A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes

We prove the convergence of a semi-implicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two different inhomogeneous flux-type boundary conditions. This problem arises in the modeling of the sedimentation-consolidation process. We formulate the definition of entropy solution of the model in the sense of Kru kov and prove convergence of the scheme to the unique entropy solution of the problem, up to satisfaction of one of the boundary conditions.

     

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.     

A Three-Dimensional Model for Fiber Lay-Down Processes

We present an improved stochastic model concerning the lay-down of fibers on a conveyor belt in the production of nonwovens. The model is based on stochastic differential equations describing the resulting position of the fiber on the belt having regard to its motion in the deposition region under influence of turbulent air flow. Our aim is to generalize an existing model to 3D. By introducing a parameter we have an alternative to consider both isotropic and anisotropic orientation of the fibers generating the nonwoven. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystal chemistry of the G-phases in the {Ti, Zr, Hf}-Ni-Si systems

Ternary compounds M₆Ni₁₆Si₇ (M=Ti, Zr, Hf) have been investigated by X-ray powder/single crystal and neutron powder diffraction. Compounds with Zr and Hf crystallize in the ordered Th₆Mn₂₃ type (Mg₆Cu₁₆Si₇-type, space group ), whereas Ti₆Ni_16.7Si₇ contains an additional Ni atom partially occupying the 24e site (M2 site, x=0.4637,0,0; occ.=0.119) inside a Ti octahedron; Ti atoms occupy a split position. Ti₆Ni_16.7Si₇ represents a new variant of the filled Th₆Mn₂₃ type structure. Ab initio calculations confirm the structural difference: additional Ni atoms favour the 24e site for Ti₆Ni_16.7Si₇, however, for the Zr and Hf-based compounds the unoccupied site renders an energetically lower ground state. Enthalpies of formation of Ti₆Ni₁₇Si₇, Zr₆Ni₁₆Si₇, and Hf₆Ni₁₆Si₇ were calculated to be −68.65, −74.78, and −78.59 kJ/(mol of atoms), respectively.     

Completely J —positive linear systems of finite order

Completely J — positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J — positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J — symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J — symmetric realizations are discussed.     

Numerical Simulations of Arterial Walls Based on IVUS-Data

Atherosclerosis has become one of the most frequent causes of death in the last decades. So the analysis and improvement of corresponding medical treatments, e.g., balloon-angioplasty or stenting, are significant tasks in the fields of biomechanics and biomedical engineering. One important component of the simulation of arterial walls, especially of atherosclerotically degenerated ones, is the knowledge of their anatomical and physiological composition. The intravascular ultrasound and the interpretation by the Virtual Histology provide cross-sectional images of the diseased arterial walls where the different components are characterized by color-coding. The topic of this contribution is the 3D reconstruction and discretization of the artery using these color-coded images and the biplane angiography. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ligand-, structure- and pharmacophore-based molecular fingerprints: a case study on adenosine A1, A2A, A2B, and A3 receptor antagonists

FLAP fingerprints are applied in the ligand-, structure- and pharmacophore-based mode in a case study on antagonists of all four adenosine receptor (AR) subtypes. Structurally diverse antagonist collections with respect to the different ARs were constructed by including binding data to human species only. FLAP models well discriminate ??active?? (=highly potent) from ??inactive?? (=weakly potent) AR antagonists, as indicated by enrichment curves, numbers of false positives, and AUC values. For all FLAP modes, model predictivity slightly decreases as follows: A_2BR?>?A_2AR?>?A₃R?>?A₁R antagonists. General performance of FLAP modes in this study is: ligand-?>?structure-?>?pharmacophore- based mode. We also compared the FLAP performance with other common ligand- and structure-based fingerprints. Concerning the ligand-based mode, FLAP model performance is superior to ECFP4 and ROCS for all AR subtypes. Although focusing on the early first part of the A_2A, A_2B and A₃ enrichment curves, ECFP4 and ROCS still retain a satisfactory retrieval of actives. FLAP is also superior when comparing the structure-based mode with PLANTS and GOLD. In this study we applied for the first time the novel FLAPPharm tool for pharmacophore generation. Pharmacophore hypotheses, generated with this tool, convincingly match with formerly published data. Finally, we could demonstrate the capability of FLAP models to uncover selectivity aspects although single AR subtype models were not trained for this purpose.