A modified method of characteristics incorporating streamline diffusion

A hybrid finite-element method, combining ideas from a modified method of characteristics and the streamline diffusion method, delivers accurate solutions to the advection–diffusion equation. An error analysis for the case of tensorial diffusion shows that the lowest-order version of the scheme, which allows one to use a symmetric linear solvers at each time step, possesses first-order accuracy in time and space. Numerical experiments demonstrate the scheme's ability to model advection-dominated transport of solute plumes without distorting sharp fronts. © 1995 John Wiley & Sons, Inc.     

Synchronization through system interconnections

An interconnection strategy with built-in adaptive controllersis presented which achieves synchronization of scalar linearsystems: the closed-loop network forces all outputs to followthe same signal asymptotically while maintaining the open-loopcharacteristics. In the design of the output feedback controllers,no knowledge of system parameters is assumed, but each systemmust have the same poles and be high-gain-stable. The proofof the main theorem relies critically on derived systems-theoreticresults and the special system topology as a network of interconnectedsystems. The topology is explained by first solving the simplerproblem of signal synchronization.     

Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains

We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.     

Nitroxide‐mediated radical polymerization in miniemulsion: Bimolecular termination in monomer‐free model systems

Bimolecular termination in nitroxide‐mediated radical polymerization in miniemulsion has been investigated through the heating of a polystyrene–2,2,6,6‐tetramethylpiperidinyl‐1‐oxy macroinitiator and its 4‐hydroxy‐2,2,6,6‐tetramethylpiperidinyl‐1‐oxy analogue in an aqueous toluene dispersion with sodium dodecyl benzenesulfonate as a surfactant at 125 °C. The level of bimolecular termination by combination, evaluated from the high‐molecular‐weight shoulder, was higher in miniemulsion than in solution and increased with decreasing particle size. Quantitative analysis revealed that these results cannot be rationalized solely by nitroxide partitioning to the aqueous phase. The results are explained by an interface effect, by which nitroxide is adsorbed or located at the aqueous–organic interface. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4995–5004, 2007     

An implicit characteristic-flux-averaging method for the euler equations for real gases

A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.     

Interference inspection of the aspherical components of an objective for nanolithography

Methods and schemes to inspect the EUV mirror shape are developed on the basis of a point diffraction interferometer with computer processing of interferograms. A measurement accuracy to within 0.001 of a wavelength in the visual range is achieved.