A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non{diierentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constra...

The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that optimal procedure of replacement matrix elements by the integer quantities with the limited number of gradations exist, and the efficient of minimization does not...

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...

Historically, our understanding of the air-sea surface stress has been derived from engineering studies of turbulent flows over flat solid surfaces, and more recently, over rigid complex geometries. Over the ocean however, the presence of a free, deformable, moving surface gives rise to a more complicated drag formulation. In fact, within the constant-stress turbulent atmospheric boundary layer...

Brushless DC (BLDC) motors are used in a wide range of applications due to their high efficiency and high power density. In this paper, sensorless four-switch direct power control (DPC) method with the sector to sector commutations ripple minimization for BLDC motor control is proposed. The main features of the proposed DPC method are: (1) fast dynamic response (2) easy implementation (3) use o...

We show that when water droplets gently impact on a hydrophobic surface, the droplet shoots out a violent jet, the velocity of which can be up to 40 times the drop impact speed. As a function of the impact velocity, two different hydrodynamic singularities are found that correspond to the collapse of the air cavity formed by the deformation of the drop at impact. It is the collapse that subsequ...

Pumps are designed and manufactured to operate well away from the cavitation condition and thus the factors affecting the onset of cavitation are important. A specially designed test rig was and constructed so that the onset of cavitation could be studied visually while obtaining actual NPSH data. The magnitude of the NPSH level at 3% drop in total discharge head of a pump was determined at dif...

By using a Danes̆’ drop theorem in locally convex spaces we obtain a vectorial form of Ekelandtype variational principle in locally convex spaces. From this theorem, we derive some versions of vectorial Caristi-Kirk’s fixed-point theorem, Takahashi’s nonconvex minimization theorem, and Oettli-Théra’s theorem. Furthermore, we show that these results are equivalent to each other. Also, the existen...

We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result. We consider the minimization problem E(A) = inf{E(Ω): |Ω| = A} over all measurable set Ω ⊂ R with the energy functional E [Ω] = PerΩ + 1 2 ∫∫

In this paper, a nonlinear loss minimization control strategy for an interior permanent magnet synchronous motor (IPMSM) based on a newly developed sliding mode approach is presented. This control method sets force the speed control of the IPMSM drives and simultaneously ensures the minimization of the losses besides the uncertainties exist in the system such as parameter variations which have ...