Patch coupling with the isogeometric dual mortar approach

The use of a common set of basis functions for design and analysis is the main paradigm of isogeometric analysis. The characteristics of the commonly used non-uniform rational B-splines (NURBS) surfaces require methods to handle non-conforming meshes to attain an efficient computational framework. The isogeometric mortar method uses constrained approximation spaces to enforce a coupling of deformations at the interface between patches in a weak manner. This method neither requires additional degrees of freedom nor the choice of empirical parameters. The main drawback of the standard isogeometric mortar approach is the non-local support of the mortar basis functions along the interface. This yields a large number of nodes per element for elements adjacent to the interface. Thus, the computational costs increase significantly for mesh refinement. This issue is remedied by the use of dual basis functions for the mortar method, which is referred to as dual mortar method. In this contribution several choices for the dual basis functions for B-splines are proposed and compared. A special focus is set on the support of the dual basis functions and on the support of the resulting mortar basis functions. Numerical examples show the influence of the choice for the dual basis functions on the accuracy of the global stress distribution, on the fulfillment of the interface conditions and on numerical efficiency. The use of approximate dual basis functions is shown to be competitive to computations of conforming meshes in terms of accuracy and efficiency. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ternäre Thallium-Indium-Sulfide: Eine Zusammenfassung

Ternary Thallium Indium Sulfides: A Summary Combined thermal and X-Ray analyses in the ternary system Thallium—Indium—Sulfur show, that the two binary sections Tl₂S? In₂S₃ and TlS? InS contain ternary compounds with unique crystal structures. The chemical formulas of these ternary solids are TlIn₅S₈, TlIn₃S₅, TlInS₂ and Tl₃InS₃ for the section Tl₂S? In₂S₃ and TlIn₅S₆ as well as Tl₃In₅S₈ (metastable high temperature phase) for the section TlS? InS respectively. With TlIn₅S₇ an additional ternary solid could be detected, which is located outside the two sections. It is derived from the binary mixed valence compound In₆S₇ by complete substitution of In⁺ by Tl⁺. The following ionic formulations make the mixed valence character of the ternary Thallium—Indium-Sulfides reasonable: TlIn₅S₈ = Tl⁺(In³⁺)₅(S^2?)₈, TlIn₃S₅ = Tl⁺ (In³⁺)₃(S^2?)₅, TlInS₂ = Tl⁺In³⁺(S^2?)₂, Tl₃InS₃ = (Tl⁺)₃In³⁺ · (S^2?)₃, TlIn₅S₆ = Tl⁺([In₂]⁴⁺)₂In³⁺ (S^2?)₆, Tl₃In₅S₈ = 4 × [(Tl⁺)_0,75 · (In⁺)_0,25In³⁺(S^2?)₂], TlIn₅S₇ = Tl⁺[In₂]⁴⁺ (In³⁺)₃(S^2?)₇. All compounds contain Tl⁺-ions in a characteristic “lone pair coordination” of S^2? ions. Indium atoms however occur with the oxidation numbers +2 (formal, In₂ dumb bells with covalent In? In bonding) and +3 (with In³⁺ in tetrahedral and octahedral coordination of S^2?). Chemical preparation, crystal chemistry and general properties of the ternary solids are discussed, summarized and compared to each other.     

Trans-cis isomerization is responsible for the red-shifted fluorescence in variants of the red fluorescent protein eqFP611

An important class of red fluorescent proteins (RFPs) feature a 2-iminomethyl-5-(4-hydroxybenzylidene)imidazolinone chromophore. Among these proteins, eqFP611 has the chromophore in a coplanar trans orientation, whereas the cis isomer is preferred by other RFPs such as DsRed and its variants. In the photoactivatable protein asFP595, the chromophore can even be switched from the nonfluorescent trans to the fluorescent cis state by light. By using X-ray crystallography, we have determined the structure of dimeric eqFP611 at high resolution (up to 1.1 A). In the far-red emitting eqFP611 variant d2RFP630, which carries an additional Asn143Ser mutation, the chromophore resides predominantly (approximately 80%) in the cis isomeric state, and in RFP639, which has Asn143Ser and Ser158Cys mutations, the chromophore is found completely in the cis form. The pronounced red shift of excitation and emission maxima of RFP639 can thus unambiguously be assigned to trans-cis isomerization of the chromophore. Among RFPs, eqFP611 is thus unique because its chromophore is highly fluorescent in both the cis and trans isomeric forms.     

On the Validity of Stokes–Einstein and Stokes–Einstein–Debye Relations in Ionic Liquids and Ionic‐Liquid Mixtures

Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations in the neat ionic liquid (IL) [C₂mim][NTf₂] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)? H bond in the cation C₂mim⁺, and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non‐Gaussian parameter α(t). If α(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.     

Electrophoresis of soft particles at high electrolyte concentrations: an interpretation by the Henry theory

The existence of electrophoretic mobility at high electrolyte concentrations defines a remarkable peculiarity in the electrosurface characteristics of soft particles. According to Ohshima [H. Ohshima, Colloids Surf. 103 (1995) 249], this effect is caused by the electroosmotic flow within the soft particle shell. An explanation supporting Ohshima's conclusion can be derived from classic electrokinetic theories. Based on the Henry theory [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106], we demonstrate that the electrophoretic mobility of soft particles does not disappear at decinormal concentration.     

Thermophysical properties and material modelling of acrylic bone cements used in vertebroplasty

The stabilization of osteoporotic vertebrae with acrylic bone cement, called vertebroplasty, is a common procedure in modern surgery. However, the thermomechanical-chemically coupled material behaviour of curing bone cements makes the application even for experienced surgeons difficult and can lead to potential complications like heat necrosis, leaking bone cement, embolisms and postoperative load shifting. In order to reduce these potential complications, to minimize the risks and to better understand the occurring effects, the thermophysical properties of a commercial acrylic bone cement were investigated in detail using differential scanning calorimetry, volumetric dilatometry and temperature controlled rheometry. More specifically, the reaction kinetics, the specific heat, the thermal conductivity, the thermal expansion, the chemical shrinkage as well as the mechanical behaviour was studied during the reaction process of the bone cement. Furthermore, the explored material behaviour is described by a customized material model that takes into account all observed effects. With the aid of this model the inhomogeneous chemical, thermal and mechanical states that appear during the application and curing of acrylic bone cements, can be studied by finite element treatment.     

Transient innermolecular carbene-hemicarcerand complex of fluorophenylcarbene

Laser flash photolysis of fluorophenyldiazirine incarcerated in hemicarcerand 2 affords incarcerated fluorophenylcarbene [2⊙3], which forms a metastable, innermolecular π-complex with aryl moieties of 2. This carbene complex can be observed spectroscopically. Extensive computational studies provide insights into the structure, spectroscopy, energetics, and kinetics of the 2⊙3 carbene complex.