Systematic Field-Theory for the Hard-Core One-Component Plasma

An accurate and systematic equation of state for the hard-core one-component plasma (HCOCP) is obtained. The result is based on the Hubbard-Schofield transformation which yields the field-theoretical Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of the reference hard-core fluid. Explicit calculations were performed using the Gaussian approximation for the effective Hamiltonian and known thermodynamic and structural properties of the reference hard-core fluid. For small values of the plasma parameter G and packing fraction the Debye-Huckel result is recovered, while for G>>1, the excess free energy F_ex and internal U_{ex} energy depend linearly on G. The obtained expression for U_ex is in a good agreement with the available Monte Carlo data for the HCOCP. We also analyse the validity of the widely used approximation, which represents the free energy as a sum of the hard-core and electrostatic part.Comment: 14 pages, 3 figure

Fracture and Friction: Stick-Slip Motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs, when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear viscous friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first order phase transitions we discuss a ``soft'' selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as function of the driving velocity. The relevance of our results to recent experiments is discussed.Comment: 12 pages, 7 figure