Wave propagation in groove guides

Wave propagation in groove guide

Cutoff frequencies of eccentric waveguides

Boundary value problem solved by point matching method in study of circular eccentric waveguide cut-off frequencie

On the application and extension of Harten's high resolution scheme

Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme

On spurious steady-state solutions of explicit Runge-Kutta schemes

The bifurcation diagram associated with the logistic equation v sup n+1 = av sup n (1-v sup n) is by now well known, as is its equivalence to solving the ordinary differential equation u prime = alpha u (1-u) by the explicit Euler difference scheme. It has also been noted by Iserles that other popular difference schemes may not only exhibit period doubling and chaotic phenomena but also possess spurious fixed points. Runge-Kutta schemes applied to both the equation u prime = alpha u (1-u) and the cubic equation u prime = alpha u (1-u)(b-u) were studied computationally and analytically and their behavior was contrasted with the explicit Euler scheme. Their spurious fixed points and periodic orbits were noted. In particular, it was observed that these may appear below the linearized stability limits of the scheme and, consequently, computation may lead to erroneous results

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit

On dielectric lenses

Dielectric lens for correction of curved field lines in electromagnetic wave propagatio

The dynamics of z~1 clusters of galaxies from the GCLASS survey

We constrain the internal dynamics of a stack of 10 clusters from the GCLASS survey at 0.87<z<1.34. We determine the stack cluster mass profile M(r) using the MAMPOSSt algorithm of Mamon et al., the velocity anisotropy profile beta(r) from the inversion of the Jeans equation, and the pseudo-phase-space density profiles Q(r) and Qr(r), obtained from the ratio between the mass density profile and the third power of the (total and, respectively, radial) velocity dispersion profiles of cluster galaxies. Several M(r) models are statistically acceptable for the stack cluster (Burkert, Einasto, Hernquist, NFW). The total mass distribution has a concentration c=r200/r-2=4.0-0.6+1.0, in agreement with theoretical expectations, and is less concentrated than the cluster stellar-mass distribution. The stack cluster beta(r) is similar for passive and star-forming galaxies and indicates isotropic galaxy orbits near the cluster center and increasingly radially elongated with increasing cluster-centric distance. Q(r) and Qr(r) are almost power-law relations with slopes similar to those predicted from numerical simulations of dark matter halos. Combined with results obtained for lower-z clusters we determine the dynamical evolution of galaxy clusters, and compare it with theoretical predictions. We discuss possible physical mechanisms responsible for the differential evolution of total and stellar mass concentrations, and of passive and star-forming galaxy orbits [abridged].Comment: 12 pages, 7 figures. Version accepted for publication in A&A after minor modification