Lattice Knots in a Slab

In this paper the number and lengths of minimal length lattice knots confined to slabs of width $L$, is determined. Our data on minimal length verify the results by Sharein et.al. (2011) for the similar problem, expect in a single case, where an improvement is found. From our data we construct two models of grafted knotted ring polymers squeezed between hard walls, or by an external force. In each model, we determine the entropic forces arising when the lattice polygon is squeezed by externally applied forces. The profile of forces and compressibility of several knot types are presented and compared, and in addition, the total work done on the lattice knots when it is squeezed to a minimal state is determined

BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

In this paper the elementary moves of the BFACF-algorithm for lattice polygons are generalised to elementary moves of BFACF-style algorithms for lattice polygons in the body-centred (BCC) and face-centred (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice. Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices

Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe

The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

Suitable rootstocks for organically grown tomato and cucumber in relation to Meloidogyne SPP.

In organic greenhouse vegetable production, significant yield loss occurs due to root-knot nematodes (Meloidogyne spp.). Soil steaming is effective; however, it is not preferred, since beneficial soil micro organisms are eliminated. An inclusion of resistant hosts within the crop rotation is complicated by the broad host range of the nematode and the high level of specialization of companies towards production of fruit vegetables. Nearly all species of fruit vegetables are susceptible to a varying degree and complete resistance is absent. Even when rootstocks show partial resistance, this is broken down at high temperatures and with an increase in nematode densities. In addition, a lack of compatibility between the rootstock and graft is reported. The objective of the research was to find a rootstock with a high resistance against the most important Meloidogyne species in greenhouses in the Netherlands, M. incognita and M. hapla. Secondly, rootstocks should combine resistance with high yield and quality. In five experiments, 16 to 28 rootstocks per vegetable crop were tested for susceptibility, based on the number and size of root-knots and degree of nematode reproduction. In tomato (Solanum lycopersicum L.), one of the best performing rootstocks was ‘PG76’; in cucumber (Cucumis sativus L.) ‘RZ64-10’ and ‘Harry’ performed well. In general, tomato rootstocks have a higher level of resistance against M. incognita compared with M. hapla. However, cucumber rootstocks seem to be more susceptible to M. incognita than to M. hapla

Multiple configuration shell-core structured robotic manipulator with interchangeable mechatronic joints : a thesis presented in partial fulfilment of the requirements for the degree of Masters of Engineering in Mechatronics at Massey University, Turitea Campus, Palmerston North, New Zealand

With the increase of robotic technology utilised throughout industry, the need for skilled labour in this area has increased also. As a result, education dealing with robotics has grown at both the high-school and tertiary educational level. Despite the range of pedagogical robots currently on the market, there seems to be a low variety of these systems specifically related to the types of robotic manipulator arms popular for industrial applications. Furthermore, a fixed-arm system is limited to only serve as an educational supplement for that specific configuration and therefore cannot demonstrate more than one of the numerous industrial-type robotic arms. The Shell-Core structured robotic manipulator concept has been proposed to improve the quality and variety of available pedagogical robotic arm systems on the market. This is achieved by the reconfigurable nature of the concept, which incorporates shell and core structural units to make the construction of at least 5 mainstream industrial arms possible. The platform will be suitable, but not limited to use within the educational robotics industry at high-school and higher educational levels and may appeal to hobbyists. Later dubbed SMILE (Smart Manipulator with Interchangeable Links and Effectors), the system utilises core units to provide either rotational or linear actuation in a single plane. A variety of shell units are then implemented as the body of the robotic arm, serving as appropriate offsets to achieve the required configuration. A prototype consisting of a limited number of ‘building blocks’ was developed for proof-of-concept, found capable of achieving several of the proposed configurations. The outcome of this research is encouraging, with a Massey patent search confirming the unique features of the proposed concept. The prototype system is an economic, easy to implement, plug and play, and multiple-configuration robotic manipulator, suitable for various applications

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Etheenbehandeling aan het einde van de tomatenteelt: Een consultancyonderzoek

The effect of ethylene on tomato ripening was investigated in a treatment in a small glasshouse experiment at Wageningen UR Greenhouse Horticulture. An ethylene generator (Restrain Ltd.) was used for the production of ethylene. Under the climatic conditions during the experiment, the ripening was clearly increased by 1.3 ppm ethylene during three days. The ethylene concentration in the harvested fruits was similar to that in untreated fruits and the shelf life was not decreased

Donkere vlekjes bij gele courgettevruchten

Referaat In gele courgettes komen regelmatig grijsbruine vlekjes in de vruchtschil voor, deze zijn vaak pas in het handelskanaal te zien. In een door het Productschap Tuinbouw gefinancierd onderzoek heeft Wageningen UR Glastuinbouw onderzocht wat de oorzaken zouden kunnen zijn. Er is een duidelijk raseffect geconstateerd. Ook is er een effect van handling gevonden. Van andere factoren die zijn onderzocht, zowel in de teeltherkomst als tijdens de bewaring na de oogst, zijn nauwelijk of geen effecten gevonden. De bruinverkleuring wordt waarschijnlijk veroorzaakt door oxidatie van polyfenolen in de vruchten. Abstract Yellow zucchini fruits can have problems with grey-brown spots in the skin. Often they appear in the post-harvest chain. Financed by the Dutch Product Board for Horticulture, Wageningen UR Greenhouse Horticulture explored some possible causes for this problem. A cultivar effect was found. Also handling influenced the appearance of the spots. Other factors examined, both in growth conditions and in post harvest treatment, didn’t seem to cause the problems. It is assumed that oxidation of polyfenols in the fruit is the biochemical cause of the appearance of the spots