Precession Of Equinoxes Research Articles

Evolution of localized states in Lieb lattices under time-dependent magnetic fields

We study the slow time evolution of localized states of the open-boundary Lieb lattice when a magnetic flux is applied perpendicularly to the lattice and increased linearly in time. In this system, Dirac cones periodically disappear, reappear and touch the flat band as the flux increases. We show that the slow time evolution of a localized state in this system is analogous to that of a zero-energy state in a three-level system whose energy levels intersect periodically and that this evolution can be mapped into a classical precession motion with a precession axis that rotates as times evolves. Beginning with a localized state of the Lieb lattice, as the magnetic flux is increased linearly and slowly, the evolving state precesses around a state with a small itinerant component and the amplitude of its localized component oscillates around a constant value (below but close to 1), except at multiples of the flux quantum where it may vary sharply. This behavior reflects the existence of an electric field (generated by the time-dependent magnetic field) which breaks the C4 symmetry of the constant flux Hamiltonian.

HOW AGN JETS HEAT THE INTRACLUSTER MEDIUM—INSIGHTS FROM HYDRODYNAMIC SIMULATIONS

ABSTRACT Feedback from active galactic nuclei (AGNs) is believed to prevent catastrophic cooling in galaxy clusters. However, how the feedback energy is transformed into heat, and how the AGN jets heat the intracluster medium (ICM) isotropically, still remain elusive. In this work, we gain insights into the relative importance of different heating mechanisms using three-dimensional hydrodynamic simulations including cold gas accretion and momentum-driven jet feedback, which are the most successful models to date in terms of reproducing the properties of cool cores. We find that there is net heating within two “jet cones” (within ∼30° from the axis of jet precession) where the ICM gains entropy by shock heating and mixing with the hot thermal gas within bubbles. Outside the jet cones, the ambient gas is heated by weak shocks, but not enough to overcome radiative cooling, therefore, forming a “reduced” cooling flow. Consequently, the cluster core is in a process of “gentle circulation” over billions of years. Within the jet cones, there is significant adiabatic cooling as the gas is uplifted by buoyantly rising bubbles; outside the cones, energy is supplied by the inflow of already-heated gas from the jet cones as well as adiabatic compression as the gas moves toward the center. In other words, the fluid dynamics self-adjusts such that it compensates and transports the heat provided by the AGN, and hence no fine-tuning of the heating profile of any process is necessary. Throughout the cluster evolution, turbulent energy is only at the percent level compared to gas thermal energy, and thus turbulent heating is not the main source of heating in our simulation.

Semiclassical Quantization of Spinning Quasiparticles in Ballistic Josephson Junctions.

A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semiclassic limit. The spectrum of Andreev bound states is obtained from the single valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position-particle-hole-spin space is constructed and shown to depend on only two parameters, namely, a magnetic phase shift and a local precession axis for the spin. The details of the Andreev-Wilson loop can be extracted via measuring the spin-resolved density of states. A Josephson junction can thus be viewed as an analog computer of closed-path-ordered exponentials.

96-65: Types of Thebesian valve in Cardiac Magnetic Resonance

Visualization of the Thebesian valve - guard of the coronary sinus (CS) - can be possible in the cardiac magnetic resonance (CMR). Such pre-visualization can potentially be valuable before cannulation of the CS. Methods: 122 patients (aged 49.2 ± 17.2; 41W) were included. CMR was performed on all participants using a GE Optima MR450w 1.5T (GEM) with a 3D cardiac coil. A standard steady-state free precession and 4-channel long axis sequences were used for the basic evaluation of the Thebesian valve. Our original sequence or navigator gated 3D free breathing CMR were performed on selected patients. The classification of the Thebesian valve in CMR was based on anatomical characteristics. Results: Examples of the Thebesian valve in CMR are presented in the figure below. Average diameter of the CS ostium was 9.9 ± 9.3 mm. Thebesian valve was found in 56 patients (45.9%). Average diameter of the CS ostium in patients with a valve present was 11.9 ± 17.9 and without Thebesian valve was 8.9 ± 0.4; p = 0.429 NS. In 21 patients (37.5%) the valve almost totally covered the CS ostium (type D); this can potentially create problems during CS cannulation. In 20 (35.7%) cases, the valve was visible from the right atrium wall (types A1, A2) and in one case (1.8%), it was visible from the inter-atrial septum (type B1). In 12 (21.4%) cases, the valve had two parts with a gap between them (type C).

Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical Surface; A Nonequilibrium Keldysh Green Function Approach

In this paper, we investigate theoretically the spin–orbit torque (SOT) as well as the Gilbert damping for a two band model of a 2D helical surface state with a ferromagnetic (FM) exchange coupling. We decompose the density matrix into the Fermi sea and Fermi surface components and obtain their contributions to the electronic transport as well as the SOT. Furthermore, we obtain the expression for the Gilbert damping due to the surface state of a 3D topological insulator (TI) and predict its dependence on the direction of the magnetization precession axis.

On turbulence driven by axial precession and tidal evolution of the spin–orbit angle of close-in giant planets

The spin axis of a rotationally deformed planet is forced to precess about its orbital angular momentum vector, due to the tidal gravity of its host star, if these directions are misaligned. This induces internal fluid motions inside the planet that are subject to a hydrodynamic instability. We study the turbulent damping of precessional fluid motions, as a result of this instability, in the simplest local computational model of a giant planet (or star), with and without a weak internal magnetic field. Our aim is to determine the outcome of this instability, and its importance in driving tidal evolution of the spin-orbit angle in precessing planets (and stars). We find that this instability produces turbulent dissipation that is sufficiently strong that it could drive significant tidal evolution of the spin-orbit angle for hot Jupiters with orbital periods shorter than about 10-18 days. If this mechanism acts in isolation, this evolution would be towards alignment or anti-alignment, depending on the initial angle, but the ultimate evolution (if other tidal mechanisms also contribute) is expected to be towards alignment. The turbulent dissipation is proportional to the cube of the precession frequency, so it leads to much slower damping of stellar spin-orbit angles, implying that this instability is unlikely to drive evolution of the spin-orbit angle in stars (either in planetary or close binary systems). We also find that the instability-driven flow can act as a system-scale dynamo, which may play a role in producing magnetic fields in short-period planets.

Precessing Ferromagnetic Needle Magnetometer.

A ferromagnetic needle is predicted to precess about the magnetic field axis at a Larmor frequency Ω under conditions where its intrinsic spin dominates over its rotational angular momentum, Nℏ≫IΩ (I is the moment of inertia of the needle about the precession axis and N is the number of polarized spins in the needle). In this regime the needle behaves as a gyroscope with spin Nℏ maintained along the easy axis of the needle by the crystalline and shape anisotropy. A precessing ferromagnetic needle is a correlated system of N spins which can be used to measure magnetic fields for long times. In principle, by taking advantage of rapid averaging of quantum uncertainty, the sensitivity of a precessing needle magnetometer can far surpass that of magnetometers based on spin precession of atoms in the gas phase. Under conditions where noise from coupling to the environment is subdominant, the scaling with measurement time t of the quantum- and detection-limited magnetometric sensitivity is t^{-3/2}. The phenomenon of ferromagnetic needle precession may be of particular interest for precision measurements testing fundamental physics.

Two spinning ways for precession dynamo.

It is numerically demonstrated by means of a magnetohydrodynamic code that precession can trigger dynamo action in a cylindrical container. Fixing the angle between the spin and the precession axis to be 1/2π, two limit configurations of the spinning axis are explored: either the symmetry axis of the cylinder is parallel to the spin axis (this configuration is henceforth referred to as the axial spin case), or it is perpendicular to the spin axis (this configuration is referred to as the equatorial spin case). In both cases, the centro-symmetry of the flow breaks when the kinetic Reynolds number increases. Equatorial spinning is found to be more efficient in breaking the centro-symmetry of the flow. In both cases, the average flow in the reference frame of the mantle converges to a counter-rotation with respect to the spin axis as the Reynolds number grows. We find a scaling law for the average kinetic energy in term of the Reynolds number in the axial spin case. In the equatorial spin case, the unsteady asymmetric flow is shown to be capable of sustaining dynamo action in the linear and nonlinear regimes. The magnetic field is mainly dipolar in the equatorial spin case, while it is is mainly quadrupolar in the axial spin case.

Surprising Behavior of Spinning Tops and Eggs on an Inclined Plane

A spinning top or a spinning hard-boiled egg is fascinating to observe since both objects can remain upright for a relatively long time without falling over. If spun at sufficient speed on a horizontal surface, the spin axis rises to a vertical position and the bottom end tends to remain fixed in position on the surface. If the initial spin is insufficient, then the spin axis will not rise all the way to the vertical, in which case a spinning top or a spinning egg will precess slowly around a vertical axis. If the bottom end is rounded, as it is with an egg or with a top having a round rather than a pointed peg, then the vertical precession axis does not necessarily pass through the center of mass. Instead, the precession axis may be located several centimeters away from the center of mass, depending on the radius of the bottom end. As a result, the whole egg or the whole top then rolls along the surface in an approximately circular path, several centimeters in diameter. The essential physics is described in Ref. 1 and the references therein, and in the many more books and papers since the early 1900s quoted in each of the references therein.

Quantitative Study of Lunisolar Precession Mechanism

According to Xiaodong Song et al.’s study about difference rotation in the Earth’s inner core, a physical model of lunar motion changing the angular momentum of the Earth’s circles is presented in this work. The Lunar motion makes there be a huge gap existing in the core angular momentum between far lunar hemisphere and near lunar hemisphere. The gap results in the difference rota-tion in the Earth’s inner core, meanwhile, it increases the angular velocity of far lunar hemisphere and decreases the angular velocity of near lunar hemisphere. The Earth’s liquid outer core gene-rates an astro-geodynamical effect including the difference rotation among the Earth’s circles. It is found that when the moon moves into the apogee or the perigee of the lunar orbit, and the moon phase is the upper and lower chords (i.e. semi-diameter place), the true anomaly of the moon will change from 270-degree back (or forward) to 90-degree; this results in the mantle shell of the Earth westward, and forms lunisolar precession, the vernal equinox westward and Chandler polar motion.

Lowering of technological risks of hypersound aeronavigation

The study reveals the mechanism of an acoustic error of an inertial sensor with a float static liquid suspension. The paper presents a numerical analysis of the autonomous positioning error that used to pose a technological risk. We have disclosed the characteristics of the device dynamics in a non-inertial frame of reference and revealed the dependence of kinematic parameters in the base and the mobile systems.The paper describes the nature of additional precession in the inertial sensor in the operating conditions of a hypersonic flight caused bythe Euler force and analyses the device’s gyroscopic response to the moments of the Coriolis effect on the precession axis in the impedance float surface.The findings can be used in hypersonic aircraft for assault and foreign intelligence. They can improveserial production of hypersonic technologies to the desired level, reducing technological risks of the vehicles’operational use.

Triadic resonances in precessing rapidly rotating cylinder flows

Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with $45^{\circ }$ nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.

THE SAPTARISHIS CALENDAR: 'THE INDIAN TROPICAL ZODIAC'!

The Saptarishis Calendar of ancient India is based on precession of the equinoxes. It employs the tropical zodiac of the Greeks and the precessional rate of Hipparchus. The Saptarishis era has to be determined by naked eye observation of the sky. The line of reference goes through the stars Dubhe and Merak in the constellation of Ursa Major, touching both of them, and crosses the ecliptic in the sidereal Purvaphalguni Nakshatra¹ of Simha Rashi at a point close to the star 59 Leonis. The angular difference between this 'Saptarishis pointer' and the vernal equinox gives the tropical lunar mansion in which Saptarishis resides at a given point in time.

On the regular precession of an asymmetric rigid body acted upon by uniform gravity and magnetic fields

In 1947 Grioli discovered that an asymmetric heavy rigid body moving about a fixed point can perform a regular precession, which is the rotation of the body about an axis fixed in it, while that axis precesses with the same uniform angular velocity about a non-vertical axis fixed in space.In the present note, we show that a magnetized asymmetric rigid body moving about a fixed point while acted upon by uniform gravity and magnetic fields can perform a regular precession about a horizontal axis fixed in space orthogonal to the magnetic field. This motion does not contain Grioli's as a special case since the gravity and magnetic effects are coupled and can vanish only simultaneously.

The spin, the nutation, and the precession of the Earth's axis revisited from a (numerical) mechanics perspective

Modeling the motion of the Earth's axis, i.e., its spin, nutation and its precession, is a prime example of our ongoing effort to simulate the behavior of complex mechanical systems. In fact, models of increasing complexity of this motion have been presented for more than 400 years leading to an increasingly accurate description. The objective of this paper is twofold namely, first, to provide a review of these efforts and, second, to provide an improved analysis, if possible, based on today's numerical possibilities. Newton himself treated the problem of the precession of the Earth, a.k.a. the precession of the equinoxes, in Liber III, Propositio XXXIX of his Principia 1. He decomposed the duration of the full precession into a part due to the Sun and another part due to the Moon, which would lead to a total duration of 25,918 years. This agrees fairly well with the experimentally observed value. However, Newton does not really provide a concise rational derivation of his result. This task was left to Chandrasekhar in Chapter 26 of his annotations to Newton's book 2. He follows an approach suggested by Scarborough 3 starting from Euler's equations for the gyroscope and by calculating the torques due to the Sun and to the Moon on a tilted spheroidal Earth. These differential equations can be solved approximately in an analytic fashion, yielding something close to Newton's more or less fortuitous result. However, the equations can also be treated more properly in a numerical fashion by using a Runge-Kutta approach allowing for a study of their general non-linear behavior. This paper will show how and discuss the outcome of the numerical solution. A comparison to actual measurements will also be attempted. When solving the Euler equations for the aforementioned case numerically it shows that besides the precessional movement of the Earth's axis there is also a nutational one present. However, as we shall show, if Scarborough's procedure is followed, the period of this nutation turns out to be roughly half a year with a very small amplitude whereas the observed (main) nutational period is much longer, namely roughly nineteen years, and much more intense amplitude-wise. The reason for this discrepancy is based on the assumption that the torques of both the Sun and the Moon are due to gravitational actions within the equinoctial plane. Whilst this is true for the Sun, the revolution of the Moon around the Earth occurs in a plane, which is inclined by roughly 5° w.r.t. the equinoctial. Moreover, this plane rotates such that the ascending and descending nodes of the moon precede with a period of roughly 18 years. If all of this is taken into account the analytically predicted nutation period will be of the order of the observed value 4, 5. As in the case of the precession we will provide a more stringent analysis based on a numerical solution of the Euler equations, which leads beyond the results presented in Sect.12.10 of 5.

El Niño evolution during the Holocene revealed by a biomarker rain gauge in the Galápagos Islands

The El Niño-Southern Oscillation (ENSO) represents the largest perturbation to the climate system on an inter-annual time scale, but its evolution since the end of the last ice age remains debated due to the lack of unambiguous ENSO records lasting longer than a few centuries. Changes in the concentration and hydrogen isotope ratio of lipids produced by the green alga Botryococcus braunii, which blooms during El Niño rains in the Galápagos Islands, indicate that the early Holocene (9200–5600 yr BP) was characterized by alternating extremes in the intensity and/or frequency of El Niño events that lasted a century or more. Our data from the core of the ENSO region thus calls into question earlier studies that reported a lack of El Niño activity in the early Holocene. In agreement with other proxy evidence from the tropical Pacific, the mid-Holocene (5600–3500 yr BP) was a time of consistently weak El Niño activity, as were the Early Middle Ages (∼1000–1500 yr BP). El Niño activity was moderate to high during the remainder of the last 3500 years. Periods of strong or frequent El Niño tended to occur during peaks in solar activity and during extended droughts in the United States Great Plains linked to La Niña. These changing modes of ENSO activity at millennial and multi-centennial timescales may have been caused by variations in the seasonal receipts of solar radiation associated with the precession of the equinoxes and/or changes in solar activity, respectively.

Resolution of a modulated structure by electron and powder X-ray diffraction

These past few years, many new structures have been solved using electron diffraction methods: zone axis precession electron diffraction (PED) and tomography in reciprocal space. Both methods enable to reduce importantly the multiple scattering, so that the reflection intensities can be used for structure determination by direct methods. The ferrite Sr25Fe30O77 belongs to a family of phases whose structures consist of an intergrowth of m perovskite layers with complex rocksalt type layers [1,2]. The compound of interest is the member m = 4 of this family and its structure has been solved by combining both electron diffraction methods cited above. This oxide crystallizes in an orthorhombic system with the sub-cell parameters a ≍ b ≍ 5.4 Å and c ≍ 42 Å in a F type lattice. The structure exhibits modulation along a axis with a modulation vector q = 2/5 a. The commensurate nature of the modulation enables to describe the structure in a supercell with the cell parameters a ≍ 27 Å, b ≍ 5.4 Å and c ≍ 42 Å. PED patterns were recorded in zone axis with a Spinning Star unit using a precession angle of 20. The intensities were extracted with CRISP software and the resulting dataset was then implemented in SIR2008 for structure solution. The tomography data collection, recorded by tilting manually every 0.5 degree from -30 to +30 degrees, was inserted in a "3D Electron Diffraction Tomography" software, which reconstructs the 3D reciprocal space and extracts automatically the reflection intensities. The intensity file was then used on SIR2008 for structure determination. In order to confirm and refine the structural model, a powder X-ray diffraction pattern was performed on a laboratory diffractometer with Cu Ka1 radiation. Cell parameters were refined with the WinPlotr and FullProf Softwares using both LeBail and Rietveld methods [3]. The structural model obtained with electron diffraction data was tried and confirmed as the correct structure by the Rietveld refinements.

Identifying almost identical phases by 3D electron diffraction

Magnetically frustrated materials have been the subject of many studies over the last decades. In search for a 3-dimensional quantum spin liquid, where quantum-mechanical fluctuations prevent magnetic order, different phases of stoichiometry Ba3NiSb2O9 have recently [1] been synthesized some of them at high pressure. Two of these phases are hexagonal. The hexagonal phases (space groups P63/mmc and P63mc, respectively) have different structures but cell parameters that differ by less than 1%. Similar phases have been obtained with Cu [2] or Co [3]. These phases are well distinguished by powder X-ray diffraction when they appear in sufficient quantity in a newly synthesized powder. When these phases are present only in minor quantities, which is a common situation when synthesizing new materials, only transmission electron microscopy can give structural information on a very local scale. However, the accuracy of unit cell parameter determination by electron diffraction (usually 1% or worse) and the identical extinction conditions for the 2 space groups don't permit to distinguish between the two phases. Convergent beam electron diffraction could show the difference between the centrosymmetric and non-centrosymmetric space groups provided a suitably oriented particle can be found. In this work we propose a different method of distinguishing structures in such complicated cases by actually solving the structure. Sufficient in-zone axis precession electron diffraction and/or electron diffraction tomography data can be obtained from any crystal regardless of its orientation. In the subsequent structure solution we have tested both space groups. The quality (or absence thereof) of the structure solutions obtained clearly makes it possible to distinguish between the two hexagonal structures.

A new Li-Mn-Ge-O phase solved by combining 3D electron diffraction methods

Pyroxene compounds are a common form of natural minerals and have been studied as such for a long time. More recently the research on quasi-one-dimensional magnetic and multiferroïc materials has renewed the interest in pyroxenes of the stoichiometry AMX2O6 (A = alkali metal, M = transition metal, X = Si or Ge), since the magnetic M3+ ions form chains. Chemical substitution on the A and M sites can change the magnetic coupling along these chains making this system a rich field for the exploration of new phases of interesting magnetic properties [1]. In this work we report the discovery of a new phase in the Li-Mn-Ge-O system. A HP-HT solid state reaction was performed on a mixture of nominal stoichiometry LiMnGe2O6 during 1 h at a temperature of 8500C and a pressure of 3 GPa in a belt press. Powder X-ray diffraction yielded a diffractogram that could not be indexed by known phases of this system. An electron diffraction study in a transmission electron microscope was conducted in order to identify any unknown phases. In the case of structures that promise interesting properties a more targeted synthesis can then be undertaken. For the purpose of this work, we studied one of several unknown phases in the powder in more detail. From standard selected area electron diffraction the unit cell was determined to be triclinic with cell parameters a = 2.51 nm, b = 1.30 nm, c = 1.30 nm, α = 96.00, β = 98.80and γ = 80.80. No comparable unit cell could be found in the databases neither in this system nor with different A, M or X ions. Intensities were recorded by in-zone axis precession electron diffraction and by electron diffraction tomography. Combining the data from both methods yielded the first model of the structure which we will present here.

Spin Axis Precession of LARES Measured by Satellite Laser Ranging

Satellite laser ranging (SLR) is an efficient technique to measure spin parameters of the fully passive satellite LARES. Analysis of the laser range measurements gives information about the spin rate of the spacecraft and the orientation of its spin axis. A frequency analysis applied to the SLR data indicates an exponential increase of the satellite's spin period: T = 11.7612 ·exp(0.00293327 ·D) , RMS = 0.115 s, where D is in days since launch. The initial spin period of LARES is calculated from the spin observations during the first 30 days after launch and is equal to T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 11.7131, RMS = 0.073 s. The spin axis of the satellite is precessing around the initial coordinates of right ascension RA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">initial</sub> = 186.5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , RMS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RA</sub> = 3.1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , and Declination Decinitial = - 73.0 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> , RMS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dec</sub> = 0.7 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> (J2000 inertial reference frame), with a period of 211.7 days. The precession of the spin axis may be responsible for the observed oscillation of the slowing down rate: the spin half-life period (the time after which the spin period has doubled) varies between 209 and 267 days. The measured spin parameters of LARES are compared-and show good agreement-with the theoretical predictions given by the satellite spin model. Information about the spin parameters of LARES is necessary for the accurate modeling of the forces and torques that are affecting the orbital motion of the satellite.