What’s New with the Neutron and Proton

The existence and importance of the proton radius puzzle, observed via a Lamb shift measurement in muonic atoms, is discussed. Possible resolutions of the puzzle are discussed. Then the broader question of the meaning of the proton radius is addressed and examples of correctly defined charge densities are presented.     

A comparison of the Discontinuous-Galerkin- and Spectral-Difference-Method on triangulations using PKD polynomials

This paper gives a first numerical comparison of the Discontinuous-Galerkin-(DG) and Spectral-Difference-Method (SD) under almost equivalent conditions for smooth test cases.     

Highly oriented and ordered microstructures in block copolymer films

Block copolymer (BCP) films with long-range lateral ordering and orientation are crucial for many applications. Here, we report a simple, versatile strategy based on a solution casting procedure, to produce millimeter thick film of BCPs with highly oriented nanostructures. Transmission electron microscope (TEM), small angle X-ray scattering (SAXS), and Hansen solubility parameters were used to study the morphology and interactions of the system. A variety of BCP-solvent pairs were investigated. Factors including set-up geometry, BCP characteristics, solvent evaporation, surface tension, and interactions, such as solvent-BCP, solvent-substrate, and BCP-substrate were examined. A mechanism is proposed to describe the observed long-range lateral ordering and orientation in films up to 1 mm in thickness. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1369–1375     

Estimating satisfiability

The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its neighborhood in a way that the total weight is at least 1 for each satisfiable instance. We define in this paper a general weighting scheme for the estimation of satisfiability of general CSPs. First we give some sufficient conditions for a weighting system to be correct. Then we show that this scheme allows for an improvement on the upper bound on the existence of non-trivial cores in 3-SAT obtained by Maneva and Sinclair (2008) [17] to 4.419. Another more common way of estimating satisfiability is ordering. This consists in putting a total order on the domain, which induces an orientation between neighboring solutions in a way that prevents circuits from appearing, and then counting only minimal elements. We compare ordering and weighting under various conditions.     

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.