Fluid Core Research Articles

Investigation of damping characteristics onPLArobotic gripper fingers with magnetorheological fluid core and unimorph piezoelectricMFC

AbstractPolylactic acid (PLA) is an environmentally friendly, biodegradable, and low‐cost thermoplastic material suitable for 3D printing. Complex shapes can be easily produced and hence PLA has been used for many applications. This study presents the damping characteristics of two robotic gripper fingers. The first gripper is composed of a PLA surface layer and a magnetorheological (MR) fluid core and the second gripper is composed of a PLA surface layer bonded to a surface of unimorph piezoelectric Macro Fiber Composite (MFC). The magnetic field is applied by using permanent magnets while the magnetic field strength is varied by changing the distance between the permanent magnets. The electric field is applied by using a micro‐amplifier and regulated using data acquisition systems. The natural frequency and damping ratio of the PLA gripper finger are determined by free vibration analysis using LabVIEW software. The damping ratio and vibration amplitude suppression for the PLA grippers was increased as the magnetic field strength changed from 0G to 600G (MR) and as the electric field changed from 0V to 360V (MFC).

Deviation of Mercury's Spin Axis From an Exact Cassini State Induced by Dissipation

AbstractWe compute predictions of the deviation of Mercury's spin axis from an exact Cassini state caused by tidal dissipation as well as viscous and electromagnetic (EM) friction at the core‐mantle boundary (CMB) and inner core boundary (ICB). Viscous friction at the CMB generates a phase lead; viscous and EM friction at the ICB produce a phase lag; the magnitude of the deviation depends on the inner core size, kinematic viscosity, and magnetic field strength, but cannot exceed an upper bound. For a small inner core, viscous friction at the CMB results in a maximum phase lead of 0.027 arcsec. For a large inner core (radius >1,000 km), EM friction at the ICB generates the largest phase lag, but it does not exceed 0.1 arcsec. Elastic deformations induced by the misaligned fluid and solid cores play a first‐order role in the phase lead/lag caused by viscous and EM coupling and contribute to a perturbation in mantle obliquity on par with that caused by tidal deformations. Tidal dissipation results in a phase lag and its magnitude (in units of arcsec) is given by the empirical relation (80/Q), where Q is the quality factor; Q = 80 results in a phase lag of ∼1 arcsec. A large inner core with a low viscosity of the order of 1017 Pa s or lower can significantly affect Q and thus the resulting phase lag. The limited mantle phase lag suggested by observations (<10 arcsec) implies a lower limit on the bulk mantle viscosity of approximately 1017 Pa s.

Free vibration analysis of multi-layer rectangular plate containing magnetorheological fluid and flexible core layers rested on Winkler-Pasternak foundation

Magneto-rheological (MR) fluids viscosity can be varied by changing the magnetic field intensity. Therefore, they can improve structural rigidity and damping property. The current study presents a free vibration analysis of a multilayer rectangular plate with two layers of MR fluid and a flexible core layer, rested on a Winkler-Pasternak foundation based on exponential shear deformation theory (ESDT). In this theory, the exponential functions are applied in terms of thickness coordinates to include the effect of transverse and inertial rotational shear deformation. The flexible core displacement is modeled via the second-order Frostig model. The Hamilton’s principle is used to derive the equations of motion. These equations are solved using the Navier method to obtain the natural frequencies of the plate. The accuracy of the derived equations is validated, and the obtained results are compared with a specific case. Finally, the results show that by applying and increasing the magnetic field intensity, the natural frequencies and loss factor increase. With the increase in the mode number for each specific magnetic field intensity, the natural frequency increases and the loss factor decreases. The natural frequencies and loss factor decrease with the increase of the MR layer thickness to overall thickness ratio and the flexible core layer thickness to overall thickness ratio. The natural frequencies increase when the parameters of the foundation increase.

Librations of a body composed of a deformable mantle and a fluid core

We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Plan\'{e}taire de l'Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those related to the "permanent deformation", have a physical interpretation. The paper also contains: 1) A physical model to explain the usual lack of hydrostaticity of the mantle (permanent deformation). 2) Formulas for free librations of bodies in and out-of spin-orbit resonance that are valid for any linear viscoelastic rheology of the mantle. 3) Formulas for the offset between the mantle and the idealized rigid-body motion (Peale's Cassini states). 4) Applications to the librations of Moon, Earth, and Mercury that are used for model validation.

A Cylindrical Grip Type of Tactile Device Using Magneto-Responsive Materials Integrated with Surgical Robot Console: Design and Analysis.

This paper proposes a cylindrical grip type of tactile device that is effectively integrated to a surgical robot console so that a surgeon can easily touch and feel the same stiffness as the operating organs. This is possible since the yield stress (or stiffness) of magnetic-responsive materials can be tuned or controlled by the magnetic field intensity. The proposed tactile device consists of two main parts: a magnetorheological elastomer (MRE) layer and a magnetorheological fluid (MRF) core. The grip shape of the device to be positioned on the handle part of the master of the surgical robot is configured and its operating principle is discussed. Then, a couple of equations to calculate the stiffness from the gripping force and the field-dependent yield stress of MRF are derived and integrated using the finite element analysis (FEA) model. After simulating the stiffness of the proposed tactile device as a function of the magnetic field intensity (or current), the stiffnesses of various human organs, including the liver and heart, are calculated from known data of an elastic modulus. It is demonstrated from comparative data between calculated stiffness from human tissues and simulated stiffness from FEA that the proposed tactile device can generate sufficient stiffness with a low current level to recognize various human organs which are significantly required in the surgical robot system.

Towards Understanding the Interconnection between Celestial Pole Motion and Earth's Magnetic Field Using Space Geodetic Techniques.

The understanding of forced temporal variations in celestial pole motion (CPM) could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), i.e., 1 mm accuracy and 0.1 mm/year stability on global scales in terms of the Earth orientation parameters. Besides astronomical forcing, CPM excitation depends on the processes in the fluid core and the core–mantle boundary. The same processes are responsible for the variations in the geomagnetic field (GMF). Several investigations were conducted during the last decade to find a possible interconnection of GMF changes with the length of day (LOD) variations. However, less attention was paid to the interdependence of the GMF changes and the CPM variations. This study uses the celestial pole offsets (CPO) time series obtained from very long baseline interferometry (VLBI) observations and data such as spherical harmonic coefficients, geomagnetic jerk, and magnetic field dipole moment from a state-of-the-art geomagnetic field model to explore the correlation between them. In this study, we use wavelet coherence analysis to compute the correspondence between the two non-stationary time series in the time–frequency domain. Our preliminary results reveal interesting common features in the CPM and GMF variations, which show the potential to improve the understanding of the GMF’s contribution to the Earth’s rotation. Special attention is given to the corresponding signal between FCN and GMF and potential time lags between geomagnetic jerks and rotational variations.

Viscous Dissipation in the Fluid Core of the Moon

AbstractThe spin axes of the mantle, fluid core, and solid inner core of the Moon precess at frequency Ωp = 2π/18.6 years−1 though with different orientations, leading to viscous friction at the core‐mantle boundary (CMB) and inner core boundary (ICB). Here, we use a rotational model of the Moon and consider a range of inner core and outer core radii to investigate the relative importance of viscous dissipation at the CMB and ICB, and to show how this dissipation is connected to the phase lead angle (ϕp) of the mantle ahead of its Cassini state. We show that when the inner core radius is km and the free inner core nutation frequency Ωficn approaches Ωp, viscous dissipation at the ICB can be comparable to that at the CMB, and in the most extreme cases exceed it by as much as a factor of 10. If so, the viscous dissipation in the lunar core projected back in time depends on how Ωficn has evolved relative to Ωp. We further show that constraints on the CMB and ICB radii of the lunar core can in principle be extracted by matching the observed phase lead of ϕp = 0.27 arcsec; this requires an improved estimate of tidal dissipation and an accurate model of the turbulent viscous torque. Finally, when our rotational model is constrained to match ϕp = 0.27 arcsec, our results suggest that the viscous dissipation at the ICB is likely insufficient to have ever been above the threshold to power a thermally driven dynamo.

Comparison of the application of smart electrorheological and magnetorheological fluid cores to damp sandwich panels’ vibration behavior, based on a novel higher-order shear deformation theory

Background: Magnetorheological and electrorheological materials show variations in their rheological properties when subjected to magnetic and electric fields. We analyzed the vibration control behavior of a sandwich panel with elastic face sheets and an electrorheological or magnetorheological fluid core, using an improved higher-order theory. The theory was applied to the analysis of the structure's components as a combination of exponential, trigonometric, and polynomial functions. The core's flexibility was analyzed based on Frostig's second model, which has attracted material science researchers’ attention. Methods: Using the new theory, we analyzed the transverse shear and rotary inertia effects of the cover sheets. The governing equations and boundary conditions were derived by Hamilton's principle. The natural frequencies and loss factors were derived by solving the eigenvalue problem. The effects of changing the geometric parameters, the thickness of the magnetorheological or electrorheological layer, and thickness ratios on the vibration behavior of the panel were determined. Results: The panel's natural frequencies increased when the magnetic or electric field strength, and the panel's aspect ratio increased. It decreased when the core to panel thickness ratio increased. The magnetorheological material showed higher strength and lower sensitivity to external impurities than did the electrorheological material. Conclusions: We conclude that the magnetorheological materials minimize the structure's vibration at high-frequency operation, and the electrorheological materials are optimal for minimizing the structure's vibration at lower frequency operation. The findings of this study are useful to better understand the vibration behavior of sandwich panels with laminates under free vibration conditions.

Revisiting neutron starquakes caused by spin-down

Context. Pulsars show a steady decrease in their rotational frequency, occasionally interrupted by sudden spin-ups called glitches, whose physical origin is still a mystery. One suggested explanation for at least the small glitches are starquakes, that is, failures of the solid neutron star crust, in which the progressive reduction in the centrifugal force deforms the star, stressing the solid until it breaks. This produces a spin-up, dissipating energy inside the star. Aims. We explore this suggestion by analyzing a mostly analytical model in order to understand the possible consequences of starquakes, particularly whether they can explain at least the small glitches. Methods. We analyze the deformations and strains produced by the decreasing centrifugal force, modeling the neutron star with a fluid core and a solid crust, each with uniform density and with the core possibly denser than the crust, as a simple approximation to the strong density gradient present in real neutron stars. Results. The deformation of a star with very different densities in the core and crust is qualitatively different from the previously studied case of equal densities. The former more closely resembles the behavior of a fluid star, in which the core-crust interface is a surface of constant gravitational plus centrifugal potential. Conclusions. Regardless of the uncertain breaking strain, the glitch activity in this model is several orders of magnitude smaller than observed, even if only small glitches are considered. For a large breaking strain, suggested by simulations, glitches due to starquakes could be roughly of the correct size but much less frequent than observed glitches. The energy released in each such glitch is much larger than in the standard model of angular momentum transfer from a faster rotating superfluid in the inner crust. On the other hand, we cannot rule out that the heating produced by small starquakes could trigger glitches by allowing neutron superfluid vortices to move. We also confirm that stresses in the neutron star crust can in principle support an ellipticity much larger than some observational upper limits from pulsar timing and continuous gravitational wave searches.

Polygenic Effects of the Lipid Metabolic Pathway Accelerated Pathological Changes and Disrupted Default Mode Network Trajectory Across the Alzheimer's Disease Spectrum.

Objective: Dyslipidemia is a controversial risk for Alzheimer's disease (AD) with unknown mechanisms. This study aimed to investigate polygenic effects of the lipid metabolic pathway on cerebrospinal fluid (CSF) core biomarkers, cognition, and default mode network (DMN).Methods: Cross-sectional data on serum lipids, CSF core biomarkers, and functional MRI findings for 113 participants (25 cognitively normal, 20 with subjective cognitive decline, 24 early amnestic, 23 with late mild cognitive impairment, and 21 with AD) from the Alzheimer's Disease Neuroimaging Initiative were included. Different cognitive stages were categorized based on neuropsychological assessments. Multivariable linear regression analyses were conducted to investigate the polygenic and interactive effects on the DMN. The correlations of lipid-related polygenes and serum lipids with cognitive performance were also studied via regression analyses.Results: The polygenic scores were significantly correlated with CSF levels of core biomarkers (P < .05) but not with cognition. Several serum lipids were associated with total tau. CSF core biomarkers and 6 serum lipids both could impact cognition in a nonlinear manner. Polygenic effects exhibited diverse trajectories on the DMN subsystems across the AD spectrum. Extensive genetic and interactive effects were mainly concentrated in the cortical frontal-parietal network and subcortical regions. Brain regions of lipid metabolites linking to DMN involved sensorimotor network and occipital lobe.Conclusions: Polygenic effects of the lipid metabolic pathway could accelerate pathological changes and disrupted DMN subsystem trajectory across the AD spectrum. These results deepen the understanding of the mechanism of lipid metabolism affecting the neural system and provide several lipid indicators that enable the impairments of lipid metabolism on the brain to be monitored.

Mechanical and topographic factors influencing lava dome growth and collapse

Lava dome collapse hazards are intimately linked with their morphology and internal structure. We present new lava dome emplacement models that use calibrated rock strengths and allow material behaviour to be simulated for three distinct units: (1) a ductile, fluid core; (2) a solid upper carapace; and (3) disaggregated talus slopes. We first show that relative proportions of solid and disaggregated rock depend on rock strength, and that disaggregated talus piles can act as an unstable substrate and cause collapse, even in domes with a high rock strength. We then simulate sequential dome emplacement, demonstrating that renewed growth can destabilise otherwise stable pre-existing domes. This destabilisation is exacerbated if the pre-existing dome has been weakened following emplacement, e.g., through processes of hydrothermal alteration. Finally, we simulate dome growth within a crater and show how weakening of crater walls can engender sector collapse. A better understanding of dome growth and collapse is an important component of hazard mitigation at dome-forming volcanoes worldwide.

EXPERIMENTAL RESEARCH ON QUANTIFICATION OF COUNTERCURRENT IMBIBITION DISTANCE FOR TIGHT SANDSTONE

China has an unbelievable number of tight oil reserves in storage, but a large majority of the tight oil reservoirs are in low sweep efficiency and in poor depletion development. Countercurrent imbibition is an important recovery mechanism for enhancing oil recovery during water injection development of tight oil reservoirs. At present, a large number of scholars have mainly conducted research on the imbibition recovery of tight oil reservoirs as well as the factors that may have influences on that, but actually there are few research on the imbibition distance that characterizes the range of imbibition effect in tight oil reservoirs. In this paper, the CT online scanning device is employed to establish a quantification method for countercurrent imbibition distance (CID) of tight cores, determining the range of countercurrent imbibition, and it also can make a further study on the influence of fluid pressure, water saturation, core permeability and surfactant on CID. In addition, it can be utilized to determine the relationship between CID and imbibition recovery. As a result, this study also provides theoretical guidance for enhancing oil recovery of tight oil reservoirs. The research results show that the CID scale of tight core with the permeability of about 0.3 mD is only 1.25 ~ 1.625 cm, and CID of the tight core with 0.302 mD under the condition of 5 MPa is 1.375 cm. Under the experimental conditions in this article, fluid pressure and initial water saturation have little effect on the CID of tight cores, while permeability and surfactant have significant effect on the CID of tight cores. What’s more, the CID of the core with 0.784 mD is 2.63 times higher than that of the core with 0.302 mD. In conclusion, the CID is a crucial parameter for the characterization of imbibition recovery, and it determines the range of countercurrent imbibition.

Modeling of flow coastdown transient of a reactor coolant system under different pump failures

The flow coastdown transient calculation is important for the safety analysis of a nuclear reactor. An accurate transient analysis during coastdown is necessary and important for the design and manufacture of a reactor coolant pump, since only the reliable work of reactor coolant pumps can guarantee the safety of a nuclear power plant during this important period.In the present work, mathematical models are solved for the non-dimensional transient flow rates in four loops and a reactor core under different power failures of reactor coolant pumps. Python 3.6, high level programming language, is used to solve the mathematical equations of core thermal-hydraulics for the flow coastdown transient. A standard 4-Loop Westinghouse design pressurized water reactor is used in the analysis. Three cases are studied; failure of one of the four pumps, sequential failure of the four pumps and simultaneous failure of the four pumps due to loss of off-site power. The important parameters for the safety analysis of the reactor are flow coastdown time, flow rates, and coolant temperature. The model results for a single pump failure are compared with the published experimental data during flow coastdown of Qinshan reactor coolant pump. The comparison results show acceptable agreements. Sensitivity analyses for two different parameters during flow coastdown transient are investigated. These two parameters are the fluid inertia ratio, α and core time constant, τ. Effects of each of the parameters on the flow coastdown transient, are given separately.

Improved High-order Analysis of Linear Vibrations of a Thick Sandwich Panel With an Electro-rheological Core by Using Exponential Shear Deformation Theory

In In this paper, the behavior of free vibrations of the thick sandwich panel with multi-layer face sheets and an electrorheological (ER) fluid core using Exponential Shear Deformation Theory were investigated. For the first time, Exponential shear deformation theory is used for the face sheets while the Displacement field based on the second Frostig's model is used for the core. The governing equations and the boundary conditions are derived by Hamilton’s principle. Closed form solution is achieved using the Navier method and solving the eigenvalues. Primary attention is focused on the effects of electric field magnitude, geometric aspect ratio,and ER core layer thickness on the dynamic characteristics of the sandwich plate. The rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. When an electric field is applied, the damping of the system is more effective. The effects of the natural frequencies and loss factors on the dynamic behaviorof the sandwich plate are studied.the natural frequency of the sandwich plate increases and the modal loss factor decreases. With increasing the thickness of the ER layer, the natural frequencies of the sandwich plate are decreased.

Time to Diagnosis in Young Onset Alzheimer's Disease: A Population-Based Study from Central Norway.

Background:Young onset dementia is associated with a longer time to diagnosis compared to late onset dementia. Earlier publications have indicated that atypical presentation is a key contributing factor to the diagnostic delay. Our hypothesis was that even the most common presentation of Alzheimer’s disease is associated with a substantial diagnostic delay in patients < 65 years.Objective:To determine the time to diagnosis, and time lags in the diagnostic pathway in typical young onset Alzheimer’s disease in central Norway.Methods:The main sources of patients were the databases at the Department of Neurology, University Hospital of Trondheim (St. Olav’s Hospital), and Department of Psychiatry, Levanger Hospital. Other sources included key persons in the communities, collaborating hospital departments examining patients with suspected cognitive impairment, and review of hospital records of all three hospitals in the area. Information on the time lags, and the clinical assessment, including the use of biomarkers, was collected from hospital notes. Caregivers were interviewed by telephone.Results:Time from first symptom to diagnosis in typical young onset Alzheimer’s disease was 5.5 years (n = 223, SD 2.8). Time from onset to contact with healthcare services (usually a general practitioner) was 3.4 years (SD 2.3). Time from contact with healthcare services to the first visit at a hospital was 10.3 months (SD 15.5). Time from first visit at a hospital to diagnosis was 14.8 months (SD 22.6). The analysis of cerebrospinal fluid core biomarkers was performed after 8.3 months (SD 20.9).Conclusion:Typical Alzheimer’s disease is associated with a substantial diagnostic delay in younger patients. Raising public awareness, and education of healthcare professionals on the aspects of young onset Alzheimer’s disease is warranted. CSF core biomarkers should be performed earlier in the hospital evaluation process.

3D pore-scale modeling of nanofluids-enhanced oil recovery

The numerical modeling of oil displacement by nanofluid based on three-dimensional micromodel of cores with different permeability was carried out by the volume of fluid (VOF) method with experimentally measured values of interfacial tension, contact angle and viscosity. Water-based suspensions of SiO 2 nanoparticles with a concentration of 0–1% and different particle sizes were considered to study the effect of concentration and size of nanoparticles, displacement fluid flow rate, oil viscosity and core permeability on the efficiency of oil displacement by nanofluid. The oil recovery factor (ORF) increases with the increase of mass fraction of nanoparticles. An increase in nanoparticles' concentration to 0.5% allows an increase in ORF by about 19% compared to water flooding. The ORF increases with the decrease of nanoparticle size, and declines with the increase of displacing rate. It has been shown that the use of nanosuspensions for enhanced oil recovery is most effective for low-permeable reservoirs with highly viscous oil in injection modes with capillary number close to the immobilization threshold, and the magnitude of oil recovery enhancement decreases with the increase of displacement speed. The higher the oil viscosity, the lower the reservoir rock permeability, the higher the ORF improved by nanofluids will be.

Making sense of micro-fractures to the Longmaxi shale reservoir quality in the Jiaoshiba area, Sichuan Basin, China: Implications for the accumulation of shale gas

The processes of shale gas transport and enrichment are closely related to the micro-fractures structure. Here, porosity, permeability test, gas adsorption, scanning electron microscopy (SEM), fluid spontaneous imbibition, Nano-CT, Micro-CT, and core observations were used to determine the types and characteristics of micro-fractures in the Longmaxi shales, Jiaoshiba area. The effects of micro-fractures on shale reservoir properties and shale gas accumulation were also analyzed. Diverse sizes of intra-particle (intraP), particle-edge, and transparticle micro-fractures were widely developed in shales. The difference of micro-fracture characteristics was mainly controlled by the mineral composition. The well-developed micro-fractures in the Longmaxi shales can act as a “bridge” to link nano-pores and macro-fractures. In such cases, a large-scale “escape network” composed of “nano-pores, micro-fractures, and macro-fractures” was formed. The escape of hydrocarbons along this network results in lower pore pressure. Most pores were dramatically compressed due to the compaction of overlying strata. As a result, the pore space and seepage capacity of organic-rich shales were disappointed, which is not benefit to the enrichment and production of shale gas. However, the limited development of micro-fractures will reduce the probability of forming “escape network”. Thus, some of the pores could be remained and act as storage space along with micro-fractures for shale gas even within the tectonically deformed area.

Tau pathologies mediate the association of blood pressure with cognitive impairment in adults without dementia: The CABLE study.

This study delineated the interrelationships among blood pressure (BP), cerebrospinal fluid (CSF) core biomarkers of Alzheimer's disease (AD), and cognition. The linear regression analyses were conducted in 1546 non-demented participants (mean age of 61.58 years, range 40 to 89 years; 40% female; average days of BP measurement, 9.10 days). Mediation analyses with 10,000 bootstrapped iterations were used to explore the mediation effects. A clear age-related pattern of BP was delineated. Mid-life hypertension (especially systolic BP), late-life lower diastolic BP, as well as mid- and late-life higher pulse pressure were associated with cognitive impairment and tau-related biomarkers. BP variability was associated only with cognition but not with CSF biomarkers. Overall, the associations between BP and cognition were partially mediated (proportion: 11% to 30%) by tau pathologies, independently of amyloid pathology. Tau pathologies might play important roles in the relationship between BP and cognition, with significant age- and BP-type dependences.

Reasons Why Geomagnetic Field Generation is Physically Impossible in Earth’s Fluid Core

Despite the importance for understanding the nature of the geomagnetic field, and especially its potential for radically disrupting modern civilization [1], virtually all scientific publications relating to it are based upon the false assumption that the geomagnetic field is generated in the Earth’s fluid core. By adhering to an outmoded paradigm, members of the geoscience community have potentially exposed humanity to globally devastating risks, leaving it unprepared for an inevitable geomagnetic field collapse.&#x0D; There is no scientific reason to believe that the geomagnetic field is generated within the fluid core. Convection is physically impossible in the fluid core due to its compression by the weight above and its inability to sustain an adverse temperature gradient. There is no evidence of ongoing inner core growth to provide energy to drive thermal convection or to cause compositional convection. Moreover, there is no mechanism to account for magnetic reversals and no means for magnetic seed-field production within the fluid core to initiate dynamo amplification.&#x0D; Earth’s nuclear georeactor, seat of the geomagnetic field, has none of the problems inherent in putative fluid-core geomagnetic field production. With a mass of about one ten-millionth that of the fluid core, georeactor sub-shell convection can potentially be disrupted by great planetary trauma, such as an asteroid impact, or by major solar outbursts or even by human activities, for example, by deliberate electromagnetic disturbance of the near-Earth environment, including the Van Allen belts. Furthermore, sub-shell convection disruption might trigger surface geophysical disasters, such as super-volcano eruptions [2-4].&#x0D; Scientists have a fundamental responsibility to tell the truth and to provide scientific understanding that benefits humanity.

The Rotation of the Nonrigid Earth at the Second Order. II. The Poincaré Model: Nonsingular Complex Canonical Variables and Poisson Terms

Abstract We develop a Hamiltonian analytical theory for the rotation of a Poincaré Earth model (rigid mantle and liquid core) at the second order with respect to the lunisolar potential and moving ecliptic term. Since the Andoyer variables considered in the first-order solution present virtual singularities, i.e., vanishing divisors, we introduce a set of nonsingular complex canonical variables. This choice allows for applying the Hori canonical perturbation method in a standard way. We derive analytical expressions for the first- and second-order solutions of the precession and nutation of the angular momentum axis (Poisson terms). Contrary to first-order theories, there is a part of the Poisson terms that does depend on the Earth’s structure. The resulting numerical amplitudes, not incorporated in the International Astronomical Union nutation standard, are not negligible considering current accuracies. They are at the microarcsecond level for a few terms, with a very significant contribution in obliquity of about 40 μas for the nutation argument with period −6798.38 days. The structure-dependent amplitudes present a large amplification with respect to the rigid model due to the fluid core resonance. The features of such resonance, however, are different from those found in first-order solutions. The most prominent is that it does not depend directly on the second-order nutation argument but rather on the combination of first-order arguments generating it. It entails that some first-order approaches, like those based on the transfer function, cannot be applied to obtain the second-order contributions.