An adjoint sensitivity method is presented for parameter-dependent differentialalgebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In...

We construct mollification operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are Lp stable for any real number p ∈ [1,∞], and commute with the differential operators ∇, ∇×, and ∇·. We also construct mollification operators satisfying boundary conditions and use them to characterize the kernel of traces related to the tangential and normal trace of vector fields....

The thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid in the presence of uniform vertical magnetic field is considered. For the case of stationary convection, Rivlin-Ericksen viscoelastic fluid behaves like a Newtonian fluid. It is found that rotation has a stabilizing effect, whereas the magnetic field has both stabilizing and destabilizing effects. Graphs have been plotted ...

We present a two-step method for the localization of displays using cameras and visual markers on screens. Displays can attract attention by flashing in a characteristic pattern and color. Once they’re found by a camera, their exact position can be calculated robustly from a set of markers they show. To make the method numerically stable, a certain degree of redundancy must exist in the environ...

The geometrical structure of electrodynamics is reviewed following the analogy with gravity. It is found that the vector potentials that represent magnetic fields can be identified as connections. As a consequence, these potentials should be assigned to the links of discretization grids. A ghost field is introduced to guarantee numerical stability in the solution scheme of solving electromagnet...

Two efficient and numerically stable methods for the computation of the largest p Lyapunov characteristic exponents of an n dimensional discrete dynamical systems are presented.

We examine the case of a coupled two-cell Sherman network with electrical and inhibitory coupling. A region of stable synchrony exists when both inhibitory coupling and electrical coupling are nonzero but very weak; notably, this region is bounded on all sides by instability. We present an explanation for this curious effects as well as a detailed numerical stability analysis of phase-locking i...

In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the improved convergence theorem for planar clusters developed in [CLM14] with an ad hoc analysis of the problem, which addresses the delicate interaction between the (possible) dislocation of singularities and the multiple-volumes constraint.

We derive a new algorithm for computing the action f(A)V of the cosine, sine, hyperbolic cosine, and hyperbolic sine of a matrix A on a matrix V , without first computing f(A). The algorithm can compute cos(A)V and sin(A)V simultaneously, and likewise for cosh(A)V and sinh(A)V , and it uses only real arithmetic when A is real. The algorithm exploits an existing algorithm expmv of Al-Mohy and Hi...