On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond.
We study the behavior of the chemical reactions A+A-->A+S and A+A-->S+S (where the reactive species A and the inert species S are both assumed to be immobile) embedded on Bethe lattices of arbitrary coordination number z and on a two-dimensional (2D) square lattice. For the Bethe lattice case, exact solutions for the coverage in the A species in terms of the initial condition are obtained. In particular, our results hold for the important case of an infinite one-dimensional (1D) lattice (z=2). The method is based on an expansion in terms of conditional probabilities which exploits a Markovian property of these systems. Along the same lines, an approximate solution for the case of a 2D square lattice is developed. The effect of dilution in a random initial condition is discussed in detail, both for the lattice coverage and for the spatial distribution of reactants.
Role of density fluctuations in bimolecular reaction kinetics
Abstract The influence of initial thermal density fluctuations of reactants on the bimolecular reaction kinetics (A + B→C) is considered. It is shown that the
Actuating Principle of Online Automatic Balancer with Counter Weight Driven by Magnetic Force
Kinematic precept of mass block in automatic balancer is proposed following the principle of online automatic dynamic balancing.By combination of electromagnet and permanent magnet,the magnetic circuit of the balancer with ring coil and rare earth permanent magnet is designed.Actuating process of the balancer is discussed and then a step drive voltage waveform is defined.For the high-speed grinding motorized spindle 170MD12Y16,the mechanical structure and dimensions of the balancer are schemed out.The electromagnetic simulations for the designed balancer are conducted and the better coil ampere-turns and reluctance adjusting ring thickness are then determined.The validity of simulation results is verified by a balancer driving experiment and the desired voltage value and its duration time are also determined.the designed balancer has a stable operation process without out-of-step and fluctuation around balanced position when the ampere-turns are considered as 1 kA,the reluctance adjusting ring thickness 0.2 mm,the driving voltage 12.4 V and the voltage duration time 120 ms.