Interacting electrical conductors self-assemble to form tree like networks in the presence of applied voltages or currents. Experiments have shown that the degree distribution of the steady state networks are identical over a wide range of network sizes. In this work we develop a new model of the self-assembly process starting from the underlying physical interaction between conductors. In agreement with experimental results we find that for steady state networks, our model predicts that the fraction of endpoints is a constant of 0.252, and the fraction of branch points is 0.237. We find that our model predicts that these scaling properties also hold for the network during the approach to the steady state as well. In addition, we also reproduce the experimental distribution of nodes with a given Strahler number for all steady state networks studied.
The efficiency of conventional techniques used to harvest energy in nuclear reactors lies around 35%. This limit exists, because the nuclear energy is converted to electrical energy via heat engines. We study an alternative approach where the kinetic energy of nuclear reaction products is directly converted into electric energy in a stack of charged capacitors with a gap size of 500 nm and graphene electrodes. Graphene is expected to be chemically and mechanically stable in high‐radiation environments, because its tensile strength of 130 GPa is very large, about 100 times larger than most metals. The dielectric strength of such nanocapacitors exceeds 1 GV/m, because avalanching is suppressed at small gap sizes. In a 1 GV/m electric field charged nuclear reaction products, such as 5.6 MeV alpha particles, come to rest in of a stack with 5000 nanocapacitors. We show that during the deceleration process more than 90% of kinetic energy of charged nuclear reaction products is converted to electric energy and stored as electric energy in the stack. Each stack is 2.5‐mm thick and produces a high‐voltage DC current. A device with a 1‐Ci241Am source is expected to generate 22 mW of electric power.
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