Optimal Capacity of the Blume-Emery-Griffiths perceptron

A Blume-Emery-Griffiths perceptron model is introduced and its optimal capacity is calculated within the replica-symmetric Gardner approach, as a function of the pattern activity and the imbedding stability parameter. The stability of the replica-symmetric approximation is studied via the analogue of the Almeida-Thouless line. A comparison is made with other three-state perceptrons.Comment: 10 pages, 8 figure

A molecular dynamics computer simulation study of room-temperature ionic liquids. I. Equilibrium solvation structure and free energetics

Solvation in 1-ethyl-3-methylmidazolium chloride and in 1-ethyl-3-methylimidazolium hexafluorophosphate near equilibrium is investigated via molecular dynamics computer simulations with diatomic and benzenelike molecules employed as probe solutes. It is found that electrostriction plays an important role in both solvation structure and free energetics. The angular and radial distributions of cations and anions become more structured and their densities near the solute become enhanced as the solute charge separation grows. Due to the enhancement in structural rigidity induced by electrostriction, the force constant associated with solvent configuration fluctuations relevant to charge shift and transfer processes is also found to increase. The effective polarity and reorganization free energies of these ionic liquids are analyzed and compared with those of highly polar acetonitrile. Their screening behavior of electric charges is also investigated.Comment: 12 page

Analytic study of the urn model for separation of sand

We present an analytic study of the urn model for separation of sand recently introduced by Lipowski and Droz (Phys. Rev. E 65, 031307 (2002)). We solve analytically the master equation and the first-passage problem. The analytic results confirm the numerical results obtained by Lipowski and Droz. We find that the stationary probability distribution and the shortest one among the characteristic times are governed by the same free energy. We also analytically derive the form of the critical probability distribution on the critical line, which supports their results obtained by numerically calculating Binder cumulants (cond-mat/0201472).Comment: 6 pages including 3 figures, RevTe

Analytic study of the three-urn model for separation of sand

We present an analytic study of the three-urn model for separation of sand. We solve analytically the master equation and the first-passage problem. We find that the stationary probability distribution obeys the detailed balance and is governed by the {\it free energy}. We find that the characteristic lifetime of a cluster diverges algebraically with exponent 1/3 at the limit of stability.Comment: 5pages, 4 figures include