We report a superconducting transition in the fully conserving fluctuation exchange approximation for a two-dimensional attractive Hubbard model. The transition temperature agrees well with quantum Monte Carlo calculations, but the superfluid density and specific heat near $T_c$ have anomalous temperature dependences for lattice sizes up to $64\times 64$.

Recent research has examined the possibility of recovering energy from mechanical vibration induced by a vehicle shock absorber using piezoelectric and electromagnetic transducers. In terms of automotive applications, piezoelectric vibration energy harvesting shows promise for recapturing some (even if small) amounts of vehicle vibration energy, which would otherwise be wasted through the vehicle dampers. Functional materials, such as piezoelectric materials, are capable of converting mechanical energy into useful electrical energy and vice versa. In this paper, an innovative rotational piezoelectric vibration-energy-harvesting device is presented that employs a magnetic coupling mechanism and provides robust performance over a range of frequencies. The piezoelectric energy harvester is driven by a unidirectional suspension system. An experimental investigation was carried out to study the performance of the manufactured prototype. We observed no damage to the prototype after operating continuously at a vibration amplitude of 5 mm at a frequency of 2.5 Hz for over 10,000 cycles. In addition, the presented regenerative suspension system is capable of producing high and relatively steady open-circuit voltages, irrespective of excitation frequencies. The results demonstrate that regenerative shock absorber is robust and has a broad frequency range.

We show that the exact 1/${\mathrm{\varepsilon }}_{\mathrm{n}}$ dependence of the self-energy for the Hubbard model for large ${\mathrm{\varepsilon }}_{\mathrm{n}}$ is obtained entirely from the second-order skeleton diagram evaluated with the exact propagator. Explicit calculation demonstrates that contributions from higher-order skeleton diagrams cancel exactly as a consequence of the crossing symmetry of the renormalized four-point vertex function. From an analysis of the skeleton diagram expansion and direct numerical calculation, we show that an imperfect cancellation of contributions from higher-order skeleton diagrams appears at third and fourth order in U for the shielded potential approximation and the fluctuation exchange approximation, respectively. By itself, this indication of crossing symmetry violation of the vertex function says little about the accuracy of the resulting self-energy and propagator, particularly at low frequency.