On the nature and origin of complexity in discrete,homogeneous, locally-interacting systems

The observed complexity of nature is often attributed to an intrinsic propensity of matter to self-organize under certain (e.g., dissipative) conditions. In order better to understand and test this vague thesis, we define complexity as logical depth, a notion based on algorithmic information and computational time complexity. Informally, logical depth is the number of steps in the deductive or causal path connecting a thing with its plausible origin. We then assess the effects of dissipation, noise, and spatial and other symmetries of the initial conditions and equations of motion on the asymptotic complexity-generating abilities of statistical-mechanical model systems. We concentrate on discrete, spatially-homogeneous, locally-interacting systems such as kinetic Ising models and cellular automata.     

Singlet–triplet splittings as obtained from the Xα-scattered wave method: A theoretical analysis

The theoretical determination of singlet–triplet splittings of the excited states of closed-shell molecules is discussed with emphasis on the use of the Xα–scattered wave method. With this method, splittings can be computed in two independent ways. Both will have corrections due to orbital relaxation effects. The singlet–triplet splittings obtained with the Xα–scattered wave method for several large organic molecules are reviewed. It is seen that the results using the two splitting formulas differ by a large amount; in fact, they differ by the magnitude of the computed splitting. We provide a criterion for choosing the results obtained with one method over the other by showing that they both give upper bounds to the best result obtainable within the framework of the model. However, because of the large differences between the two methods, the quantitative value of the splitting should be viewed with caution.     

Radiochemical methods in nuclear waste management

Radiochemical techniques play an important role in nuclear waste management studies at the Centre for Analytical Research in the Environment. Current research includes the measurement of atmospheric emissions from a reprocessing plant, modelling of environmental pathways, and evaluation of reactor materials for the prediction of releases from ultimate disposal sites. A radiochemical separation procedure has been developed for¹²⁹I, which has been applied to a study of emissions from the Sellafield nuclear reprocessing plant. Atmospheric emissions, rainfall, grass, milk and wild food are analysed to model the ultimate fate of¹²⁹I. A new procedure has been developed for measuring sub-ppm concentrations of chlorine in archive steel samples as part of programme to produce an inventory of arisings of³⁶Cl from nuclear power stations. The method has been extended to other reactor materials and this paper describes the application of the radiochemical method for Magnox alloys, mild steel and cast iron.     

Bis(1,2-bis(diphenylphosphino)ethane)tungsten(0) Complexes Containing Electron-Saturated Metal Centers and Singly-Coordinated Bridging Ligands

Reaction of 1,4-diisocyanobenzene or 4-isocyanobenzonitrile with trans-W(N(2))(2)(DPPE)(2) (DPPE = 1,2-bis(diphenylphosphino)ethane) produced cis-WL(2)(DPPE)(2), where L = 1,4-diisocyanobenzene or 4-isocyanobenzonitrile. cis-(CNC(6)H(4)NC)(2)W(DPPE)(2) crystallizes in the triclinic space group P&onemacr;, with a = 12.848(3) ?, b = 13.596(3) ?, c = 19.072(3) ?, alpha = 78.99(2) degrees, beta = 70.66(2) degrees, gamma = 65.26(2) degrees, V = 2849.8(11) ?(3), and Z = 2. cis-(NCC(6)H(4)NC)(2)W(DPPE)(2) crystallizes in the triclinic space group P&onemacr;, with a = 12.712(3) ?, b = 13.700(3) ?, c = 19.109(3) ?, alpha = 77.91(2) degrees, beta = 70.63(2) degrees, gamma = 64.76(2) degrees, V = 2830.7(13) ?(3), and Z = 2. Both compounds possess a distorted octahedral geometry about the metal center, with the two isocyanide ligands cis to one another. The isocyanide ligands are substantially bent along the CNC axis of the isocyanide group coordinated to tungsten. For the complex containing the symmetric ligand, CNC(6)H(4)NC, the mean CNC angle for the coordinated end of the isocyanide is 139.1(11) degrees, the average W-C bond length is 1.86(1) ?, and the C&tbd1;N bond lengths have a mean value of 1.30(2) ?. These data indicate substantial back-donation from an electron-saturated tungsten atom. This is supported spectroscopically, with substantial shifts to lower wavenumbers for the C-N stretching frequencies of the coordinated isocyanide groups. Similar trends are observed in cis-(NCC(6)H(4)NC)(2)W(DPPE)(2). Both compounds contain electron-rich metals surrounded by large ligands which apparently protect the metals from atmospheric oxidation. The isocyanide ligands in both complexes contain a second coordinating group pointing away from the metal into the environment surrounding the molecules, providing the potential for polymetallic complexes containing metals in a variety of oxidation states.     

Study of the direct detection of crosslinks in hydrocarbons by 13C-NMR. I. Preparation and characterization of model compound 1,1,2,2-tetra(tridecyl) ethane

The present series of papers is the commencement of a study aimed at the direct detection and quantification of crosslinking in hydrocarbons with the ultimate objective of a precise study of radiation-induced crosslinking in polyethylene. The subject of the present paper is the synthesis of a model compound containing a crosslink in a well-defined position sufficiently remote from the chain ends to be representative of an average crosslink in polyethylene. Such a compound in the form of 1,1,2,2-tetra(tridecyl) ethane has been synthetized and isolated in pure form in the course of the present work. Melting points and x-ray spacings of the new compound have been determined, and a comparison with the corresponding linear paraffins has been made. Effects are noted relating to the influence of molecular shape on the GPC elution volume, in which context an observation on a cyclic paraffin is also quoted.     

Incomplete idempotent Schröder quasigroups and related packing designs

Summary In this paper it is proved that, for any positive integern 2, 3 (mod 4),n 7, there exists an incomplete idempotent Schröder quasigroup with one hole of size two IISQ(n, 2) except forn = 10. It is also proved that for any positive integern 0, 1 (mod 4), there exists an idempotent Schröder quasigroup ISQ(n) except forn = 5 and 9. These results completely determine the spectrum of ISQ(n) and provide an application to the packing of a class of edge-coloured block designs.Research supported by NSERC grant A-5320.Research supported by NSFC grant 19231060-2.