Trajectory stabilization of a model car via fuzzy control

This paper deals with trajectory stabilization of a computer simulated model car via fuzzy control. Stability conditions of fuzzy systems are given in accordance with the definition of stability in the sense of Lyapunov. First, we approximate a computer simulated model car, whose dynamics is nonlinear, by T-S (Takagi and Sugeno) fuzzy model. Fuzzy control rules, which guarantee stability of the control system under a condition, are derived from the approximated fuzzy model. The simulation results show that the fuzzy control rules effectively realize trajectory stabilization of the model car along a given reference trajectory from all initial positions under a condition and the dynamics of the approximated fuzzy model agrees well with that of the model car.     

Peroxide generation and decomposition on polymer surface

Polymer peroxides were generated onto polypropylene and polyurethane films, and polyester fibers by ozonization, UV irradiation, and plasma treatment. Their thermal and redox decompositions were studied using two assays: peroxidase and iodide. They may differ in the sensitivity to access the peroxides, depending on their localization in the polymer substrates. It was found that the generated peroxides are likely to be distributed not only on the outermost surface, but also in the subsurface of the polymer substrates. Plasma treatment provided polyurethane film with easily accessible peroxides, while UV irradiation and ozonization generated peroxides that were mostly incapable of reacting with aqueous solution of peroxidase. Redox decomposition of the peroxide groups by ferrous ions at 25°C showed that less than 50% of peroxides could react with ferrous ions with a rate constant similar to that of hydrogen peroxide in aqueous solution. Thermal decomposition of the peroxides did not obey the first-order kinetics, probably due to formation of not single peroxide species with different decomposition rate constants. The lowest decomposition rate constant observed at 65°C was 3 × 10^?3 min^?1, which did not depend on the polymer substrate nature and the method of peroxide generation. © 1995 John Wiley & Sons, Inc.     

Statistical properties of actions of periodic orbits

We investigate statistical properties of unstable periodic orbits, especially actions for two simple linear maps (p-adic Baker map and sawtooth map). The action of periodic orbits for both maps is written in terms of symbolic dynamics. As a result, the expression of action for both maps becomes a Hamiltonian of one-dimensional spin systems with the exponential-type pair interaction. Numerical work is done for enumerating periodic orbits. It is shown that after symmetry reduction, the dyadic Baker map is close to generic systems, and the p-adic Baker map and sawtooth map with noninteger K are also close to generic systems. For the dyadic Baker map, the trace of the quantum time-evolution operator is semiclassically evaluated by employing the method of Phys. Rev. E 49, R963 (1994). Finally, using the result of this and with a mathematical tool, it is shown that, indeed, the actions of the periodic orbits for the dyadic Baker map with symmetry reduction obey the uniform distribution modulo 1 asymptotically as the period goes to infinity. (c) 2000 American Institute of Physics.     

A synthesis of 3-phenyl-1,2,3,4-tetrahydroisoquinoline and 2-phenyl-1,2,4,5-tetrahydro-3H-3-benzazepine via Pummerer-type cyclization: enhancing effect of boron trifluoride diethyl etherate on the cyclization

A synthesis of 6,7-dimethoxy-3-phenyl-1,2,3,4-tetrahydroisoquinoline (14a) and 7,8-dimethoxy-2-phenyl-1,2,4,5-tetrahydro-3H-3-benzazepine (14b) was achieved via the cyclization of N-(3,4-dimethoxyphenyl)methyl-1-phenyl-2-(phenylsulfinyl)ethylformamide (6a) and N-2-(3,4-dimethoxyphenyl)ethyl-1-phenyl-2-(phenylsulfinyl)-ethylformamide (6b) using the Pummerer reaction as a key step, respectively. The Pummerer reaction of 6a,b under usual conditions using trifluoroacetic anhydride yielded the vinyl sulfides (8a, b), non-cyclized products, as a major product. The cyclization proceeded when boron trifluoride diethyl etherate was used as an additive reagent, thus giving rise to the corresponding cyclized products (7a) and (7b) in moderate yields. We propose that the enhancing effect of the Lewis acid on the cyclization may be attributable to the involvement of a dicationic intermediate, sulfonium-carbenium dication (23).     

A Generalization of Opsut’s Lower Bounds for the Competition Number of a Graph

The notion of a competition graph was introduced by Cohen in 1968. The competition graph C(D) of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. In 1978, Roberts defined the competition number k(G) of a graph G as the minimum number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of the important research problems in the study of competition graphs to characterize a graph by its competition number. In 1982, Opsut gave two lower bounds for the competition number of a graph. In this paper, we give a generalization of these two lower bounds for the competition number of a graph.     

Directed percolation criticality in turbulent liquid crystals

We experimentally investigate the critical behavior of a phase transition between two topologically different turbulent states of electrohydrodynamic convection in nematic liquid crystals. The statistical properties of the observed spatiotemporal intermittency regimes are carefully determined, yielding a complete set of static critical exponents in full agreement with those defining the directed percolation class in 2+1 dimensions. This constitutes the first clear and comprehensive experimental evidence of an absorbing phase transition in this prominent nonequilibrium universality class.     

Elastic convection in vibrated viscoplastic fluids

We observe a new type of behavior in a shear-thinning yield stress fluid: freestanding convection rolls driven by vertical oscillation. The convection occurs without the constraint of container boundaries, yet the diameter of the rolls is spontaneously selected for a wide range of parameters. The transition to the convecting state occurs without hysteresis when the amplitude of the plate acceleration exceeds a critical value. We find that a nondimensional stress, the stress due to the inertia of the fluid normalized by the yield stress, governs the onset of the convective motion.