996, ed. M.-L. Ge, Y. Saint-Aubin and L. Vinet (Springer-Verlag

A Dynamical Analysis of the Kepler-80 System of Five Transiting Planets

Kepler has discovered hundreds of systems with multiple transiting exoplanets which hold tremendous potential both individually and collectively for understanding the formation and evolution of planetary systems. Many of these systems consist of multiple small planets with periods less than ~50 days known as Systems with Tightly-spaced Inner Planets, or STIPs. One especially intriguing STIP, Kepler-80 (KOI-500), contains five transiting planets: f, d, e, b, and c with periods of 1.0, 3.1, 4.6, 7.1, 9.5 days, respectively. We provide measurements of transit times and a transit timing variation (TTV) dynamical analysis. We find that TTVs cannot reliably detect eccentricities for this system, though mass estimates are not affected. Restricting the eccentricity to a reasonable range, we infer masses for the outer four planets (d, e, b, and c) to be $6.75^{+0.69}_{-0.51}$, $4.13^{+0.81}_{-0.95}$, $6.93^{+1.05}_{-0.70}$, and $6.74^{+1.23}_{-0.86}$ Earth masses, respectively. The similar masses but different radii are consistent with terrestrial compositions for d and e and $\sim$2% H/He envelopes for b and c. We confirm that the outer four planets are in a rare dynamical configuration with four interconnected three-body resonances that are librating with few degree amplitudes. We present a formation model that can reproduce the observed configuration by starting with a multi-resonant chain and introducing dissipation. Overall, the information-rich Kepler-80 planets provide an important perspective into exoplanetary systems.Comment: Accepted to AJ. 19 pages, 7 figures. Additional animations available here[http://mmacdonald.altervista.org/kepler-80.html

Permanent annihilation of thermally activated defects which limit the lifetime of float-zone silicon

We have observed very large changes in the minority carrier lifetime when high purity float-zone (FZ) silicon wafers are subject to heat-treatments in the range of 200– 1100˚C. Recombination centres were found to become activated upon annealing at 450–700˚C, causing significant reductions in the bulk lifetime, detrimental for high efficiency solar cells and stable high powered devices. Photoluminescence imaging of wafers annealed at 500˚C revealed concentric circular patterns, with lower lifetimes occurring in the centre, and higher lifetimes around the periphery. Deep level transient spectroscopy measurements on samples extracted from the centre of an n-type FZ silicon wafer annealed at 500˚C revealed a large variety of defects with activation energies ranging between 0.16– 0.36eV. Our measurements indicate that vacancy related defects are causing the severe degradation in lifetime when FZ wafers are annealed at 450–700˚C. Upon annealing FZ silicon at temperatures >800°C, the lifetime is completely recovered, whereby the defect-rich regions vanish and do not reappear (permanently annihilated). Our results indicate that, in general, as-grown FZ silicon should not be assumed to be defect lean, nor can it be assumed that the bulk lifetime will remain stable during thermal processing, unless annealed at temperatures >1000°C

The generating function for a particular class of characters of SU(n)

We compute the generating function for the characters of the irreducible representations of SU(n) whose associated Young diagrams have only two rows with the same number of boxes. The result is a rational determinantal expression in which both the numerator and the denominator have a simple structure when expressed in terms of Schur polynomials.Comment: 7 pages, no figure

Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems

The relationship (resemblance and/or contrast) between quantum and classical integrability in Ruijsenaars-Schneider systems, which are one parameter deformation of Calogero-Moser systems, is addressed. Many remarkable properties of classical Calogero and Sutherland systems (based on any root system) at equilibrium are reported in a previous paper (Corrigan-Sasaki). For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all "integer valued". In this paper we report that similar features and results hold for the Ruijsenaars-Schneider type of integrable systems based on the classical root systems.Comment: LaTeX2e with amsfonts 15 pages, no figure

Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials

A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model that decomposes triangularly in terms of the symmetric monomial superfunctions. Many explicit examples are displayed. Furthermore, various new results have been obtained for the supersymmetric version of the CMS models: the Lax formulation, the construction of the Dunkl operators and the explicit expressions for the conserved charges. The reformulation of the models in terms of the exchange-operator formalism is a crucial aspect of our analysis.Comment: Minor corrections in tables; 30 page

Explicit solution of the quantum three-body Calogero-Sutherland model

Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a deformation of the Clebsch-Gordan series. This yields recursion relations for the wave functions of those systems. In this note, this approach is used to compute the explicit expressions for the three-body Calogero-Sutherland wave functions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation introduced by Macdonald.Comment: 10 page

Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model

We algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. For this purpose, we derive the raising and lowering operators which increase and decrease eigenvalues of pseudomomenta. The operators exchanging eigenvalues of two pseudomomenta have been known. All the eigenstates are systematically produced by starting from the ground state and multiplying these operators to it.Comment: 11 pages, Latex, no figure