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Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders ; ; Rahm, Alexander et al in Physical Review. E. (2018), 98 Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models ... [more ▼] Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe nonmonotonic behavior of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. The relative conductivity enhancement increases exponentially with volume fraction in the nematic phase. Moreover, we observe that the orientational ordering of the rods in the nematic phase induces an anisotropy in the conductivity, i.e., enhanced values in the direction of the nematic director field. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in order to get a qualitative estimate. [less ▲] Detailed reference viewed: 49 (4 UL)Sequencing chess ; Schilling, Tanja ; in Europhysics Letters (2016), 116(10009), We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulations. Based on the typical number of moves required to transpose a given configuration of chess ... [more ▼] We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulations. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both the size of the state space and the size of the tree of legal moves are not unique indicators of the complexity of the game, but that considerations regarding the connectedness of states are equally important. [less ▲] Detailed reference viewed: 75 (3 UL) |
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