We examine the equilibrium configurations of a nematic liquid crystal with an immersed body in two dimensions. A complex variables formulation provides means for finding analytical solutions case strong anchoring. Local tractions, forces and torques on are discussed general setting. For weak (finite) anchoring strengths, effective boundary technique is proposed which used to determine asymptoti...

In this paper it is shown that if μ is an n-dimensional Ahlfors-David regular measure in R which satisfies the so-called weak constant density condition, then μ is uniformly rectifiable. This had already been proved by David and Semmes in the cases n = 1, 2 and d − 1, and it was an open problem for other values of n. The proof of this result relies on the study of the n-uniform measures in R. I...

Focal adhesions (FAs) connect the cellular actin cytoskeleton via integrin with the extracellular matrix. They comprise of many structural and signaling proteins which are highly dynamic, well regulated, and responsible for the sensing of physical properties from the environment. Vinculin is a protein that incorporates all these functions. Here, we investigated the phosphorylation of Y1065 in t...

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach-Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energi...

in this paper, we propose a parametric uniform approximation method to solve np-hard absolute value equations. for this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. by solving the parametric smooth nonlinear equation using newton method, for a decreasing sequence of parameters, we can get the ...