Semi-Classical Dynamics in Quantum Spin Systems

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes.     

Ultrasonic degradation of aqueous carboxymethylcellulose: effect of viscosity, molecular mass, and concentration

It is well established that prolonged exposure of solutions of macromolecules to high-energy ultrasonic waves produces a permanent reduction in viscosity. It is generally agreed as well and also this study proved the hydrodynamic forces to have the primary importance in degradation. According to this study the sonolytic degradation of aqueous carboxymethylcellulose polymer or polymer mixtures is mainly depended on the initial dynamic viscosity of the polymer solution when the dynamic viscosity values are in the area range enabling intense cavitation. The higher was the initial dynamic viscosity the faster was the degradation. When the initial dynamic viscosities of the polymer solutions were similar the sonolytic degradation was dependent on the molecular mass and on the concentration of the polymer. The polymers with high molecular mass or high polymer concentration degraded faster than the polymers having low molecular mass or low polymer concentration. The initial dynamic viscosities were adjusted using polyethyleneglycol.     

A general screening method for doping agents in human urine by solid phase extraction and liquid chromatography/time-of-flight mass spectrometry

A general screening method based on solid phase extraction (SPE) and liquid chromatography/time-of-flight mass spectrometry (LC/TOFMS) was developed and investigated with 124 different doping agents, including stimulants, -blockers, narcotics, -adrenergic agonists, agents with anti-estrogenic activity, diuretics and cannabinoids. Mixed mode cation exchange/C8 cartridges were applied to SPE, and chromatography was based on gradient elution on a C18 column. Ionization of the analytes was achieved with electrospray ionization in the positive mode. Identification by LC/TOFMS was based on retention time, accurate mass and isotopic pattern. Validation of the method consisted of analysis of specificity, analytical recovery, limit of detection and repeatability. The minimum required performance limit (MRPL), established by World Anti-Doping Agency (WADA), was attained to 97 doping agents. The extraction recoveries varied between 33 and 98% and the median was 58%. Mass accuracy was always better than 5 ppm, corresponding to a maximum mass error of 0.7 mDa. The repeatability of the method for spiked urine samples, expressed as median of relative standard deviations (RSD%) at concentrations of MRPL and 10 times MRPL, were 14% and 9%, respectively. The suitability of the LC/TOFMS method for doping control was demonstrated with authentic urine samples.     

Brake squeal: a literature review

Brake squeal, which usually falls in the frequency range between 1 and 16 kHz, has been one of the most difficult concerns associated with automotive brake systems since their inception. It causes customer dissatisfaction and increases warranty costs. Although substantial research has been conducted into predicting and eliminating brake squeal since the 1930s, it is still rather difficult to predict its occurrence. In this paper, the characteristics and current difficulties encountered in tackling brake squeal are first described. A review of the analytical, experimental and numerical methods used for the investigation of brake squeal is then given. Some of the challenges facing brake squeal research are outlined.     

A new a posteriori error estimate for convection–reaction–diffusion problems

A new a posteriori error estimate is derived for the stationary convection–reaction–diffusion equation. In order to estimate the approximation error in the usual energy norm, the underlying bilinear form is decomposed into a computable integral and two other terms which can be estimated from above using elementary tools of functional analysis. Two auxiliary parameter-functions are introduced to construct such a splitting and tune the resulting bound. If these functions are chosen in an optimal way, the exact energy norm of the error is recovered, which proves that the estimate is sharp. The presented methodology is completely independent of the numerical technique used to compute the approximate solution. In particular, it is applicable to approximations which fail to satisfy the Galerkin orthogonality, e.g. due to an inconsistent stabilization, flux limiting, low-order quadrature rules, round-off and iteration errors, etc. Moreover, the only constant that appears in the proposed error estimate is global and stems from the Friedrichs–Poincaré inequality. Numerical experiments illustrate the potential of the proposed error estimation technique.     

Eigenvalue confinement and spectral gap for random simplicial complexes

We consider the adjacency operator of the Linial‐Meshulam model for random simplicial complexes on n vertices, where each d‐cell is added independently with probability p to the complete ‐skeleton. Under the assumption , we prove that the spectral gap between the smallest eigenvalues and the remaining eigenvalues is with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. The main ingredient of the proof is a Füredi‐Komlós‐type argument for random simplicial complexes, which may be regarded as sparse random matrix models with dependent entries. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 506–537, 2017     

The [U2F12]2− Anion of Sr[U2F12]

The D_2h‐symmetric dinuclear complex anion [U₂F₁₂]^2? of pastel green Sr[U₂F₁₂] shows a hitherto unknown structural feature: The coordination polyhedra around the U atoms are edge‐linked monocapped trigonal prisms, the U^V atoms are therefore seven‐coordinated. This leads to a U–U distance of 3.8913(6) Å. A weak U^V–U^V interaction is observed for the dinuclear [U₂F₁₂]^2? complex and described by the antiferromagnetic exchange J_exp of circa ?29.9 cm^?1. The crystalline compound can be easily prepared from SrF₂ and β‐UF₅ in anhydrous hydrogen fluoride (aHF) at room temperature. It was studied by means of single crystal X‐ray diffraction, IR, Raman and UV/VIS spectroscopy, magnetic measurements, and by molecular as well as by solid‐state quantum chemical calculations.     

Size‐Selective Encapsulation of Hydrophobic Guests by Self‐Assembled M4L6 Cobalt and Nickel Cages

Subtle differences in metal–ligand bond lengths between a series of [M₄L₆]^4? tetrahedral cages, where M=Fe^II, Co^II, or Ni^II, were observed to result in substantial differences in affinity for hydrophobic guests in water. Changing the metal ion from iron(II) to cobalt(II) or nickel(II) increases the size of the interior cavity of the cage and allows encapsulation of larger guest molecules. NMR spectroscopy was used to study the recognition properties of the iron(II) and cobalt(II) cages towards small hydrophobic guests in water, and single‐crystal X‐ray diffraction was used to study the solid‐state complexes of the iron(II) and nickel(II) cages.