A localized hybrid method of stress analysis: A combination of moiré interferometry and FEM

A method of combining moiré interferometry and the finite-element method to effect localized stress analysis is presented. The displacement data from local regions of interest in the optical experiment are used as boundary conditions for the finite-element stress analysis. The stability of the method is examined with data from simple numerical models one of which corresponded to the stress analysis of a pin-loaded plate with friction. These studies show that the method requires the sensivity of moiré interferometry for successful implementation, i.e., displacement data accuracy within 0.1 μm or 4 μin. This localized hybrid method of stress analysis provides a powerful and efficient method for the reduction of experimental data.     

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.     

An algebraic interpretation of the multivariate <Emphasis Type="Italic">q</Emphasis>-Krawtchouk polynomials

The multivariate quantum q-Krawtchouk polynomials are shown to arise as matrix elements of “q-rotations” acting on the state vectors of many q-oscillators. The focus is put on the two-variable case. The algebraic interpretation is used to derive the main properties of the polynomials: orthogonality, duality, structure relations, difference equations, and recurrence relations. The extension to an arbitrary number of variables is presented.     

Corneal studies by photoelasticity

Freshly enucleated andin vivo eyes of cats were analyzed to determine the detailed distribution of birefringence across the cornea and through its thickness, and to determine the change of birefringence with intraocular pressure. Scattered light and oblique-incidence photoelasticity were used. The experiments are summarized and special considerations are discussed. These include the necessity for a laser-light source; diffraction limitation in producing a narrow ribbon of light; rotation of the plane of polarization; inequalities in reflected components of polarized light.     

Photoelastic-fringe multiplication—For tenfold increase in sensitivity

Slices from three-dimensional frozen-stress models were collected from numerous photoelastic laboratories and these diverse samples were used to demonstrate fringe multiplication. Multiplied isochromatic patterns of excellent clarity and fidelity are presented. Maximum multiplication factors of 9 or 11 are exhibited for most demonstrations, but multiplications by 17 and 25 are exhibited for special cases. Speed, accuracy and simplicity of the method are discussed, and benefits of full-field data retrieval are emphasized.     

New optical methods of moiré fringe multiplication

Photographs or other replicas of relatively coarse specimen screens can be analyzed with sensitivities corresponding to screens of many thousands of lines per inch (lpi). Moiré fringe multiplication is accomplished by collecting specific groups of diffracted beams emanating from two moiré screens in series. Three methods are described and multiplication by factors as high as 30 are demonstrated. Sensitivity and accuracy are increased by the fringe-multiplication factor. Usefulness of full-field mechanical differentiation techniques is extended to cases of correspondingly lower strains. These fringe-multiplication methods apply to both bar-and-space screens and transparent diffraction gratings.     

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.