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

Acute mental health care according to recent mental health legislation. Part III. Structuring space for acute mental health care

Objective: This is the third of three reports on the follow-up review of mental health care at Helen Joseph Hospital (HJH). The study reviewed existing South African standards for mental health care facilities. Architectural principles and implications for the use of space were deducted from recent legislation. Objectives were to evaluate the use of space in the existing physical facilities, to identify appropriate architectural solutions considering identified human rights requirements and to provide provisional cost estimates to align the unit towards its designated functions. Method: Personal interviews were conducted. An on-site assessment and survey was made of existing and potential new spaces. Results: Spatial requirements for implementing the Mental Health Act, No. 17 of 2002 (MHCA) were explored. Principles for spatial design of acute facilities include that: - spaces should communicate clear individual identity; - space should be segregated into zones according to user functionality and privacy; - communal leisure spaces should open into safe contained outdoor spaces; - circulation routes should preferably be circular; - sufficient visual connection should exist between circulation space and group activities; and - open lines of sight should be provided to all access points. The potential options for extension included: - an extensive unused single storey structural shell for a potential office wing on the same floor; - a huge vacant double volume space which could be accessed across the existing flat roof for potential occupational therapy activities; and - the existing roof area could be altered and secured to become an adequate outside leisure and garden area. A proposed concept design in two phases – based on these principles - was submitted to hospital and provincial management. Conclusion: To implement the MHCA without violating the human rights of mental health care users at HJH will require specific adjustment and extension of the current use of space at HJH.Key words: Architecture; Hospitals; Mental health services; Human right

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