A curious phenomenon when it comes to solving the linear system formulation of the PageRank problem is that while the convergence rate of Gauss–Seidel shows an improvement over Jacobi by a factor of approximately two, successive overrelaxation (SOR) does not seem to offer a meaningful improvement over Gauss–Seidel. This has been observed experimentally and noted in the literature, but to the be...

Linear multistep methods using higher derivatives are discussed. The order of damping at infinity which measures the stability behavior of a fc-step method for large h is introduced. ,4-stable methods with positive damping order are most suitable for stiff problems. A method for computing the damping order is given. Necessary and sufficient conditions for A -stability, A (a) -stability and stif...

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources" (2015). This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u t t − ∆ p u − ∆u t = f (u), in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f (u) is a source feedback t...

The high resolution observations (TRACE and SOHO) of waves in coronal structures have revealed a rapid damping of modes, sometimes their damping length being of the same order as their wavelength. The rapid damping of modes in coronal loops permits us to derive values for magnetic field and transport coefficients. In this contribution we study the damping of linear compressional waves consideri...

The nonlinear damping behavior is usually ignored in the design of a miniature moving-coil loudspeaker. But when the loudspeaker operated in air, the damping parameter varies with the voice-coil displacement corresponding due to viscous air flow. The present paper presents an identification model as inverse problem to identify the nonlinear damping parameter in the lumped parameter model for th...

We analyze the eeect of weak residual disorder in microstructures deened on high-mobility heterojunctions, where the classical electron motion is ballistic. We parameterize the disorder by its correlation length and the elastic mean-free-path l, which can be estimated from microscopic models. For the experimentally relevant case in which is not negligible with respect to the size of the microst...

We present systematic, unique linear and nonlinear shear rheology data of an experimentally pure ring polystyrene and its linear precursor. This polymer was synthesized anionically and characterized by interaction chromatography and fractionation at the critical condition. Its weight-average molar mass is 84 kg/mol; i.e., it is marginally entangled (entanglement number Z ≈ 5). Its linear viscoe...

Propagating transverse waves are thought to be a key transporter of Poynting flux throughout the Sun's atmosphere. Recent studies have shown that these motions, interpreted as magnetohydrodynamic kink mode, prevalent corona. The associated energy estimates suggest carry enough meet demands coronal radiative losses in quiescent Sun. However, it is still unclear how deposit their into plasma. We ...