A new Petrie-like construction for abstract polytopes

This article introduces a new construction for polytopes, that may be seen as a generalisation of the Petrie dual to higher ranks. Some theoretical results are derived regarding when the construction can be expected to work, and the construction is applied to some special cases. In particular, the generalised Petrie duals of the hypercubes are enumerated.     

Noncommutative Dynamical Models with Quantum Symmetries

We define dynamical models on the q-Minkowski space algebra (which is a particular case of the Reflection Equation Algebra) as deformations (quantizations) of dynamical models with rotational symmetries, and we find their integrals. In particular, we introduce a q-analog of the Runge-Lenz vector and a q-analog of the dynamics in space-time with a spherically symmetric metric.     

Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition

Currently there is a strong interest in plasmonic materials operating in the near‐infrared (NIR), however, conventional metals such as gold and silver possess high optical losses in this region. In this work we demonstrate localized surface plasmon resonances (LSPRs) with low loss in the NIR region by utilizing atomic layer deposition to deposit thin films of aluminium doped zinc oxide onto silicon nanopillars created via nanopshere lithography. The deposited films have excellent conformality and the LSPRs can be tuned from the mid‐infrared to the NIR by controlling the doping concentration, deposition temperature and nanostructure morphology. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

The density matrix renormalization group for ab initio quantum chemistry

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational cost are given special attention: the orbital choice and ordering, and the exploitation of the symmetry group of the Hamiltonian. With these considerations, the QC-DMRG algorithm allows to find numerically exact solutions in active spaces of up to 40 electrons in 40 orbitals.     

Approximating Lyapunov exponents and Sacker–Sell spectrum for retarded functional differential equations

We consider Lyapunov exponents and Sacker–Sell spectrum for linear, nonautonomous retarded functional differential equations posed on an appropriate Hilbert space. A numerical method is proposed to approximate such quantities, based on the reduction to finite dimension of the evolution family associated to the system, to which a classic discrete QR method is then applied. The discretization of the evolution family is accomplished by a combination of collocation and generalized Fourier projection. A rigorous error analysis is developed to bound the difference between the computed stability spectra and the exact stability spectra. The efficacy of the results is illustrated with some numerical examples.     

Comparison of extraction efficiencies and LC–MS–MS matrix effects using LLE and SPE methods for 19 antipsychotics in human blood

Antipsychotic drugs are frequently associated with sudden death investigations. Detection of these drugs is necessary to establish their use and possible contribution to the death. LC–MS(MS) methods are common; however accurate and precise quantification is assured by using validated methods. This study compared extraction efficiency and matrix effects using common liquid–liquid and solid-phase extraction procedures in both ante-mortem and post-mortem specimen using LC–MS–MS. Extraction efficiencies and matrix effects were determined in five different blank blood specimens of each blood type. The samples were extracted using a number of different liquid–liquid extraction methods and compared with a standard mixed-mode solid-phase extraction method. Matrix effects were determined using a post-extraction addition approach—the blank blood specimens were extracted as described above and the extracts were reconstituted in mobile phase containing a known amount of analytes. The extraction comparison of ante-mortem and post-mortem blood showed considerable differences, in particular the extraction efficiency was quite different between ante-mortem and post-mortem blood. Quantitative methods used for determination of antipsychotic drugs in post-mortem blood should establish that there are no differences in extraction efficiency and matrix effects, particularly if using ante-mortem blood as calibrator.     

Comparative study of various normal mode analysis techniques based on partial Hessians

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine‐stretch, the spectrum of quinine and a bis‐cinchona derivative, and the low frequency modes of the LAO binding protein. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Multiscale Modeling for the Simulation of Damage Processes at Refractory Materials under Thermal Shock

A brittle damage model based on multiscale considerations and homogenisation procedures is presented. Cell models are developed as RVE including different microstructural features. The material laws themselves are formulated on the continuum level. Local failure occurs if the damage variable reaches a critical value. For simple configurations of the microstructure, the relation between stress, strain und temperature is derived from analytical considerations. In order to properly model the thermo-mechanical coupling, the temperature-dependence of material constants is taken into account. Fracture and damage mechanical approaches are combined using different techniques. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of SnS nanoflowers for lithium ion batteries

SnS nanoflowers containing hierarchically organized nanosheet subunits were synthesized using a simple solution route, and they function as lithium ion battery anodes that maintain high capacities and coulombic efficiencies over 30 cycles.