The presence of a few poor-quality mesh elements can negatively affect the stability and efficiency of a finite element solver and the accuracy of the associated partial differential equation solution. We propose a mesh quality improvement method that improves the quality of the worst elements. Mesh quality improvement of the worst elements can be formulated as a nonsmooth unconstrained optimiz...

We analyze convergence properties of the Modiied Barrier Function Method (MBFM), which operates like the usual Augmented Lagrangian method, except that it uses a shifted logarithmic barrier function in place of the usual quadratic penalty function. The MBFM avoids some of the drawbacks of classical barrier methods. The convergence of the MBFM had previously been established under strict regular...

The vascular barrier is an important function of the endothelium and its dysfunction is involved in several diseases. The barrier function of the endothelial cell monolayer is governed by cell-cell, cell-extracellular matrix (cell-ECM) contacts, and inflammatory factors such as thrombin, histamine or vascular endothelial growth factor. Several in vivo and in vitro assays that measure the vascul...

A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety verification based on barrier certificate has the benefit of avoiding explicit computation of the exact reachable set which is usually intractable for nonlinear hybrid systems. In this paper, we propose a new barrier certificate condition, called Exponential Conditio...

With a help of the selfconsistent Hartree-Fock-Bogoliubov (HFB) approach with the D1S effective Gogny interaction and the Generator Coordinate Method (GCM) we incorporate the transverse collective vibrations to the one-dimensional model of the fission-barrier penetrability based on the traditional WKB method. The average fission barrier corresponding to the least-energy path in the two-dimensio...

In this paper, a new model based on differential-algebraic equations(DAEs) for solving convex quadratic programming(CQP) problems is proposed. It is proved that the new approach is guaranteed to generate optimal solutions for this class of optimization problems. This paper also shows that the conventional interior point methods for solving (CQP) problems can be viewed as a special case of the n...

environmental noise pollution is among the most urban problems which can be caused due to real sources like traffic, train and virtual sources provided by rigid surfaces. one of the urban structures in which can perform as a virtual noise source are the installed gutters alongside highways. these structures are mostly used to pass the wastewater or the rainfall. in this research, the acoustical...

We present an advanced and novel control method to enable actuated Spring Loaded Inverted Pendulum model walk over rough challenging terrains. The high-level philosophy is the decoupling of controls vertical horizontal states. state controlled via Backstepping-Barrier Function (BBF) based quadratic programs: a combination Lyapunov backstepping barrier function, both which provide inequality con...