On some aspects of the geometry of differential equations in physics

In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular differential equations, and partial differential equations in field theories. The geometric structures underlying these systems are presented and commented. The main results concerning these structures are stated and discussed, as well as their influence on the study of the differential equations with which they are related. Furthermore, research to be developed in these areas is also commented.Comment: 21 page

Improving the vibration suppression capabilities of a magneto-rheological damper using hybrid active and semi-active control

This paper presents a new hybrid active & semi-active control method for vibration suppression in flexible structures. The method uses a combination of a semi-active device and an active control actuator situated elsewhere in the structure to suppress vibrations. The key novelty is to use the hybrid controller to enable the magneto-rheological damper to achieve a performance as close to a fully active device as possible. This is achieved by ensuring that the active actuator can assist the magneto-rheological damper in the regions where energy is required. In addition, the hybrid active & semi-active controller is designed to minimize the switching of the semi-active controller. The control framework used is the immersion and invariance control technique in combination with sliding mode control. A two degree-of-freedom system with lightly damped resonances is used as an example system. Both numerical and experimental results are generated for this system, and then compared as part of a validation study. The experimental system uses hardware-in-the-loop to simulate the effect of both the degrees-of-freedom. The results show that the concept is viable both numerically and experimentally, and improved vibration suppression results can be obtained for the magneto-rheological damper that approach the performance of an active device

Modification of cell surface properties of Pseudomonas alcaligenes S22 during hydrocarbon biodegradation

Biodegradation of water insoluble hydrocarbons can be significantly increased by the addition of natural surfactants one. Very promising option is the use of saponins. The obtained results indicated that in this system, after 21 days, 92% biodegradation of diesel oil could be achieved using Pseudomonas alcaligenes. No positive effect on the biodegradation process was observed using synthetic surfactant Triton X-100. The kind of carbon source influences the cell surface properties of microorganisms. Modification of the surface cell could be observed by control of the sedimentation profile. This analytical method is a new approach in microbiological analysis