Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Thermodynamic properties of Pb2PtO4 and PbPt2O4 and phase equilibria in the system Pb–Pt–O

The compounds Pb2PtO4 and PbPt2O4 were synthesized from an intimate mixture of yellow PbO and Pt metal powders by heating under pure oxygen gas at 973 K for periods up to 600 ks with intermediate grinding and recompacting. Both compounds were found to decompose on heating in pure oxygen to PbO and Pt, apparently in conflict with the requirements for equilibrium phase relations in the ternary system Pb–Pt–O. The oxygen chemical potential corresponding to the three-phase mixtures, Pb2PtO4 + PbO + Pt and PbPt2O4 + PbO + Pt were measured as a function of temperature using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the solid electrolyte and pure oxygen gas at 0.1 MPa pressure as the reference electrode. The standard Gibbs free energies of formation of the ternary oxides were derived from the measurements. Analysis of the results indicated that the equilibrium involving three condensed phases Pb2PtO4 + PbO + Pt is metastable. Under equilibrium conditions, Pb2PtO4 should have decomposed to a mixture of PbO and PbPt2O4. Measurement of the oxygen potential corresponding to this equilibrium decomposition as a function of temperature indicated that decomposition temperature in pure oxygen is 1014(±2) K. This was further confirmed by direct determination of phase relations in the ternary Pb–Pt–O by equilibrating several compositions at 1023 K for periods up to 850 ks and phase identification of quenched samples using X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). Only one ternary oxide PbPt2O4 was stable at 1023 K under equilibrium conditions. Alloys and intermetallic compounds along the Pb–Pt binary were in equilibrium with PbO.

NMR spectrum of pyridine-N-oxide in a thermotropic nematic phase

Absract is not available.

NMR studies of phase transition in ammonium hydrogen bischloroacetate, NH4H(CH2ClCOOO)2

Proton second moment (M2) and spin-lattice relaxation time (T1) of Ammonium Hydrogen Bischloroacetate (ABCA) have been measured in the range 77-350 K. A value of 6.5 G2 has been observed for the second moment at room temperature, which is typical of NH4+ reorientation and also a second moment transition in the range 170-145 K indicates the freezing of NH4+ motion. The NMR signal disappears dicontinuously at 128 K. Proton spin-lattice relaxation time (T1) Vs temperature, yielded only one sharp miniumum of 1.9 msec which is again typical of NH4+ reorientation. A slope change at 250 K is also observed, prbably due to CH2 motion. Further, the FID signal disappears at 128 K. Thus the Tc appears to be 128 K (of two reported values 120 K and 128 K). Activation energies have been calculated and the mechanism of the phase transition is discussed.

Lotte Stern and Dr. Alfred Stern with Otto Wallerstein, a relative of Lotte's father; Berkeley, California.

From left to right: Lotte Stern, Otto Wallerstein, Alfred Stern; Photograph taken shortly after arrival in Berkeley, California

Quantitative and molecular genetics of juvenile wood traits in radiata and slash/Caribbean pines.

The Juvenile Wood Initiative (JWI) project has been running successfully since July 2003 under a Research Agreement with FWPA and Letters of Association with the consortium partners STBA (Southern Tree Breeding Association), ArborGen and FPQ (Forestry Plantations Queensland). Over the last five and half years, JWI scientists in CSIRO, FPQ, and STBA have completed all 12 major milestones and 28 component milestones according to the project schedule. We have made benchmark progress in understanding the genetic control of wood formation and interrelationships among wood traits. The project has made 15 primary scientific findings and several results have been adopted by industry as summarized below. This progress was detailed in 10 technical reports to funding organizations and industry clients. Team scientists produced 16 scientific manuscripts (8 published, 1 in press, 2 submitted, and several others in the process of submission) and 15 conference papers or presentations. Primary Scientific Findings. The 15 major scientific findings related to wood science, inheritance and the genetic basis of juvenile wood traits are: 1. An optimal method to predict stiffness of standing trees in slash/Caribbean pine is to combine gravimetric basic density from 12 mm increment cores with a standing tree prediction of MoE using a time of flight acoustic tool. This was the most accurate and cheapest way to rank trees for breeding selection for slash/Caribbean hybrid pine. This method was also recommended for radiata pine. 2. Wood density breeding values were predicted for the first time in the STBA breeding population using a large sample of 7,078 trees (increment cores) and it was estimated that selection of the best 250 trees for deployment will produce wood density gains of 12.4%. 3. Large genetic variation for a suite of wood quality traits including density, MFA, spiral grain, shrinkage, acoustic and non-acoustic stiffness (MoE) for clear wood and standing trees were observed. Genetic gains of between 8 and 49% were predicted for these wood quality traits with selection intensity between 1 to 10% for radiata pine. 4. Site had a major effect on juvenile-mature wood transition age and the effect of selective breeding for a shorter juvenile wood formation phase was only moderate (about 10% genetic gain with 10% selection intensity, equivalent to about 2 years reduction of juvenile wood). 5. The study found no usable site by genotype interactions for the wood quality traits of density, MFA and MoE for both radiata and slash/Caribbean pines, suggesting that assessment of wood properties on one or two sites will provide reliable estimates of the genetic worth of individuals for use in future breeding. 6. There were significant and sizable genotype by environment interactions between the mainland and Tasmanian regions and within Tasmania for DBH and branch size. 7. Strong genetic correlations between rings for density, MFA and MoE for both radiata and slash/Caribbean pines were observed. This suggests that selection for improved wood properties in the innermost rings would also result in improvement of wood properties in the subsequent rings, as well as improved average performance of the entire core. 8. Strong genetic correlations between pure species and hybrid performance for each of the wood quality traits were observed in the hybrid pines. Parental performance can be used to identify the hybrid families which are most likely to have superior juvenile wood properties of the slash/Caribbean F1 hybrid in southeast Queensland. 9. Large unfavourable genetic correlations between growth and wood quality traits were a prominent feature in radiata pine, indicating that overcoming this unfavourable genetic correlation will be a major technical issue in progressing radiata pine breeding. 10. The project created the first radiata pine 18 k cDNA microarray and generated 5,952 radiata pine xylogenesis expressed sequence tags (ESTs) which assembled into 3,304 unigenes. 11. A total of 348 genes were identified as preferentially expressed genes in earlywood or latewood while a total of 168 genes were identified as preferentially expressed genes in either juvenile or mature wood. 12. Juvenile earlywood has a distinct transcriptome relative to other stages of wood development. 13. Discovered rapid decay of linkage disequilibrium (LD) in radiata pine with LD decaying to approximately 50% within 1,700 base pairs (within a typical gene). A total of 913 SNPS from sequencing 177,380 base pairs were identified for association genetic studies. 14. 149 SNPs from 44 genes and 255 SNPs from a further 51 genes (total 95 genes) were selected for association analysis with 62 wood traits, and 30 SNPs were shortlisted for their significant association with variation of wood quality traits (density, MFA and MoE) with individual significant SNPs accounting for between 1.9 and 9.7% of the total genetic variation in traits. 15. Index selection using breeding objectives was the most profitable selection method for radiata pine, but in the long term it may not be the most effective in dealing with negative genetic correlations between wood volume and quality traits. A combination of economic and biological approaches may be needed to deal with the strong adverse correlation.

Photoacoustic investigation of phase transitions in solids

The use of the photoacoustic effect in the investigation of first- and second-order phase transitions has been examined. Changes in the amplitude of the photoacoustic signal across the phase transition are compared with changes in thermal properties such as specific heat and thermal diffusivity. The systemsstudied include NaN02, TlN03, CsN03, NH4N03, BaTiO,, COO, Cu,HgI,, V02 andV305. The current photoacoustic studies are discussed in the light of the theoretical models available.

Electrochemical phase formation (ECPF) and macrogrowth Part I. Hemispherical models

The phenomenological theory of hemispherical growth is generalised to time-dependent nucleation and growth-rates. Special cases, which include models with diffusion-controlled rates, are analysed. Expressions are obtained for small and large time behaviour and peak characteristics of potentiostatic transients, and their use in model parameter estimation is discussed. Two earlier equations are corrected. Numerically calculated transients which are presented exhibit some interesting features such as a maximum preceding the steady state, oscillations and shoulder.

Electrochemical phase formation (ECPF) and macrogrowth Part II. Two-rate models

A general theory is evolved for a class of macrogrowth models which possess two independent growth-rates. Relations connecting growth-rates to growth geometry are established and some new growth forms are shown to result for models with passivation or diffusion-controlled rates. The corresponding potentiostatic responses, their small and large time behaviours and peak characteristics are obtained. Numerical transients are also presented. An empirical equation is derived as a special case and an earlier equation is corrected. An interesting stochastic result pertaining to nucleation events in the successive layers is proved.

Enhancement of organic phase controlled extraction of copper by activated carbon

The addition of activated carbon particles (Darco-G, average size 4.3,μm) is shown to enhance the initial rate of extraction of copper in a Lewis cell by a mixture of α- and β-hydroxyoximes, when the rate of extraction is controlled by resistances in the organic phase. It is likely that the copper complex is adsorbed by carbon near the interace and partially released in the bulk. The enhancing effect of carbon vanishes when toluene is used as a diluent instead of heptane, presumably because toluene preferentially adsorbs on its surface.

Relative host plant species use by the lantana biological control agent Aconophora compressa (Membracidae) across its native and introduced ranges

Aconophora compressa Walker (Hemiptera: Membracidae) was released in 1995 against the weed lantana in Australia, and is now found on multiple host plant species. The intensity and regularity at which A. compressa uses different host species was quantified in its introduced Australian range and also its native Mexican range. In Australia, host plants fell into three statistically defined categories, as indicated by the relative rates and intensities at which they were used in the field. Fiddlewood (Citharexylum spinosum L.: Verbenaceae) was used much more regularly and at higher densities than any other host sampled, and alone made up the first group. The second group, lantana (Lantana camara L.: Verbenaceae; pink variety) and geisha girl (Duranta erecta L.: Verbenaceae), were used less regularly and at much lower densities than fiddlewood. The third group, Sheena’s gold (another variety of D. erecta), jacaranda (Jacaranda mimosifolia D. Don: Bignoniaceae) and myoporum (Myoporum acuminatum R. Br.: Myoporaceae), were used infrequently and at even lower densities. In Mexico, the insect was found at relatively low densities on all hosts relative to those in Australia. Densities were highest on L. urticifolia, D. erecta and Tecoma stans (L.) Juss. ex Kunth (Bignoniaceae), which were used at similar rates to one another. It was found also on a few other verbenaceous and non-verbenaceous host species but at even lower densities. The relative rate at which Citharexylum spp. and L. urticifolia were used could not be assessed in Mexico because A. compressa was found on only one plant of each species in areas where these host species co-occurred. The low rate at which A. compressa occurred on fiddlewood in Mexico is likely to be an artefact of the short-term nature of the surveys or differences in the suites of Citharexylum and Lantana species available there. These results provide further incentive to insist on structured and quantified surveys of non-target host use in the native range of potential biological control agents prior to host testing studies in quarantine.

The influence of HIV infection to the periodontium; a clinical, microbiological, and enzymological study

The main targets of human immunodeficiency virus (HIV) are CD4 receptors of CD4+ lymphocytes and many other cells such as monocytes/macrophages, megakaryocytes, peripheral blood dendritic cells, follicular dendritic cells (DC), epidermal Langerhans cells, and astrocytes. Infection and killing of CD4+ lymphocytes or false reaction of the body to HIV infection and the spontaneous apoptosis of CD4+ lymphocytes decrease CD4+ lymphocyte counts leading to immunosuppression, further disease progression, and appearance of opportunistic infections and malignancies. Oral manifestations are considered to be among the first signs of HIV infection. Enhanced degradation of extracellular matrix and basement membrane components in oral diseases including periodontitis is caused by Zn-dependent enzymes called matrix metalloproteinases (MMPs). The levels and degrees of activation of MMP-1, -2, -3, -7, -8, -9, -25, -26, tissue inhibitors of MMPs (TIMP)-1 and -2, and myeloperoxidase (MPO) and collagenolytic/gelatinolytic activities, and also Ig A, -G, and -M, total protein, and albumin levels in a two-year follow-up were studied from salivary samples. The expression of MMP-7, -8, -9, -25, and -26 immunoreactivities in gingival tissue specimens were studied. Healthy HIV-negative subjects served as controls. All studied clinical periodontal parameters and microbiological evaluation of the periodontopathogens showed that periodontal health of the HIV-positive patients was moderately decreased in comparison to the healthy controls. The levels of Candida in the periodontal pockets and salivary MPO increased with the severity of HIV infection. Immunoreactivities and levels of MMPs and TIMPs, and MMP activities (collagenase, gelatinase) were enhanced in the HIV-positive patient salivary samples relative to the healthy controls regardless of the phase of HIV infection. However, these parameters did not reflect periodontal status in a similar way as in the generally healthy periodontitis patients. Salivary total protein, albumin, IgA, -G, and -M levels were significantly higher in all phases of HIV infection compared to the controls, and salivary total protein, IgG and IgM levels remained higher after two years follow-up, partly correlating with the disease progression and which may reflect the leakage of serum components into the mouth and thus a decreased mucosal barrier. Salivary analyses of MMPs and TIMPs with immunohistochemical analyses showed that HIV infection could predispose to periodontal destruction when compared with healthy controls or the body s defence reactions associated with HIV infection may have been reflected or mediated by MMPs.

A novel investigation of vapor-phase charge-transfer complexes of halogens with n-donors by electron energy loss spectroscopy

Complexes of I2 with diethyl ether and triethylamine and of Br, with diethyl ether have been investigated in the vapor phase for the first time by employing electron energy loss spectroscopy. Besides the CT bands, blue-shifted vacuum-UV bands of the halogens have been assigned; the amine-I, system appears to exhibit two CT bands,associated with two different excited states of the complex.

Lotte Stern and Dr. Alfred Stern with Otto Wallerstein, a relative of Lotte's father; Berkeley, California.

From left to right: Lotte Stern, Otto Wallerstein, Alfred Stern; Photograph taken shortly after arrival in Berkeley, California