International Journal of Modern Physics C

Boltzmann–Gibbs (BG) distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In this paper, we implement these exchange rules on networks and we find that these stationary probability distributions are robust and they are not affected by the topology of the underlying network. We introduce a new family of interactions: random but directed ones. In this case, it is found the topology to be determinant and the mean money per economic agent is related to the degree of the node representing the agent in the network. The relation between the mean money per economic agent and its degree is shown to be linear.

We study the impact of heterogeneous aspirations on the spatial public goods game (PGG) in a square lattice. An aspiration parameter u is introduced to decide who will be more probably to become the potential strategy source in structured population. Individuals are divided into two groups A(u > 0) and B(u = 0) by fraction v and 1 - v. We study how u and v affect cooperation in the PGG. For low values of u, the cooperation level monotonously increases as v increases. However, for large values of u, there exist an intermediate v ≈ 0.5 for which cooperation thrives best. The influence of noise is also investigated. We find that the highest threshold of phase transition is reached at the middle value of noise.

With the consideration of the Brownian motion of nanoparticles in fluids, the probability model for the size of nanoparticles and the model for convective heat transfer of nanofluids are derived based on the fractal character of nanoparticles. The proposed model is expressed as a function of the size of nanoparticles, the volumetric nanoparticle concentration, the thermal conductivity of base fluids, fractal dimension of nanoparticles and the temperature, as well as the random number. It is found that the convective heat flux of nanofluids decreases with increasing of the average diameter of nanoparticles. This model has the characters of both analytical and numerical solutions. The Monte Carlo simulations combined with the fractal geometry theory are performed. Every parameter of the proposed formula on convective heat transfer of nanofluids has clear physical meaning. So the proposed model can reveal the physical mechanisms of convective heat transfer of nanofluids.

This study calculated the crossing time in the diploid mutation–selection model in an infinite population limit for various dominance parameters, h, and selective advantages, by switching on a diploid, asymmetric, sharply-peaked landscape, from an initial state which is the steady state in a diploid, sharply-peaked landscape. The crossing time for h < 1 was found to diverge at the critical fitness parameter, which increased with increasing selective advantage and decreased with increasing sequence length. When the sequence length was increased with a fixed extension parameter, there was no crossing time for h < 1 when the sequence length was longer than the critical sequence length, which increased with increasing selective advantage. The crossing time for h ≤ 1 was found to be an exponentially increasing function of the sequence length, and the crossing time for h > 1 became saturated at a long sequence length. The crossing time decreased with increasing selective advantage, mainly because the larger selective advantage caused the increase in relative density of the reversal allele to grow exponentially at an earlier time.

We have developed a procedure that characterizes the land use pattern of an urban system using: (a) Spatial entropy that measures the extent of spread of residential, business and industrial sectors; and (b) Index of dissimilarity that quantifies the degree of mixing in space of different sectors. The approach is illustrated by using the land use zoning maps of the city state of Singapore and a selection of North American cities. We show that a common feature of most cities is for the industrial areas to be highly clustered while at the same time segregated from the residential or business districts. We also demonstrate that the combination of entropy of residential and dissimilarity index between residential and business areas provides a quantitative and potentially useful means of differentiating the land use pattern of different cities.

The negative externalities from an individual bank failure to the whole system can be huge. One of the key purposes of bank regulation is to internalize the social costs of potential bank failures via capital charges. This study proposes a method to evaluate and allocate the systemic risk to different countries/regions using a Susceptible-Infected-Removable (SIR) type of epidemic spreading model and the Shapley value (SV) in game theory. The paper also explores features of a constructed bank network using real globe-wide banking data.

A lattice Boltzmann model (LBM) for a moving body in shallow waters is developed. Three different schemes, FH's, Guo's and MMP's schemes, for a curved boundary condition at second-order accuracy are used in the study and compared in detail. The multiple-relaxation-time (MRT) is adopted for better stability. In order to deal with the moving body boundary, a certain momentum is added to reflect the interaction between the fluid and the solid; and a refill method for new wetted nodes moving out from solid nodes has been proposed. The described method is applied to simulate static and moving cylinders in shallow waters. The corresponding experiments are further performed for validation of the present model. It is found that all of the three schemes produce similar results that agree well with the experimental data for the static cylinder. However, for the moving boundary, MMP's scheme performs best. Overall, the proposed modeling approach is able to simulate both, static and moving cylinders in shallow water flows at acceptable accuracy.

To find the discrete symmetries of a Hamilton operator Ĥ is of central importance in quantum theory. Here, we describe and implement a brute force method to determine the discrete symmetries given by permutation matrices for Hamilton operators acting in a finite-dimensional Hilbert space. Spin and Fermi systems are considered as examples. A computer algebra implementation in SymbolicC++ is provided.