Algebraic methods in quantum mechanics: from molecules to polymers

We present a brief review of algebraic techniques developed and applied in molecular spectroscopy in the last five years. We also outline perspectives for new applications of the Lie algebraic method in the first decade of the new century. Received 21 November 2001     

A biogenetically patterned enantiospecific synthesis of allopupukeanones

The first enantiospecific synthesis of allopupukeanones has been accomplished starting from 6-methylcarvone. A biogenetically patterned rearrangement of a pupukeanane to allopupukeanane was employed as the key step.     

Sub-Doppler and Doppler spectroscopy of DCN isotopomers in the terahertz region: ground and first excited bending states (v1v2v3)=(0 1 0)

The rotational spectra of the deuterium cyanide isotopic species DCN, D¹³CN, DC¹⁵N, and D¹³C¹⁵N were recorded in the vibrational ground and first excited bending state (v₂=1) up to 2 THz. The R-branch transitions from J=3←2 to J=13←12 were measured with sub-Doppler resolution. These very high resolution (∼70 kHz) and precise (±3-10 kHz) saturation dip measurements allowed for resolving the underlying hyperfine structure due to the ¹⁴N nucleus in DCN and D¹³CN for transitions as high as J=10←9. Additional high JR-branch (J=25←24 to J=28←27) transitions around 2 THz and direct l-type (ΔJ=0, J=19 to J=25) transitions from 66 to 118 GHz were recorded in Doppler-limited resolution. For the ground state of D¹³C¹⁵N, the J=1←0 transition was measured for the first time. The transition frequency accuracies for the other deuterated species were significantly improved. These new experimental data, together with the available infrared rovibrational data and previously measured direct l-type transitions, were subjected to a global least squares analysis for each isotopomer. This yielded precise sets of molecular constants for the ground and first excited vibrational states, including the nuclear quadrupole and magnetic spin-rotation coupling constants of the ¹⁴N nucleus for DCN and D¹³CN. The hyperfine structure due to the D, ¹³C, and ¹⁵N nuclei have not been resolved, but led to a broadening of the observed saturation dips.     

Decreasing the Displacements of a Composite Saddle-Shaped Cable Roof

The structural possibilities of decreasing the compliance of a composite saddle-shaped cable roof having a compliant support contour are investigated. The use of a supporting contour consisting of cables joined together with tie-bars is considered as a structural method enabling one to decrease the compliance of the roof. Each cable of the support has its own initial flexure. The method is most efficient from the viewpoint of material consumption per unit of covered area relative to the increasing rigidity and prestress level of the cable net.The efficiency of the method was evaluated by a numerical experiment, which was carried out for a composite saddle-shaped cable roof 50 × 50 m in the plan. The roof was formed by two orthogonal cable groups joined with a compliant supporting contour. A hybrid composite cable based on a carbon-fiber-reinforced plastic, a glass-fiber-reinforced plastic, and steel was considered as a material for the cable net in combination with steel. The material consumption and the maximum vertical displacement of the cable net in relation to the initial geometrical characteristics of the supporting contour were obtained. A possibility of decreasing the maximum vertical displacements of the roof by 8% was established.     

Photoluminescence linewidth broadening due to alloy/thickness fluctuation of CdxZn1 − xSe/ZnSe triple quantum wells

Photoluminescence (PL) linewidth broadening of Cd_xZn_{1 − x}Se/ZnSe triple quantum wells, grown on GaAs substrates by molecular beam epitaxy (MBE), has been investigated. Various quantum well (QW) samples have been prepared with different QW thickness and composition (Cd-composition). Measured and calculated PL linewidth are compared. Both composition and thickness fluctuations are considered for the calculation with the parameters such as the volume of exciton, nominal thickness and composition of QWs. Surface roughness measured by atomic force microscopy (AFM) is used to estimate the interface roughness. Results show that when Cd-composition increases additional linewidth broadening due to Zn/Cd interdiffusion is enhanced.     

Atomic-scale simulation of nano-grains:structure and diffusion properties

Nanograins are characterized by a typical grain size from lto 100 nm.Mclecular dynamics aimubations have been carried out for the nanograin sphere with the diameters from 1.45 to 10.12 nm.We study the influence of grain size on structure and diffusion properties of the nanograins.The results reveal that as the grain size is reduced,the fraction of grain surface increases significantly,and the surface width is approximately constant；the diffusicn coefficlent is increased sharply,and the relation of the diffusion coefficient and the grain size is close to exponential relation below 10nm.     

Altered expression of polyhydroxyalkanoate synthase gene and its effect on poly[(R)-3-hydroxybutyrate] synthesis in recombinant Escherichia coli

Polyhydroxyalkanoate (PHA) synthase (PhaC) from Wautersia eutropha was expressed in a wide range of production level in Escherichia coli XL1-Blue cells and its effects on PhaC activity, poly[(R)-3-hydroxybutyrate] [P(3HB)] production and its molecular weights were investigated. The production level of PhaC was controlled both by the amount of chemical inducer (isopropyl-β-d-thiogalactopyranoside, IPTG) added into the medium and the use of different copy number of plasmids. In a flask experiment, as PhaC production level in the cells increased, the PhaC activity also increased in the range of low PhaC concentration. However, PhaC activity did not further increase in the range of high PhaC concentration, probably due to the formation of inclusion body in the cells. The molecular weight of P(3HB) was found to decrease with increasing PhaC activity. This trend was also verified in high cell density cultivation using 10-l jar fermentor. Furthermore, we demonstrated that the use of low copy number plasmid and appropriate induction of PhaC expression were effective in achieving both high productivity and high molecular weight of P(3HB).     

Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.     

Numerical Prediction of the Strain State of Thermoset Matrix/Mineral Filler Composite Plates

The numerical prediction of the fields of inelastic strains (the linear invariant of the tensor of inelastic strains) in thermoset polyester/marble filler composite plates is discussed. A uniformly distributed load is applied to the plates, which lie on a steel base. The strain fields are predicted by means of the boundary element method by using creep test data for the composites and the polyester matrix itself. Identical creep tests were performed for two ages of the materials (1 month and 13 years), which allowed evaluating the aging effect. The study is carried out in two stages. At the first stage, the application of the generalized Maxwell-Gurevich equation to the thermoset matrix/mineral filler composite is demonstrated. The model parameters determined from the experimental creep data is used for the second stage, where the state of inelastic strains in the plates is predicted by applying the boundary element method. The influence of composite formulation (filler content) and physical aging of the polyester matrix on the state of inelastic strains in the plates is shown.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 145–156, March–April, 2005.     

Small and high-density GeSiC dots stacked on buried Ge hut-clusters in Si

Self-assembled GeSiC dots stacked on a Ge hut-cluster layer buried in Si have been investigated. The critical thickness for formation of GeSiC dots is reduced owing to the strain fields from the buried hut-clusters. By utilizing the stacked structure, the dot size is decreased and the uniformity is improved. The highest density of the GeSiC dots with stacked structures is 7.4×10¹⁰ cm⁻², which is six times larger than that of single GeSiC dots. The formation of the self-assembled GeSiC dots is strongly influenced by being stacked with buried Ge dots as well as C incorporation.