Symplectic integration of space debris motion considering several Earth's shadowing models

In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones. Indeed, it has already been demonstrated that such objects could stay there for hundreds of years. Our model takes into account the Earth's gravitational potential, luni-solar and planetary gravitational perturbations and direct solar radiation pressure. Based on the analysis of the energy conservation and on a comparison with a high order non-symplectic integrator, we show that our algorithm allows us to use large time steps and keep accurate results. We also propose an innovative method to model Earth's shadow crossings by means of a smooth shadow function. In the particular framework of symplectic integration, such a function needs to be included analytically in the equations of motion in order to prevent numerical drifts of the energy. For the sake of completeness, both cylindrical shadows and penumbra transitions models are considered. We show that both models are not equivalent and that big discrepancies actually appear between associated orbits, especially for high area-to-mass ratios

Orbital similarity functions - application to asteroid pairs

The paper expands the idea of Vokrouhlický and Nesvorný who used a modified Zappalà et al. metric with osculating elements in search for pairs of asteroids suspected of having a common origin. Using six different orbital similarity functions, we find that five of them display a similar excess of close pairs in the catalogue of osculating elements. The excess is even higher when mean orbital elements are used. Similarly, when the mean elements are applied, there is a better agreement between the closest pairs found in the same catalogue using different metrics. The common subset of 62 pairs from five lists of 100 closest pairs according to different distance functions is provided. Investigating an artificial sample of asteroid orbital pairs with a known initial orbital velocity difference we find that the Drummond metric best preserves orbital proximity over long time intervals

The transition from granite to banded aplite-pegmatite sheet complexes: An example from Megiliggar rocks, Tregonning topaz granite, Cornwall

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The genetic relationship between a granite pluton and adjacent complex of rare-metal pegmatite-aplite-banded sheets (Megiliggar Sheet Complex - MSC) has been studied at the border of the Tregonning topaz granite at Megiliggar Rocks, Cornwall, SW England. Similarities in whole-rock chemical and mineralogical compositions, together with a gradual change in textures away from the granite margin, provide strong evidence for a genetic link between the Tregonning Granite and MSC. The sheets are likely to represent apophyses of residual melt which escaped from the largely crystallised roof of the granite pluton. The escaping melt was peraluminous, had a composition near the F, B, Li slightly enriched granite minimum, and, in comparison with other Cornish granites, was enriched in F, Li, Rb, Cs, Sn, W, Nb, Ta, and U, and depleted in Fe, Mg, Ca, Sr, Th, Zr, and REE. With increasing distance from the Tregonning Granite, the silicate melt crystallised as homogeneous leucogranite sheets and banded complex sheets (i.e. combinations of bands with granitic, aplitic and pegmatitic textures), then layered aplite-pegmatites; this sequence becoming progressively more depleted in the fluxing and volatile elements F, Li, Rb, and Cs, but showing no change in Zr/Hf ratios. The fixed Zr/Hf ratio is interpreted as indicating a direct genetic link (parental melt) between all rock types, however the melt progressively lost fluxing and volatile elements with distance from the granite pluton, probably due to wall-rock reaction or fluid exsolution and migration via fractures. Differentiation of the primary melt into Na-Li-F-rich and separate K-B-rich domains was the dominant chemical process responsible for the textural and mineral diversity of the MSC. On a large (cliff-section) scale, the proximal Na-Li-F-rich leucogranite passes through complex sheets into K-B-rich aplite-pegmatites, whilst at a smaller (< 1 m) scale, the K-B-rich bands are interspersed (largely overlain) by Na-Li-F-rich segregations. The grain size differences between the aplite and pegmatite could be related to pressure fluctuations and/or undercooling.Laser-ablation ICP-MS analyses of micas and tourmaline in Masaryk University Brno were supported by the Czech Science Foundation project No. GA14-13600S. All other analytical work for this contribution was supported by the RVO 67985831 in the Institute of Geology of the Czech Academy of Sciences, Praha. We are grateful to P. Davidson and an anonymous referee for their reviews

Neural correlates of enhanced visual short-term memory for angry faces: An fMRI study

Copyright: © 2008 Jackson et al.Background: Fluid and effective social communication requires that both face identity and emotional expression information are encoded and maintained in visual short-term memory (VSTM) to enable a coherent, ongoing picture of the world and its players. This appears to be of particular evolutionary importance when confronted with potentially threatening displays of emotion - previous research has shown better VSTM for angry versus happy or neutral face identities.Methodology/Principal Findings: Using functional magnetic resonance imaging, here we investigated the neural correlates of this angry face benefit in VSTM. Participants were shown between one and four to-be-remembered angry, happy, or neutral faces, and after a short retention delay they stated whether a single probe face had been present or not in the previous display. All faces in any one display expressed the same emotion, and the task required memory for face identity. We find enhanced VSTM for angry face identities and describe the right hemisphere brain network underpinning this effect, which involves the globus pallidus, superior temporal sulcus, and frontal lobe. Increased activity in the globus pallidus was significantly correlated with the angry benefit in VSTM. Areas modulated by emotion were distinct from those modulated by memory load.Conclusions/Significance: Our results provide evidence for a key role of the basal ganglia as an interface between emotion and cognition, supported by a frontal, temporal, and occipital network.The authors were supported by a Wellcome Trust grant (grant number 077185/Z/05/Z) and by BBSRC (UK) grant BBS/B/16178

Application of the MEGNO technique to the dynamics of Jovian irregular satellites

We apply the MEGNO (Mean Exponential Growth of Nearby Orbits) technique to the dynamics of Jovian irregular satellites. We demonstrate the efficiency of applying the MEGNO indicator to generate a mapping of relevant phase-space regions occupied by observed jovian irregular satellites. The construction of MEGNO maps of the Jovian phase-space region within its Hill-sphere is addressed and the obtained results are compared with previous studies regarding the dynamical stability of irregular satellites. Since this is the first time the MEGNO technique is applied to study the dynamics of irregular satellites we provide a review of the MEGNO theory. We consider the elliptic restricted three-body problem in which Jupiter is orbited by a massless test satellite subject to solar gravitational perturbations. The equations of motion of the system are integrated numerically and the MEGNO indicator computed from the systems variational equations. An unprecedented large set of initial conditions are studied to generate the MEGNO maps. The chaotic nature of initial conditions are demonstrated by studying a quasi-periodic orbit and a chaotic orbit. As a result we establish the existence of several high-order mean-motion resonances detected for retrograde orbits along with other interesting dynamical features. The computed MEGNO maps allows to qualitatively differentiate between chaotic and quasi-periodic regions of the irregular satellite phase-space given only a relatively short integration time. By comparing with previous published results we can establish a correlation between chaotic regions and corresponding regions of orbital instability.Comment: 15 pages, 13 figures, 2 tables, submitted to MNRA

FUNCTIONAL MR OF BRAIN ACTIVITY AND PERFUSION IN PATIENTS WITH CHRONIC CORTICAL STROKE

PURPOSE: (1) To determine whether functional MR can reliably map functional deficits in patients with stroke in the primary visual cortex; (2) to determine whether functional MR can reliably map perfusion deficits; and (3) to determine whether functional MR can give any additional diagnostic information beyond conventional MR. METHODS: Seven patients who had had a stroke in their primary visual system were examined using two functional MR techniques: (1) dynamic susceptibility contrast imaging, and (2) cortical activation mapping during full-field visual stimulation. Maps of relative cerebral blood volume and activation were created and compared with visual field examinations and conventional T2-weighted images on a quadrant-by-quadrant basis in five of these patients. RESULTS: Visual field mapping matched with both T2-weighted conventional images and activation mapping of 16 of 18 quadrants. In two quadrants, the activation maps detected abnormalities that were present on the visual field examination but not present on the T2-weighted images nor on the relative cerebral blood volume maps, which may indicate abnormal function without frank infarction. In addition, the activation maps demonstrated decreased activation in extrastriate cortex and had normal T2 signal and relative cerebral blood volume but was adjacent to infarcted primary cortex, mapping in vivo how stroke in one location can affect the function of distant tissue. CONCLUSION: Functional MR techniques can accurately map functional and perfusion deficits and thereby provide additional clinically useful information. Additional studies will be needed to determine the prognostic utility of functional MR in stroke patients

The Affective Impact of Financial Skewness on Neural Activity and Choice

Few finance theories consider the influence of “skewness” (or large and asymmetric but unlikely outcomes) on financial choice. We investigated the impact of skewed gambles on subjects' neural activity, self-reported affective responses, and subsequent preferences using functional magnetic resonance imaging (FMRI). Neurally, skewed gambles elicited more anterior insula activation than symmetric gambles equated for expected value and variance, and positively skewed gambles also specifically elicited more nucleus accumbens (NAcc) activation than negatively skewed gambles. Affectively, positively skewed gambles elicited more positive arousal and negatively skewed gambles elicited more negative arousal than symmetric gambles equated for expected value and variance. Subjects also preferred positively skewed gambles more, but negatively skewed gambles less than symmetric gambles of equal expected value. Individual differences in both NAcc activity and positive arousal predicted preferences for positively skewed gambles. These findings support an anticipatory affect account in which statistical properties of gambles—including skewness—can influence neural activity, affective responses, and ultimately, choice

Microstructural Abnormalities in Subcortical Reward Circuitry of Subjects with Major Depressive Disorder

Previous studies of major depressive disorder (MDD) have focused on abnormalities in the prefrontal cortex and medial temporal regions. There has been little investigation in MDD of midbrain and subcortical regions central to reward/aversion function, such as the ventral tegmental area/substantia nigra (VTA/SN), and medial forebrain bundle (MFB).We investigated the microstructural integrity of this circuitry using diffusion tensor imaging (DTI) in 22 MDD subjects and compared them with 22 matched healthy control subjects. Fractional anisotropy (FA) values were increased in the right VT and reduced in dorsolateral prefrontal white matter in MDD subjects. Follow-up analysis suggested two distinct subgroups of MDD patients, which exhibited non-overlapping abnormalities in reward/aversion circuitry. The MDD subgroup with abnormal FA values in VT exhibited significantly greater trait anxiety than the subgroup with normal FA values in VT, but the subgroups did not differ in levels of anhedonia, sadness, or overall depression severity.These findings suggest that MDD may be associated with abnormal microstructure in brain reward/aversion regions, and that there may be at least two subtypes of microstructural abnormalities which each impact core symptoms of depression

Motor Preparatory Activity in Posterior Parietal Cortex is Modulated by Subjective Absolute Value

For optimal response selection, the consequences associated with behavioral success or failure must be appraised. To determine how monetary consequences influence the neural representations of motor preparation, human brain activity was scanned with fMRI while subjects performed a complex spatial visuomotor task. At the beginning of each trial, reward context cues indicated the potential gain and loss imposed for correct or incorrect trial completion. FMRI-activity in canonical reward structures reflected the expected value related to the context. In contrast, motor preparatory activity in posterior parietal and premotor cortex peaked in high “absolute value” (high gain or loss) conditions: being highest for large gains in subjects who believed they performed well while being highest for large losses in those who believed they performed poorly. These results suggest that the neural activity preceding goal-directed actions incorporates the absolute value of that action, predicated upon subjective, rather than objective, estimates of one's performance

The tumbling rotational state of 1I/‘Oumuamua

The discovery of 1I/2017 U1 (1I/‘Oumuamua) has provided the first glimpse of a planetesimal born in another planetary system. This interloper exhibits a variable colour within a range that is broadly consistent with local small bodies, such as the P- and D-type asteroids, Jupiter Trojans and dynamically excited Kuiper belt objects. 1I/‘Oumuamua appears unusually elongated in shape, with an axial ratio exceeding 5:1. Rotation period estimates are inconsistent and varied, with reported values between 6.9 and 8.3 h. Here, we analyse all the available optical photometry data reported to date. No single rotation period can explain the exhibited brightness variations. Rather, 1I/‘Oumuamua appears to be in an excited rotational state undergoing non-principal axis rotation, or tumbling. A satisfactory solution has apparent lightcurve frequencies of 0.135 and 0.126 h−1 and implies a longest-to-shortest axis ratio of ≳5:1, although the available data are insufficient to uniquely constrain the true frequencies and shape. Assuming a body that responds to non-principal axis rotation in a similar manner to Solar System asteroids and comets, the timescale to damp 1I/‘Oumuamua’s tumbling is at least one billion years. 1I/‘Oumuamua was probably set tumbling within its parent planetary system and will remain tumbling well after it has left ours