Quantum hydrodynamics with trajectories: The nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry

We present a solution to the conservation form (Eulerian form) of the quantum hydrodynamic equations which arise in chemical dynamics by implementing a mixed/discontinuous Galerkin (MDG) finite element numerical scheme. We show that this methodology is stable, showing good accuracy and a remarkable scale invariance in its solution space. In addition the MDG method is robust, adapting well to various initial-boundary value problems of particular significance in a range of physical and chemical applications. We further show explicitly how to recover the Lagrangian frame (or pathline) solutions.     

Global Regularity of Solutions to Systems of Reaction–Diffusion with Sub-Quadratic Growth in Any Dimension

This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without smallness assumptions, in any dimension N. The proof is based on blow-up techniques. The natural entropy of the system plays a crucial role in the analysis. It allows us to use of De Giorgi type methods introduced for elliptic regularity with rough coefficients. In spite these systems are entropy supercritical, it is possible to control the hypothetical blow-ups, in the critical scaling, via a very weak norm. Analogies with the Navier–Stokes equation are briefly discussed in the introduction.     

Some Remarks on the Eigenvalue Multiplicities of the Laplacian on Infinite Locally Finite Trees

We consider the continuous Laplacian on an infinite uniformly locally finite network under natural transition conditions as continuity at the ramification nodes and the classical Kirchhoff flow condition at all vertices in a L ^∞-setting. The characterization of eigenvalues of infinite multiplicity for trees with finitely many boundary vertices (von Below and Lubary, Results Math 47:199–225, 2005, 8.6) is generalized to the case of infinitely many boundary vertices. Moreover, it is shown that on a tree, any eigenspace of infinite dimension contains a subspace isomorphic to ${\ell^\infty({\mathbb N})}$ . As for the zero eigenvalue, it is shown that a locally finite tree either is a Liouville space or has infinitely many linearly independent bounded harmonic functions if the edge lengths do not shrink to zero anywhere. This alternative is shown to be false on graphs containing circuits.     

Theory of the non-planar surface phase in tilted smectic films under electric field

We present a phenomenological theory of the non-planar tilted surface phase recently observed in freely suspended smectic films. We show that the three phases —Synclinic, Anticlinic, and non-planar (Axial)— stable in non-chiral systems, merge into a single phase in chiral systems. We discuss some experimental consequences of this specific chiral feature. We predict the effects of electric field application parallel to the smectic layers on the stability of the various zero-field surface phases, and determine the conditions for the observation of field-induced chiral Anticlinic/Synclinic crossovers. In thin films they depend only on the ratio between the bulk electroclinic coupling energy and the surface electric-field-tilt coupling.     

Some Remarks on Large-Time Asymptotic of the Lifshitz–Slyozov Equations

We obtain an entropy functional for the Lifshitz–Slyozov system. This can be used to investigate the time asymptotics of the system. In particular, we describe situations in which the monomers concentration either tend to 0 or saturate as time becomes large. The latter situation can be excluded under assumptions on the support of the initial data.     

Mixed convection and conduction heat transfer in open cavities

A numerical study has been carried out on mixed convection and conduction in open cavities. The study covers the Rayleigh number from 10 to 10⁶, the Reynolds number from 1 to 10³ andk _r =k _w /k _a from 1 to 100 forPr=0.72 (air) and cavity aspect ratioB from 0.8 to 1.3. The flow is assumed to be laminar and two-dimensional. The density variation is taken into account by the Boussinesq approximation. The controlvolume approach is used for solving the governing equations of conjugate heat transfer involving conduction in the walls. Streamlines and isotherms in the system are produced and the results are represented in terms of the Nusselt number as function of other parameters. Correlations are derived to calculate heat transfer through the cavity openings.     

Strontium ferrite nanoparticles synthesized in presence of polyvinylalcohol: Phase composition,microstructural and magnetic properties

Systematic study was devoted to the synthesis of hexagonal strontium ferrite nanoparticles employing polyvinylalcohol as stabilizing agent. Preliminary experiments allowed to select an optimal sol having molar ratio Sr²⁺/Fe³⁺=12${\mathrm{Sr}}^{2+}/{\mathrm{Fe}}^{3+}=12$, weight ratio PVA/[Sr²⁺+Fe³⁺]=1.4$\mathrm{PVA}/[{\mathrm{Sr}}^{2+}+{\mathrm{Fe}}^{3+}]=1.4$ and pH=2.1$\mathrm{pH}=2.1$. The obtained sol were transformed to gels by an evaporation of water at 100 °C and drying at 112 °C under vacuum. The subsequent calcination was carried out for 3 h at 400 °C, achieved by heating rate of 17 K/min. The obtained precursor was used for a detail study of influence of annealing conditions (temperature range 600–700 °C, annealing time 10–190 min) on the resulting properties. Semiquantitative X-ray phase analysis approved a gradual increase of the M-phase content and a gradual growth of M-phase crystallites with temperature and time. Magnetic measurements showed a distinct influence of the phase composition, namely ratio of the contents of M-phase and maghemite on the shape of the magnetic loops, while the crystallite sizes have only a slight effect.     

Differential protein expression by Pseudomonas fragi submitted to various stresses.

We have analyzed the impact of various stressing conditions on the physiological and molecular responses of the main psychrotrophic spoilage bacterium of refrigerated meat and meat products, Pseudomonas fragi. A survival study using conventional plating was first performed to select the stressing agents and parameters. Some of these mimicked cleaning-disinfection processes but with less drastic conditions in order to keep alive enough bacterial cells for the protein expression characterization. Cultures of P. fragi, at the beginning of the stationary phase of growth, were submitted to individual pH (5.4, 10.5), osmotic (8% Na2SO4, pH 7.0), biocide (fatty amine) shocks or combined treatments (8% Na2SO4, pH 10.5; 8% Na2SO4, pH 10.5 + biocide; pH 5.4 + pH 10.5 and pH 10.5 + pH 5.4) and the molecular responses were investigated by comparing autoradiograms of two-dimensional gel electrophoresis (2-DE) patterns of proteins radiolabeled with L-[35S]methionine. The observation of qualitative and relative quantitative variations in protein expression, determined with Melanie II image analysis software (Bio-Rad), revealed the overexpression of a total of 91 proteins for the eight challenges by comparison with the nonshocked controls. Some proteins appeared to be more or less general stress proteins whereas others were specific for one chemical treatment. The appraisal of the type of molecular response according to the type of treatment was analyzed statistically.     

A nonstandard multigrid method with flexible multiple semicoarsening for the numerical solution of the pressure equation in a Navier-Stokes solver

Numerical methods for the incompressible Reynolds-averaged Navier-Stokes equations discretized by finite difference techniques on collocated cell-centered structured grids are considered in this paper. A widespread solution method to solve the pressure-velocity coupling problem is to use a segregated approach, in which the computational work is deeply controlled by the solution of the pressure problem. This pressure equation is an elliptic partial differential equation with possibly discontinuous or anisotropic coeffficients. The resulting singular linear system needs efficient solution strategies especially for 3-dimensional applications. A robust method (close to MG-S [22,34]) combining multiple cell-centered semicoarsening strategies, matrix-independent transfer operators, Galerkin coarse grid approximation is therefore designed. This strategy is both evaluated as a solver or as a preconditioner for Krylov subspace methods on various 2- or 3-dimensional fluid flow problems. The robustness of this method is shown. This revised version was published online in June 2006 with corrections to the Cover Date.