We study a restricted solid-on-solid model involving deposition and evaporation with probabilities p and 1 - p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for p approximately 0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q identical with p - 1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear lambda - q relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for 0.55< or =p< or =0.8, which provides numerical estimates of the crossover times tc. They scale as tc approximately lambda -phi with phi=4.1+/-0.1, which is in excellent agreement with the theoretically predicted universal value phi=4 and improves previous numerical estimates, which suggested phi approximately 3.

The p-state clock model is studied, for general values of p , from simulations using a heat-bath single spin flipping Monte Carlo method, and a mapping of the corresponding spinlike configurations to a solid-on-solid growth model. The growth exponents are calculated. From the dynamics generated by this far from equilibrium kinetic roughening of the surface one is able to characterize the corresponding equilibrium magnetic properties of the original model, such as the high temperature Berezinskii-Koserlitz-Thouless (BKT) transitions, the low-temperature long-range ordered phase transitions, as well as the conventional second-order phase transitions. The present method suggests that for p>or=5 the high-temperature phase transition is indeed a BKT one, whose value is the same as that for p-->infinity ( XY model), while the low-temperature phase transition has a first-order character.

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We present an analysis of mapped surfaces obtained from configurations of two classical statistical-mechanical spin models in the square lattice: the q -state Potts model and the spin-1 Blume-Capel model. We carry out a study of the phase transitions in these models using the Monte Carlo method and a mapping of the spin configurations to a solid-on-solid growth model. The first- and second-order phase transitions and the tricritical point happen to be relevant in the kinetic roughening of the surface growth process. At the low and high temperature phases the roughness W grows indefinitely with the time, with growth exponent beta(w) approximately 0.50(W approximately tbeta(w)) . At criticality the growth presents a crossover at a characteristic time tc, from a correlated regime (with beta(w) ++ 0.50 ) to an uncorrelated one (beta(w) approximately equal 0.50) . We also calculate the Hurst exponent H of the corresponding surfaces. At criticality, beta(w) and H have values characteristic of correlated growth, distinguishing second- from first-order phase transitions. It has also been shown that the Family-Vicsek relation for the growth exponents also holds for the noise-reduced roughness with an anomalous scaling.

The steady-state charge densities, electric potential, and current densities are determined analytically in the case of the first dynamo created by Michael Faraday, which consists of a conducting disk rotating between the poles of an off-axis permanent magnet. The results obtained are compared with another work that considered the same problem using a different approach. We also obtain analytical expressions for the total current on the disk and for the dynamo's electromotive force.