Lower Cost Lightweight Cold-formed Portal Frames

Southern Africa has a dire need for housing small industries and people, and concomitantly the creation of employment. It is common to use hot-rolled steel sections for industrial structures, which are pre-manufactured and then bolted together on site. In this paper an alternative structural concept for low-rise portals for light industries is proposed, whereby the total frame is made up of standard cold-formed sections which are cut and welded together on site. The cladding material is employed as an integral structural component through the principles of stressed skin diaphragm action. A short pile footing is proposed to provide a degree of rotational fixity for the colunns of the frame. Different frame configurations are investigated and the practical application of the concept is discussed

Topological Constraints at the Theta Point: Closed Loops at Two Loops

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.Comment: 5 pages, RevTeX, typo

Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the purpose of performing a strand passage, and model this using Theta-SAPs, polygons that contain the pattern Theta at a fixed location. It is proved that the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted self-avoiding polygons, and that the same holds for subsets of n-edge Theta-SAPs that yield a specific after-strand-passage knot-type. Thus the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n, and we conjecture that instead it approaches a knot-type dependent amplitude ratio lying strictly between 0 and 1. This is supported by critical exponent estimates obtained from a new maximum likelihood method for Theta-SAPs that are generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF algorithm. We also give strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand passage site. Considering both the local structure and the crossing-sign at the strand passage site, we observe that the more "compact" the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend is consistent with results from other strand-passage models, however, we are the first to note the influence of the crossing-sign information. Two measures of "compactness" are used: the size of a smallest polygon that contains the structure and the structure's "opening" angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics

Knot localization in adsorbing polymer rings

We study by Monte Carlo simulations a model of knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent $\phi$ and the metric exponent $\nu$, are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied by a less sharp variation of the exponent related to the degree of localization. Indeed, for a whole interval below the adsorption transition, one can not exclude a contiuous variation with temperature of this exponent. Deep into the adsorbed phase we are able to verify that knot localization is strong and well described in terms of the flat knot model.Comment: 27 pages, 10 figures. Submitter to Phys. Rev.

Simulations of grafted polymers in a good solvent

We present improved simulations of three-dimensional self avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having thus only an entropic effect, or attractive. In the latter case we concentrate on the adsorption transition, We find clear evidence for the cross-over exponent to be smaller than 1/2, in contrast to all previous simulations but in agreement with a re-summed field theoretic $\epsilon$-expansion. Since we use the pruned-enriched Rosenbluth method (PERM) which allows very precise estimates of the partition sum itself, we also obtain improved estimates for all entropic critical exponents.Comment: 5 pages with 9 figures included; minor change

Early non-psychotic deviant behaviour as an endophenotypic marker in bipolar disorder, schizo-affective disorder and schizophrenia

Objective: To determine and compare the incidence of early non-psychotic deviant behaviour (i.e. under the age of ten) in Afrikaner patients with bipolar disorder, schizo-affective disorder and schizophrenia. Methods: Patients with bipolar disorder, schizo-affective disorder and schizophrenia were interviewed using a structured questionnaire probing for early deviant childhood behaviour starting before the age of 10 years. Information from close family members was also obtained where possible. Seven areas of possible deviance were probed into: social dysfunction, unprovoked aggression, extreme anxiety, chronic sadness, extreme odd behaviours, attention impairment and learning difficulties. Demographic data included: age, marital status, gender, and years of formal education. The following clinical features were also recorded: age of onset of illness and suicide attempts. Results: A total of 74 patients diagnosed with bipolar disorder, 43 patients diagnosed with schizo-affective disorder and 80 patients diagnosed with schizophrenia were interviewed. Early deviant behaviour was statistically more prevalent in schizophrenia (65%) and schizo-affective disorder (60,5%), than in the bipolar group (21,6%). Deviant childhood behaviour was grouped into 3 clusters: social functioning impairment cluster (social isolation, aggression, extreme odd behavior), mood/anxiety cluster (extreme fears, chronic sadness) and a cognitive impairment cluster (attention impairment, learning disability). Bipolar patients showed significantly less social functioning and cognitive impairment compared to patients with schizo-affective disorder and schizophrenia. Conclusion: Our findings suggest that early deviant behaviour may be a possible endophenotypic marker in schizophrenia and schizoaffective disorder. Keywords: early non-psychotic deviant behaviour, endophenotype, bipolar disorder, schizo-affective disorder, schizophrenia South African Psychiatry Review Vol. 8(4) 2005: 153-15

Equilibrium size of large ring molecules

The equilibrium properties of isolated ring molecules were investigated using an off-lattice model with no excluded volume but with dynamics that preserve the topological class. Using an efficient set of long range moves, chains of more than 2000 monomers were studied. Despite the lack of any excluded volume interaction, the radius of gyration scaled like that of a self avoiding walk, as had been previously conjectured. However this scaling was only seen for chains greater than 500 monomers.Comment: 11 pages, 3 eps figures, latex, psfi

Simulations of lattice animals and trees

The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the animal (tree) ensemble, and prune or branch the further growth according to a heuristic fitness function. In contrast to previous applications of PERM, this fitness function is {\it not} the weight with which the actual configuration would contribute to the partition sum, but is closely related to it. We obtain high statistics of animals with up to several thousand sites in all dimension 2 <= d <= 9. In addition to the partition sum (number of different animals) we estimate gyration radii and numbers of perimeter sites. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and >= 8. In addition, we present the hitherto most precise estimates for growth constants in d >= 3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy. Finally, we discuss the collapse of animals and trees, arguing that our present version of the algorithm is also efficient for some of the models studied in this context, but showing that it is {\it not} very efficient for the `classical' model for collapsing animals.Comment: 17 pages RevTeX, 29 figures include

Area distribution of the planar random loop boundary

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe

Average Structures of a Single Knotted Ring Polymer

Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of the average structure. The other type of the averages structure uses all the conformation vectors generated from those sampled in a simulation. In thecase of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N is increased. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.Comment: 15 pages, 19 figures, uses jpsj2.cl