Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Seismic activity triggered by water wells in the Parana Basin, Brazil

Triggered seismicity is commonly associated with deep water reservoirs or injection wells where water is injected at high pressure into the reservoir rock. However, earth tremors related solely to the opening of groundwater wells are extremely rare. Here we present a clear case of seismicity induced by pore-pressure changes following the drilling of water wells that exploit a confined aquifer in the intracratonic Parana Basin of southeastern Brazil. Since 2004, shallow seismic activity, with magnitudes up to 2.9 and intensities V MM, has been observed near deep wells (120-200 m) that were drilled in early 2003 near the town of Bebedouro. The wells were drilled for irrigation purposes, cross a sandstone layer about 60-80 m thick and extract water from a confined aquifer in fractured zones between basalt flow layers. Seismic activity, mainly event swarms, has occurred yearly since 2004, mostly during the rainy season when the wells are not pumped. During the dry season when the wells are pumped almost continuously, the activity is very low. A seismographic network, installed in March 2005, has located more than 2000 microearthquakes. The events are less than 1 km deep (mostly within the 0.5 km thick basalt layer) and cover an area roughly 1.5 km x 5 km across. The seismicity generally starts in a small area and expands to larger distances with an equivalent hydraulic diffusivity ranging from 0.06 to 0.6 m(2)/s. Geophysical and geothermal logging of several wells in the area showed that water from the shallow sandstone aquifer enters the well at the top and usually forms waterfalls. The waterfalls flow down the sides of the wells and feed the confined, fractured aquifer in the basalt layer at the bottom. Two seismic areas are observed: the main area surrounds several wells that are pumped continuously during the dry season, and a second area near another well (about 10 km from the first area) that is not used for irrigation and not pumped regularly. The main area displays cyclic annual activity, but the second area does not. We explain the earthquake swarms as being triggered by pore pressure diffusion in the fractured basalt layer due to additional pressure from the newly connected surface aquifer. This reaches critically prestressed areas up to a few kilometers away from the wells. During periods of continuous pumping, the reduction of pore pressure in the confined aquifer stops the seismic activity. Our study suggests that this kind of activity may be more common than previously thought and implies that many other cases of small tremors associated with the drilling of water wells may have gone unnoticed.

Dielectric Dispersion of Water in the Frequency Range from 10 mHz to 30 MHz

We investigate the dielectric dispersion of water, specially in the low-frequency range, by using the impedance spectroscopy technique. The frequency dependencies of the real R and imaginary Z parts of the impedance Could not be explained by means of the Usual description of the dielectric properties of the water as all insulating liquid containing ions. This is due to the incomplete knowledge of the parameters entering in the fundamental equations describing the evolution of the system, and oil the mechanisms regulating the exchange of charge of the cell with the external circuit. We propose a simple description of our experimental data based on the model of Debye, by invoking a dc conductivity of the cell, related to the nonblocking character of the electrodes. A discussion on the electric Circuits able to simulate the cell under investigation, based oil bulk and Surface elements, is also reported. We find that the simple circuit formed by a series of two parallels of resistance and capacitance is able to reproduce the experimental data concerning the real and imaginary part of the electrical impedance of the cell for frequency larger than 1 Hz. According to this description, one of the parallels takes into account the electrical properties of interface between the electrode and water, and the other of the bulk. For frequency lower than 1 Hz, a good agreement with the experimental data is obtained by simulating the electrical properties of the interface by means of the constant phase element.