International Journal of Modern Physics C

We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing with locally conserving money transactions, the money distribution goes to the Gibb's distribution of statistical mechanics. We then consider the effects of savings, etc. and see how the distribution changes. We also propose a new model where the agents invest equal amounts of money in each transaction. We find that for short time-period, the money distribution obeys a power-law with an exponent very close to unity, and has an exponential tail; after a very long time, this distribution collapses and the entire amount of money goes to a tiny fraction of the population.

The Tobin tax is an often discussed method to tame speculation and get a source of income. The discussion is especially heated when the financial markets are in crisis. In this article we refer to the foreign exchange markets. The Tobin tax should be a small international tax affecting all currency transactions and thus consequently reducing destabilizing speculations. In this way this tax should take over a control function. By including the Tobin tax in the microscopic model of Cont and Bouchaud one finds that this tax could be the right method to control foreign exchange operations and to get a good source of income.

In this paper a dissipative trigonometrically-fitted two-step explicit hybrid method is developed. This method is based on a dissipative explicit two-step method developed recently by Papageorgiou, Tsitouras and Famelis.⁶ Numerical examples show that the procedure of trigonometrical fitting is the only way in one to produce efficient dissipative methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions.

Given a continuous function f(x), suppose that the sign of f has only finitely many discontinuous points in the interval [0, 1]. We show how to use a sequence of one-dimensional deterministic binary cellular automata to determine the sign of f(ρ) where ρ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that f satisfies certain technical conditions.

We introduce a new Monte Carlo algorithm which incorporates a guiding function to the conventional Monte Carlo method. In this way, the efficiency of Monte Carlo methods is drastically improved. Two more ingredients, namely, the elimination of irrelevant degrees of freedom and the concept of optimal temperature are also introduced which can further speed up the search process. We use this algorithm to search for the optimal path of the traveling salesman problem and the ground state energy of the Anderson–Edwards spin glass model and demonstrate that its performance is comparable with more elaborate and heuristic methods.

A model of the dynamics of appearance of a new collective feeling, in addition and opposite to an existing one, is presented. Using percolation theory, the collective feeling of insecurity is shown to be able to coexist with the opposite collective feeling of safety. Indeed this coexistence of contradictory social feelings result from the simultaneous percolation of two infinite clusters of people who are respectively experiencing a safe and unsafe local environment. Therefore opposing claims on national debates over insecurity are shown to be possibly both valid.

We provide an asymmetrical quantum key distribution protocol based on the correlations of EPR pairs. It is a variant of the modified Lo–Chau protocol where the EPR pair is not in the state Φ⁺ but is in one of the four states {Φ^±, Ψ^±}. The two sides communicating with each other are not equal in the process of establishing the key. A public key system can be built on the protocol. It differs from classical public key system in that there are three keys: the public key, the secret key and the real key.

Mobile phones are very useful devices. One can phone with them and one can also use them to reach and teach students in high schools as well as in universities. To this end, with an example, the feasibility of the approach was demonstrated. A science simulation using the processing power of the phone was also shown.

The Taylor series expansion- and least squares-based lattice Boltzmann method (TLLBM) was used in this paper to extend the current thermal model to an arbitrary geometry so that it can be used to solve practical thermo-hydrodynamics in the incompressible limit. The new explicit method is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least squares approach. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Numerical simulations of natural convection in a square cavity on both uniform and nonuniform grids have been carried out. Favorable results were obtained and compared well with the benchmark data. It was found that, to get the same order of accuracy, the number of mesh points used on the nonuniform grid is much less than that used on the uniform grid.

We found that numbers of densely connected clusters in Barabási–Albert (BA) networks follow the exponential distribution. Heuristic arguments presented in the paper allow us to deduce that the critical temperature of the Ising model on the BA network is closely related to critical temperature of the largest densely connected cluster within the network. The arguments explain the logarithmic dependence of the critical temperature on the size of the network.

We have analyzed the lifetimes of states by considering the relaxation trajectories following a quench. The average lifetimes, as a function of the quench depth into the two-phase region, shows a very sharp drop defining a limit of stability for metastable states. Using the limit of stability we define a line similar to a spinodal in the two-phase region.