The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

Approximating exponential and logarithmic functions using polynomial interpolation

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

Reinvestigation of the ν2 + 2ν3 subband in the overtone icosad of 12CH4 using cavity ring-down (CRD) spectroscopy of a supersonic jet expansion

We report a detailed reinvestigation of the ν₂?+?2ν₃ combination band of methane ¹²CH₄ centred at (7510.3378?±?0.003)?cm^?1 ((225.154263?±?0.0001)?THz) within the icosad of the overtone absorption. A new experimental setup is described, allowing us to carry out cw-laser cavity ring-down spectroscopy (cw-CRDS) at instrumental resolution in the MHz range in seeded supersonic jet expansions down to rotational temperature of 7?K compared to previous cw-CRDS measurements in our group achieving about 50?K in expansions of neat CH₄. We provide a careful re-analysis on the basis of our new experimental results for the Q and R branch transitions including data obtained between about 7 and 300?K under various conditions. We resolve previously observed discrepancies of assignments and are able to present a definitive assignment for lines involving angular momentum quantum numbers up to J?=?4. The analysis of relative intensities in spectra taken at rotational and effective translational temperatures between about 50?K and less than 10?K indicate conservation of nuclear spin symmetry upon supersonic jet expansion, in agreement with previous results using other techniques and covering other spectral ranges.     

Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a,b and z

In a recent paper (Temme, 2021) new asymptotic expansions are given for the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed and special attention for the case $a～b$. In this paper we extend the approach and also accept large values of $z$. The new expansions are valid when at least one of the parameters $a$, $b$, or $z$ is large. We provide numerical tables to show the performance of the expansions.     

处理噪声问题的泰勒展开交替最小化算法

为了处理图像、计算机视觉和生物信息等领域中广泛存在的稀疏大噪声和高斯噪声问题,提出了一种利用交替方向最小化思想求解主成分追求松弛模型的泰勒展开交替最小化算法(TEAM).采用推广泰勒展开和收缩算子等技术推导出低秩矩阵和稀疏大噪声矩阵的迭代方向矩阵,加入连续技术提高算法的收敛速率,设计出TEAM算法的求解步骤.实验中,将TEAM算法与该领域的顶级算法作分析对比.结果表明,TEAM算法时间优势明显,误差优势略好.     

Non-convergent perturbation theory and misleading inferences about parameter relationships: The case of superexchange

We discuss the well-known three-centre cation–anion–cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson–Hubbard model. We find that due to the interfering energy scales in the model, a limiting expression for the superexchange J$J$ for the idealized Mott–Hubbard (M–H) case t?U?Δ$t?U?\Delta$ cannot be formally defined. We further show that the decomposition of the superexchange into range-dependent components is formally invalid. The well-known t⁴$t^4$ superexchange expression, obtained from path-dependent series expansions, is not unique to these systems as it can also be obtained with many other different expansions, in which either the d$d$–p$p$ energy difference Δ$\Delta$ or the d$d$-electron correlation U$U$ can actually be small. Particularly for milder relationships between the parameters, i.e.  t?U?Δ$t?U?\Delta$, the reverse from the usual form of the series expansions can yield better agreement with the exact results. This implies that the fitting of experimental data to the simple expressions derived from path-dependent series expansions can lead to qualitatively incorrect relationships between the parameters, fictitiously within the M–H regime.     

An improved capillary electrophoresis method for in vitro monitoring of the challenging early steps of Aβ1–42 peptide oligomerization: Application to anti‐Alzheimer's drug discovery

We report an improved CE method to monitor in vitro the self‐assembly of monomeric amyloid β‐peptide (42 amino acids amyloid β‐peptide, Aβ_1–42) and in particular the crucial early steps involved in the formation of the neurotoxic oligomers. In order to start the kinetics from the beginning, sample preparation was optimized to provide samples containing exclusively the monomeric form. The CE method was also improved using a dynamic coating and by reducing the separation distance. Using this method, the disappearance of the monomer as well as the progressive formation of four species during the self‐assembly process can now be monitored and quantified over time. The hydrodynamic radius of the species present at the initial kinetics step was estimated around 1.8 nm by Taylor dispersion analysis while SDS‐PAGE analyses showed the predominance of the monomer. These results confirmed that the Aβ_1–42 species present at this initial time was the monomer. Methylene blue, an anti‐Alzheimer disease candidate, was then evaluated. In spite of an oligomerization inhibition, the enhanced disappearance of the Aβ_1–42 monomer provoked by methylene blue was demonstrated for the first time. This method, allowing the monomeric and smallest oligomeric species to be monitored, represents a new accurate and precise way to evaluate compounds for drug discovery.