On Stability and Strong Convergence for the Spatially Homogeneous Boltzmann Equation for Fermi-Dirac Particles

 The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under a cutoff condition on the collision kernel, we prove a strong stability in L ¹ topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L ¹ to equilibrium under a high temperature condition. The basic tools used are moment-production estimates and the strong compactness of the collision gain term. (Accepted 25, October 2002) Published online March 14, 2003 Communicated by P.-L. Lions     

Stability and exponential convergence for the Boltzmann equation

We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L ¹, and extend previous results in L for the non-homogeneous equation, as well as the more developed L ^p -theory for the spatially homogeneous Boltzmann equation.We also give new L -estimates for the spatially homogeneous equation in the case of Maxwellian interactions.     

Carboxymethylated nanofibrillated cellulose: effect of monovalent electrolytes on the rheological properties

The effect of the ionic strength on the properties of a carboxymethylated nanofibrillated cellulose (NFC) system was investigated through rheological studies. It was shown that homogenization of pulp suspensions containing a high amount of a monovalent electrolyte leads to the production of NFC systems displaying a lower magnitude in the rheological response as compared with systems prepared at lower ionic strengths conditions. It was further shown that increasing the ionic strength of NFC suspensions after their manufacturing also results in a lowering of the rheological response. The decreased rheological response in the former case was postulated to be caused by a lowering of the delamination deficiency of the homogenization process, due to decreased swelling of the carboxymethylated pulp, caused by the screening of the charges. In the latter case (post-addition of the electrolyte), the lowering of the rheological response was postulated to be due to the compression of the electrostatic double layer, when the electrostatic repulsion between the charged fibrils diminished in the presence of the electrolyte.     

Carboxymethylated nanofibrillated cellulose: rheological studies

The rheological properties of carboxymethylated nanofibrillated cellulose (NFC), investigated with controlled shear rate- and oscillatory measurements, are reported for the first time. It was shown that the rheological properties of the studied system are similar to those reported for other NFC systems. The carboxymethylated NFC systems showed among other things high elasticity and a shear thinning behaviour when subjected to increasing shear rates. Further, the shear viscosity and storage modulus of the system displayed power-law relations with respect to the dry content of the NFC suspension. The exponential values, 2 and 2.4 respectively, were found to be in good agreement with both theoretical predictions and published experimental work. Furthermore, it was found that the pulp consistency at which NFC is produced affects the properties of the system. The rheological studies imply that there exists a critical pulp concentration below which the efficiency of the delamination process diminishes; the same adverse effect is also observed when the critical concentration is significantly exceeded due to a lower energy input during delamination.     

Topological Structure of the Set of Weighted Composition Operators on Weighted Bergman Spaces of Infinite Order

We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H^∞) and L(H^∞_v) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.     

Simulation of two‐phase flow with moving immersed boundaries

A two‐dimensional multi‐phase model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible Navier–Stokes equation coupled with a phase‐field model based on van der Waals' free energy density and the Cahn–Hilliard equation. A new phase‐field boundary condition was implemented with minimization of the free energy in a direct way, to specifically improve the physical behavior of the contact line dynamics for moving immersed objects. Numerical stability and execution time were significantly improved by the use of the new boundary condition. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the Lucas–Washburn theory and Stefan's problem. The proposed model may be used for multi‐phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium. Copyright © 2010 John Wiley & Sons, Ltd.     

Systematic Study of the Interaction Between VIV Centres and LnIII Ions in Well Defined {V 2 IV LnIII}{AsIIIW9O33}2 Sandwich-Type Clusters: Part 2

The gadolinium (Gd) member of a new type of heteropolytungstates that contain one lanthanide and two transition metal ions in a triangular arrangement is reported. The compound NaK₆Gd_0.33 [((VO)₂Gd(H₂O)₄K₂(H₂O)₂(Na)(H₂O)₂)(α-B-AsW₉O₃₃)₂]·24H₂O (1) was prepared from acidified aqueous solutions of Na₂WO₄·2H₂O, As₂O₃ and VOSO₄·5H₂O to which Gd³⁺ ions were added. The single crystal X-ray structure analysis (monoclinic, space group P2₁/m) shows that the anion consists of two [α-B-As^IIIW₉O₃₃]^9? trilacunary Keggin-type units linked by two VO²⁺, one Gd³⁺ as well as weakly by two K⁺ and one Na⁺ ions, resulting in a sandwich-type structure with idealized C _2v symmetry. The problem of positioning crystal lattice and special polyoxometalate sites with different cations is discussed also in connection with supramolecular chemistry aspects and as an option for further research. A fit of the magnetic susceptibility yielded exchange coupling constants of J _VV = ?2.55 cm^?1 (anti-ferromagnetic) between the vanadium ions and J _GdV = 0.6 cm^?1 (ferromagnetic) between the Gd and each of the two vanadium ions. The complete magnetochemical analysis also revealed a partial occupancy of the Na⁺ sites in the counter-cation–water system by Gd³⁺ ions (0.33 Gd³⁺ ions in total).     

The surface charge of regenerated cellulose fibres

In this paper the influence of charged species on the sheet strength of viscose fibres was investigated. Four samples of chemical modified viscose fibres, as well as a reference fibre were studied. The swelling of these viscose fibres and the breaking length of hand sheets have been determined. Comparing the results, the influence of both, swelling and surface charge on the bonding force, is evident. The allocation of the charges, induced by cationic starch and Carboxmethylcellulose, has been analyzed by Titration, attenuated total reflection spectroscopy (ATR) and X-ray photoelectron spectroscopy (XPS). Titration was used to make a first estimation of the charge distribution within the fibre. Using ATR and XPS, more detailed information about the surface charge has been achieved. All measurement methods showed a significant amount of charge on the fibre surface.     

Odd-even effects in the alignment of ferroelectric liquid crystals

Nine different poly-n-alkylterphthalamides have been synthesized, and their properties as alignment layers for chiral smectic C liquid crystals have been determined. Poly-n-hexylterphthalamide is found to be particularly well suited for one of the room temperature mixtures used in this study. The contrast between relaxed states shows an odd-even effect that can probably be explained by the crystal form of the different polymers. The tilt angle found between the relaxed states depends only on the polymer used, not on the inherent tilt of the chiral smectic C phases.