Small Angular Momentum Research Articles

Effects of pairing correlation on the quasiparticle resonance in neutron-rich Ca isotopes

We investigated the effects of the pairing correlation on the quasiparticle resonant energy and width in the neutron-rich Ca isotopes by using the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov theory with Green's function method. The resonant energy and width can be read from three kinds of quasiparticle spectra, including the quasiparticle-state probability density, the occupation probability density, and the pair probability density. The results read from different quasiparticle spectra calculated with the same potential are exactly the same for the narrow resonances, while for the broad resonances, the difference among the results are relatively larger. From the comparison between the quasiparticle-state probability density calculated with and without the pairing field, we could separate the effect only from the pairing correlation on the quasiparticle resonances. We found that the pairing correlation can increase the resonant energy and width for both the hole-like and particle-like quasiparticle resonances. And this increase is larger when the state is closer to the Fermi energy, especially for the particle-like quasiparticle resonance originated from the unbound single-particle states with smaller angular momentum $l$ in weakly bound nucleus.

Manifold path selection steering law for pyramid-type single-gimbal control moment gyros

The properties of singularities for pyramid-type single-gimbal control moment gyro (SGCMG) configuration are investigated in this paper. Manifold theory is applied to the SGCMG system and singular surfaces are classified by passability and directionality. A terminal domain is introduced as a small angular momentum space wrapped by internal elliptic singular surfaces and intersected hyperbolic singular surfaces. The hyperbolic singular surfaces in a terminal domain can provide the SGCMG system with a chance to select a manifold path containing no internal elliptic singularity. Thereafter, a manifold path selection (MPS) steering law based on a modified gradient method is proposed, which can achieve internal elliptic singularity avoidance without introducing torque errors. Compared with the other two steering laws, the effectiveness of the proposed method is demonstrated using attitude maneuver examples.

A Local Energy Estimate for Wave Equations on Metrics Asymptotically Close to Kerr

In this article we prove a local energy estimate for the linear wave equation on metrics with slow decay to a Kerr metric with small angular momentum. As an application, we study the quasilinear wave equation $\Box_{g(u, t, x)} u = 0$ where the metric $g(u, t, x)$ is close (and asymptotically equal)to a Kerr metric with small angular momentum $g(0,t,x)$. Under suitable assumptions on the metric coefficients, and assuming that the initial data for $u$ is small enough, we prove global existence and decay of the solution $u$.

Episodic accretion onto a protostar

AbstractWe introduce hydrodynamic simulations in which a protostar captures a cloudlet with a relatively small angular momentum. The cloudlet accretes onto the protostar and perturbs the gas disk rotating around the protostar. This cloudlet capture can reproduce some features observed in the molecular emission lines from TMC-1A. First, the cloudlet can reproduce the blue asymmetry observed in the CS emission. Second, the cloudlet can explain the slow infall observed in the C18O emission. Third, the impact of the cloudlet can explain the offset of the SO emission from the disk center. We also argue that a warm gas should confine the cloudlet through pressure. A protostar may obtain substantial mass by capturing cloudlets.

New energy levels of atomic lanthanum with small total angular momentum quantum number discovered by laser spectroscopic methods in the near IR

Optogalvanic spectroscopy as well as laser-induced fluorescence spectroscopy were applied in order to find new energy levels of atomic lanthanum. A hollow-cathode lamp and a tuneable continuous wave titanium-sapphire laser in the wavelength range from 750 nm to 850 nm were used for the measurements. Three energy levels of even parity with small values of total angular momentum quantum number J were discovered: 38 519.18 cm−1with J=1/2,40 392.80 cm−1with J=3/2,and 42 191.24 cm−1with J=3/2. The existence of these three levels was confirmed by laser excitations of several spectral lines as well as by spectral lines from a Fourier transform spectrum. Magnetic dipole hyperfine structure constants of the three new levels were determined from fits of the experimental spectra of the laser lines.

Описание сценария развития протогалактик с малыми угловыми моментами через каскадную фрагментацию с образованием протоскоплений и протозвезд на основе теории графов

The process of proto galaxies development is considered in the period of Universe cooling, when their masses are equal to the Jeans values. As a result of further cooling, the proto systems are subjected to the cascade fragmentation mechanism under which the more and more new smaller fragments are formed. Primary fragments are future galaxies (the upper limit of the mass of fragments falls within the mass range of galaxies), the ancestors of future star clusters, stars and sub stars form in the secondary fragmentation wave. In order to describe cascade fragmentation in proto systems with an extremely small angular momentum, a directed graph is constructed based on a general idea about the evolution of stellar systems. Star formation efficiency evaluations are carried out for proto systems, which determined by power-law mass spectra and the probabilities of key events are calculated. The fractional contents of the substance leaving for the formation of a new generation of stars and sub stars are calculated, depending on the μ-th star formation cycle (for its total number N). The dependence of the mass fraction transferred from the proto system to the system is presented in graphical form as a function of the fragments number N. Four options of the evolution of stellar systems such as galaxies are obtained, which are described by mass spectra with different exponents at the first and second stages of evolution. It is shown that, depending on the evolutionary scenario determined by the combination of mass spectra at the first and second stages of evolution, galaxies at the final stage of evolution may have different populations. According to one of the scenarios, galaxies should contain stellar composition limited by the masses of dwarf stars (≤ 0.8 M⊙). For the calculated maximum value Nmax ≈ 70 and the time of one fragmentation cycle, which occurs during one-star star formation in stellar clusters of galaxies ~ 107 years, it is expected that the time of complete gas depletion in stellar systems such as elliptical galaxies will be ~ 7•109 years. Considering that the characteristic time for the beginning of the formation of galaxies is ≈ 12•109 years, the obtained result explains satisfactorily the absence of star formation in elliptical galaxies over the past 5 billion years. Further development of research in this direction shows that it possible to understand the causes of differences in the composition of populations of various types of galaxies.

A projection-based controller for fast spacecraft detumbling using magnetic actuation

Magnetic control has been used for decades for spacecraft detumbling, i.e., to bring a spacecraft to a final condition with a sufficiently small angular momentum after separation from the launcher. This task is typically achieved by controllers based on the so-called b-dot principle, which stands out thanks to its simplicity, reliability and ease of on-board implementation. In this paper, we first review existing control methods and study their convergence properties with tools borrowed from general averaging theory, which allows addressing in an accurate manner the time-varying nature of magnetic actuation. Then, some effort is devoted to showing the performance limitations of existing controllers for which increasing the gain too much deteriorates the convergence rate. To overcome this issue, a novel projection-based control law with a state-dependent time-varying gain is presented. By means of Lyapunov arguments for non-autonomous systems, we prove that the proposed controller guarantees that the spacecraft angular momentum converges exponentially fast to zero for all initial conditions, robustly with respect to sufficiently small uncertainties in the inertia matrix, and that the closed-loop solutions are globally uniformly ultimately bounded in the presence of exogenous bounded disturbances. Several numerical simulations have been carried out by referring to realistic detumbling scenarios to show the performance improvement with respect to existing controllers.

Effect of Trunk Swinging Behaviors on Planar Bipedal Walking with an Upper Body on Gentle Slope

Bipedal walking locomotion is one of the characteristics of human behavior. Both the lower body and the upper body (trunk) behaviors affect walking characteristics. To achieve a suitable gait, it is important to understand the effect of the trunk behavior. Therefore, in this paper, the effects of three types of trunk swinging behavior on planar bipedal gait in a model with an upper body – forward swinging, backward swinging, and no swinging – were evaluated using numerical simulations. To reduce control inputs and reflect the effect of upper body behavior, an underactuated bipedal walker without knee joints was adopted. This walker walked down a gentle slope using only hip actuation between the stance leg and the trunk. As a result, unique gait characteristics that depended on the direction of the trunk swinging behavior were found, including a longer step length and a lower-frequency gait with forward trunk swinging behavior and a shorter step length and higher-frequency gait with smaller angular momentum with backward trunk swinging behavior.

Chaotic Rotations of a Rigid Ellipsoidal Body Exhibiting Spin-Orbit Misalignment in a Periodic Orbit

We study chaotic rotations of a rigid ellipsoidal body due to the effects of gravitational torques, in the case where this body exhibits spin-orbit misalignment. After first deriving a simple model of a rigid ellipsoid of uniform mass distribution with principal axis of rotation directed slightly out of the orbital plane, we prove using the Melnikov method that this perturbation is sufficient to excite the ellipsoid to chaotically rotate for a circular orbit. We further verify this analytical result with numerical time series and Poincaré sections for circular orbits. We then use numerical simulations to demonstrate that elliptical orbits provide further pathways to chaos. Our primary finding is that increasing the degree of spin-orbit misalignment will increase the prevalence of initial conditions leading to chaotic dynamics, for elliptical bodies on both circular and elliptical orbits. Indeed, our results suggest that chaotic rotation of elongated bodies exhibiting spin-orbit misalignment is somewhat common for large enough deviation of the principal axis of rotation from the normal to the orbital plane, provided the rigid body lacks rotational symmetry around its spin-axis and, furthermore, exhibits sufficiently small angular momentum so that the effects of gravitational torques are nontrivial.

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Greens function method.Taking the weakly bound nucleus $^{66}$Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared.For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum.By switching off the pairing potential and/or the Hartree-Fock (HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential.The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here, especially for the partial waves with small angular momentum $\ell$.

Applications of Schauder’s fixed point theorem to singular radially symmetric systems

We study the existence of periodic orbits of radially symmetric systems with a repulsive singularity. We show that such a system has a family of orbits rotating around the origin with small angular momentum. Our proofs are based on the use of topological degree theory and Schauder’s fixed point theorem.

Existence of the Blandford-Znajek monopole for a slowly rotating Kerr black hole

The Blandford-Znajek monopole is a conjectured solution of force-free electrodynamics in the vicinity of a slowly rotating Kerr black hole, supposedly defined as a perturbation in small angular momentum. It is used to argue for the extraction of energy from rotating black holes by the Blandford-Znajek process. We set up a careful analysis of the perturbative definition of the Blandford-Znajek monopole, showing in particular that the regime in which it is defined allows to use the technique of matched asymptotic expansions. Our conclusion is that the Blandford-Znajek monopole, as it is defined, is not consistent with demanding physically reasonable boundary conditions far away from the event horizon. This puts into question the existence of the Blandford-Znajek monopole, at least in the limit of slow rotation of the Kerr black hole.

Asymptotics for the wave equation on differential forms on Kerr–de Sitter space

We study asymptotics for solutions of Maxwell's equations, in fact of the Hodge-de Rham equation $(d+\delta)u=0$ without restriction on the form degree, on a geometric class of stationary spacetimes with a warped product type structure (without any symmetry assumptions), which in particular include Schwarzschild-de Sitter spaces of all spacetime dimensions $n\geq 4$. We prove that solutions decay exponentially to $0$ or to stationary states in every form degree, and give an interpretation of the stationary states in terms of cohomological information of the spacetime. We also study the wave equation on differential forms and in particular prove analogous results on Schwarzschild-de Sitter spacetimes. We demonstrate the stability of our analysis and deduce asymptotics and decay for solutions of Maxwell's equations, the Hodge-de Rham equation and the wave equation on differential forms on Kerr-de Sitter spacetimes with small angular momentum.

Initial angular momentum and flow in high energy nuclear collisions

We study the transfer of angular momentum in high energy nuclear collisions from the colliding nuclei to the region around midrapidity, using the classical approximation of the Color Glass Condensate (CGC) picture. We find that the angular momentum shortly after the collision (up to times ~ 1/Q_s, where Q_s is the saturation scale) is carried by the "beta-type" flow of the initial classical gluon field, introduced by some of us earlier. beta^i ~ mu_1 nabla^i mu_2 - mu_2 nabla^i mu_1 (i=1,2) describes the rapidity-odd transverse energy flow and emerges from Gauss' Law for gluon fields. Here mu_1 and mu_2 are the averaged color charge fluctuation densities in the two nuclei, respectively. Interestingly, strong coupling calculations using AdS/CFT techniques also find an energy flow term featuring this particular combination of nuclear densities. In classical CGC the order of magnitude of the initial angular momentum per rapidity in the reaction plane, at a time 1/Q_s, is |dL_2/d eta| ~ R_A/Q_s^3 epsilon_0/2 at midrapidity, where R_A is the nuclear radius, and epsilon_0 is the average initial energy density. This result emerges as a cancellation between a vortex of energy flow in the reaction plane aligned with the total angular momentum, and energy shear flow opposed to it. We discuss in detail the process of matching classical Yang-Mills results to fluid dynamics. We will argue that dissipative corrections should not be discarded to ensure that macroscopic conservation laws, e.g. for angular momentum, hold. Viscous fluid dynamics tends to dissipate the shear flow contribution that carries angular momentum in boost-invariant fluid systems. This leads to small residual angular momentum around midrapidity at late times for collisions at high energies.

Echoes of Kerr-like wormholes

Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal frequencies of the wormhole, which we characterize. We illustrate this in the static Damour-Solodukhin wormhole and in a new, rotating generalization that approximates a Kerr black hole outside the throat. Rotation gives rise to a potential with an intermediate plateau region that breaks the degeneracy of the quasinormal frequencies. Rotation also leads to late-time instabilities which, however, fade away for small angular momentum.

Pairing correlations and symmetries in odd-A nuclei.

The pairing correlations in odd-A nuclei are analyzed in the mean field approximation and beyond. In particular the role of symmetry conservation is investigated. We find that particle number projection after the variation (PN-PAV) has little effect on the pairing correlations specially in the weak pairing regime. This is in contrast to the variation after particle number projection (PN-VAP) approach where a strong effect is found. The situation is specially critical in odd nuclei because the pairing correlations vanish due to the blocking effect and the Hartree-Fock-Bogoliubov wave function collapses to the Hartree-Fock one. The PN-VAP, however, handles perfectly the exact blocking providing highly correlated wave functions. The role of the angular momentum projection is studied only in the PAV approach. We find small changes of the pairing correlation, at least at small angular momentum. In the calculations we use the Gogny interaction well suited to this kind of studies.

Hot Accretion onto Black Holes with Outflow

Classic Bondi accretion flow can be generalized to rotating viscous accretion flow. Study of hot accretion flow onto black holes show that its physical charateristics change from Bondi-like for small gas angular momentum to disk-like for Keperian gas angular momentum. Especially, the mass accretion rate divided by the Bondi accretion rate is proportional to the viscosity parameter alpha and inversely proportional to the gas angular momentum divided by the Keplerian angular momentum at the Bondi radius for gas angular momentum comparable to the Keplerian value. The possible presence of outflow will increase the mass inflow rate at the Bondi radius but decrease the mass accretion rate across the black hole horizon by many orders of magnitude. This implies that the growth history of supermassive black holes and their coevolution with host galaxies will be dramatically changed when the accreted gas has angular momentum or develops an outflow.

One thousand and one bubbles

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.

Uniqueness of Kerr–Newman–de Sitter Black Holes with Small Angular Momenta

We show that a stationary solution of the Einstein–Maxwell equations which is close to a non-degenerate Reissner–Nordstrom–de Sitter solution is in fact equal to a slowly rotating Kerr–Newman–de Sitter solution. The proof uses the nonlinear stability of the Kerr–Newman–de Sitter family of black holes with small angular momenta, recently established by the author, together with an extension argument for Killing vector fields. Our black hole uniqueness result only requires the solution to have high but finite regularity; in particular, we do not make any analyticity assumptions.

Spin Interaction under the Collision of Two Kerr-(Anti-)de Sitter Black Holes

We investigate herein the spin interaction during collisions between Kerr-(anti-)de Sitter black holes. The spin interaction potential depends on the relative rotation directions of the black holes, and this potential can be released as gravitational radiation upon collision. The energy of the radiation depends on the cosmological constant and corresponds to the spin interaction potential in the limit that one of the black holes has negligibly small mass and angular momentum. We then determine the approximate overall behaviors of the upper bounds on the radiation using thermodynamics. The results indicate that the spin interaction can consistently contribute to the radiation. In addition, the radiation depends on the stability of the black hole produced by the collision.