Null Rotation Research Articles

The Flow-geodesic Curvature and the Flow-evolute of Hyperbolic Plane Curves

We introduce a new type of curvature function and associated evolute curve for a given curve in the hyperboloid model of plane hyperbolic geometry. A special attention is devoted to the examples, particularly to a horocycle provided by the null Lorentzian rotation.

Chronology of the chemical enrichment of the old Galactic stellar populations

Context. Over its history, the Milky Way has accreted several smaller satellite galaxies. These mergers added stars and gas to the Galaxy and affected the properties of the pre-existing stellar populations. Stellar chemical abundances and ages are needed to establish the chronological order of events that occur before, during, and after such mergers. Aims. We report the precise ages (∼6.5%) and chemical abundances for the TITANS, a sample of old metal-poor dwarfs and subgiants with accurate atmospheric parameters. We also obtain ages with an average precision of 10% for a selected sample of dwarf stars from the GALAH survey. We use these stars, located within ∼1 kiloparsec of the Sun, to analyse the chronology of the chemical evolution of in situ and accreted metal-poor stellar populations. Methods. We determined ages via isochrone fitting. For the TITANS, we determined Mg, Si, Ca, Ti, Ni, Ba, and Eu abundances using spectrum synthesis. The [Mg/Fe] abundances of the GALAH stars were re-scaled to be consistent with the abundances of the TITANS. We separated stellar populations by primarily employing chemical abundances and orbits. Results. We find that star formation in the so-called Gaia-Enceladus or Gaia-Sausage galaxy, the last major system to merge with the Milky Way, lasted at least 3 billion years and got truncated 9.6 ± 0.2 billion years ago. This marks with a very high level of precision the last stage of its merging process. We also identified stars of a heated metal-poor in-situ population with virtually null net rotation, probably disturbed by several of the early Milky Way mergers. We show that this population is more metal-rich than Gaia-Enceladus at any moment in time. Conclusions. The sequence of events uncovered in our analysis supports the hypothesis that Gaia-Enceladus truncated the formation of the high-α disc and caused the gas infall that forms the low-α disc.

Spacetimes with continuous linear isotropies III: null rotations

It is shown that in many of the possible cases local null rotation invariance of the curvature and its first derivatives is sufficient to ensure that there is an isometry group G_r with rge 3 acting on (a neighbourhood of) the spacetime and containing a null rotation isotropy. The exceptions where invariance of the second derivatives is additionally required to ensure this conclusion are Petrov type N Einstein spacetimes, spacetimes containing “pure radiation” (a Ricci tensor of Segre type [(11,2)]), and conformally flat spacetimes with a Ricci tensor of Segre type [1(11,1)] (a “tachyon fluid”).

Holographic integral geometry with time dependence

We write down Crofton formulas — expressions that compute lengths of space- like curves in asymptotically AdS3 geometries as integrals over kinematic space — which apply when the curve and/or the background spacetime is time-dependent. Relative to their static predecessor, the time-dependent Crofton formulas display several new features, whose origin is the local null rotation symmetry of the bulk geometry. In pure AdS3 where null rotations are global symmetries, the Crofton formulas simplify and become integrals over the null planes, which intersect the bulk curve.

Single-Pulse TMS over the Parietal Cortex Does Not Impair Sensorimotor Perturbation-Induced Changes in Motor Commands.

Intermittent exposure to a sensorimotor perturbation, such as a visuomotor rotation, is known to cause a directional bias on the subsequent movement that opposes the previously experienced perturbation. To date, it is unclear whether the parietal cortex is causally involved in this postperturbation movement bias. In a recent electroencephalogram study, Savoie et al. (2018) observed increased parietal activity in response to an intermittent visuomotor perturbation, raising the possibility that the parietal cortex could subserve this change in motor behavior. The goal of the present study was to causally test this hypothesis. Human participants (N = 28) reached toward one of two visual targets located on either side of a fixation point, while being pseudorandomly submitted to a visuomotor rotation. On half of all rotation trials, single-pulse transcranial magnetic stimulation (TMS) was applied over the right (N = 14) or left (N = 14) parietal cortex 150 ms after visual feedback provision. To determine whether TMS influenced the postperturbation bias, reach direction was compared on trials that followed rotation with (RS + 1) and without (R + 1) TMS. It was hypothesized that interfering with parietal activity would reduce the movement bias following rotated trials. Results revealed a significant and robust postrotation directional bias compared with both rotation and null rotation trials. Contrary to our hypothesis, however, neither left nor right parietal stimulation significantly impacted the postrotation bias. These data suggest that the parietal areas targeted here may not be critical for perturbation-induced motor output changes to emerge.

Principal configurations around umbilics of spacelike surfaces in null hypersurfaces of [formula omitted

We study the principal configurations around an isolated η-umbilical point on a generic spacelike surface S immersed in a null hypersurface M of Minkowski space R14 relative to a well-defined null vector field η orthogonal to the surface S. In the particular case of M being a null rotation hypersurface of R14 we also recover the local Darbouxian principal configurations around that kind of η-umbilical points.

Shearless bifurcation on symplectic maps of magnetic field lines in tokamaks with reversed current

We introduce two-dimensional symplectic maps to describe the Poincaré maps of magnetic field lines in large aspect ratio tokamak equilibria with reversed non-monotonic plasma current density profiles. For these maps, we investigate the effect of the symmetry breaking due to the toroidal correction with a peculiar invariant, namely, a magnetic surface with a null rotation number, enclosing a vanishing current. We find that this rotationless invariant surface is surrounded by many small island chains. Furthermore, near such invariant, the symmetry breaking gives rise to two magnetic shearless invariants surrounded by twin island chains. We also find chaotic lines adjacent to all the observed islands created by the considered structurally unstable equilibria.

Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space

We examine curvature properties of twisted surfaces with null rotation axis in Minkowski 3-space. That is, we study surfaces that arise when a planar curve is subject to two synchronized rotations, possibly at different speeds, one in its supporting plane and one of this supporting plane about an axis in the plane. Moreover, at least one of the two rotation axes is a null axis. As is clear from its construction, a twisted surface generalizes the concept of a surface of revolution. We classify flat, constant Gaussian curvature, minimal and constant mean curvature twisted surfaces with a null rotation axis. Aside from pseudospheres, pseudohyperbolic spaces and cones, we encounter B-scrolls in these classifications. The appearance of B-scrolls in these classifications is of course the result of the rotation about a null axis. As for the cones in the classification of flat twisted surfaces, introducing proper coordinates, we prove that they are determined by so-called Clelia curves. With a Clelia curve we mean a curve that has linear dependent spherical coordinates.

An extension of the Newman–Janis algorithm

The Newman–Janis algorithm is supplemented with a null rotation and applied to the tensors of the Reissner–Nordström spacetime to generate the metric, Maxwell, Ricci and Weyl tensors for the Kerr–Newman spacetime. This procedure also provides a mechanism whereby the Carter Killing tensor arises from the geodesic angular momentum tensor of the underlying Reissner–Nordström metric. The conformal Killing tensor in the Kerr–Newman spacetime is generated in a similar fashion. The extended algorithm is also applied to the Killing vectors of the Reissner–Nordström spacetime with interesting consequences. The Schwarzschild to Kerr transformation is a special case.

Null probability, dominance and rotation

New arguments against Bayesian regularity and an otherwise plausible domination principle are offered on the basis of rotational symmetry. The arguments against Bayesian regularity work in very general settings.

Geometry of massless cosmic strings

We study the geometry generated by a massless cosmic string. We find that this is given by a Riemann flat spacetime with a conical singularity along the world sheet of the string. The geometry of such a spacetime is completely fixed by the holonomy of a simple loop wrapping the conical singularity. In the case of a massless cosmic string, this holonomy is a null rotation or parabolic Lorentz transformation with a parabolic angle given by the linear energy density of the cosmic string. This description explicitly shows that there is no gravitational shockwave accompanying the massless cosmic string as has been suggested in the past. To illustrate the nonsingular nature of the surrounding geometry, we construct a metric for the massless cosmic string that is smooth everywhere outside the conical singularity.

Wideband Pattern Nulling With Multiarmed Spiral Antennas

The wideband modes of multiarmed spiral antennas are studied, with the goal of obtaining insight into their potential for stable pattern nulling over extremely wide bandwidths. Using the mode theory, it is found that for stable and extremely wideband operation, a maximum of N-2 nulls may be inserted into an N-armed spiral's pattern. Single and multiple null insertions are demonstrated numerically and experimentally, using three-, four-, and eight-armed spirals. Spiral mode theory is also utilized to determine limitations imposed by the unequal mode impedances of the multiarmed spiral. Techniques for compensation of frequency-dependent null rotation are also discussed, where it is shown that a simple delay-line compensation technique is satisfactory for stabilizing the null locations over modest bandwidths. It is also shown that the number of nulls that can be practically inserted in the pattern is limited not only by the number of arms, but also by the size of the antenna.

Gyrokinetic simulations with external resonant magnetic perturbations: Island torque and nonambipolar transport with plasma rotation

Static external resonant magnetic field perturbations (RMPs) have been added to the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comp. Phys. 186, 545 (2003)]. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr, and the corresponding j→×B→ plasma torque (density) R[jrBp/c], induced by magnetic islands that break the toroidal symmetry of a tokamak. This extends the previous GYRO formulation for the transport of toroidal angular momentum (TAM) [R. E. Waltz, G. M. Staebler, J. Candy, and F. L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)]. The focus is on electrostatic full torus radial slice simulations of externally induced q=m/n=6/3 islands with widths 5% of the minor radius or about 20 ion gyroradii. Up to moderately strong E×B rotation, the island torque scales with the radial electric field at the resonant surface Er, the island width w, and the intensity I of the high-n micro-turbulence, as ErwI. The radial current inside the island is carried (entirely in the n=3 component) and almost entirely by the ion E×B flux, since the electron E×B and magnetic flutter particle fluxes are cancelled. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that while the expected magnetic braking of the toroidal plasma rotation occurs at strong co- and counter-current rotation, at null toroidal rotation, there is a small co-directed magnetic acceleration up to the small diamagnetic (ion pressure gradient driven) co-rotation corresponding to the zero Er and null torque. This could be called the residual stress from an externally induced island. At zero Er, the only effect is the expected partial flattening of the electron temperature gradient within the island. Finite-beta GYRO simulations demonstrate almost complete RMP field screening and n=3 mode unlocking at strong Er.

Bending of the Bolivian orocline and growth of the central Andean plateau: Paleomagnetic and structural constraints from the Eastern Cordillera (22–24°S, NW Argentina)

We report new paleomagnetic and structural data from late Cretaceous to Mio‐Pliocene continental sandy/silty sedimentary rocks from the Eastern Cordillera (central Andes). Here, N–S to NNE–SSW ridges hosting Paleozoic basement and upper Cretaceous continental red beds overthrust thick adjacent Cenozoic basins. Pretilting (and likely primary) reliable directions gathered at 15 sites document 45.9° ± 9.4, 30.1° ± 23.9°, and 15.4° ± 19.3° clockwise (CW) rotations with respect to South America occurring after the late Cretaceous (∼80 Ma), Oligo‐Miocene (20–30 Ma), and late Miocene‐Pliocene (5–10 Ma), respectively. Conversely, four upper Cretaceous sites from the walls of a N–S left‐lateral strike‐slip fault (Yavi–Abra Pampa fault) yield a null rotation. About 20 km to the west, flower structures and subvertical syntectonic strata dated at 14.26 ± 0.19 Ma are exposed along the subparallel Abra Moreta left‐lateral strike‐slip fault. Relying on data from the literature on the period when deformation began, we suggest that since Eo‐Oligocene times (30–40 Ma) the Eastern Cordillera has undergone a regional CW rotation of 40°–50°, synchronous with crustal shortening and large‐scale bending of the Andean salient. The CW rotation is possibly still active today, as documented by regional GPS data from the Andes. Since ∼15 Ma ago, the activity of N–S left‐lateral strike‐slip faults induced counterclockwise rotations along the fault zone, locally annulling the regional CW rotation. In agreement with a previous model, we speculate that mid‐Miocene strike‐slip activity accommodated the progressive southward spreading of the Altiplano‐Puna high‐altitude plateau, laterally migrating from the overthickened crustal region of the salient apex.

New half supersymmetric solutions of the heterotic string

We describe all supersymmetric solutions of the heterotic string which preserve eight supersymmetries and show that these are distinguished by the holonomy, , of the connection, , with skew-symmetric torsion. The solutions are principal bundles over a four-dimensional hyper-Kähler manifold equipped with an anti-self-dual connection and fibre group G which has a Lie algebra, or . Some of the solutions have the interpretation as 5-branes wrapped on G with transverse space any hyper-Kähler four-dimensional manifold. We construct new solutions for and show that they are characterized by three integers and have continuous moduli. There is also a smooth family in this class with one asymptotic region and the dilaton is bounded everywhere on the spacetime. We also demonstrate that the worldvolume theory of the backgrounds with holonomy SU(2) can be understood in terms of gauged WZW models for which the gauge fields are composite. The solutions are superpositions of fundamental strings and pp-waves in flat space, which may also include a null rotation. The heterotic string backgrounds which preserve eight supersymmetries are Lorentzian group manifolds.

Two-dimensional gravity with a dynamical aether

We investigate the two-dimensional behavior of gravity coupled to a dynamical unit timelike vector field, i.e. ``Einstein-aether theory.'' The classical solutions of this theory in two dimensions depend on one coupling constant. When this coupling is positive the only solutions are (i) flat spacetime with constant aether, (ii) de Sitter or anti-de Sitter spacetimes with a uniformly accelerated unit vector invariant under a two-dimensional subgroup of $SO(2,1)$ generated by a boost and a null rotation, and (iii) a nonconstant curvature spacetime that has no Killing symmetries and contains singularities. In this case the sign of the curvature is determined by whether the coupling is less or greater than one. When instead the coupling is negative only solutions (i) and (iii) are present. This classical study of the behavior of Einstein-aether theory in $1+1$ dimensions may provide a starting point for further investigations into semiclassical and fully quantum toy models of quantum gravity with a dynamical preferred frame.

The geometry of null rotation identifications

The geometry of flat spacetime modded out by a null rotation (boost+rotation) is analysed. When embedding this quotient spacetime in String/M-theory, it still preserves one half of the original supersymmetries. Its connection with the BTZ black hole, supersymmetric dilatonic waves and one possible resolution of its singularity in terms of nullbranes are also discussed.

(Conformal) Killing Vectors in the Newman-Penrose Formalism

Finding (conformal) Killing vectors of a given metric can be a difficult task. This paper presents an efficient technique for finding Killing, homothetic, or even proper conformal Killing vectors in the Newman-Penrose (NP) formalism. Leaning on, and extending, results previously derived in the GHP formalism we show that the (conformal) Killing equations can be replaced by a set of equations involving the commutators of the Lie derivative with the four NP differential operators, applied to the four coordinates. It is crucial that these operators refer to a preferred tetrad relative to the (conformal) Killing vectors, a notion to be defined. The equations can then be readily solved for the Lie derivative of the coordinates, i.e. for the components of the (conformal) Killing vectors. Some of these equations become trivial if some coordinates are chosen intrinsically (where possible), i.e. if they are somehow tied to the Riemann tensor and its covariant derivatives. If part of the tetrad, i.e. part of null directions and gauge, can be defined intrinsically then that part is generally preferred relative to any Killing vector. This is also true relative to a homothetic vector or a proper conformal Killing vector provided we make a further restriction on that intrinsic part of the tetrad. If because of null isotropy or gauge isotropy, where part of the tetrad cannot even in principle be defined intrinsically, the tetrad is defined only up to (usually) one null rotation parameter and/or a gauge factor, then the NP-Lie equations become slightly more involved and must be solved for the Lie derivative of the null rotation parameter and/or of the gauge factor as well. However, the general method remains the same and is still much more efficient than conventional methods. Several explicit examples are given to illustrate the method.

Age of the Corsica–Sardinia rotation and Liguro–Provençal Basin spreading: new paleomagnetic and Ar/Ar evidence

The age of spreading of the Liguro–Provençal Basin is still poorly constrained due to the lack of boreholes penetrating the whole sedimentary sequence above the oceanic crust and the lack of a clear magnetic anomaly pattern. In the past, a consensus developed over a fast (20.5–19 Ma) spreading event, relying on old paleomagnetic data from Oligo–Miocene Sardinian volcanics showing a drift-related 30° counterclockwise (CCW) rotation. Here we report new paleomagnetic data from a 10-m-thick lower–middle Miocene marine sedimentary sequence from southwestern Sardinia. Ar/Ar dating of two volcanoclastic levels in the lower part of the sequence yields ages of 18.94±0.13 and 19.20±0.12 Ma (lower–mid Burdigalian). Sedimentary strata below the upper volcanic level document a 23.3±4.6° CCW rotation with respect to Europe, while younger strata rapidly evolve to null rotation values. A recent magnetic overprint can be excluded by several lines of evidence, particularly by the significant difference between the in situ paleomagnetic and geocentric axial dipole (GAD) field directions. In both the rotated and unrotated part of the section, only normal polarity directions were obtained. As the global magnetic polarity time scale (MPTS) documents several geomagnetic reversals in the Burdigalian, a continuous sedimentary record would imply that (unrealistically) the whole documented rotation occurred in few thousands years only. We conclude that the section contains one (or more) hiatus(es), and that the minimum age of the unrotated sediments above the volcanic levels is unconstrained. Typical back-arc basin spreading rates translate to a duration ≥3 Ma for the opening of the Liguro–Provençal Basin. Thus, spreading and rotation of Corsica–Sardinia ended no earlier than 16 Ma (early Langhian). A 16–19 Ma, spreading is corroborated by other evidences, such as the age of the breakup unconformity in Sardinia, the age of igneous rocks dredged west of Corsica, the heat flow in the Liguro–Provençal Basin, and recent paleomagnetic data from Sardinian sediments and volcanics. Since Corsica was still rotating/drifting eastward at 16 Ma, it presumably induced significant shortening to the east, in the Apennine belt. Therefore, the lower Miocene extensional basins in the northern Tyrrhenian Sea and margins can be interpreted as synorogenic “intra-wedge” basins due to the thickening and collapse of the northern Apennine wedge.

Interpretation and deperturbation of the Λ-type doubling in the a 3Π state of GaH

The unusual J dependence of the Λ doubling splitting that separates e and f levels in the a 3Π state of GaH has been interpreted using a deperturbation study carried out in an effective Hamiltonian point of view and based on a case (c) partition of the Hamiltonian: rather than limiting the zeroth-order part of the Hamiltonian to electronic and vibrational motions, spin-orbit interaction is also included, leaving outside just those effects linked with nuclear rotational motion. Thus the reasons for the peculiar behavior of the Λ splitting come out in a simple and appealing way. Essentially, with such a procedure, the variation with increasing rotation of the Λ-doubling splitting, i.e., the variations of the energy differences between e and f levels, are directly connected with fairly large differences between the rotational parameters (including mandatorily first and second order centrifugal distorsion) occurring in the off-diagonal Coriolis matrix elements within the 3Π block. To a lesser extent, smaller differences between the e and f rotational constants in the diagonal elements also contribute to the pattern of splittings. The consistency of the resulting values of the main fitted difference parameters (3Π0 e/f splitting at null rotation and first-order diagonal and off-diagonal rotational constant differences) is examined on the basis of experimental data on the one hand and new ab initio calculations on the other. Correct orders of magnitude are obtained although rotational constant differences but one are experimentally larger than expected theoretically from a model restricted to the four electronic states dissociating into ground state products.