Mean field model for spatially extended systems in the presence of multiplicative noise

We present a mean field model that describes the effect of multiplicative noise in spatially extended systems. The model can be solved analytically. For the case of the phi4 potential it predicts that the phase transition is shifted. This conclusion is supported by numerical simulations of this model in two dimensions.

Relations between soil surface roughness, tortuosity, tillage treatments, rainfall intensity and soil and water losses from a red yellow latosol

The soil surface roughness increases water retention and infiltration, reduces the runoff volume and speed and influences soil losses by water erosion. Similarly to other parameters, soil roughness is affected by the tillage system and rainfall volume. Based on these assumptions, the main purpose of this study was to evaluate the effect of tillage treatments on soil surface roughness (RR) and tortuosity (T) and to investigate the relationship with soil and water losses in a series of simulated rainfall events. The field study was carried out at the experimental station of EMBRAPA Southeastern Cattle Research Center in São Carlos (Fazenda Canchim), in São Paulo State, Brazil. Experimental plots of 33 m² were treated with two tillage practices in three replications, consisting of: untilled (no-tillage) soil (NTS) and conventionally tilled (plowing plus double disking) soil (CTS). Three successive simulated rain tests were applied in 24 h intervals. The three tests consisted of a first rain of 30 mm/h, a second of 30 mm/h and a third rain of 70 mm/h. Immediately after tilling and each rain simulation test, the surface roughness was measured, using a laser profile meter. The tillage treatments induced significant changes in soil surface roughness and tortuosity, demonstrating the importance of the tillage system for the physical surface conditions, favoring water retention and infiltration in the soil. The increase in surface roughness by the tillage treatments was considerably greater than its reduction by rain action. The surface roughness and tortuosity had more influence on the soil volume lost by surface runoff than in the conventional treatment. Possibly, other variables influenced soil and water losses from the no-tillage treatments, e.g., soil type, declivity, slope length, among others not analyzed in this study.

Studying Avalanches in the ground-state of the two-dimensional random field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation ¿ of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of ¿. The corresponding exponents are compared.