Optimal control of the Stokes equations: conforming and non-conforming finite element methods under reduced regularity

This paper deals with a control-constrained linear-quadratic optimal control problem governed by the Stokes equations. It is concerned with situations where the gradient of the velocity field is not bounded. The control is discretized by piecewise constant functions. The state and the adjoint state are discretized by finite element schemes that are not necessarily conforming. The approximate control is constructed as projection of the discrete adjoint velocity in the set of admissible controls. It is proved that under certain assumptions on the discretization of state and adjoint state this approximation is of order 2 in L ²(Ω). As first example a prismatic domain with a reentrant edge is considered where the impact of the edge singularity is counteracted by anisotropic mesh grading and where the state and the adjoint state are approximated in the lower order Crouzeix-Raviart finite element space. The second example concerns a nonconvex, plane domain, where the corner singularity is treated by isotropic mesh grading and state and adjoint state can be approximated by a couple of standard element pairs.     

Characterizing geometric designs, II

We provide a characterization of the classical point-line designs PG₁(n,q), where n?3, among all non-symmetric 2-(v,k,1)-designs as those with the maximal number of hyperplanes. As an application of this result, we characterize the classical quasi-symmetric designs PGn−2(n,q), where n?4, among all (not necessarily quasi-symmetric) designs with the same parameters as those having line size q+1 and all intersection numbers at least qn−4+?+q+1. Finally, we also give an explicit lower bound for the number of non-isomorphic designs having the same parameters as PG₁(n,q); in particular, we obtain a new proof for the known fact that this number grows exponentially for any fixed value of q.     

Direct numerical simulation of thermocapillary flow based on the Volume of Fluid method

A numerical method for direct simulation of thermal Marangoni effects at dynamically deformable interface of two-phase incompressible fluids is developed. The approach is based on the Volume of Fluid (VOF) method with special focus on the numerical treatment of the temperature surface gradient because of its decisive role as the driving force of the flow. The surface gradient calculation is split into computing its length and direction in order to satisfy the correct thermal boundary condition at the interface without losing mobility of the interface. The method is applied to three different types of thermocapillary flow, namely thermocapillary migration of a droplet in an ambient fluid with linear temperature gradient, thermocapillary convection in a liquid layer under linear temperature gradient along the interface, and Marangoni convection due to Bénard–Marangoni instability. In the first case, different aspects of the dynamics of the migration are considered for validation such as the terminal migration velocity, the initial acceleration and quantification of the wall effects. The simulation also considers high convective heat transfer and covers a wide range of Marangoni numbers up to 5000, where good agreement with both theoretical and experimental results is achieved. In the second case, the convection velocity in the liquid layer is compared with an analytical result. In the final application, pattern formation due to the Bénard–Marangoni instability in a liquid layer in square geometry of small aspect ratio is investigated for realistic Biot number and dynamically deformable fluid interface. The results show good agreement with experiments from literature, where our numerical simulation also predicts cell pattern for a particular aspect ratio which is outside the limitation of the above cited experimental work.     

Analytical study of the interface in fibre-reinforced 2D composite material

Imperfect bonding between the constitutive components can greatly affect the properties of the composite structures.An asymptotic analysis of different types of imperfect interfaces arising in the problem of 2D fibrereinforced composite materials are proposed.The performed study is based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems.All solutions are obtained in a closed analytical form.The obtained results can be used for the calculation of pull-out and pushout tests,as well as for the investigation of the fracture of composite materials.     

Impact of sorption phenomena on multiphase conveying processes

Twin-screw multiphase pumps are employed increasingly to convey multiphase mixtures of crude oil, accompanying fluids, associated gas and solid particles. They are positive displacement pumps and suitable for handling products containing liquid accompanied by large amounts of gas. Experimental investigations on the conveying characteristic, namely measuring the delivered volume flow as a function of the pressure difference, provide results for selected mixtures. By means of the on hand work, the influence of sorption phenomena occurring due to pressure variations alongside the conveying process on the conveying characteristics of twin-screw pumps delivering mixtures of oil and gases is measured. The employed gases are air and carbon dioxide, which differ strongly in solubility in oil. All experiments are conducted in a closed loop test facility, where oil and gas volume flows are mixed before the inlet and separated after the outlet of the multiphase pump. In order to simulate the influence of the suction side pressure drop in the reservoir on the conveying characteristic, packed beds are employed as oil-filed model. Sorption processes inside of the oil-field model and within the multiphase pump affect the conveying behaviour significantly. The two-phase flow in the inlet and outlet pipe is visualised by means of a capacitance tomography system. Results show that the oil fraction of the total delivered volume flow is decreased due to desorption at the pump inlet. The gas fraction at the pump outlet is further decreased due to absorption. Experimental results are compared to calculated solubilities of the on-hand gases in oil and to the theoretically derived gas volume flow fraction expected at the multiphase pump.     

Initiation of Protein Synthesis with Non‐Canonical Amino Acids In Vivo

By transplanting identity elements into E. coli tRNA^fMet, we have engineered an orthogonal initiator tRNA (itRNA^Ty2) that is a substrate for Methanocaldococcus jannaschii TyrRS. We demonstrate that itRNA^Ty2 can initiate translation in vivo with aromatic non‐canonical amino acids (ncAAs) bearing diverse sidechains. Although the initial system suffered from low yields, deleting redundant copies of tRNA^fMet from the genome afforded an E. coli strain in which the efficiency of non‐canonical initiation equals elongation. With this improved system we produced a protein containing two distinct ncAAs at the first and second positions, an initial step towards producing completely unnatural polypeptides in vivo. This work provides a valuable tool to synthetic biology and demonstrates remarkable versatility of the E. coli translational machinery for initiation with ncAAs in vivo.     

Formation of H3+ in Collisions of H2+ with H2 Studied in a Guided Ion Beam Instrument

In order to study collisions between ions and neutrals, a new Guided Ion Beam (GIB) apparatus, called NOVion, has been assembled and tested. The primary purpose of this instrument is to measure absolute cross sections at energies relevant for technical or inter- and circumstellar plasmas. New and improved results are presented for forming H₃⁺ in collisions of H₂⁺ with H₂. Between 0.1 eV and 2 eV, our measured effective cross sections are in good overall agreement with most previous measurements. However, at higher energies, our results do not show the steep decline, recommended in the standard literature. After critical evaluation of all experimental and theoretical data, a new analytical function is proposed, describing properly the dependence of the title reaction on the collision energy up to 10 eV.     

Contamination of therapeutic human immunoglobulin preparations with apolipoprotein H (β2‐glycoprotein I)

Polyclonal immunoglobulin (Ig) concentrates are important biological medicinal products and the assurance of their quality and safety is crucial. In our present approach we used proteomic methods to check the purity of commercial Ig products of different origin. The experimental setup included nonreducing 2DE or DIGE combined with MALDI‐TOF and the thrombin generation assay, a routine safety test for pharmaceutical Ig preparations, and was complemented by a specific immunoassay. 2DE patterns displayed contaminations with trace amounts of human apolipoprotein H (Apo‐H), transferrin, albumin, and its fragments. In contrast to the latter, Apo‐H is a protein that is active in the coagulation cascade, and thus a potential involvement in thromboembolic events in vivo cannot be excluded. It was found by 2DE and MALDI‐TOF to be a contaminant of several Ig preparations. Spiking experiments of Ig preparations with pure Apo‐H demonstrated an Apo‐H concentration dependent increase in thrombin generation assay values. Traces of Apo‐H are possibly also contributing to unwanted side effects, as already known for factor XIa. The significance of Apo‐H contaminations for these side effects might be verified by detailed analyses of pharmacovigilance data.