Contact mechanics modeling of piezo-actuated stick-slip microdrives

This paper draws a line from early attempts of modeling stick-slip microdrives to open questions from today’s research. As a basis, it contains a collection of substantial investigations on piezo-actuated stick-slip microdrives for nanomanipulation purposes. Friction models showing special characteristics and their mathematical representations are reviewed. It is found that the working properties of stick-slip drives strongly depend on friction characteristics of the contact points between the guiding elements, which is known for years. However, numerous publications in the field of friction and remaining problems — which cannot be explained by known friction models — indicate that there is a demand for even more friction-related research.Former attempts to model stick-slip drives are based on the so-called LuGre friction model, which is shortly presented. An empirical model called CEIM is also analyzed. It is an adaption of the elastoplastic model. The latter can cover not only the phenomenon “0-amplitude’ (described by the authors in recent publications), but also stick-slip based force generation scenarios. Nevertheless, interesting friction characteristics such as the generation of μN forces with stick-slip drives, which are already proven, cannot be covered by known friction models. It is pointed out which characteristics have to be considered.     

Scalar field collapse with an exponential potential

An analogue of the Oppenheimer–Synder collapsing model is treated analytically, where the matter source is a scalar field with an exponential potential. An exact solution is derived followed by matching to a suitable exterior geometry, and an analysis of the visibility of the singularity. In some situations, the collapse indeed leads to a finite time curvature singularity, which is always hidden from the exterior by an apparent horizon.     

Synthesis of high-performance superabsorbent glycerol acrylate-cross-linked poly (acrylic acid)

Glycerol acrylate (GA) is synthesised by an acryloylation reaction with acryloyl chloride. An ester was used as a cross-linking agent at varying proportions in the synthesis of poly acrylic acid (PAA). The amount of cross-linking density in the product (GA-PAA) and degree of neutralisation determine the absorbency of the polymer samples. A sample of GA-PAA containing 0.8 % GA was discovered to absorb 395 and 66 g/g of water and saline solution, respectively. Different solvent uptakes were tested with the sample showing varying capacity for different solvents. The temperature of the reaction was maintained at 60 °C and a reaction time of 2½ h. FTIR, TGA, SEM and XRD analyses were used to characterise the products.     

Kinetic and thermodynamic modeling of Portland cement hydration at low temperatures

Portland cement have to hydrate in cold climates in some particular conditions. Therefore, a better understanding of cement hydration under low temperatures would benefit the cement-based composites application. In this study, Portland cement was, therefore, kinetically and thermodynamically simulated based on a simple kinetics model and minimization of Gibbs free energy. The results of an evaluation indicate that Portland cement hydration impact factors include the water–cement ratio (w/c), temperature, and specific surface area, with the latter being an especially remarkable factor. Therefore, increasing the specific surface area to an appropriate level may be a solution to speed the delayed hydration due to low temperatures. Meanwhile, the w/c ratio is believed to be controlled under cold climates with consideration of durability. The thermodynamic calculation results suggest that low-temperature influences can be divided into three levels: irrevocable effects (<0 °C), recoverable effects (0–10 °C), and insignificant effects (10–20 °C). Portland cement was additionally measured via X-ray diffraction, thermal gravity analysis, and low-temperature nitrogen adsorption test in a laboratory and comparisons were drawn that validate the simulation result.     

Open Quantum Random Walks on the Half-Line: The Karlin–McGregor Formula,Path Counting and Foster’s Theorem

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin–McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler’s ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster’s Theorem for the expected return time together with applications.