Quadrupolar ordering of phospholipid molecules in narrow necks of phospholipid vesicles

Shapes of phospholipid vesicles that involve narrow neck(s) were studied theoretically. It is taken into account that phospholipid molecules are intrinsically anisotropic with respect to the membrane normal and that they exhibit quadrupolar orientational ordering according to the difference between the local principal membrane curvatures. Direct interactions between oriented molecules were considered within a linear approximation of the energy coupling with the deviatoric field. The equilibrium shapes of axisymmetric closed vesicles were studied by minimization of the free energy of the phospholipid bilayer membrane under relevant geometrical constraints. The variational problem was stated by a system of Euler-Lagrange differential equations that revealed a singularity in the derivative of the meridian curvature at points where the effect of the orientational ordering exactly counterbalances the effect of the isotropic bending. The system of Euler-Lagrange differential equations was solved numerically to yield consistently related equilibrium orientational distribution of the phospholipid molecules and vesicle shape. According to our estimation of the model constants the formation of the neck is promoted if direct interactions between the oriented molecules are taken into account. It was shown that the energy of the equilibrium shapes is considerably affected by the quadrupolar ordering of phospholipid molecules.     

Analysis of the Kleiser-Schumann method

Summary The Kleiser-Schumann algorithm for the approximation of the Stokes problem by Fourier/Legendre polynomials is analized. Stability when the degree of the polynomials increases is established, whereas error estimates in Sobolev spaces are proven.The research of this author has been partially supported by the U.S. Army through its European Research Office under contract No. DAJA-84-C-0035     

Many-body perturbation theory and polarization propagator studies of the structure, energetics and excitation spectrum of CO3

Geometry optimization has been performed on CO₃ in the SCF approximation and in the second-, third-, and fourth-order MBPT approximations limited to single and double substitutions using a double-zeta plus polarization basis set. The energetics of the formation and decomposition of CO₃ from the reactions CO₂ + O(¹D) → CO₃ and CO₃ + CO → 2CO₂, respectively, have been calculated in several approximations including full fourth-order MBPT. In addition first-order polarization propagator calculations have been performed to identify the low-lying excited states.     

Good reduction of elliptic curves defined over\mathbb{Q}(\sqrt[3]{2})

Partially supported by Ministero della Pubblica istruzione—Italia. Consiglio Nazionale delle Ricerche—Italia.     

Perspectives on bioenergy and biotechnology in Brazil

Brazil is one of the world’s largest producers of alcohol from biomass at low cost and is responsible for more than 1 million direct jobs. In 1973, the Brazilian Program of Alcohol (Proalcool) stimulated the creation of a bioethanol industry that has led to large economic, social, and scientific improvements. In the year 1984, 94.5% of Brazil’s cars used bioethanol as fuel. In 2003/2004, 350.3 million of sugarcane produced 24.2 million t of sugar and 14.4 billion L of ethanol for an average 4.3 million cars using ethanol. Since its inception, cumulative investment in Proalcool totals US$11 billion, and Brazil has saved US$27 billion in oil imports. The ethanol production industry from sugarcane generates 152 times more jobs than would have been the case if the same amount of fuel was produced from petroleum, and the use of ethanol as a fuel is advantageous for environmental reasons. In 2003, one of the biggest Brazilian ethanol industries started consuming 50% of the residual sugarcane bagasse to produce electrical energy (60 MW), a new alternative use of bioenergy for the Brazilian market. Other technologies for commercial uses of bagasse are in development, such as in the production of natural fibers, sweeteners (glucose and xylitol), single-cell proteins, lactic acid, microbial enzymes, and many other products based on fermentations (submerged and semisolid). Furthermore, studies aimed at the increase in the biosynthesis of sucrose and, consequently, ethanol productivity are being conducted to understand the genetics of sugarcane. Although, at present, there remain technical obstacles to the economic use of some ethanol industry residues, several research projects have been carried out and useful data generated. Efficient utilization of ethanol industry residues has created new opportunities for new value-added products, especially in Brazil, where they are produced in high quantities.     

Atomic and gravitational clock

Atomic and gravitational clocks are governed by the laws of electrodynamics and gravity, respectively. While the strong equivalence principle (SEP) assumes that the two clocks have been synchronous at all times, recent planetary data seem to suggest a possible violation of the SEP. Our past analysis of the implications of an SEP violation on different physical phenomena revealed no disagreement. However, these studies assumed that the two different clocks can be consistently constructed within the framework. The concept of scale invariance, and the physical meaning of different systems of units, are now reviewed and the construction of two clocks that do not remain synchronous—whose rates are related by a nonconstant function _a—is demonstrated. The cosmological character of _a is also discussed.This paper is reprinted with minor editorial modifications fromNature,296, 709 (1982).