Topological analysis of polymeric melts: Chain length effects and fast-converging estimators for entanglement length

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for N_e from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.Comment: Major revisions. Developed near-ideal estimators which operate on multiple chain lengths. Now test these on two very different model polymers

Nucleation of cracks in a brittle sheet

We use molecular dynamics to study the nucleation of cracks in a two dimensional material without pre-existing cracks. We study models with zero and non-zero shear modulus. In both situations the time required for crack formation obeys an Arrhenius law, from which the energy barrier and pre-factor are extracted for different system sizes. For large systems, the characteristic time of rupture is found to decrease with system size, in agreement with classical Weibull theory. In the case of zero shear modulus, the energy opposing rupture is identified with the breakage of a single atomic layer. In the case of non-zero shear modulus, thermally activated fracture can only be studied within a reasonable time at very high strains. In this case the energy barrier involves the stretching of bonds within several layers, accounting for a much higher barrier compared to the zero shear modulus case. This barrier is understood within adiabatic simulations

Ideal contribution to the macroscopic quasiequilibrium entropy of anisotropic fluids

The Landau-de Gennes free energy plays a central role in the macroscopic theory of anisotropic fluids. Here, the ideal, entropic contribution to this free energy—that is always present in these systems, irrespectively of the detailed form of interactions or applied fields—is derived within the quasiequilibrium ensemble and successfully tested. An explicit and compact form of the macroscopic, ideal entropy is derived. This entropy is nonpolynomial in the order parameter, diverging logarithmically near the fully oriented state and therefore restricting the order parameter to physical admissible values. As an application, it is shown that the isotropic-nematic transition within the Maier-Saupe model is described in a simple and very accurate manner

The adsorption structure of furan on Pd(1 1 1)

The structure of molecular furan, C4H4O, on Pd(1 1 1) has been investigated by O K-edge near-edge X-ray absorption fine structure (NEXAFS) and C 1s scanned-energy mode photoelectron diffraction (PhD). NEXAFS shows the molecule to be adsorbed with the molecular plane close to parallel to the surface, a conclusion confirmed by the PhD analysis. Chemical-state specific C 1s PhD data were obtained for the two inequivalent C atoms in the furan, the α-C atoms adjacent to the O atom, and the β-C atoms bonded only to C atoms, but only the PhD modulations for the α-C emitters were of sufficiently large amplitude for detailed evaluation using multiple scattering calculations. This analysis shows the α-C atoms to be located approximately 0.6 Å off-atop surface Pd atoms with an associated C–Pd bondlength of 2.13 ± 0.03 Å. Two alternative local geometries consistent with the data place the O atom in off-atop or near-hollow locations, and for each of these local structures there are two equally-possible registries relative to the fcc and hcp hollow sites. The results are in good agreement with earlier density functional theory calculations which indicate that the fcc and hcp registries are equally probable, but the PhD results fail to distinguish the two distinct local bonding geometries

Test of Quantum Action for Inverse Square Potential

We present a numerical study of the quantum action previously introduced as a parametrisation of Q.M. transition amplitudes. We address the questions: Is the quantum action possibly an exact parametrisation in the whole range of transition times ($0 < T < \infty$)? Is the presence of potential terms beyond those occuring in the classical potential required? What is the error of the parametrisation estimated from the numerical fit? How about convergence and stability of the fitting method (dependence on grid points, resolution, initial conditions, internal precision etc.)? Further we compare two methods of numerical determination of the quantum action: (i) global fit of the Q.M. transition amplitudes and (ii) flow equation. As model we consider the inverse square potential, for which the Q.M. transition amplitudes are analytically known. We find that the relative error of the parametrisation starts from zero at T=0 increases to about $10^{-3}$ at $T=1/E_{gr}$ and then decreases to zero when $T \to \infty$. Second, we observe stability of the quantum action under variation of the control parameters. Finally, the flow equation method works well in the regime of large $T$ giving stable results under variation of initial data and consistent with the global fit method.Comment: Text (LaTeX), Figures(ps

Simulation-based Testing for Early Safety-Validation of Robot Systems

Industrial human-robot collaborative systems must be validated thoroughly with regard to safety. The sooner potential hazards for workers can be exposed, the less costly is the implementation of necessary changes. Due to the complexity of robot systems, safety flaws often stay hidden, especially at early design stages, when a physical implementation is not yet available for testing. Simulation-based testing is a possible way to identify hazards in an early stage. However, creating simulation conditions in which hazards become observable can be difficult. Brute-force or Monte-Carlo-approaches are often not viable for hazard identification, due to large search spaces. This work addresses this problem by using a human model and an optimization algorithm to generate high-risk human behavior in simulation, thereby exposing potential hazards. A proof of concept is shown in an application example where the method is used to find hazards in an industrial robot cell

Two dimensional Berezin-Li-Yau inequalities with a correction term

We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas.Comment: 6 figure