An evaluation of the economic benefits of active cooling and carbon dioxide enrichment of greenhouse cucumbers (Cucumis sativus L.) : a thesis presented in partial fulfilment of the requirements for the degree of Master of Horticultural Science at Massey University

Cooling a greenhouse with a refrigeration system rather than conventional ventilation makes it possible to maximise the fractional enrichment time for carbon dioxide, and more importantly enrich during periods of high photosynthetically active radiation. Using conventional climate control methods, enrichment is limited to periods when the greenhouse is not being ventilated, thus reducing the potential enrichment time of the crop. The objective of this study was to develop a simulation model of a greenhouse crop growing with a closed cycle climate control system, using a heat pump, with a reversible (dual) cycle, for heating and cooling. A computer implemented mathematical model developed by Wells (1992) was modified to simulate cucumber crop growth in a greenhouse of commercial size and allowing certain parameters to be set. These parameters included: two types of control system, four levels of enrichment, three crop periods, and at two locations, Auckland and Christchurch. The three crop periods chosen were 26 Jan to 26 April, 25 May to 23 August, and 20 September to 19 December. The two types of control involved conventional fan ventialtion and electric heating, and closed cycle climate control using a reverse cycle heat pump. Greenhouse carbon dioxide enrichment levels used were 350, 600, 900, 1200 μ1.1-1 . The two locations chosen were Auckland and Christchurch. An economic analysis of the results was carried out calculating Annual Marginal Return (AMR) and Internal Rate of Return (IRR) for treatments compared to control. It was concluded that carbon dioxide enrichment combined with conventional control is a worthwhile investment in Christchurch but less so in Auckland. Due to the high capital cost, carbon dioxide enrichment combined with closed cycle climate control is a less attractive investment. However, as considerable energy savings are possible with closed cycle climate control, it is worthwhile investigating other less expensive forms of closed cycle climate control. The economic feasibility of the application of this technology to other, higher value, crops is worthwhile investigating

Rotating flow in a cylinder with a circular barrier on the bottom

The relative flow of a homogeneous, slightly viscous fluid in a rotating cylinder is induced by differential rotation of the bottom disk, on which a thin circular strip of small height is fixed. The axis of symmetry of the strip coincides with the rotation axis of the cylinder.\ud \ud At the strip a Stewartson layer exists which is partially free, partially attached to the strip. The structure of the Stewartson E1/4-layer E being the Ekman number) is not affected by the height of the strip, but the E1/3-layer problem has to be solved in the two separate intervals. The fact that both solutions do not match at the strip edge necessitates the presence of an intermediate region that exhibits some characteristic features of an Ekman layer

The algebraic square peg problem

The square peg problem asks whether every continuous curve in the plane that starts and ends at the same point without self-intersecting contains four distinct corners of some square. Toeplitz conjectured in 1911 that this is indeed the case. Hundred years later we only have partial results for curves with additional smoothness properties. The contribution of this thesis is an algebraic variant of the square peg problem. By casting the set of squares inscribed on an algebraic plane curve as a variety and applying Bernshtein's Theorem we are able to count the number of such squares. An algebraic plane curve defined by a polynomial of degree m inscribes either an infinite amount of squares, or at most (m4 - 5m2 + 4m)= 4 squares. Computations using computer algebra software lend evidence to the claim that this upper bound is sharp for generic curves. Earlier work on Toeplitz's conjecture has shown that generically an odd number of squares is inscribed on a smooth enough Jordan curve. Examples of real cubics and quartics suggest that there is a similar parity condition on the number of squares inscribed on some topological types of algebraic plane curves that are not Jordan curves. Thus we are led to conjecture that algebraic plane curves homeomorphic to the real line inscribe an even number of squares

Development in a biologically inspired spinal neural network for movement control

In two phases, we develop neural network models of spinal circuitry which self-organises into networks with opponent channels for the control of an antagonistic muscle pair. The self-organisation is enabled by spontaneous activity present in the spinal cord. We show that after the process of self-organisation, the networks have developed the possibility to independently control the length and tension of the innerated muscles. This allows the specification of joint angle independent from the specification of joint stiffness. The first network comprises only motorneurons and inhibitory interneurons through which the two channels interact. The inhibitory interneurons prevent saturation of the motorneuron pools, which is a necessary condition for independent control. In the second network, however, the neurons in the motorneuron pools obey the size-principle, which is a threat to the desired invariance of joint angle for varying joint stiffness, because of the different amplification of inputs in the case these inputs are not equal. To restore the desired invariance the second network ha.s been expanded with Renshaw cells. The manner in which they are included in the circuitry corrects the problem caused by the addition of the size-principle. The results obtained from the two models compare favourably with the FLETE-model for spinal circuitry (Bullock & Grossberg, 1991; Bullock et al., HJ93; Bullock & Contreras-Vidal, 1993) which has been successful in explaining several phenomena related to motor control.Fulbright Scholarship; Office of Naval Research (N00014-92-J-1309, N00014-95-1-0409

A model for vortical plumes in rotating convection

In turbulent rotating convection a typical flow structuring in columnar vortices is observed. In the internal structure of these vortices several symmetries are approximately satisfied. A model for these columnar vortices is derived by prescribing these symmetries. The symmetry constraints are applied to the Navier¿Stokes equations with rotation in the Boussinesq approximation. It is found that the application of the symmetries results in a set of linearized equations. An investigation of the linearized equations leads to a model for the columnar vortices and a prediction for the heat flux (Nusselt number) that is very appropriate compared to the results from direct numerical simulations of the full governing equation

On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions

Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z ∝ Re0.8 and P ∝ Re2.25 for 5 × 102 ≤ Re ≤ 2 × 104 and Z ∝ Re0.5 and P ∝ Re1.5 for Re ≥ 2 × 104 (with Re based on the velocity and size of the dipole). A critical Reynolds number Rec(here, Rec ≈ 2 × 104) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following scaling relations are obtained: Z ∝ Re^3/4, P ∝ Re^9/4, and dP/dt ∝ Re11/4 in agreement with the numerically obtained scaling laws. For Re ≥ Rec the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate boundary-layer theory, this yields: Z ∝ Re1/2 and P ∝ Re3/2