Implicit–explicit schemes for nonlinear nonlocal equations with a gradient flow structure in one space dimension

Nonlinear convection–diffusion equations with nonlocal flux and possibly degenerate diffusion arise in various contexts including interacting gases, porous media flows, and collective behavior in biology. Their numerical solution by an explicit finite difference method is costly due to the necessity of discretizing a local spatial convolution for each evaluation of the convective numerical flux, and due to the disadvantageous Courant–Friedrichs–Lewy (CFL) condition incurred by the diffusion term. Based on explicit schemes for such models devised in the study of Carrillo et al. a second‐order implicit–explicit Runge–Kutta (IMEX‐RK) method can be formulated. This method avoids the restrictive time step limitation of explicit schemes since the diffusion term is handled implicitly, but entails the necessity to solve nonlinear algebraic systems in every time step. It is proven that this method is well defined. Numerical experiments illustrate that for fine discretizations it is more efficient in terms of reduction of error versus central processing unit time than the original explicit method. One of the test cases is given by a strongly degenerate parabolic, nonlocal equation modeling aggregation in study of Betancourt et al. This model can be transformed to a local partial differential equation that can be solved numerically easily to generate a reference solution for the IMEX‐RK method, but is limited to one space dimension.     

Quantitative HPLC-MS analysis of nucleotide sugars in plant cells following off-line SPE sample preparation

An analytical workflow was developed for the absolute quantification of uridine diphosphate (UDP)-sugars in plant material in order to compare their metabolism both in wild-type Arabidopsis thaliana and mutated plants (ugd2,3) possessing genetic alterations within the UDP-glucose dehydrogenase genes involved in UDP-sugar metabolism. UDP-sugars were extracted from fresh plant material by chloroform-methanol-water extraction and further purified by solid-phase extraction with a porous graphitic carbon adsorbent with extraction efficiencies between 80?±?5 % and 90?±?5 %. Quantitative determination of the UDP-sugars was accomplished through HPLC separation with a porous graphitic carbon column (Hypercarb^TM) which was interfaced to electrospray ionization Orbitrap mass spectrometry. The problem of instable retention times due to redox processes on the stationary phase were circumvented by grounding of the column effluent and incorporation of a column regeneration procedure using acetonitrile-water containing 0.10 % trifluoroacetic acid. The method was calibrated using external calibration and UDP as internal standard. Calibration functions were approximated by first- or second-order regression analysis for concentrations spanning three orders of magnitude. Upon injecting sample volumes of 2.65 μL, the limits of detection for the UDP-sugars were in the 70 nmol L^?1 range. Six different UDP-sugars, including UDP-glucose, UDP-galactose, UDP-arabinose, UDP-xylose, UDP-glucuronic acid, and UDP-galacturonic acid were found in concentrations of 0.4 to 38 μg/g plant material. Data evaluation by analysis of variance (ANOVA) revealed statistically significant differences in UDP-sugar concentrations between wild-type and mutant plants, which were found to conclusively mirror the impaired metabolic pathways in the mutant plants.

Survey of chemical residues and biological evaluation of photochemically pre-vulcanized surgical gloves

Abstract  

Latex allergies arise from the presence of latex proteins as well as noxious rubber additives (mainly accelerators and activators used in conventional sulfur-accelerated vulcanization processes) in medical devices (e.g., medical gloves, catheters) made from natural rubber latex. As a new approach the ultraviolet (UV) light-initiated pre-vulcanization of natural rubber latex makes efficient cross-linking feasible without using any toxic, mutagenic, or irritating chemicals. The cross-linking in the latex particles is accomplished via the thiol-ene addition reaction in the presence of a polyfunctional thiol and a photoinitiator. The new process is carried out in a falling film photoreactor on a pilot scale which provides a continuous irradiation of the latex emulsion. The UV technique is suitable for an easy up-scaling and represents the entrance into large-volume industrial production. The surgical gloves are then made by a conventional coagulant dipping process comprising good physical properties and high ageing stabilities. The aim of this study was to evaluate the biological properties and skin compatibility of UV-pre-cured gloves in skin sensitization, skin irritation studies, and cytotoxic tests. In addition the biologically available chemical residues in the gloves were characterized by UV–visible spectroscopy, elementary analyses, and high-performance liquid chromatography coupled with mass spectroscopy. The results of the studies revealed that UV-cross-linked surgical gloves exhibit good skin compatibility together with low cytotoxicity and residual chemical levels in the range of 60 and 120 μg/g_glove.     

On the role of reachability and observability in NMR experimentation

It is shown that the system theoretic concepts of reachability and observability are relevant to the analysis of NMR experiments. Moreover, the sets of reachable states are examined and Lie theoretic criteria are given for the reachability of the system. The question is investigated how the set of reachable states depends on the class of input functions that are allowed. Both one‐dimensional and multi‐dimensional NMR experiments are considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mechanical Properties of Bacterially Synthesized Nanocellulose Hydrogels

The mechanical characteristics of bacterially synthesized nano-cellulose (BNC) were studied with uniaxial compression and tensile tests. Compressive loads result in a release of water and the deformation of the water-saturated network corresponds approximately to the volume of released water. The BNC hydrogel exhibits a mainly viscous response under compression. The strain response under tensile loads has an elastic and a viscous component. This can be described with a Maxwell model, where the viscosity is strain rate-dependent. When the aqueous phase of the BNC hydrogel is stabilized with an additional alginate hydrogel matrix, the system exhibits an elastic response under compressive loads. The analysis of the ‘alginated’ BNC network with the Maxwell model shows that the alginate matrix increases the viscosity of the composite system. The results of the mechanical tests show that the water absorbed in the BNC hydrogel strongly influences its mechanical behavior.     

Second-order schemes for conservation laws with discontinuous flux modelling clarifier–thickener units

Continuously operated clarifier–thickener (CT) units can be modeled by a non-linear, scalar conservation law with a flux that involves two parameters that depend discontinuously on the space variable. This paper presents two numerical schemes for the solution of this equation that have formal second-order accuracy in both the time and space variable. One of the schemes is based on standard total variation diminishing (TVD) methods, and is addressed as a simple TVD (STVD) scheme, while the other scheme, the so-called flux-TVD (FTVD) scheme, is based on the property that due to the presence of the discontinuous parameters, the flux of the solution (rather than the solution itself) has the TVD property. The FTVD property is enforced by a new nonlocal limiter algorithm. We prove that the FTVD scheme converges to a BV _t solution of the conservation law with discontinuous flux. Numerical examples for both resulting schemes are presented. They produce comparable numerical errors, while the FTVD scheme is supported by convergence analysis. The accuracy of both schemes is superior to that of the monotone first-order scheme based on the adaptation of the Engquist–Osher scheme to the discontinuous flux setting of the CT model (Bürger, Karlsen and Towers in SIAM J Appl Math 65:882–940, 2005). In the CT application there is interest in modelling sediment compressibility by an additional strongly degenerate diffusion term. Second-order schemes for this extended equation are obtained by combining either the STVD or the FTVD scheme with a Crank–Nicolson discretization of the degenerate diffusion term in a Strang-type operator splitting procedure. Numerical examples illustrate the resulting schemes.     

Mit der Untersuchung von Erbsen hat sich

Ohne Zusammenfassung     

On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

Polydisperse suspensions consist of particles differing in size or density that are dispersed in a viscous fluid. During sedimentation, the different particle species segregate and create areas of different composition. Spatially one-dimensional mathematical models of this process can be expressed as strongly coupled, nonlinear systems of first-order conservation laws. The solution of this system is the vector of volume fractions of each species as a function of depth and time, which will in general be discontinuous. It is well known that this system is strictly hyperbolic provided that the Masliyah–Lockett–Bassoon (MLB) flux vector is chosen, the particles have the same density, and the hindered-settling factor (a multiplicative algebraic expression appearing in the flux vector) does not depend on the particle size but is the same for all species. It is the purpose of this paper to prove that this hyperbolicity result remains valid in a fairly general class of cases where the hindered-settling factor does depend on particle size. This includes the common power-law type hindered-settling factor in which the exponent, sometimes called Richardson–Zaki exponent, is determined individually for each species, and is a decreasing function of particle size. The importance of this paper is two-fold: it proves stability for a class of polydisperse suspensions that was not covered in previous work, and it offers a new analysis of real data.