Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Pigment orientation changes detected by low temperature linear dichroism spectroscopy: cold-hardening transition in phycobilisome-containing organisms

Low temperature (77K) linear dichroism spectroscopy was used to characterize pigment orientation changes accompanying the light state transition in the cyanobacterium, Synechococcus sp. pee 6301, and cold-hardening in winter rye (Secale cereale L. cv. Puma). Samples were oriented for spectroscopy using the gel squeezing method (Abdourakhmanov et aI., 1979) and brought to 77K in liquid nitrogen. The linear dichroism (LD) spectra of Synechococcus 6301 phycobilisome/thylakoid membrane fragments cross-linked in light state 1 and light state 2 with glutaraldehyde showed differences in both chlorophyll a and phycobilin orientation. A decrease in the relative amplitude of the 681nm chlorophyll a positive LD peak was observed in membrane fragments in state 2. Reorientation of the phycobilisome (PBS) during the transition to state 2 resulted in an increase in core allophycocyanin absorption parallel to the membrane, and a decrease in rod phycocyanin parallel absorption. This result supports the "spillover" and "PBS detachment" models of the light state transition in PBS-containing organisms, but not the "mobile PBS" model. A model was proposed for PBS reorientation upon transition to state 2, consisting of a tilt in the antenna complex with respect to the membrane plane. Linear dichroism spectra of PBS/thylakoid fragments from the red alga, Porphyridium cruentum, grown in green light (containing relatively more PSI) and red light (containing relatively more PSll) were compared to identify chlorophyll a absorption bands associated with each photosystem. Spectra from red light - grown samples had a larger positive LD signal on the short wavelength side of the 686nm chlorophyll a peak than those from green light - grown fragments. These results support the identification of the difference in linear dichroism seen at 681nm in Synechococcus spectra as a reorientation of PSll chromophores. Linear dichroism spectra were taken of thylakoid membranes isolated from winter rye grown at 20°C (non-hardened) and 5°C (cold-hardened). Differences were seen in the orientation of chlorophyll b relative to chlorophyll a. An increase in parallel absorption was identified at the long-wavelength chlorophyll a absorption peak, along with a decrease in parallel absorption from chlorophyll b chromophores. The same changes in relative pigment orientation were seen in the LD of isolated hardened and non-hardened light-harvesting antenna complexes (LHCII). It was concluded that orientational differences in LHCII pigments were responsible for thylakoid LD differences. Changes in pigment orientation, along with differences observed in long-wavelength absorption and in the overall magnitude of LD in hardened and non-hardened complexes, could be explained by the higher LHCII monomer:oligomer ratio in hardened rye (Huner et ai., 1987) if differences in this ratio affect differential light scattering properties, or fluctuation of chromophore orientation in the isolated LHCII sample.

The salvo combat model with area fire

This paper analyzes versions of the salvo model of missile combat where area fire is used by one or both sides in a battle. While these models share some properties with the area fire Lanchester model and the aimed fire salvo model, they also display some interesting differences, especially over the course of several salvos. Whereas the relative size of each force is important with aimed fire, with area fire it is the absolute size that matters. Similarly, while aimed fire exhibits square law behavior, area fire shows approximately linear behavior. When one side uses area and the other uses aimed fire, the model displays a mix of square and linear law behavior.