Estimation of soil resistivity by the assembly of a vertical electrical sounding equipment at a university campus at Turbaco, Bolivar

A low-cost geoelectric equipment was implemented for academic purposes to carry out the Vertical Electrical Sounding method in order to determine the resistivity and depth of a point on the surface of a university zone and obtain the contrasts of that resistivity parameter for each type of soil. A model was reproduced at the laboratory to calibrate the equipment, and then the technique was tested in the field. Among the results, layers of sandy loam, soft limestone and dark clay with thicknesses of 0.3 m, 0.75 m and 12 m respectively were obtained, finally a clear clay was obtained whose thickness is unknown. These were compared with reference samples by well drilling method. There was a concordance between the results through the method of statistical confidence intervals with a normal distribution. The data behaved according to a soil model of lower-higher-lower resistivity. © Published under licence by IOP Publishing Ltd

Morphodynamic evolution of an estuary inlet

This paper presents the application of a morphodynamic model based on 2D reduced-physics principles to investigate morphology change of a complex estuary inlet system in the United Kingdom. The model combines a simple governing equation with a set of measured bathymetry data in order to model morphology change. The modelling method suggests that this simplified approach is able to recognise principal medium term morphodynamic trends in the estuary. However, the length and quality of the estuary bathymetry data set limits the applicability of the model to inter-annual scale

Pullback Attractors for Stochastic Heat Equations in Materials with Memory

We study the asymptotic behaviour of a non-autonomous stochastic reaction-diffusion equation with memory. In fact, we prove the existence of a random pullback attractor for our stochastic parabolic PDE with memory. The randomness enters in our model as an additive Hilbert valued noise. We first prove that the equation generates a random dynamical system (RDS) in an appropriate phase space. Due to the fact that the memory term takes into account the whole past history of the phenomenon, we are not able to prove compactness of the generated RDS, but its asymptotic compactness, ensuring thus the existence of the random pullback attractor

Synchronization of a Stochastic Reaction-Diffusion System On a Thin Two-Layer Domain

A system of semilinear parabolic stochastic partial differential equations with additive space-time noise is considered on the union of thin bounded tubular domains D1,ε := Γ × (0, ε) and D2,ε := Γ × (−ε, 0) joined at the common base Γ ⊂ Rd, where d ≥ 1. The equations are coupled by an interface condition on Γ which involves a reaction intensity k(x , ε), where x = (x , xd+1) ∈ Rd+1 with x ∈ Γ and |xd+1| < ε. Random influences are included through additive space-time Brownian motion, which depend only on the base spatial variable x ∈ Γ and not on the spatial variable xd+1 in the thin direction. Moreover, the noise is the same in both layers D1,ε and D2,ε. Limiting properties of the global random attractor are established as the thinness parameter of the domain ε → 0, i.e., as the initial domain becomes thinner, when the intensity function possesses the property limε→0 ε−1k(x , ε) = +∞. In particular, the limiting dynamics is described by a single stochastic parabolic equation with the averaged diffusion coefficient and a nonlinearity term, which essentially indicates synchronization of the dynamics on both sides of the common base Γ. Moreover, in the case of nondegenerate noise we obtain stronger synchronization phenomena in comparison with analogous results in the deterministic case previously investigated by Chueshov and Rekalo [EQUADIFF-2003, F. Dumortier et al., eds., World Scientific, Hackensack, NJ, 2005, pp. 645–650; Sb. Math., 195 (2004), pp. 103–128]