On the Thermodynamic Limit in Random Resistors Networks
نویسنده
چکیده
We study a random resistors network model on a euclidean geometry Z. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions. PACS numbers: 1315, 9440 Short title: Random Resistors Networks February 6, 2008 † e-mail: [email protected] ‡ e-mail: [email protected] 2
منابع مشابه
Relation Between RNA Sequences, Structures, and Shapes via Variation Networks
Background: RNA plays key role in many aspects of biological processes and its tertiary structure is critical for its biological function. RNA secondary structure represents various significant portions of RNA tertiary structure. Since the biological function of RNA is concluded indirectly from its primary structure, it would be important to analyze the relations between the RNA sequences and t...
متن کاملSpectral densities of scale-free networks.
The spectral densities of the weighted Laplacian, random walk, and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent beta. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and beta.
متن کاملIncrease in Complexity in Random Neural Networks
We study trie dynamics of a discrete time, continuous state neural network with random asymmetric couplings and random thresholds. Trie evolution of trie neurons is given m the thermodynamic limit by a set of dynamic mean-field equations obtained by
متن کاملRigorous Results on the Hopfield Model Ofneural Networks
We review some recent rigorous results in the theory of neural networks, and in particular on the thermodynamic properties of the Hoppeld model. In this context, the model is treated as a Curie-Weiss model with random interactions and large deviation techniques are applied. The tractability of the random interactions depends strongly on how the number, M, of stored patterns scales with the size...
متن کاملNonequilibrium transitions in complex networks: a model of social interaction.
We analyze the nonequilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small-world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-...
متن کامل