Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

Influence and role of metal ions in enzymatic catalysis with e.c. 1.2.3.2. xanthine oxidase Application to trace analysis

The effect of metal ions on the reductive half-reaction of xanthine oxidase (XOD) in the catalytic conversion of xanthine into uric acid has been studied spectrophotometrically in Tris-HCl buffer at pH 7.4, 37 +/- 0.1 degrees and ionic strength 0.04M. Some metal ions display inhibitor properties, the sequence of inhibiting efficiency being Ag(I) > Hg(II) > Cu(II) > Cr(VI) > V(V) > Au(III) > Tl(I) and for these the I(50) values were determined. Only Tl(I), V(V) and Cu(II) showed reversible inhibition and therefore for these the mechanisms were assessed [competitive for V(V) and Tl(I); uncompetitive for Cu(II)]. The conditional inhibition constants (K(i)) were also determined. The effect of EDTA for protection of the enzyme against metal inhibition, and for its reactivation after inhibition, was also investigated. Utilization of the linear relationship between relative enzyme activity and inhibitor concentration allowed sensitive and selective (though not specific) determination of Ag(I) and Hg(II) (10(-9)-10(-8)M), and of Cu(II) and Cr(VI) (10(-7)-10(-6)M), the maximum relative error being +/- 4%. For a few metal ions, e.g., Ag(I) and Cr(VI), in the presence of EDTA, a certain specificity is observed.     

A variational principle for doubly nonlinear evolution

The weighted energy-dissipation principle stands as a novel variational tool for the study of dissipative evolution and has already been applied to rate-independent systems and gradient flows. We provide here an example of its application to a specific yet critical doubly nonlinear equation featuring a super-quadratic dissipation.     

Overview of the current spectroscopy effort on the Livermore electron beam ion traps

An overview is given of the current spectroscopic effort on the Livermore electron beam ion trap facilities. The effort focuses on four aspects: spectral line position, line intensity, temporal evolution, and line shape. Examples of line position measurements include studies of the K-shell transitions in heliumlike Kr³⁴⁺ and the 2s-2p intrashell transitions in lithiumlike Th⁸⁷⁺ and U⁸⁹⁺, which provide benchmark values for testing the theory of relativistic and quantum electrodynamical contributions in high-Z ions. Examples of line intensity measurements are provided by measurements of the electron-impact excitation and dielectronic recombination cross sections of the heliumlike transition-metal ions Ti²⁰⁺ through Co²⁵⁺. A discussion of radiative lifetime measurements of metastable levels in heliumlike ions is given to illustrate our time-resolved spectroscopy techniques in the microsecond range. We also present a measurement of the spectral lineshape that illustrates the very low ion temperatures that can be achieved in an EBIT.     

Nearly-integrable dissipative systems and celestial mechanics

The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KAM theorems to prove the existence of quasi-periodic tori and invariant attractors. We conclude by reviewing some dissipative models of Celestial Mechanics. Among the rotational dynamics we consider the Yarkovsky and YORP effects; within the three-body problem we introduce the so-called Stokes and Poynting–Robertson effects.     

A macroscopic model for magnetic shape-memory single crystals

A rate-independent model for the quasi-static magneto-elastic evolution of a magnetic shape-memory single crystal is presented. In particular, the purely mechanical Souza–Auricchio model for shape-memory alloys is here combined with classical micro-magnetism by suitably associating magnetization and inelastic strain. By balancing the effect of conservative and dissipative actions, a nonlinear evolution PDE system of rate-independent type is obtained. We prove the existence of so-called energetic solutions to this system. Moreover, we discuss several limits for the model corresponding to parameter asymptotics by means of a rigorous Γ-convergence argument.     

Separation of N1- and N8-acetylspermidine isomers by reversed-phase column liquid chromatography after derivatization with dansyl chloride

The separation of dansyl derivatives of N1- and N8-acetylspermidine by reversed-phase column liquid chromatography is reported. The influence of organic solvents on the retention of acetylspermidines was studied. Best resolutions were achieved using a C18 column and a ternary mobile phase composed of water, methanol and acetonitrile. The precolumn derivatization method permitted the detection of picomole quantities. A method for the determination of acetylspermidines in rat tissues is described.     

Nonlocal quasivariational evolution problems

This note addresses a class of abstract quasivariational evolution equations taking into account nonlocality with respect to time. We present an existence result for suitably weak solutions to such problems, which extend previous contributions. The existence argument relies on some order technique and exploits a fixed point result for multivalued applications in ordered spaces. Moreover, we discuss the application of our results to classes of ODE and parabolic PDE problems.