The effect of long-range forces on the dynamics of a bar

The one-dimensional dynamic response of an infinite bar composed of a linear “microelastic material” is examined. The principal physical characteristic of this constitutive model is that it accounts for the effects of long-range forces. The general theory that describes our setting, including the accompanying equation of motion, was developed independently by Kunin (Elastic Media with Microstructure I, 1982), Rogula (Nonlocal Theory of Material Media, 1982) and Silling (J. Mech. Phys. Solids 48 (2000) 175), and is called the peridynamic theory. The general initial-value problem is solved and the motion is found to be dispersive as a consequence of the long-range forces. The result converges, in the limit of short-range forces, to the classical result for a linearly elastic medium. Explicit solutions in elementary form are given in a broad class of special cases. The most striking observations arise in the Riemann-like problem corresponding to a constant initial displacement field and a piecewise constant initial velocity field. Even though, initially, the displacement field is continuous, it involves a jump discontinuity for all later times, the Lagrangian location of which remains stationary. For some materials the magnitude of the discontinuity-jump oscillates about an average value, while for others it grows monotonically, presumably fracturing the material when it exceeds some critical level.     

Analysis of a new drug of abuse: Cathinone derivative 1‐(3,4‐dimethoxyphenyl)‐2‐(ethylamino)pentan‐1‐one

Recently, novel psychoactive drugs for human abuse such as amphetamines, phenethylamines, benzofuries, and tryptamines, cathinones have gained high popularity. These designer drugs are mainly sold via online stores as “bath salts” and are labeled “not for human consumption.” Due to the novelty of the compounds, only a little information about pharmacology, toxicology, and the long‐term damage they may cause is available. Moreover, there are only few analytical methods for their identification and analysis. Among new cathinone derivatives, 1‐(3,4‐dimethoxyphenyl)‐2‐(ethylamino)pentan‐1‐one (DL‐4662), became available via an internet shop. A sample of this compound was purchased and investigated. The first aim of our study was an identity check by NMR spectroscopy and gas chromatography with mass spectrometry. As many of the recreational drugs are chiral and are mainly sold as racemates, a further goal of our research was enantioseparation by gas chromatography with mass spectrometry and high‐performance liquid chromatography with UV detection, to prove whether DL‐4662 was traded enantiomerically pure or as racemic mixture. Both chiral separation methods showed the presence of a racemate.     

A spectral method for nonlinear elliptic equations

Let Ω be an open, simply connected, and bounded region in \(\mathbb {R}^{d}\), d ≥ 2, and assume its boundary ?Ω is smooth and homeomorphic to \(\mathbb {S}^{d-1}\). Consider solving an elliptic partial differential equation L u = f(?, u) over Ω with zero Dirichlet boundary value. The function f is a nonlinear function of the solution u. The problem is converted to an equivalent elliptic problem over the open unit ball \(\mathbb {B}^{d}\) in \(\mathbb {R}^{d}\), say \(\widetilde {L}\widetilde {u} =\widetilde {f}(\cdot ,\widetilde {u})\). Then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials \(\widetilde {u} _{n}\) of degree ≤ n that is convergent to \(\widetilde {u}\). The transformation from Ω to \(\mathbb {B}^{d}\) requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For \(u\in C^{\infty } \left (\overline {\Omega }\right ) \) and assuming ?Ω is a C ^∞ boundary, the convergence of \(\left \Vert \widetilde {u} -\widetilde {u}_{n}\right \Vert _{H^{1}}\) to zero is faster than any power of 1/n. The error analysis uses a reformulation of the boundary value problem as an integral equation, and then it uses tools from nonlinear integral equations to analyze the numerical method. Numerical examples illustrate experimentally an exponential rate of convergence. A generalization to ?Δu + γ u = f(u) with a zero Neumann boundary condition is also presented.     

Power‐to‐Gas

The power‐to‐gas concept is a promising technology to chemically store energy and therefore a feasible approach to mitigate the challenges of energy transition. Heterogeneous catalysis plays a crucial role in CO₂ conversion to methane using nickel based catalysts. A thorough catalyst characterization facilitates the synthesis of optimized catalyst systems. The determination of reaction kinetics is fundamental for industrial reactor design.     

Adaptive space-time boundary element methods for the wave equation

For the solution of the wave equation a space-time energetic boundary integral formulation is used. The resulting single layer boundary integral equation is discretised by a conforming ansatz space on the lateral boundary. To derive an adaptive scheme an a posteriori error estimator based on the representation formula is used. Finally, numerical examples for a one-dimensional spatial domain are presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid Structure Interaction of Blood Vessels in Circle of Willis

This work involves studying the role of the Brain Blood Barriers (BBB) on damping the stress applied on brain tissue through blood pressure that is the main cause of brain aneurysm. The numerical simulations are focused on the geometry of the Anterior Communicating Artery (ACoA) because there is a 30 % higher probability for a brain aneurysm in this location. A linear elastic model is used to model the structure part including BBB and brain tissue. Regarding the fluid properties, blood is assumed to behave as a Newtonian fluid. The stress and deformation of the brain tissue is analyzed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The coordination chemistry of the proton

It is well known that an acidic hydrogen atom can form hydrogen bonds to a hydrogen bond acceptor, a Lewis base. It is considerably less known that the proton can coordinate two or more atoms conveniently in bonding modes that cannot be described as hydrogen bonding. Agostic interactions, bridging hydrides, 3-centre-2-electron bonds in boranes, bifurcated hydrogen atoms, they are all elements of the coordination chemistry of the proton and, of course, the hydrogen bond comes in more than one facette as well.     

Azobenzene-containing triazatriangulenium adlayers on Au(111): structural and spectroscopic characterization

Adlayers of different azobenzene-functionalized derivatives of the triazatriangulenium (TATA) platform on Au(111) surfaces were studied by scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), gap-mode surface-enhanced Raman spectroscopy (gap-mode SERS), and cyclic voltammetry (CV). The chemical composition of the adlayers is in good agreement with the molecular structure, i.e., different chemical groups attached to the azobenzene functionality were identified. Furthermore, the presence of the azobenzene moieties in the adlayers was verified by the vibration spectra and electrochemical data. These results indicate that the molecules remain intact upon adsorption with the freestanding functional groups oriented perpendicularly to the TATA platform and thus also to the substrate surface.