Revisiting natural and laboratory electron spin resonance (ESR) dose response curves of quartz from Chinese loess

Natural and laboratory ESR dose response curves (DRCs) of [AlO₄/h]⁰ and [TiO₄/M⁺]⁰ were investigated for samples of quartz from the Luochuan loess-palaeosol master section, Chinese Loess Plateau. The natural and laboratory DRCs show a clear divergence above ∼1000 Gy, with much lower D₀ values and saturation levels observed for the natural DRCs, which is in agreement with the previous study by Tsukamoto et al. (2018). Young (<15 ka) samples from Luochuan and Jingbian – another site of the Chinese Loess Plateau, together with two modern samples of Chinese loess, were used to investigate the residual signals of [AlO₄/h]⁰ and [TiO₄/M⁺]⁰ centres. Our results are in line with published studies and show that the significant residual signals corresponding to several tens to hundreds of Gy are present in both Al and Ti centres. These need to be taken into account before laboratory DRC construction. ESR pulse annealing experiments performed on samples irradiated with different doses show an apparent dose-dependent thermal instability of [AlO₄/h]⁰ and [TiO₄/M⁺]⁰, with the signals for higher doses decaying faster with increasing temperature. We attribute the change in D₀ with preheat reported in Tsukamoto et al.2018, as well as the difference between laboratory and natural DRCs, to this apparent dose-dependent thermal instability of the signals. The saturation level of the natural DRC, being the result of reaching the equilibrium between filling of the traps and emptying them due to thermal decay, is therefore additionally affected at higher doses, due to the increased thermal instability. The inability to recreate in the laboratory the same response to irradiation as the one observed in nature questions the accuracy of dating samples beyond ∼1000 Gy.     

Resonance trapping and evolution of particles subject to poynting-robertson drag: Adiabatic and non-adiabatic approaches

The problem of resonance trapping for particles subject to Poynting-Robertson drag is approached initially from an adiabatic regime theory. A simplified Hamiltonian system is presented for simple eccentricity-type resonances up to order 3, and expressions related to the trapping process are deduced. The fast dissipation provoked by Poynting-Robertson leads to the employment of a numerical approach for the computation of resonance capture probabilities, for particles in the size range of practical importance. Some aspects of the dynamical evolution of a particle after capture are noticed from results of numerical integrations. Analytical methods are used in order to confirm the numerical results.     

On Motions Near the Lagrange Equilibrium Point L 4 in the Case of Routh's Critical Mass Ratio

We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L ₄ when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L ₄. We also show that in the case of instability of L ₄ the trajectories starting in a vicinity of L ₄ remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date.     

Partial Reduction in the N-Body Planetary Problem using the Angular Momentum Integral

We present a new set of variables for the reduction of the planetary n-body problem, associated to the angular momentum integral, which can be of any use for perturbation theory. The construction of these variables is performed in two steps. A first reduction, called partial is based only on the fixed direction of the angular momentum. The reduction can then be completed using the norm of the angular momentum. In fact, the partial reduction presents many advantages. In particular, we keep some symmetries in the equations of motion (d'Alembert relations). Moreover, in the reduced secular system, we can construct a Birkhoff normal form at any order. Finally, the topology of this problem remains the same as for the non-reduced system, contrarily to Jacobi's reduction where a singularity is present for zero inclinations. For three bodies, these reductions can be done in a very simple way in Poincaré's rectangular variables. In the general n-body case, the reduction can be performed up to a fixed degree in eccentricities and inclinations, using computer algebra expansions. As an example, we provide the truncated expressions for the change of variable in the 4-body case, obtained using the computer algebra system TRIP.     

The integrable cases of the general spatial three-body problem at third-order resonance

For the general three-body problem at third-order resonance an analytical solution is obtained by the use of the Weierstrass functions.     

Assessing the Vibrational Frequencies of the Holweide Hospital in the City of Cologne (Germany) by Means of Ambient Seismic Noise Analysis and FE modelling

Ambient seismic noise measurements were conducted inside the Holweide Hospital (Cologne) for checking whether its frequencies of vibration fall into the range where soil amplification is expected. If this is the case, damage might increase in case of an earthquake due to an amplified structural response of the building. Two different techniques were used: the ratio between the horizontal and vertical components of the spectra recorded at stations located inside the building and the ratio between the corresponding components of the spectra recorded simultaneously inside the building and at a reference station placed outside. While the former method might be preferred because of less equipment involved, the latter has the advantage of producing more stable results and deleting automatically the influence of the sedimentary cover, which might obscure some eigenfrequencies of vibration of the building. An independently performed finite-element analysis of the hospital showed a good correlation between measured and calculated eigenmodes.     

A web of secondary resonances for large <Emphasis Type="Italic">A</Emphasis>/<Emphasis Type="Italic">m</Emphasis> geostationary debris

The dynamics of space debris with very high A/m near the geostationary orbit is dominated by the gravitational coefficient C ₂₂ and the solar radiation pressure. An analysis of the stability of the orbits by the chaos indicator MEGNO and frequency analysis map FAM shows chaotic layers around the separatrix and reveals a web of sub-structures associated to resonances with the annual period of the Sun. This succession of stable thin islands and chaotic layers can be reproduced and explained by a quite simple toy model, based on a pendulum approach, perturbed, through the eccentricity, by the external (Sun) frequency. The use of suitable action-angle variables in the circulation and libration regions of the pendulum allows to point out new resonances between the geostationary libration angle and the Sun’s longitude. They correspond very well (positions, shape, width) to the structures visible on the FAM representations.     

Polarization of resonance lines in the case of a Voigt absorption profile

Multiple resonance scattering of radiation in a spectral line is considered in the case of a Voigt absorption profile. The scattering is assumed to take place in a nonmagnetic semi-infinite atmosphere with uniformly distributed sources of unpolarized radiation. Polarization characteristics have been obtained for the emergent radiation by numerically solving the Ambartsumian-Chandrasekhar matrix integral equation.     

大气中粘性效应对三维地形波及其波动阻力的影响

采用两层大气模式, 通过引入瑞利摩擦系数来定性描述大气中粘性机制, 讨论了粘性效应对三维简单地形波及其波动阻力的影响。结果表明,无论低层大气为稳定层结还是不稳定层结, 大气中粘性的存在将减弱地形波的强度, 减小其产生的波动阻力     

凹坑地形风流结构对污染物散布的模拟研究

利用建立的三维非静力高分辨率高阶湍流闭合模式与随机游动扩散模式研究了一个深凹露天矿区污染物散布的规律,同时在风洞中进行了示踪实验。结果表明,由于凹坑内复环流结构的存在,使得坑内污染物浓度较大,且浓度最大值出现在源的上风侧。数值试验与风洞试验结果吻合较好。