Effects of Saving and Spending Patterns on Holding Time Distribution

The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution can also be obtained by proposing a new model where the preferential spending behavior is considered. The association of the distribution with the probability of money to be exchanged has also been discussed.Comment: 9 pages, 6 figure

Adaptive Guaranteed-Performance Consensus Control for Multiagent Systems With an Adjustable Convergence Speed

Adaptive guaranteed-performance consensus control problems for multi-agent systems are investigated, where the adjustable convergence speed is discussed. This paper firstly proposes a novel adaptive guaranteed-performance consensus protocol, where the communication weights can be adaptively regulated. By the state space decomposition method and the stability theory, sufficient conditions for guaranteed-performance consensus are obtained, as well as the guaranteed-performance cost. Moreover, since the convergence speed is usually adjusted by changing the algebraic connectivity in existing works, which increases the communication burden and the load of the controller, and the system topology is always given in practical applications, the lower bound of the convergence coefficient for multi-agent systems with the adaptive guaranteed-performance consensus protocol is deduced, which is linearly adjustable approximately by changing the adaptive control gain. Finally, simulation examples are introduced to demonstrate theoretical results

Comparison of two efficient methods for calculating partition functions

In the long-time pursuit of the solution to calculate the partition function (or free energy) of condensed matter, Monte-Carlo-based nested sampling should be the state-of-the-art method, and very recently, we established a direct integral approach that works at least four orders faster. In present work, the above two methods were applied to solid argon at temperatures up to $300$K, and the derived internal energy and pressure were compared with the molecular dynamics simulation as well as experimental measurements, showing that the calculation precision of our approach is about 10 times higher than that of the nested sampling method.Comment: 6 pages, 4 figure