Chaos control by using Motor Maps

In this paper a new method for chaos control is proposed, consisting of an unsupervised neural network, namely a Motor Map. In particular a feedback entrainment scheme is adopted: a chaotic system with a given parameter set generates the reference trajectory for another chaotic system with different parameters to be controlled: the Motor Map is required to provide the appropriate time-varying gain value for the feedback signal. The state of the controlled system is considered as input to the Motor Map. Particular efforts have been paid to the feasibility of the implementation. Indeed, the simulations performed have been oriented to design a Motor Map suitable for an hardware realization, thus some restrictive hypotheses, such as for example a low number of neurons, have been assumed. A huge number of simulations has been carried out by considering as system to be controlled a Double Scroll Chua Attractor as well as other chaotic attractors. Several reference trajectories have also been considered: a limit cycle generated by a Chua's circuit with different parameters values, a double scroll Chua attractor, a chaotic attractor of the family of the Chua's circuit attractors. In all the simulations instead of controlling the whole state space, only two state variables have been fed back. Good results in terms of settling time (namely, the period in which the map learns the control task) and steady state errors have been obtained with a few neurons. The Motor Map based adaptive controller offers high performances, specially in the case when the reference trajectory is switched into another one. In this case, a specialization of the neurons constituting the Motor Map is observed: while a group of neurons learns the appropriate control law for a reference trajectory, another group specializes itself to control the system when the other trajectory is used as a reference. A discrete components electronic realization of the Motor Map is presented and experimental results confirming the simulation results are shown. (c) 2002 American Institute of Physics.     

Nonrelativistic Geodesic Motion

We show that any second-order dynamic equationon a configuration space X R ofnonrelativistic time-dependent mechanics can be seen asa geodesic equation with respect to some (nonlinear)connection on the tangent bundle TX X of relativisticvelocities. We compare relativistic and nonrelativisticgeodesic equations, and study the Jacobi vector fieldsalong nonrelativistic geodesics.     

On the Specific Heat of Fermi–Pasta–Ulam Systems and Their Glassy Behavior

The specific heat of Fermi–Pasta–Ulam systems has until now been estimated through the energy fluctuations of a suitable subsystem, and opposite answers were apparently provided concerning its possible vanishing for vanishing temperatures. In the present paper a more realistic numerical implementation of the specific heat measurement is discussed, which mimics the interaction of the FPU system with a calorimeter. It is found that there exists a freezing critical temperature below which the relaxation times to equilibrium between FPU system and calorimeter become relevant, so that the system presents aging and hysteresis features very similar to those familiar in glasses and spin glasses. In particular, in the framework of such a point of view involving finite long times, the specific heat appears to vanish for vanishing temperatures.     

Invariant Metrics on Cohomogeneity One Manifolds

Let G be one of the connected subgroups of the orthogonal group of ⁿ which acts transitively on the unit sphere S ^n–1. We get the necessary and sufficient condition for G-invariant metrics g on ⁿ \{0} to be extendend to the origin. For n=2 this is a classical result of Berard–Bergery. The curvature tensor and the sectional curvature of any such Riemannian G-manifold ( ⁿ , g) are described in terms of the length of the Killing vector fields, as well as the second fundamental form of the regular orbits G(P)=S ^n–1. As an application we describe all G-invariant metrics which are Kähler, hyperKähler or have constant principal curvatures. Some of these results are generalized to the case of any cohomogeneity one G-manifold which, in a neighbourhood of a singular orbit, can be identified with a twisted product.     

Reactions of water, dihydrogen, dinitrogen, dinitrogen oxide, methane over illuminated ultraclean graphite

Some photocatalytic reactions of different gases on ultraclean graphite have been studied by means of quadrupole mass spectrometry. With water vapor, dihydrogen, dinitrogen and dinitrogen oxide, the UV-illuminated graphite acts as a reducing agent. TPD measurements indicate that photocatalytic processes are strongly affected by adsorption-desorption equilibria.     

EFFECT OF U.V.-IRRADIATION ON SEDIMENTATION BEHAVIOR OF VARIOUS PROTEINS

Abstract— Moderate u.v.-doses (2537 Å) sufficient to reduce enzymatic activities of native enzymes up to about 90 per cent, in general do not produce measurable amounts of smaller dialyzable fragments.
The disappearance of the original boundary in sedimentation diagrams is mostly due to the formation of rapidly sedimenting polydispersed material. Generally the sedimentation constants of the native proteins are not significantly changed. The boundaries, however, often loose their symmetry. The quantum yields for the disappearance of the original boundaries are roughly inversely proportional to the molecular weights. The number of molecules disappearing from the main peak is smaller than the number of molecules inactivated by a given dose. The data indicate that ultracentrifugation provides no satisfactory method for separation of native molecules from the damaged and inactivated. Proteins with labile quaternary structures (e.g. thyroglobulin or hemocyanine) which tend to dissociate under very mild conditions show an enhanced dissociation after u. v.-irradiation.     

2∶1 Complex of desoxycholic acid and ethyl acetate: Disorder in the structure at 298 and 163 K

The crystal structure of the 21 channel complex of desoxycholic acid and ethyl acetate has been investigated at 298 and 163 K. The space group isP2₁2₁2₁(No. 19) with four molecules of desoxycholic acid in the unit cell. The ethyl acetate molecules are enclathrated along the 2₁ axes parallel toc and exhibit differing degrees of disorder in the low- and room-temperature structures. Differences in the disorder imply that it is both statistical and dynamic in nature. Our best model for each structure yieldsR=0.064 [R _w =0.058,w=( ₂ F)^–1] andR=0.068 [R _w =0.064,w=( ² F) ^–1 ] for the ambient- and low-temperature studies respectively.IUPAC Nomenclature: 3, 12-dihydroxy-5-cholan-24-oic acid.