Comparing performance of instrumental drift correction by linear and quadratic adjusting in inductive electromagnetic data

Electromagnetic induction (EMI) method results are shown for vertical magnetic dipole (VMD) configuration by using the EM38 equipment. Performance in the location of metallic pipes and electrical cables is compared as a function of instrumental drift correction by linear and quadratic adjusting under controlled conditions. Metallic pipes and electrical cables are buried at the IAG/USP shallow geophysical test site in Sao Paulo City. Brazil. Results show that apparent electrical conductivity and magnetic susceptibility data were affected by ambient temperature variation. In order to obtain better contrast between background and metallic targets it was necessary to correct the drift. This correction was accomplished by using linear and quadratic relation between conductivity/susceptibility and temperature intending comparative studies. The correction of temperature drift by using a quadratic relation was effective, showing that all metallic targets were located as well deeper targets were also improved. (C) 2010 Elsevier B.V. All rights reserved.

An extension of the concept of gradient semigroups which is stable under perturbation

In this article we introduce the concept of a gradient-like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup (those possessing a Lyapunov function, see [J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, Amer. Math. Soc., 1989]) and a nonlinear semigroup possessing a gradient-like attractor. We prove that a perturbation of a gradient-like nonlinear semigroup remains a gradient-like nonlinear semigroup. Moreover, for non-autonomous dynamical systems we introduce the concept of a gradient-like evolution process and prove that a non-autonomous perturbation of a gradient-like nonlinear semigroup is a gradient-like evolution process. For gradient-like nonlinear semigroups and evolution processes, we prove continuity, characterization and (pullback and forwards) exponential attraction of their attractors under perturbation extending the results of [A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suarez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations 236 (2007) 570-603] on characterization and of [A.V. Babin, M.I. Vishik, Attractors in Evolutionary Equations, Stud. Math. Appl.. vol. 25, North-Holland, Amsterdam, 1992] on exponential attraction. (C) 2009 Elsevier Inc. All rights reserved.

On the concept of electrical impedance for an electrolytic cell

The analysis of the electrical impedance of an electrolytic cell in the shape of a slab is performed. We have solved, numerically, the differential equations governing the phenomenon of the redistribution of the ions in the presence of an external electric field, and compared the results with the ones obtained by solving the linear approximation of these equations. The control parameters in our study are the amplitude and the frequency of the applied voltage, assumed a simple harmonic function of the time. We show that for the large amplitudes of the applied voltage, the actual current is no longer harmonic at low frequencies. From this result it follows that the concept of electrical impedance of a cell is a useful quantity only in the case where the linear approximation of the fundamental equations of problem work well.

The concept of quasi-integrability: a concrete example

We use the deformed sine-Gordon models recently presented by Bazeia et al [1] to take the first steps towards defining the concept of quasi-integrability. We consider one such definition and use it to calculate an infinite number of quasi-conserved quantities through a modification of the usual techniques of integrable field theories. Performing an expansion around the sine-Gordon theory we are able to evaluate the charges and the anomalies of their conservation laws in a perturbative power series in a small parameter which describes the ""closeness"" to the integrable sine-Gordon model. We show that in the case of the two-soliton scattering the charges, up to first order of perturbation, are conserved asymptotically, i.e. their values are the same in the distant past and future, when the solitons are well separated. We indicate that this property may hold or not to higher orders depending on the behavior of the two-soliton solution under a special parity transformation. For closely bound systems, such as breather-like field configurations, the situation however is more complex and perhaps the anomalies have a different structure implying that the concept of quasi-integrability does not apply in the same way as in the scattering of solitons. We back up our results with the data of many numerical simulations which also demonstrate the existence of long lived breather-like and wobble-like states in these models.