Stability and Dissipation of Many Components’ LC Systems and Application to Metamaterials

Dykhne’s method, based on rotational symmetry of two-dimensional equations of constant direct current, was applied to study the properties of the medium, consisting of reactances—of inductors and capacitors (nondissipative elements). The exact solution for the 4-component system consisting of the two different types of 2 inductors and 2 capacitors, randomly placed and connected, was obtained. The obtained solution for investigated system has the two features: (1) the finite dissipation in the nondissipative system of inductors and capacitors; (2) appearance of plateau—the constant value of effective conductivity in a wide range of concentrations of components. The obtained results were useful for description of composite metamaterials.

Seismic Q—Stratigraphy or dissipation

The basic problems encountered in extracting estimates of seismic dissipation from data recorded on vertical seismic profiles are analyzed. Because anomalous dissipation in the subsurface is likely to be associated with conditions or lithologies of limited vertical extent, a knowledge of the factors which influence the spatial resolution of an attenuation measurement is of considerable importance. By introducing a statistical perspective, it is possible to simulate multiple measurements in an inhomogeneous interval and to draw conclusions which apply to an entire class of impedance structures. Theoretical seismograms are analyzed to demonstrate that for small receiver separations neither a single measurement nor the mean value determined from multiple measurements is likely to give a good estimate of the attenuation for an inhomogeneous depth interval. For small receiver separations, the attenuation computed from the amplitude ratios method is much more strongly influenced by the local stratigraphy in the immediate vicinity of the seismometer than by the attenuation in the depth interval between seismometers. As the seismometer separation increases, there is a dramatic decrease in the variability in the attenuation values determined from multiple measurements. A critical distance can be defined which is a measure of the spatial resolution. Beyond the critical distance the mean value approaches a quantity which is the sum of two components: the effective dissipation for an inhomogeneous interval and a stratigraphic term which describes the attenuation in a nondissipative system.