Current Research

		University of Connecticut School of Engineering Jan 2010 to present
		Computer Graphics/Haptics & Applications
		I am currently researching on integrating computer graphics and haptics to create a sophisticated and efficient infrastructure for virtual experiments. Among the potential applications are touch-enabled CAD/CAE systems for design and assembling mechincal parts, interactive design of compliant mechanisms, substance removal (cutting/drilling) simulation for heterogeneous materials as in computer-aided surgery and dentistry, interactive molecular dynamics, protein folding and RNA docking, etc. We are now in the process of programming the graphics and haptics elements for a general purpose interactive software package than can serve as our virtual environment for any stimulatory purposes. The haptic device that we use for beginning is SensAble Technologies' well-known PHANTOM™ Omni which provides 6 DOF position and orientation input and 3 DOF force feedback. we are using OpenGL and OpenHaptics APIs integrated with fast tessellation and collision detection algorithms in C++. Click here to learn more about haptics.

Previous Research

		University of Tehran School of Engineering Sep 2004 to Sep 2008
		Theory of Wing Sections of Arbitrary Shapes
		I have been researching on the theory of sequential conformal transformations and its applications in potential theory, theoretical aerodynamics, orthogonal grid generation and inverse airfoil design. The idea is to employ a multi-step conformal mapping to transform a known potential field around a simple boundary geometry - a circle or a half-space, in particular, with known solutions for Laplace boundary-value equation - into the desired potential filed around a given arbitrary airfoil. This method, which was first introduced in 1931 by Norwegian-American theoretical aerodynamicist Theodore Theodorsen (1897 - 1978), provides an exact solution for evaluation of pressure and velocity distribution around an airfoil of arbitrary shape with an explicit expression that uses the so-called "shape factors". These parameters are functions of shape only, which is arbitrarily provided by a matrix of discretely located coordinates, and can be evaluated with a fundamental integration using specific computational algorithms. Once these shape factors are found, the potential flow solver explicitly determines the pressure distribution with an exact formula, unlike any other available method in computational fluid dynamics that is fundamentally bound to method-dependent approximations and computational errors. The shape of the boundary is not limited to any restrictions, yet the sequence of transformations is designed specifically to give most computationally efficient and accurate results for the class of airfoils within practical geometric ratios. The following improvements and contributions have been accomplished in our research program:
		Improving the theoretical framework to enhance the generality of the method as well as computational robustness; so that it is applicable to a larger class of airfoil shapes without sacrificing computational time or accuracy when evaluating the shape factors. Two new sequences of affine transformations are added to the original two, which are not affine; adding 6 degree of mapping freedom. This trick allows for airfoils of large camber and/or thickness, or airfoils of less smooth shapes to be represented with the same order of accuracy and computational effort as small camber and/or thickness smooth airfoils; at the expense of increased rigorous mathematical complexity. Setting those six parameters into trivial values reduces the affine transformations to identity and gives Theodorsen's method as a very special simple case.
		Extending the approach from a method specifically designed for airfoils - taking advantage of their almost similar stream-lined  shapes for computational efficiency - and placed in specific boundary conditions at infinity, to a general theory for the exact solution of general Laplace boundary-value problem outside or inside a wide class of boundary shapes as well as arbitrary boundary conditions at infinity. This theory leads to broad applications in applied mathematics, fluid mechanics and electromagnetics.
		In addition to evaluating the field on the boundary itself, our extended theory also evaluates the field everywhere around the object. In addition to fluid flow problems, this offers more applications that come directly from properties of orthogonality preservation of conformal mapping. One such application is orthogonal grid generation around arbitrary wing sections, ranging from O-grid to H- and C-grid, obtained from the grids around simple geometries with the same sequence of conformal transformations.
		Finally, the improved theory offers a high robustness and computational stability that allows for an innovative methodology for the inverse problem of airfoil design. This time we sought a method to obtain the unknown airfoil section from given pressure distribution for an specified angle of attack. We use the same approach of representing the airfoil with a series of diminishing so-called Fourier shape coefficients that are obtained from a systematic shape optimization of airfoil's conformal equivalent.