Stretching of polymer chains by fluctuating flow fields

We investigate polymer stretching by fluctuating flow fields via numerical solutions of the Brownian dynamics of multibead polymer chains taking into account nonlinear elasticity, hydrodynamic interactions and good solvent, excluded volume interaction effects. By varying the scaling exponent of the energy spectrum whilst keeping the same Reynolds and Deborah numbers, as well as microscale length and turnover times, we show that steeper spectra are associated with stronger stretching. We compute the probability density functions of chain length, and explain their main features by examining explicit molecular histories. We quantify the interaction between strain rate tensor structure and chain geometry as a means of understanding better the different stretching mechanisms in mild, moderate and strong polymer stretching regimes.     

Feynman-Diagrammatic Description of the Asymptotics of the Time Evolution Operator in Quantum Mechanics

We describe the “Feynman diagram” approach to nonrelativistic quantum mechanics on \({\mathbb{R}^n}\), with magnetic and potential terms. In particular, for each classical path γ connecting points q ₀ and q ₁ in time t, we define a formal power series V _γ (t, q ₀, q ₁) in \({\hbar}\), given combinatorially by a sum of diagrams that each represent finite-dimensional convergent integrals. We prove that exp(V _γ ) satisfies Schrödinger’s equation, and explain in what sense the \({t \to 0}\) limit approaches the δ distribution. As such, our construction gives explicitly the full \({\hbar\to 0}\) asymptotics of the fundamental solution to Schrödinger’s equation in terms of solutions to the corresponding classical system. These results justify the heuristic expansion of Feynman’s path integral in diagrams.     

Dark-field optical coherence microscopy

Dark-field illumination is known to enhance scattering contrast in optical microscopy. We combined this concept with Fourier domain optical coherence microscopy (OCM). The detection and illumination paths are decoupled, and only the scattered light originating from the sample generates the tomogram signal, whereas any specular reflection is highly suppressed. We analyze and discuss this dark-field OCM concept and present its superior imaging quality on live cell samples.     

Easy knapsacks and the complexity of energy allocation problems in the smart grid

Motivated by the growing interest in the smart grid and intelligent energy management mechanisms we study two classes of domestic energy allocation problems. In the first case we work with a system that is tasked with scheduling the work on a number of appliances over a given time window. In the second one a collection of air conditioning appliances is used to control the temperature of a given domestic environment. Our framework for this case includes a simplified mechanism for modelling the heat exchange between the interior and the exterior of the given environment. We present various polynomial time algorithms and NP-hardness proofs. In particular the main result of the paper is a proof that although it is NP-hard to schedule the operation of a single air-conditioning unit, working at various temperature levels in a variable energy price regime, there is a polynomial time algorithm for controlling one such device working at a single temperature level, for houses with low thermal inertia. The algorithm analysis hinges on the properties of a polynomial time variant of the minimisation version of the knapsack problem which may be of independent interest.     

A note on the nucleolus for 2-convex TU games

For 2-convex n-person cooperative TU games, the nucleolus is determined as some type of constrained equal award rule. Its proof is based on Maschler, Peleg, and Shapley’s geometrical characterization for the intersection of the prekernel with the core. Pairwise bargaining ranges within the core are required to be in equilibrium. This system of non-linear equations is solved and its unique solution agrees with the nucleolus.     

Fast Algorithms for Nonparametric Curve Estimation

Abstract

Naive implementations of local polynomial fits and kernel estimators require almost O(n ²) operations. In this article two fast O(n) algorithms for nonparametric local polynomial fitting are presented. They are based on updating normal equations. Numerical stability is guaranteed by controlling ill-conditioned situations for small bandwidths and data-tuned restarting of the updating procedure. Restarting at every output point results in a moderately fast but highly stable O(n ^7/5) algorithm. Applicability of algorithms is evaluated for estimation of regression curves and their derivatives. The idea is also applied to kernel estimators of regression curves and densities.     

Intrinsic relaxation rates of polarized Cs vapor in miniaturized cells

The intrinsic relaxation rates of the vector magnetization of cesium vapor enclosed in microfabricated atomic magnetometer cells are investigated. Two methods—the optically detected magnetic resonance and the ground-state Hanle effect—are used to carry out automated measurements in dependence on cell temperature and nitrogen buffer gas pressure. The experimental results are compared with expected contributions of the different relaxation processes and in this way allow the discrimination between them to help further optimization of cell design. The methods are compared in terms of basic features, data quality, and practical applicability.     

Strong optical nonlinearities of self-assembled polymorphic microstructures of phenylethynyl functionalized fluorenones

The polymorphs of a phenylethynyl functionalized fluorenone derivative, and their controlled self-assembly for microstructures with different morphologies have been studied. These polymorphic microcrystals exhibit very distinctive NLO properties, which are highly correlated to their electronic and supramolecular structures.     

Fast Exfoliation and Functionalisation of Two‐Dimensional Crystalline Carbon Nitride by Framework Charging

Two‐dimensional (2D) layered graphitic carbon nitride (gCN) nanosheets offer intriguing electronic and chemical properties. However, the exfoliation and functionalisation of gCN for specific applications remain challenging. We report a scalable one‐pot reductive method to produce solutions of single‐ and few‐layer 2D gCN nanosheets with excellent stability in a high mass yield (35 %) from polytriazine imide. High‐resolution imaging confirmed the intact crystalline structure and identified an AB stacking for gCN layers. The charge allows deliberate organic functionalisation of dissolved gCN, providing a general route to adjust their properties.