Oscillating reactions are one of the most interesting topics in chemistry and analytical chemistry. Fluctuations in concentrations of one the reacting species (usually a reaction intermediate) create an oscillating chemical reaction. In oscillating systems, the reaction is far from thermodynamic equilibrium. In these systems, at least one autocatalytic step is required. Developing an instinctiv...

Flows in the neighborhood of spinning or oscillating bodies are of interest to both academic workers and industry. Among them, the flows between oscillating cylinders are some of the most important and interesting problems of motion near oscillating bodies. As early as 1886, Stokes [1] established an exact solution for the rotational oscillations of an infinite rod immersed in a classical linea...

In this study, factors controlling autonomous vesicle oscillations exhibited by self-oscillating diblock copolymers were investigated. The self-oscillating diblock copolymer contains poly(ethylene oxide) (PEO) as the hydrophilic block and a random copolymer composed of N-isopropylacrylamide (NIPAAm) with side chains of ruthenium tris(2,2'-bipyridine) (Ru(bpy)3), which catalyzes the Belousov-Zha...

In this paper, we investigated the activation energies of the aggregation−disaggregation self-oscillation induced by the Belousov-Zhabotinsky (BZ) reaction by utilizing the nonthermoresponsive polymer chain in a wide temperature range. This is because the conventional type self-oscillating polymer chain, with thermoresponsive poly(Nisopropylacrylamide) (poly(NIPAAm) main-chain covalently bonded...

‎The controlled harmonic oscillator with retarded damping‎, ‎is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems‎. ‎In this paper‎, ‎to solve this problem‎, ‎we presented an analytical method‎. ‎This approach is based on the homotopy perturbation method‎. ‎The solution procedure becomes easier‎, ‎simpler and mor...

A Hamiltonian approach to the solution of the VlasovPoisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new Hamiltonian that contains slowly varying terms only. The formalism has been applied to the coherent beam-beam interaction, and a stationary solution to the transform...

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the uniform convergence of the solution of the oscillating systems to the bounded uniformly continuous solution of the homogenized system.

A time-free, drift-free, multi-dimensional model of friction is introduced. A discrete implementation is developed which exhibits four solution regimes: sticking, creeping, oscillating, and sliding. Its computational solution is efficient to compute online and is robust to noise. It is applied to haptic rendering.