Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given positive function under which we prove the existene of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.Comment: 20 page

The Paneitz Curvature Problem on Lower Dimensional Spheres

In this paper we prescribe a fourth order conformal invariant 9the Paneitz Curvature) on five and six spheres. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results.Comment: 34 page

Some Existence Results for a Paneitz Type Problem Via the Theory of Critical Points at Infinity

In this paper a fourth order equation involving critical growth is considered under Navier boundary condition. We give some topological conditions on a given function to ensure the existence of solutions. Our methods involve the study of the critical points at infinity and their contribution to the topology of the level sets of the associated Euler Lagrange functionalComment: 26 page

Comparative Study of Different Active Control Systems of High Rise Buildings under Seismic Excitation

Large number of active vibration control systems existing in the literature has brought lot of confusion for engineers and junior researchers. This study deals with the comparison of different active control systems of a 20-storey building under seismic excitation for three control devices: Active Mass Damper (AMD), Active Bracing System (ABS) and Connected Building Control (CBC). Two different control configurations are considered to add active damping to the building. The first one employs force actuator and displacement sensor and is examined with first and second order Positive Position Feedback, Lead compensators and Direct Velocity Feedback. The second configuration employs a displacement actuator collocated with a force sensor and an Integral Force Feedback control law. A total number of 15 control cases are compared from the point of view of stability, robustness, performance and control effort

MHD natural convection nanofluid flow in a heat exchanger: effects of brownian motion and thermophoresis for nanoparticles distribution

The free convection of Cu-water nanofluid is simulated and investigated inside a square heat exchanger chamber in the presence of MHD magnetic field. The Buongiorno model with the effects of Brownian and thermophoresis motion is considered to nanoparticles distribution inside the chamber. The geometry consists of a square chamber with two cylinders on the right and left sides as heater and cooler in order to create the buoyancy force, respectively. These cylinders represent hot and cold pipes, and the walls of the chamber are heat and mass insulation. the FVM with SIMPLE algorithm are used for velocity and pressure coupling. In current two-phase simulation, the effects of Rayleigh number, Hartmann number, inclination angle of chamber and volume fraction on streamline contours, isothermal lines, Lorentz force lines, nanoparticle distribution and Nusselt number are investigated. By modeling the motion of nanoparticles and evaluating it, a nanoparticle transport zone was observed. The diffusion effects of thermophoresis were significant in this zone. The nanoparticles were thrown from the hot cylinder to the cold cylinder. The application of a magnetic field enlarged the nanoparticle transport zone. However, increasing the Rayleigh number and decreasing the inclination angle of the enclosure caused the nanoparticles to disperse evenly