The last‐passage (LP) Monte Carlo algorithm for the charge density on a flat conducting surface held at a constant potential is further developed by deriving a generalized last‐passage Green's function on the flat surface. In the previous research, a centered Green's function on the flat surface was used. In the new last‐passage algorithm, an off‐centered point on the flat surface inside the Green's function hemisphere can also be used. To demonstrate the algorithm, the charge density on a circular disk is calculated and it is found that the result agrees very well with the analytic solution. Compared with the previous centered LP, the generalized algorithm is better in most cases and has an advantage that it can use the same potential distribution over the LP hemisphere for different locations inside of the lower flat surface including the center of the hemisphere for the charge density.

First‐passage and last‐passage Monte Carlo algorithms have been used for computing charge distribution on a conducting object. First‐passage algorithms are used for an overall charge distribution on a conducting object and Given–Hwang's last‐passage algorithms are used for a charge density at a specific point on a flat or spherical surface of a conductor. In this paper, a last‐passage algorithm for computing charge distribution over a finite region of a conducting object is presented.

We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.

The last-passage (LP) Monte Carlo algorithms for the charge density on an L-shaped conducting surface are further developed by deriving a quadrupole LP Green's function on the L-shaped flat surface. To demonstrate the algorithm, charge densities on an L-shaped conductor are computed in 3D space and it is found that these results agree very well with the ones from the Given-Hwang's original last-passage algorithm on a flat surface. Compared with the Given-Hwang's LP algorithm, the quadrupole LP one is very suitable for charge density near the L-shaped edge boundary.

We propose a method to make a highly clustered complex network within the configuration model. Using this method, we generated highly clustered random regular networks and analyzed the properties of them. We show that highly clustered random regular networks with appropriate parameters satisfy all the conditions of the small-world network: connectedness, high clustering coefficient, and small-world effect. We also study how clustering affects the percolation threshold in random regular networks. In addition, the prisoner's dilemma game is studied and the effects of clustering and degree heterogeneity on the cooperation level are discussed.Introduction. -Recently, complex networks have played important roles in various fields [1][2][3][4][5]. There are, especially, a lot of researches on the various types of realworld network structures [1,4,5]. As a result, studies to generate network models that resemble various kinds of real-world networks attract a lot of attention. Many methods were proposed to generate complex networks: rewiring model, growing model, configuration model, etc [6][7][8][9][10][11][12][13][14][15][16][17][18].The Watts-Strogatz (WS) model generates a smallworld network based on the rewiring method [6]. The small-world network has a high clustering coefficient and short average path length, but it has restriction in the degree distribution [6,7].The Barabási-Albert (BA) model generates a scale-free network using the growing model with the preferential attachment [8]. It produces the power-law degree distribution, which is frequently observed in a real-world network such as citation networks, metabolic networks, and the Internet [19][20][21][22][23]. However, the network generated by the BA model has a vanishing clustering coefficient in contrast with real-world networks. To overcome this problem of the BA model, many researchers proposed modified BA models [9][10][11][12] that have a high clustering coefficient maintaining the power-law degree distribution.The configuration model is a method to make a random network for a given arbitrary degree sequence. This (a)