Invariants of chaotic Hamiltonian systems

The invariants of chaotic bounded Hamiltonian systems and their relation to the solutions of the first variational equations of the equations of motion are studied. We show that these invariants are characterized by the fact that they either lose the property of differentiability as functions on phase space or that a certain formal power series defined in terms of the derivatives of the invariants has zero radius of convergence. For a specific example, we show that the former possibility appears to apply.     

A Facile and Convenient Method for the Synthesis of 8-Methoxy 10,11-Dihydronaphtho [1,2-b]Quinolines

Dihydronaphthoquinolines are relatively rare polycyclic heterocyclic compounds. We wish to report a simple and convenient preparative method for hitherto unknown compounds with these new structural features. 6-methoxy tetralone¹ (I) 3.5g (.02 mole) in 3 ml DMF was added slowly to 4.6g (.02 mole) of POCl₃ in 3ml DMF at 0°C. The mixture was stirred for 5 hrs. and the temp. was then gradually raised from 0° to 60–65°C. The resultant complex was treated with aq. sodium acetate solution till pH5–6 was reached. The extract on usual purification, furnished 3.2g (80°%.) of 1-chloro, 6-methoxy, 1,2,3,4 tetrahydro naphthalene-2-aldehyde(II)⁺²     

Synthesis of (±)-2-Methoxy-9a-Carbamorphinan and (±)-2-Methoxy-9a-Carba-14α-Morphinan: Acid Catalyzed Cyclizations of 1-m-Methoxybenzyl-4, 4a,5,6,7,8-Hexahydronaphthalen-2(3H)-ONE and 1 -m-Methox Ybenzyloctalins

The bridged-ethers, (±)-2-methoxy-9a-carbamorphinan (1b) and (±)-2-methoxy-9a-carba-14α-morphinan(2b) have been synthesized. The acid-catalyzed cyclizations of 1-m-methoxy benzyloctalone 3b and 1-m-methoxybenzyloctalins 4b proceed with high regio-and stereoselectivities leading mostly to the bridged-ketone 14 and ether 1b respectively, along with o-methoxy-tetracyclic ketone 15 and the ether 17, in addition to other minor products.     

Quasi-invariants and generalized Killing vectors-II

We consider here the problem of the existence of a quasi-invariant which is linear in the momenta for Hamiltonians in three degrees of freedom. We show that such quasi-invariants are more constrained in their structure than in the two degrees of freedom case. We also show that some of these quasi-invariants have to be interpreted as ‘pseudo-translations’, i.e., as translations in a non-orthogonal system of coordinates.     

Studies on the relationship between structure and electrophoretic mobility of alpha-helical and beta-sheet peptides using capillary zone electrophoresis.

The electrophoretic behaviour of a series of 33 different synthetic peptides has been investigated using free solution high-performance capillary zonal electrophoretic (HPCZE) methods. The dependency of the electrophoretic mobility, mu(em), on the peptide charge, q, and on the charge-to-size ratio parameter, zeta, determined according to several electromobility models, have been examined. Significant divergences from linearity in the mu(em) vs. q or the mu(em) vs. zeta plots were noted for several peptides, possibly due to the proclivity of specific arrangements of their amino acid sequences to assume preferred alpha-helical or beta-sheet conformational features rather than random coil structures under the HPCZE conditions. These results provide further demonstration of the facility of HPCZE procedures to probe the effects of compositional, sequential and conformational differences of closely-related peptides and their consequences on their physicochemical behaviour in solution.     

Differentiability of invariants and Liapunov equations in Hamiltonian systems

In this communication, we investigate the behavior of the derivatives of invariants for Hamiltonian systems, using information derived from an analysis of the Liapunov exponents of the system. We show that under certain conditions on the analyticity properties of the solutions of the equations of motion, it is possible to construct 2n invariants of motion which are guaranteed to beC ^∞ as functions of phase space and time in a suitably defined domainD.     

Time dependent canonical perturbation theory I: General theory

In this communication, we reanalyze the causes of the singularities of canonical perturbation theory and show that some of these singularities can be removed by using time-dependent canonical perturbation theory. A study of the local and global properties (in terms of the perturbation parameter) is also undertaken.     

Loss Reduction by Means of Two-Dimensional Roughness Elements on the Suction Surface of a Linear Turbine Rotor Cascade

This paper reports the results of experimental investigations carried out to reduce pressure losses by means of two-dimensional roughness elements (in the form of stainless steel tubes of different diameters). The roughness elements are fixed at various axial stations on the suction surface of 120° turning, 175 mm chord, impulse turbine rotor blades. Flow measurements are carried out at the exit of the cascade at five axial stations, using a five-hole probe operating in non-nulling mode. In addition, the blade surface static pressure distribution is measured. The data from the five-hole probe measurements are used to calculate pressure, velocity and flow angle distributions at the cascade exit and these results are used to calculate mass averaged values and integral parameters such as wake half-width, loss coefficient, etc. The static pressure distribution is altered very little except near the roughness element. The lift coefficient remains almost constant for all configurations and the drag coefficient is reduced for some configurations. The non-dimensional total pressure defects in the wake for all configurations followed Gaussian distribution. A two-dimensional roughness element of 0.6 mm diameter placed at 0.65 chord on the suction surface showed an appreciable reduction in pressure losses.