The Phototropism of Jurassic Petrified Wood in North China Plate

Trees on the side directly exposed to sunlight generally grow faster than on the opposite side, a phenomenon termed plant phototropism. There are in situ vertical trunks of silicified wood in the Xiadelongwan area of Yanqing County, north Beijing, where the first National Geologic Park of Petrified Wood of China has been built since 2002. A few trunks have well-preserved growth rings. One petrified stump from the formation shows a positive phototropism direction of SW230°. As compared with the modern normal growth stumps in Beijing plain area, which have a positive phototropism direction of SW210 °± 5°, the evidence of wood phototropism supports the conclusion of previous palaeomagnetic studies that the North China Plate has rotated clockwise since the Late Jurassic. The known petrified wood stumps in the Yanshan-Liaoning area are mainly found from the strata of 165-136 Ma, which corresponds to the main stage of the Yanshanian Movement.     

基于主应力轴旋转理论的修正Terzaghi松动土压力

基于土体主应力轴旋转理论,提出了Trapdoor上方土体侧向土压力系数的一般表达式,从而修正了传统的Terzaghi松动土压力计算公式。对于无黏性土,该系数是一个只与土体有效内摩擦角相关的参数,其值介于1.0和被动土压力系数Kp之间,且随着有效内摩擦角的增大而增大。黏性土的侧向土压力系数则与Trapdoor上覆土体厚度、重度、有效黏聚力和有效内摩擦角及Trapdoor宽度等参数有关。与传统计算方法相比,修正后的Terzaghi松动土压力计算结果与国内外Trapdoor模型试验结果及FLAC数值分析结果更为吻合,可广泛应用于地下管道、地基局部沉陷及隧道工程的土拱应力分析。     

Differential Rotation in Self Gravitating Filaments

The effect of differential rotation on the equilibria of self-gravitating filaments has been examined for isothermal and logatropic equations of state (EOS). Parametric regions for existence of solutions and upper limits for (the ratio of the rotational kinetic energy to the gravitational potential energy) have been worked out for the different laws of rotation. Effect of magnetic field has also been discussed.     

Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 2: Fitting to VLBI data

VLBI-based offsets of the Celestial Pole positions, as well as the variations of UT (series of Goddard Space Flight Center, 1984–2005) are processed applying the Earth’s rotation theory (ERA) 2005 constructed by the numerical integration of the differential equations of rotation of the deformable Earth. The equations were published earlier (Krasinsky 2006) as the first part of the work. The resulting weighted root mean square (WRMS) errors of the residuals , for the angles of nutation and precession are 0.136 and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for the IAU 2000 model adopted as the international standard. In ERA 2005, the angles , are related to the inertial ecliptical frame J2000, the angle including the precessional secular motion. As the published observational data are theory-dependent being related to IAU 2000, a procedure to confront the numerical theory to the observed Celestial Pole offsets and UT variations is developed. Processing the VLBI data has shown that beside the well known 435-day FCN mode of the free core nutation, there exits a second mode, FICN, caused by the inner part of the fluid core, with the period of 420 day close to that of the FCN mode. Beatings between the two modes are responsible for the apparent damping and excitation of the free oscillations, and are implicitly modeled by ERA 2005. The nutational and precessional motions in ERA 2005 are proved to be mutually consistent but only in case the relativistic correction for the geodetic precession is applied. Otherwise, the overall WRMS error of the residuals would increase by 35%. Thus, the effect of the geodetic precession in the Earth rotation is confirmed experimentally. The other finding is the reliable estimation δ_c = 3.844 ± 0.028° of the phase lag δ_c of the tides in the fluid core. When processing the UT variations, a simple model of the elastic interaction between the mantle and fluid core at their common boundary made it possible to satisfactory describe the largest observed oscillations of UT with the period of 18.6 year, reducing the WRMS error of the UT residuals to the value 0.18 ms (after removing the secular, annual and semi-annual terms).     

Rotational state of the nucleus of Comet 9P/Tempel 1: Results from Hubble Space Telescope observations in 2004

The nucleus of Comet 9P/Tempel 1 was first observed with the Hubble Space Telescope (HST) in December 1997 [Lamy, P., Toth, I., A'Hearn, M.F., Weaver, H., Weissman, P.R., 2001. Icarus 154, 337-344], but the temporal coverage was insufficient to determine its rotational period. Because the success of the Deep Impact mission was critically dependent on understanding the rotational state and approximate shape and size of the nucleus, we extensively re-observed 9P/Tempel 1, this time with the Advanced Camera for Surveys (HST/ACS), from May 7.9 to 9.5, 2004 (UT). At the mid-point of the observing window, the comet was 3.52 AU from the Sun, 4.03 AU from the Earth, and at a solar phase angle of 13.3°. The program was comprised of 18 separate visits, each one corresponding to an HST orbit filled with 3 ACS exposures of either 800 or 857 s duration with the F606W broadband filter. These very deep exposures revealed a star-like object, without any apparent coma. The light curve, defined by 49 data points, is characterized by a mean apparent V magnitude of 21.8 and an amplitude of 0.5 mag, indicating that we were viewing the varying cross-section of a rotating, elongated body. The periodicity was analyzed with seven different techniques yielding a rotational period in the range 39.40 to 43.00 h, and a mean value of 41.27±1.85 h (1σ). Using an albedo pV=0.04 and a linear phase law with a coefficient , we determined an effective radius of 3.01 km; a possible prolate spheroid solution has semi-axes a=3.71 km, b=2.36 km and a minimum axial ratio a/b∼1.57. By comparing the light curves obtained in 1997 and in 2004, we were able to constrain the phase function of the nucleus. Finally, an upper limit of Afρ<0.04 cm is set based on the non-detection of the coma.     

Orbital YORP and asteroid orbit evolution, with application to Apophis

Photon thrust from shape alone can produce quasi-secular changes in an asteroid's orbital elements. An asteroid in an elliptical orbit with a north–south shape asymmetry can steadily alter its elements over timescales longer than one orbital trip about the Sun. This thrust, called here orbital YORP (YORP = Yarkovsky–O'Keefe–Radzievskii–Paddack), operates even in the absence of thermal inertia, which the Yarkovsky effects require. However, unlike the Yarkovsky effects, which produce secular orbital changes over millions or billions of years, the change in an asteroid's orbital elements from orbital YORP operates only over the precession timescale of the orbit or of the asteroid's spin axis; this is generally only thousands or tens of thousands of years. Thus while the orbital YORP timescale is too short for an asteroid to secularly journey very far, it is long enough to warrant investigation with respect to 99942 Apophis, which might conceivably impact the Earth in 2036. A near-maximal orbital YORP effect is found by assuming Apophis is without thermal inertia and is shaped like a hemisphere, with its spin axis lying in the orbital plane. With these assumptions orbital YORP can change its along-track position by up to ±245 km, which is comparable to Yarkovsky effects. Though Apophis' shape, thermal properties, and spin axis orientation are currently unknown, the practical upper and lower limits are liable to be much less than the ±245 km extremes. Even so, the uncertainty in position is still likely to be much larger than the 0.5 km “keyhole” Apophis must pass through during its close approach in 2029 in order to strike the Earth in 2036.     

Asymmetries in the distribution of H2O and CO2 in the inner coma of Comet 9P/Tempel 1 as observed by Deep Impact

Prior to the impact event, Deep Impact monitored the ambient inner coma of Comet 9P/Tempel 1 at high spatial resolution in July 2005. Gaseous H₂O and CO₂ are unambiguously detected in the infrared spectra collected with the HRI-IR spectrometer aboard Deep Impact. Detailed distribution maps of these volatiles in the inner coma, within 60 km from the nucleus, are produced from the integrated emission bands of H₂O (2.66 μm) and CO₂ (4.26 μm). Uncorrelated asymmetries are determined in the spatial distribution of both species indicating chemical heterogeneities within the nucleus. Although present at some abundance surrounding the entire nucleus, H₂O has a pronounced enhancement in abundance in the sunward direction rotational phases, evidence that the dominant process of subliming water ice from the nucleus is solar heating. In contrast, CO₂ is enhanced in the regions near the negative rotational pole of the nucleus, suggesting localized outgassing there. Both species show an increase in radiance above the limb of the nucleus toward Ecliptic North. The distribution maps also suggest that the process of dust removal from the nucleus is strongly connected to the outgassing of volatiles. Detailed study of these coma asymmetries gives insight to the relative abundances of the dominant molecular components of the inner coma, source regions of the native volatiles, anisotropic outgassing of the nucleus, and the formation and evolution of the nucleus. A quiescent water production rate for Tempel 1 on July 4, 2005, is estimated to be .     

A ballistics analysis of the Deep Impact ejecta plume: Determining Comet Tempel 1's gravity, mass, and density

In July of 2005, the Deep Impact mission collided a 366 kg impactor with the nucleus of Comet 9P/Tempel 1, at a closing speed of 10.2 km s⁻¹. In this work, we develop a first-order, three-dimensional, forward model of the ejecta plume behavior resulting from this cratering event, and then adjust the model parameters to match the flyby-spacecraft observations of the actual ejecta plume, image by image. This modeling exercise indicates Deep Impact to have been a reasonably “well-behaved” oblique impact, in which the impactor-spacecraft apparently struck a small, westward-facing slope of roughly 1/3-1/2 the size of the final crater produced (determined from initial ejecta plume geometry), and possessing an effective strength of not more than . The resulting ejecta plume followed well-established scaling relationships for cratering in a medium-to-high porosity target, consistent with a transient crater of not more than 85-140 m diameter, formed in not more than 250-550 s, for the case of (gravity-dominated cratering); and not less than 22-26 m diameter, formed in not less than 1-3 s, for the case of (strength-dominated cratering). At , an upper limit to the total ejected mass of 1.8×¹⁰⁷ kg (1.5-2.2×¹⁰⁷ kg) is consistent with measurements made via long-range remote sensing, after taking into account that 90% of this mass would have stayed close to the surface and then landed within 45 min of the impact. However, at , a lower limit to the total ejected mass of 2.3×¹⁰⁵ kg (1.5-2.9×¹⁰⁵ kg) is also consistent with these measurements. The expansion rate of the ejecta plume imaged during the look-back phase of observations leads to an estimate of the comet's mean surface gravity of (0.17-0.90 mm s⁻²), which corresponds to a comet mass of mt=4.5×¹⁰¹³ kg (2.3-12.0×¹⁰¹³ kg) and a bulk density of (200-1000 kg m⁻³), where the large high-end error is due to uncertainties in the magnitude of coma gas pressure effects on the ejecta particles in flight.     

Dynamics of the Earth’s core from VLBI observations

The Earth’s rotation is accompanied by free circadian oscillations of its liquid core in the inner cavity of the lower mantle, which perturb the angular momentum of the entire Earth and produce an additional free nutation of the celestial pole called free core nutation (FCN). Since this nutation causes resonances in the diurnal tides and in the expansions of luni—solar nutation, its study, especially an improvement of the FCN period, is of fundamental importance for the theory of the Earth’s rotation. We have determined the FCN parameters from a joint analysis of equidistant series of coordinates of the celestial pole obtained from the combined processing of VLBI observations on global networks of stations for the interval 1984.0–2008.4 by IERS (International Earth Rotation and Reference System Service, Paris, France) and NEOS (National Earth Orientation Service, Washington, USA). Applying a moving least-squares filter (MLSF) to these data has shown that the FCN period averaged over this time interval differs significantly from the theoretical one and its phase varies over a wide range. Using the mean quadratic collocation (MQC) method, we have obtained a new, more accurate stochastic FCN model. Its analysis by the envelope method has revealed long-term linear phase trends, calling into question not only the adopted FCN period but also its stability and, hence, the stability of the resonant effects in the Earth’s luni—solar nutation.