the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

Internal stress plasticity occurs when a small external stress biases internal mismatch strains produced by, e.g., phase transformation or thermal expansion mismatch. At small applied stresses, this deformation mechanism is characterized by a deformation rate which is proportional to the applied stress and is higher than for conventional creep mechanisms. In this work, we demonstrate the operat...

Abstract. The dynamics of a free boundary problem for electrostatically actuated microelectromechanical systems (MEMS) is investigated. The model couples the electric potential to the deformation of the membrane, the deflection of the membrane being caused by application of a voltage difference across the device. More precisely, the electrostatic potential is a harmonic function in the angular ...

This is a review of my recent work. What kinds of combinations of singularities can appear in small deformation fibers of a fixed singularity? We consider this problem for hypersurface singularities on complex analytic spaces of dimension 2. Recall first that a connected Dynkin graph of type A, D or E corresponds to a surface singularity called a rational double point. (Durfee [3].) When the fi...

The effect of pre-existing nano sized precipitates on the mechanisms and rate of grain refinement has been investigated during the severe plastic deformation. A binary Al–0.2Sc alloy, containing coherent Al3Sc particles, of 3.62 nm in diameter has been deformed by accumulative roll bonding up to 10 cycles. The resulting deformed structures were quantitatively analyzed using electron backscatter...

The Lattice Boltzmann Method is used to simulate the dynamics of droplet deformation in a channel flow under various conditions. The droplet behavior has been investigated under transient conditions. For cases where the droplet remains attached to the surface, the shape deformation of the droplet during crawling is captured. It has been shown that there is a limiting value for the droplet volum...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

The internal flow circulation dynamics of a liquid drop moving in a co- or counter-flowing gas stream has been numerically studied. The present work is concerned with the time accurate numerical solution of the two phase flow field at the low Mach number limit with an appropriate volume tracking method to capture motion and deformation of a liquid drop. It is shown that relative velocity betwee...

Breast lesion visibility in static strain imaging ultimately is noise limited. When correlation and related techniques are applied to estimate local displacements between two echo frames recorded before and after a deformation, target contrast increases linearly with the amount of deformation applied. However, above some deformation threshold, decorrelation noise increases more than contrast su...