Nonspherical Perturbations Research Articles

Oscillon spectroscopy

The sine-Gordon model in 3+1 dimensions is known to admit two oscillons of different energy and frequency but comparable lifetime. We show that the oscillon spectrum includes more spherically symmetric “states”. We identify new high-amplitude oscillons by allowing the field profile to have a number of nodes. For each number of nodes, we find 2 states with a comparable lifetime to the nodeless ones. Oscillons with nodes are, however, unstable to non-spherical perturbations and so their lifetime is significantly reduced. Interestingly, these states are seen to fragment into a collection of nodeless oscillons. The heavy nodeless oscillon is quite remarkable: despite its energy, it is stable against fragmentation. Moreover, it has considerably small oscillation frequency, meaning that it can be interpreted as a rather relativistic bound state.

A deformed IR: a new IR fixed point for four-dimensional holographic theories

In holography, the IR behavior of a quantum system at nonzero density is described by the near horizon geometry of an extremal charged black hole. It is commonly believed that for systems on S3, this near horizon geometry is AdS2 × S3. We show that this is not the case: generic static, nonspherical perturbations of AdS2 × S3 blow up at the horizon, showing that it is not a stable IR fixed point. We then construct a new near horizon geometry which is invariant under only SO(3) (and not SO(4)) symmetry and show that it is stable to SO(3)-preserving perturbations (but not in general). We also show that an open set of nonextremal, SO(3)-invariant charged black holes develop this new near horizon geometry in the limit T → 0. Our new IR geometry still has AdS2 symmetry, but it is warped over a deformed sphere. We also construct many other near horizon geometries, including some with no rotational symmetries, but expect them all to be unstable IR fixed points.

Stability Analysis on the Moon’s Rotation in a Perturbed Binary Asteroid

Numerical calculation provides essential tools for deep space exploration, which are indispensable to mission design and planetary research. In a specific case of binary asteroid defense such as the DART mission, an accurate understanding of the possible dynamical responses and the system’s stability and engineers’ prerequisite. In this paper, we discuss the numeric techniques for tracking the year-long motion of the secondary after being perturbed, based upon which its rotational stability is analyzed. For long-term simulations, we compared the performances of several integrating schemes in the scenario of a post-impact full two-body system, including low- and high-order Runge–Kutta methods, and a symplectic integrator that combines the finite element method with a symplectic integral format. For rotational stability analysis of the secondary, we focus on the rotation of the secondary around its long-axis. We calculated a linearised error propagation matrix and found that, in the case of tidal locking of the secondary to the primary, the rotation is stable; as the perturbation amplitude of the spin angular velocity of the secondary increases, the rotation will lose stability and will be prone to being unstable in the long-axis direction of the secondary. Furthermore, we investigated the one-year-long influences of the non-spherical perturbations of the primary and the secondary.

Lifetime Extension of Ultra Low-Altitude Lunar Spacecraft with Low-Thrust Propulsion System

Due to the non-spherical perturbation of the Moon, the lifetime of ultra low-altitude Lunar spacecraft may be quite short. In this paper, we analyze the lifetime of about 50 km-altitude Lunar spacecraft with different initial orbit. The lifetime in low inclination orbits is much shorter than the ones in the near polar orbits. To extend the lifetime and keep the spacecraft in an appropriate range, an orbit maintenance strategy based on low-thrust propulsion system is proposed. The influence of the orbit initial conditions (e.g., semi-major axis, inclination, right ascension of the ascending node) on lifetime extension are discussed and the effect of the low-thrust magnitude in orbit maintenance is analyzed. According to the numerical simulation results, the lifetime of about 50 km-altitude 100 kg Lunar spacecraft with 10 kg fuel and 20 mN thruster can be extended from 7.958 days to over a 109.1725 days, which demonstrates the effectiveness of the strategy. Furthermore, a global perspective for ultra low-altitude Lunar spacecraft lifetime extension problem is provided in this paper, which can be applied to Moon mission designs extensively.

Natural landing dynamics near the secondary in single-tidal-locked binary asteroids

The hopping dynamics of a lander in single-tidal-locked binary asteroid systems is explored. A coupled orbit-attitude dynamical model of the lander in the body-fixed frame of the secondary is established by considering the non-spherical perturbations from the two bodies. As an approximate model, the binary system is treated as an oblate spheroid-ellipsoid system. Lander deployment to the secondary is numerically simulated to examine the motion characteristics by varying the primary mass and system period. Two dynamical parameters related to the characteristic properties of the binary system are introduced to reveal the intrinsic reasons for different landing trajectory evolutions. These two dynamical parameters can effectively provide a measure to estimate the hopping evolution in different binary systems.

Frequency Separation Control for Drag-Free Satellite With Frequency-Domain Constraints

For a drag-free satellite, one core technology required to achieve the mission requirements is drag-free control. The purpose of control is to offset the interference such as sunlight pressure, gravitational gradients of Earth and Moon, nonspherical perturbation, etc. Currently, the drag-free controller design is mainly aimed at the full frequency band. This will inevitably mix the control signal into the scientific measurement signal, thereby interfering with the processing of scientific data. Besides, the control at the full frequency band will increase fuel consumption. To solve the above problems, this article presented the controller design method for a drag-free satellite with scientific measurement constraints, which covers motion model establishing, coordinate axis decomposition, frequency separation control strategy formulation, H∞ mixed sensitivity controller design, controller stability analysis, and performance results.

Dynamical ℓ -boson stars: Generic stability and evidence for nonspherical solutions

$\ell$-boson stars are static, spherical, multi-field self-gravitating solitons. They are asymptotically flat, finite energy solutions of Einstein's gravity minimally coupled to an odd number of massive, complex scalar fields. A previous study assessed the stability of $\ell$-boson stars under spherical perturbations, finding that there are both stable and unstable branches of solutions, as for single-field boson stars ($\ell=0$). In this work we probe the stability of $\ell$-boson stars against non-spherical perturbations by performing numerical evolutions of the Einstein-Klein-Gordon system, with a 3D code. For the timescales explored, the $\ell$-boson stars belonging to the spherical stable branch do not exhibit measurable growing modes. We find, however, evidence of zero modes; that is, non-spherical perturbations that neither grow nor decay. This suggests the branching off towards a larger family of equilibrium solutions: we conjecture that $\ell$-boson stars are the enhanced isometry point of a larger family of static (and possibly stationary), non-spherical multi-field self-gravitating solitons.

Shape stability of a gas cavity surrounded by linear and nonlinear elastic media

A number of recent medical procedures such as histotripsy rely on inertially-dominated oscillating gas cavities (i.e. bubbles) inside soft tissue. As a first approximation, soft tissue can be modeled by linear or nonlinear elasticity models and the equations describing bubble dynamics in such media have been derived in previous works. However, these models assume that the bubble remains perfectly spherical at all times for all initial conditions, which is in contradiction with any practical setting or experiments. Ignoring non-spherical behavior could for instance lead to inaccurate predictions for the extent of tissue damage generated during these procedures. The use of such models in practice thus requires one to predict departures from spherical behavior. In this article, departures from sphericity are expressed by non-spherical perturbations. Two sets of equations describing the dynamics of all non-spherical modes are derived for a bubble surrounded by a medium described using linear elasticity and Neo-Hookean hyperelasticity. For both elasticity models and for given initial conditions, bubble shape stability is shown to be controlled by five dimensionless parameters: the Weber number We, the Cauchy number Ca, the dimensionless vapor pressure inside the bubble, the dimensionless initial non-condensible gas pressure inside the bubble and the dimensionless far-field pressure. A growth criterion indicating whether the amplitude of a given non-spherical mode increases exponentially with time is also derived for both models. Bubble shape stability is then compared for both elasticity models during a Rayleigh collapse. Overall, it is found that shape stability is promoted when the shear modulus of the surrounding medium is increased and when the initial step increase in the external pressure is reduced. It is also established that the bubble shape during a Rayleigh collapse is stable over a much wider range of parameters for a surrounding medium described using Neo-Hookean hyperelasticity as opposed to linear elasticity with a similar shear modulus. This could lead to the overprediction of the occurrence of bubble shape instabilities if the surrounding medium is described using linear elasticity, which is particularly problematic during violent bubble collapse.

Observability analysis of autonomous navigation using inter-satellite range: An orbital dynamics perspective

This paper focuses on the observability of the autonomous navigation for multi-satellite systems using only inter-satellite range (ISR), especially under complicated orbital dynamical model. According to previous studies, the autonomous is unobservable because the Right Ascension of Ascending Node (RAAN) can be determined, which is derived under reduced dynamics model only considering J2 non-spherical perturbation. In order to analyze this observability issue further, the ISR measurement model with respect to orbital elements and the orbital dynamical model considering several kinds of perturbations are built. Through calculating the value of the partial derivative of ISR with respect to the RAAN, we find that the RAAN is observable under complicated dynamical model considering the non-spherical, the solar pressure and third-body perturbations. This is because that the solar pressure and third-body perturbations make the RAAN change rates of satellites different, so the overall rotation does not exist. These conclusions are verified by simulation cases. Furthermore, the simulation results show that the perturbation model error has remarkable impact on the RAAN estimation accuracy.

Symplectic analysis on orbit-attitude coupling dynamic problem of spatial rigid rod

An orbit-attitude coupling dynamic model for the spatial rigid rod that is abstracted from the large-stiffness slender components widely used in spatial structures is established, and the symplectic method is used to estimate the validity of the dynamic model by analyzing the coupling dynamic behaviors of the rod in this work. Based on the Hamiltonian variational principle, the orbit-attitude dynamic model of the spatial rigid rod is proposed, and the canonical form of the model is presented first. Then, the symplectic Runge–Kutta method is developed, and the structure-preserving properties of the canonical form, including the conservation law of energy and conservative property in the phase space, are investigated to illustrate the validity of the numerical results obtained by the symplectic Runge–Kutta method subsequently. Finally, the effects of the nonspherical perturbations of the Earth on the coupling dynamic behaviors are investigated numerically. From the simulation results, it can be concluded that the main orbit-attitude coupling dynamic behaviors of the spatial large-stiffness slender component excited by the nonspherical perturbation can be described by the proposed dynamic model ignoring the deformation as well as the transverse vibration of the slender component, which provides an approach for simplifying rapid dynamic analysis on the spatial large-stiffness slender component. In addition, the validity and the structure-preserving properties of the symplectic Runge–Kutta method for the orbit-attitude coupling dynamic problem of the spatial rigid rod are also illustrated.

Characterizing space debris longitude-dependent distribution based on RAAN perturbation rate

The space debris environment is one of the major threats against payloads. Space debris orbital distribution is of great importance for space debris environment modeling. Due to perturbation factors, the Right Ascension of Ascending Node (RAAN) of space objects changes consistently, causing regular rotation of the orbit plane around Earth’s axis. Based on the investigation of the RAAN perturbation rate of concerned objects, this paper proposes a RAAN discretization method in order to present the space debris longitude-dependent distribution. Combined with two line element (TLE) data provided by the US Space Surveillance Network, the estimated value from RAAN discretization method is compared with the real case. The results suggest that using only the initial orbital data at the beginning of the time interval of interest, the RAAN discretization method is able to provide reliable longitude distribution of concerned targets in the next following period. Furthermore, spacecraft cumulative flux against space debris is calculated in this paper. The results suggest that the relevance between spacecraft RAAN setup and flux output is much smaller for LEO targets than MEO targets, which corresponds with the theory analysis. Since the nonspherical perturbation is the major factor for RAAN variation, the RAAN perturbation rate has little connection with the size of orbital objects. In other words, the RAAN discretization method introduced in this paper also applies to space debris of different size range, proposing a possible suggestion for the improvement of space debris environment engineering models.

Dynamical evolutions of -boson stars in spherical symmetry

In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars (BSs) by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number . We call such solutions ‘-boson stars’. Here, we perform a series of fully non-linear dynamical simulations of perturbed -BSs in order to study their stability, and the final fate of unstable configurations. We show that for each value of , the configuration of maximum mass separates the parameter space into stable and unstable regions. Stable configurations, when perturbed, oscillate around the unperturbed solution and very slowly return to a stationary configuration. Unstable configurations, in contrast, can have three different final states: collapse to a black hole, migration to the stable branch, or explosion (dissipation) to infinity. Just as it happens with BSs, migration to the stable branch or dissipation to infinity depends on the sign of the total binding energy of the star: bound unstable stars collapse to black holes or migrate to the stable branch, whereas unbound unstable stars either collapse to a black hole or explode to infinity. Thus, the parameter allows us to construct a new set of stable configurations. All our simulations are performed in spherical symmetry, leaving a more detailed stability analysis including non-spherical perturbations for future work.

Stable Schwarzschild stars as black-hole mimickers

The Schwarzschild star is an ultracompact object beyond the Buchdahl limit, which has Schwarzschild geometry outside its surface and positive pressure in the external layer which vanishes at the surface. Recently it has been shown that the Schwarzschild star is stable against spherically symmetric perturbations. Here we study arbitrary axial nonspherical perturbations, and show that the observable quasinormal modes can be as close to the Schwarzschild limit as one wishes, what makes the Schwarzschild star a very good mimicker of a black hole. The decaying time-domain profiles prove that the Schwarzschild star is stable against nonspherical perturbations as well. Another peculiar feature is the absence of echoes at the end of the ringdown. Instead we observe a nonoscillating mode which might belong to the class of algebraically special modes. At asymptotically late times, Schwarzschildian power-law tails dominate in the signal.

Spontaneous scalarisation of charged black holes: coupling dependence and dynamical features

Spontaneous scalarisation of electrically charged, asymptotically flat Reissner–Nordström black holes (BHs) has been recently demonstrated to occur in Einstein–Maxwell–Scalar (EMS) models. This phenomenon is allowed by a non-minimal coupling between the scalar and the Maxwell fields, and does not require non-minimal couplings of the scalar field to curvature invariants. EMS BH scalarisation presents a technical simplification over the BH scalarisation that has been conjectured to occur in extended scalar–tensor Gauss–Bonnet (eSTGB) models. It is then natural to ask: (1) how universal are the conclusions extracted from the EMS model? And (2) how much do these conclusions depend on the choice of the non-minimal coupling function? Here we address these questions by performing a comparative analysis of several different forms for the coupling function including: exponential, hyperbolic, power-law and a rational function (fraction) couplings. In all of them we obtain and study the domain of existence of fundamental, spherically symmetric, scalarised BHs and compute, in particular, their entropy. The latter shows that scalarised EMS BHs are always entropically preferred over the RN BHs with the same total charge to mass ratio q. This contrasts with the case of eSTGB, where for the same power-law coupling the spherical, fundamental scalarised BHs are not entropically preferred over the Schwarzschild solution. Also, while the scalarised solutions in the EMS model for the exponential, hyperbolic and power-law coupling are very similar, the rational function coupling leads to a transition in the domain of existence, by virtue of a pole in the coupling function, into a region of ‘exotic’ solutions that violate the weak energy condition. Furthermore, fully non-linear dynamical evolutions of unstable RN BHs with different values of q are presented. These show: (1) for sufficiently small q, scalarised solutions with (approximately) the same q form dynamically; (2) for large q, spontaneous scalarisation visibly decreases q; thus evolutions are non-conservative; (3) despite the existence of non-spherical, static scalarised solutions, the evolution of unstable RN BHs under non-spherical perturbations leads to a spherical scalarised BH.

Re-entry guidance method based on decoupling control variables and waypoint

ABSTRACTGenerally, earth rotating and non-spherical perturbation of the earth in re-entry motion model are simplified using the standard trajectory guidance method. The re-entry motion is also simplified to horizontal motion and vertical motion and controlled, respectively. The simplification of re-entry motion model will lead to loss of motion accuracy and location accuracy. The direct decomposition will lead to the reduction of control accuracy because the horizontal motion and the vertical motion are coupled in re-entry. To improve the standard trajectory guidance method, the standard trajectory guidance method based on decoupling control variables and waypoint is proposed in this paper. The proposed guidance method will not simplify earth rotating and non-spherical perturbation of the earth in motion equation or decompose the re-entry motion to horizontal motion and vertical motion. Trajectory waypoint is adopted to reduce the change frequency of tracking states, because tracking states change frequently if the entire standard trajectory is tracked in real time.

Numerical simulation of single vapor bubble dynamics in a liquid in an intense acoustic field

The possibility of increasing the calculation efficiency by the joint use of two models of the dynamics of a single weakly-nonspherical vapor bubble under its strong collapse in liquid is studied. In both models the motion of liquid and vapor is split into a spherical component and its small nonspherical perturbation. The models differ in the description of the spherical component. In the first (simplified) model, it is described by a system of ODE together with partial differential equations in temperature, derived under the assumption of weak compressibility of liquid and bubble homobaricity. In the second model, one-dimensional gas dynamics equations are applied. The advantage of the simplified model consists in determining a numerical solution with much-less computer time costs in comparison with what is required for the numerical integration of gas dynamics equations. The assumptions used in the simplified model in the final stage of collapse become incorrect, and, as a result, the numerical solution errors increase. Therefore, the simplified model is applied at the beginning of bubble collapse, whereas the gas dynamics equations are used at its end. Within this approach, the numerical solution in the final stage of collapse is dependent on the moment of transition to the gas dynamics equations. It is shown that satisfactory description of evolution of bubble sphericity distortion is achieved when the transition is made under the condition that the Mach number M of vapor in the vicinity of the bubble surface is less than 0.4. Satisfactory resolution of the shock wave in the bubble is attained when the transition is performed at M<0.2.

What sets the central structure of dark matter haloes?

Dark matter (DM) haloes forming near the thermal cut-off scale of the density perturbations are unique, since they are the smallest objects and form through monolithic gravitational collapse, while larger haloes contrastingly have experienced mergers. While standard cold dark matter (CDM) simulations readily produce haloes that follow the universal Navarro-Frenk-White (NFW) density profile with an inner slope, $\rho \propto r^{-\alpha}$, with $\alpha=1$, recent simulations have found that when the free-streaming cut-off expected for the CDM model is resolved, the resulting haloes follow nearly power-law density profiles of $\alpha\sim1.5$. In this paper, we study the formation of density cusps in haloes using idealized $N$-body simulations of the collapse of proto-haloes. When the proto-halo profile is initially cored due to particle free-streaming at high redshift, we universally find $\sim r^{-1.5}$ profiles irrespective of the proto-halo profile slope outside the core and large-scale non-spherical perturbations. Quite in contrast, when the proto-halo has a power-law profile, then we obtain profiles compatible with the NFW shape when the density slope of the proto-halo patch is shallower than a critical value, $\alpha_{\rm ini} \sim 0.3$, while the final slope can be steeper for $\alpha_{\rm ini}\ga 0.3$. We further demonstrate that the $r^{-1.5}$ profiles are sensitive to small scale noise, which gradually drives them towards an inner slope of $-1$, where they become resilient to such perturbations. We demonstrate that the $r^{-1.5}$ solutions are in hydrostatic equilibrium, largely consistent with a simple analytic model, and provide arguments that angular momentum appears to determine the inner slope.

Robustness analysis method for orbit control

Satellite orbits require periodical maintenance due to the presence of perturbations. However, random errors caused by inaccurate orbit determination and thrust implementation may lead to failure of the orbit control strategy. Therefore, it is necessary to analyze the robustness of the orbit control methods. Feasible strategies which are tolerant to errors of a certain magnitude can be developed to perform reliable orbit control for the satellite. In this paper, first, the orbital dynamic model is formulated by Gauss’ form of the planetary equation using the mean orbit elements; the atmospheric drag and the Earth's non-spherical perturbations are taken into consideration in this model. Second, an impulsive control strategy employing the differential correction algorithm is developed to maintain the satellite trajectory parameters in given ranges. Finally, the robustness of the impulsive control method is analyzed through Monte Carlo simulations while taking orbit determination error and thrust error into account.

Fuel efficient control strategy for constellation orbital deployment

– This paper aims to provide a new method to design a fuel efficient control strategy such as J2 perturbation for deploying a constellation into a specified configuration. The nonspherical perturbation, mainly J2 perturbation, is the dominant perturbation for low-Earth-orbit (LEO) satellites of a constellation. This perturbation can be utilized in the control strategy to lower fuel consumption enormously. , – The relationship of the coupled variables, the relative right ascension of ascending node (RAAN) and the relative phase (RP), are analyzed. First-order approximation expressions of the relative RAAN (RRAAN) and the relative phase (RP) with respect to the semimajor axis are derived. According to the Gauss’ variational equations, the reduced explicit functions of these variables in regard to each active control are established. Based on these functions, control strategy design methods, including the preliminary planning and iterative corrections, are proposed. The numerical simulation is carried out to verify the proposed method. , – The results indicate that the constellation can be deployed accurately about the semimajor axis, the RRAAN and the relative phase (RP) by the developed fuel efficient control strategy. , – The proposed control strategy is limited for the orbital altitude where the J2 perturbation is dominant. , – The proposed effective method is applicable for the engineers planning an orbital control strategy of deploying satellites of a constellation. , – The new control strategy can realize utilization of J2 perturbation and an accurate deployment, simultaneously. Further, this paper provides practical help for satellite engineers.

Quasi-normal acoustic oscillations in the transonic Bondi flow

In recent work, we analyzed the dynamics of spherical and nonspherical acoustic perturbations of the Michel flow, describing the steady radial accretion of a relativistic perfect fluid into a nonrotating black hole. We showed that such perturbations undergo quasi-normal oscillations and computed the corresponding complex frequencies as a function of the black hole mass M and the radius r_c of the sonic horizon. It was found that when r_c is much larger than the Schwarzschild radius r_H = 2GM/c^2 of the black hole, these frequencies scale like the surface gravity of the analogue black hole associated with the acoustic metric. In this work, we analyze the Newtonian limit of the Michel solution and its acoustic perturbations. In this limit, the flow outside the sonic horizon reduces to the transonic Bondi flow, and the acoustic metric reduces to the one introduced by Unruh in the context of experimental black hole evaporation. We show that for the transonic Bondi flow, Unruh's acoustic metric describes an analogue black hole and compute the associated quasi-normal frequencies. We prove that they do indeed scale like the surface gravity of the acoustic black hole, thus providing an explanation for our previous results in the relativistic setting.