Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homologyComment: LaTex with 10 eps figure

Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps

Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable, volume-preserving maps with one action and $d$ angles. For the area-preserving case, Greene's residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. We study a three-dimensional, reversible, volume-preserving analogue of Chirikov's standard map with one action and two angles. We investigate the preservation and destruction of tori under perturbation by computing the "residue" of nearby periodic orbits. We find tori with Diophantine rotation vectors in the "spiral mean" cubic algebraic field. The residue is used to generate the critical function of the map and find a candidate for the most robust torus.Comment: laTeX, 40 pages, 26 figure

Suppression of decoherence via strong intra-environmental coupling

We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin--spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schroedinger equation for the spin--spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in suppression of decoherence. This effect could play an important role in the construction of solid state quantum devices such as quantum computers.Comment: 4 pages, 3 figures, Revtex fil

rs5888 Variant of SCARB1 Gene Is a Possible Susceptibility Factor for Age-Related Macular Degeneration

Major genetic factors for age-related macular degeneration (AMD) have recently been identified as susceptibility risk factors, including variants in the CFH gene and the ARMS2 LOC387715/HTRA1locus. Our purpose was to perform a case-control study in two populations among individuals who did not carry risk variants for CFHY402H and LOC387715 A69S (ARMS2), called “study” individuals, in order to identify new genetic risk factors. Based on a candidate gene approach, we analyzed SNP rs5888 of the SCARB1 gene, coding for SRBI, which is involved in the lipid and lutein pathways. This study was conducted in a French series of 1241 AMD patients and 297 controls, and in a North American series of 1257 patients with advanced AMD and 1732 controls. Among these individuals, we identified 61 French patients, 77 French controls, 85 North American patients and 338 North American controls who did not carry the CFH nor ARMS2 polymorphisms. An association between AMD and the SCARB1 gene was seen among the study subjects. The genotypic distribution of the rs5888 polymorphism was significantly different between cases and controls in the French population (p<0.006). Heterozygosity at the rs5888 SNP increased risk of AMD compared to the CC genotypes in the French study population (odds ratio (OR) = 3.5, CI95%: 1.4–8.9, p<0.01) and after pooling the 2 populations (OR = 2.9, 95% CI: 1.6–5.3, p<0.002). Subgroup analysis in exudative forms of AMD revealed a pooled OR of 3.6 for individuals heterozygous for rs5888 (95% CI: 1.7–7.6, p<0.0015). These results suggest the possible contribution of SCARB1, a new genetic factor in AMD, and implicate a role for cholesterol and antioxidant micronutrient (lutein and vitamin E) metabolism in AMD

NACA Advanced Restricted Reports

Report discusses an investigation into the mechanical stability of a rotor with two vertically hinged blades mounted on symmetrical supports of equal stiffness and mass. Information about the instability regions and effect of damping is included. The two-blade rotor was found to have two shaft-critical speeds at which instability can occur as well as a second region at which self-excited vibrations occur

NACA Technical Reports

Vibrations of rotary-wing aircraft may derive their energy from the rotation of the rotor rather than from the air forces. A theoretical analysis of these vibrations is described and methods for its application are explained in Chapter one. Chapter two reports the results of an investigation of the mechanical stability of a rotor having two vertically hinged blades mounted upon symmetrical supports, that is, of equal stiffness and mass in all horizontal directions. Chapter three presents the theory of ground vibrations of a two-blade helicopter rotor on anisotropic flexible supports

NACA Technical Notes

Report presenting an extension of previous work on the theory of self-excited mechanical oscillations of hinged rotor blades. This particular report details the missing case of one or two blades on unequal supports. Results regarding types of instability, general behavior of rotor system as a function of rotor speed, and effect of damping is provided

NACA Technical Notes

Report presenting vibrations of rotary-wing aircraft, which may derive their energy from the rotation of the rotor rather than from the air forces. The theory includes the effects of unequal stiffness of the pylon for deflections in different directions and the effect of damping in the hinges and in the pylon. Some areas of further investigation include polar symmetry and two blade cases