Towards DNA-Encoded Micellar Chemistry: DNA-Micelle Association and Environment Sensitivity of Catalysis

The development of DNA-compatible reaction methodologies is a central theme to advance DNA-encoded screening library technology. Recently, we were able to show that sulfonic acid-functionalized block copolymer micelles facilitated Brønsted acid-promoted reactions such as the Povarov reaction on DNA-coupled starting materials with minimal DNA degradation. Here, the impact of polymer composition on micelle shape, and reaction conversion was investigated. A dozen sulfonic acid-functionalized block copolymers of different molar mass and composition were prepared by RAFT polymerization and were tested in the Povarov reaction, removal of the Boc protective group, and the Biginelli reaction. The results showed trends in the polymer structure-micellar catalytic activity relationship. For instance, micelles composed of block copolymers with shorter acrylate ester chains formed smaller particles and tended to provide faster reaction kinetics. Moreover, fluorescence quenching experiments as well as circular dichroism spectroscopy showed that DNA-oligomer-conjugates, although highly water-soluble, accumulated very effectively in the micellar compartments, which is a prerequisite for carrying out a DNA-encoded reaction in the presence of polymer micelles.     

Benefits of working capital sharing in supply chains

Supply chain finance and working capital management are important avenues to reduce supply chain costs. Small suppliers may not have sufficient working capital to finance their operations and efficiently supply their customers. We develop a model that captures the fundamental aspects of financial and operational planning in a two-stage supply chain, with both strong and weak members. A strong member can negotiate for more favorable financing rates, more advantageous payment terms, and shorter lead times than a weaker member. We investigate two working capital allocation scenarios. In the dedicated working capital allocation scenario, the members of the supply chain each have their own working capital. In the joint working capital allocation scenario, the members of the supply chain have a joint pool of working capital. Our results demonstrate significant benefits when the members of the supply chain share the working capital. We also show that extending payment delays to a supplier upstream results in higher overall supply chain costs.     

Reliable a posteriori error estimation for state-constrained optimal control

We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non-discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introduce an adaptation strategy for the regularisation parameter.     

Reduced C*-algebras of Fell bundles over inverse semigroups

We construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the Fell bundle. We study when the reduced C*-algebra for an inverse semigroup action on a groupoid by partial equivalences coincides with the reduced groupoid C*-algebra of the transformation groupoid, giving both positive results and counterexamples.     

Numerical investigation of the effective Skempton coefficient in fluid-saturated fractured rock

Characterization of hydro-mechanical processes in reservoir rocks is an essential issue for many geo investigations such as characterization of subsurface fluid flow or geothermal exploitation. For geothermal applications, the role of fractures as storage and transport components of a hydraulic system are highly important. In the present contribution we focus on investigating the effective Skempton coefficient of a damaged porous rock analyzing a modified Cryer problem, which provides a simple model of a porous rock containing a storage and transport pat. The effective Skempton coefficient is defined as the ratio of the increase in mean pore pressure induced by change in confining pressure for undrained boundary conditions. Using approaches from computational homogenization, we evaluate the confining pressure as the negative volume average of the total mean stress. Similarly, we compute the effective fluid pressure in terms of the volume-averaged fluid pressure in the rocks. We compare the numerical results to those from typical experiments and highlight the problems with the latter. The proposed concept for determination of an effective Skempton coefficient based on numerically evaluated volume averages helps to generate a better understanding of the process-inherent constituents. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equilibrium and nonequilibrium dynamics of the sub-Ohmic spin-boson model

Employing the nonperturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with a spectral density J(omega) proportional to omega(s). We show that, in contrast with the case of Ohmic damping, the delocalized phase of the sub-Ohmic model cannot be characterized by a single energy scale only, due to the presence of a nontrivial quantum phase transition. In the strongly sub-Ohmic regime, s<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase--this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.     

Microresonator array for high-resolution spectroscopy

We investigated the properties of an array of spherical microresonators used as a miniaturized high-resolution spectroscopic device. Sixteen spherical microspheres made from polymethyl methacrylate were placed on a microscope slide serving as an optical wave guide. Light of a tunable narrowband laser source was coupled into this slide so that an evanescent wave was excited on the topside of the slide, where the resonators were placed. This evanescent field generated a particular intensity pattern in the array that depended sensitively on the wavelength. After calibration, that pattern was recorded by a CCD camera and used to identify the wavelength with a resolution of R ~ lambda/Deltalambda = 7 x 10(4).     

Acceleration of absolute negative mobility

Recently, the counter intuitive migration phenomenon of absolute negative mobility (ANM) has been demonstrated to occur for colloidal particles in a suitably arranged post array within a microfluidic device [1]. This effect is based on the interplay of Brownian motion, nonlinear dynamics induced through microstructuring, and nonequilibrium driving, and results in a particle movement opposite to an applied static force. Simultaneously, the migration of a different particle species along the direction of the static force is possible [19], thus providing a new tool for particle sorting in microfluidic device format. The so far demonstrated maximum velocities for micrometer-sized spheres are slow, i. e., in the order of 10 nm per second. Here, we investigate numerically, how maximum ANM velocities can be significantly accelerated by a careful adjustment of the post size and shape. Based on this numerical analysis, a post design is developed and tested in a microfluidic device made of PDMS. The experiment reveals an order of magnitude increase in velocity.