Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

In this article, we propose a new class of finite volume schemes of arbitrary accuracy in space and time for systems of hyperbolic balance laws with stiff source terms. The new class of schemes is based on a three stage procedure. First a high-order WENO reconstruction procedure is applied to the cell averages at the current time level. Second, the temporal evolution of the reconstruction polynomials is computed locally inside each cell using the governing equations. In the original ENO scheme of Harten et al. and in the ADER schemes of Titarev and Toro, this time evolution is achieved via a Taylor series expansion where the time derivatives are computed by repeated differentiation of the governing PDE with respect to space and time, i.e. by applying the so-called Cauchy–Kovalewski procedure. However, this approach is not able to handle stiff source terms. Therefore, we present a new strategy that only replaces the Cauchy–Kovalewski procedure compared to the previously mentioned schemes. For the time-evolution part of the algorithm, we introduce a local space–time discontinuous Galerkin (DG) finite element scheme that is able to handle also stiff source terms. This step is the only part of the algorithm which is locally implicit. The third and last step of the proposed ADER finite volume schemes consists of the standard explicit space–time integration over each control volume, using the local space–time DG solutions at the Gaussian integration points for the intercell fluxes and for the space–time integral over the source term. We will show numerical convergence studies for nonlinear systems in one space dimension with both non-stiff and with very stiff source terms up to sixth order of accuracy in space and time. The application of the new method to a large set of different test cases is shown, in particular the stiff scalar model problem of LeVeque and Yee [R.J. LeVeque, H.C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms, Journal of Computational Physics 86 (1) (1990) 187–210], the relaxation system of Jin and Xin [S. Jin, Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics 48 (1995) 235–277] and the full compressible Euler equations with stiff friction source terms.     

Delivery by shock waves of active principle embedded in gelatin-based capsules

PURPOSE: Delivering a drug close to the targeted cells improves its benefit versus risk ratio. A possible method for local drug delivery is to encapsulate the drug into solid microscopic carriers and to release it by ultrasound. The objective of this work was to use shock waves for delivering a molecule loaded in polymeric microcapsules. MATERIAL AND METHODS: Ethyl benzoate (EBZ) was encapsulated in spherical gelatin shells by complex coacervation. A piezocomposite shock wave generator (120 mm in diameter, focused at 97 mm, pulse length 1.4 micros) was used for sonicating the capsules and delivering the molecule. Shock parameters (acoustic pressure, number of shocks and shock repetition frequency) were varied in order to measure their influence on EBZ release. A cavitation-inhibitor liquid (Ablasonic) was then used to evaluate the role of cavitation in the capsule disruption. RESULTS: The measurements showed that the mean quantity of released EBZ was proportional to the acoustic pressure of the shock wave (r2 > 0.99), and increased with the number of applied shocks. Up to 88% of encapsulated EBZ could be released within 4 min only (240 shocks, 1 Hz). However, the quantity of released EBZ dropped at high shock rates (above 2Hz). Ultrasound imaging sequences showed that cavitation clouds might form, at high shock rates, along the acoustic axis making the exposure inefficient. Measurements done in Ablasonic showed that cavitation plays a major role in microcapsules disruption. CONCLUSIONS: In this study, we designed polymeric capsules that can be disrupted by shock waves. This type of microcapsule is theoretically a suitable vehicle for carrying hydrophobic drugs. Following these positive results, encapsulation of drugs is considered for further medical applications.     

ChemInform Abstract: Structural Study of the NaCdVO4—Cd3V2O8 and CdO—V2O5 Sections of the Ternary System Na2O—CdO—V2O5.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Microdeformation in Heterogeneous Polymers,Revealed by Electron Microscopy

Recent investigations of the tensile fracture behaviour of representative glassy and semicrystalline impact-resistant polymers are reviewed, with emphasis on the microdeformation behaviour as revealed by electron microscopy of sections from bulk specimens, where the crack-tip damage zone has been embedded and/or stained under load, and on thin films deformed in situ. The insight that such techniques have provided into the toughening mechanisms is discussed.