Orbital Velocity Research Articles

Modified logarithmic distribution of wind-driven flow velocity in remote foreshore of the non-tidal sea

The paper presents the results of the novel modelling of the wind-driven current in the southern Baltic Sea. The steady current is accompanied by wave-induced orbital velocities. The bed boundary layer related to wave-induced oscillatory flow gives rise to the appearance of additional shear stresses affecting the wind-driven current. This impact included in the wind-driven current model yields a modified logarithmic velocity distribution. Theoretical velocity profiles are compared with the field data. The measurement database includes wind, wave and current parameters. The velocities and directions of the wind were collected from the anemometer installed at the Coastal Research Station (CRS) in Lubiatowo. Wave-current parameters at a depth of about 17 m were obtained from a location of approx. 1.5 Nm from the shoreline in the vicinity of CRS Lubiatowo. The study site hydrodynamics is typical of the south Baltic coast. The analysis shows good agreement between the measured flow velocities and the theoretical vertical distributions in the form of the modified logarithmic profile.

The Orbital Properties of Black Holes: Exploring the Relationship between Orbital Velocity and Distance

This research explores the concept of black holes in the physics of general relativity, including its formation and properties. The study focuses on the relationship between the orbital velocity and orbital distance of objects around a black hole, which is measured in units of the speed of light (c) and kiloparsecs (kpc), respectively. Using observational techniques, the study produces a plot showing the relationship between orbital velocity and orbital distance, which follows Kepler's law modified by the Newtonian theory of gravity and general relativity. The study also highlights the effective potential of particles in orbit around a black hole, which combines the effects of kinetic energy and gravitational potential. The effective potential shows the gravitational and relativistic properties of black holes, such as the photon orbit radius, ISCO, and the spin parameter. The resulting plot demonstrates the characteristics of the Milky Way black hole and how its spin parameter and Schwarzschild radius affect the orbital properties of surrounding particles. The study concludes that the closer the orbital distance is to the black hole, the more the orbital velocity increases, and particles with high spin parameters and small Schwarzschild radii are unlikely to escape the black hole's gravity.

Fast On-Orbit Pulse Phase Estimation of X-Ray Crab Pulsar for XNAV Flight Experiments

The recent flight experiments with Neutron Star Interior Composition Explorer (\textit{NICER}) and \textit{Insight}-Hard X-ray Modulation Telescope (\textit{Insight}-HXMT) have demonstrated the feasibility of X-ray pulsar-based navigation (XNAV) in the space. However, the current pulse phase estimation and navigation methods employed in the above flight experiments are computationally too expensive for handling the Crab pulsar data. To solve this problem, this paper proposes a fast algorithm of on-orbit estimating the pulse phase of Crab pulsar called X-ray pulsar navigaTion usIng on-orbiT pulsAr timiNg (XTITAN). The pulse phase propagation model for Crab pulsar data from \textit{Insight}-HXMT and \textit{NICER} are derived. When an exposure on the Crab pulsar is divided into several sub-exposures, we derive an on-orbit timing method to estimate the hyperparameters of the pulse phase propagation model. Moreover, XTITAN is improved by iteratively estimating the pulse phase and the position and velocity of satellite. When applied to the Crab pulsar data from \textit{NICER}, XTITAN is 58 times faster than the grid search method employed by \textit{NICER} experiment. When applied to the Crab pulsar data from \textit{Insight}-HXMT, XTITAN is 180 times faster than the Significance Enhancement of Pulse-profile with Orbit-dynamics (SEPO) which was employed in the flight experiments with \textit{Insight}-HXMT. Thus, XTITAN is computationally much efficient and has the potential to be employed for onboard computation.

Physical and Chemical Characteristics of a Plasma Flow around Descent Vehicles upon Entry in the Earth’s Atmosphere at Orbital Velocity

Physical and Chemical Characteristics of a Plasma Flow around Descent Vehicles upon Entry in the Earth’s Atmosphere at Orbital Velocity

Dynamical galactic effects induced by solitonic vortex structure in bosonic dark matter

The nature of dark matter (DM) remains one of the unsolved mysteries of modern physics. An intriguing possibility is to assume that DM consists of ultralight bosonic particles in the Bose–Einstein condensate (BEC) state. We study stationary DM structures by using the system of the Gross–Pitaevskii and Poisson equations, including the effective temperature effect with parameters chosen to describe the Milky Way galaxy. We have investigated DM structure with BEC core and isothermal envelope. We compare the spherically symmetric and vortex core states, which allows us to analyze the impact of the core vorticity on the halo density, velocity distribution, and, therefore, its gravitational field. Gravitational field calculation is done in the gravitoelectromagnetism approach to include the impact of the core rotation, which induces a gravimagnetic field. As a result, the halo with a vortex core is characterized by smaller orbital velocity in the galactic disk region in comparison with the non-rotating halo. It is found that the core vorticity produces gravimagnetic perturbation of celestial body dynamics, which can modify the circular trajectories.

Plant trait-mediated drag forces on seedlings of four tidal marsh pioneer species

Salt marshes play an important role in coastal protection by reducing the impact of waves and shoreline erosion risks. While mature vegetation is responsible for the persistence and stability of marsh ecosystems, seedling survival of pioneer species is especially crucial for marsh propagation. Marsh seedlings, however, may be threatened by climate change induced increased coastal storm surge intensity and accompanying (extreme) wave conditions, imposing stronger drag forces on marsh seedlings. We test the hypothesis that drag forces experienced by seedlings increase with horizontal orbital velocity (Uw) in a species-specific manner, and that the drag forces experienced are individual-plant trait-mediated. To test our hypotheses, seedlings of four contrasting pioneer marsh species (Bolboschoenus maritimus, Schoenoplectus tabernaemontani, Spartina anglica, and Puccinellia maritima) were exposed to storm wave conditions in a flume, where Uw and experienced drag forces were measured. Linear mixed effect models demonstrated that seedling’s susceptibility to storm wave conditions is at least partly mediated by individual plant traits. Drag forces experienced by seedlings tended to increase with Uw, and with stem length and diameter. The interplay of both traits was complex, with increasing stem length being the most important trait accounting for increases in drag forces experienced at low to moderate Uw, while the stem diameter became more important with increasing Uw. Furthermore, experienced drag forces appeared to be affected by species-specific traits such as rigidity and leaf growth, being highest for Bolboschoenus maritimus and lowest for Puccinellia maritima. Our results provide important mechanistic insights into the drivers of tidal marsh seedling vulnerability to storm wave conditions due to experienced drag, both based on the traits of individual plants and species-specific ones. This type of knowledge is of key importance when modelling saltmarsh establishment and resilience under climate change.

Patterns and drivers of macroalgal ‘blue carbon’ transport and deposition in near-shore coastal environments

The role of macroalgae (seaweed) as a global contributor to carbon drawdown within marine sediments – termed ‘blue carbon’ – remains uncertain and controversial. While studies are needed to validate the potential for macroalgal‑carbon sequestration in marine and coastal sediments, fundamental questions regarding the fate of dislodged macroalgal biomass need to be addressed. Evidence suggests macroalgal biomass may be advected and deposited within other vegetated coastal ecosystems and down to the deep ocean; however, contributions to near-shore sediments within coastal waters remain uncertain. In this study a combination of eDNA metabarcoding and surficial sediment sampling informed by seabed mapping from different physical environments was used to test for the presence of macroalgal carbon in near-shore coastal sediments in south-eastern Australia, and the physical factors influencing patterns of macroalgal transport and deposition. DNA products for a total of 68 macroalgal taxa, representing all major macroalgal groups (Phaeophyceae, Rhodophyta, and Chlorophyta) were successfully detected at 112 near-shore locations. These findings confirm the potential for macroalgal biomass to be exported into near-shore sediments and suggest macroalgal carbon donors could be both speciose and diverse. Modelling suggested that macroalgal transport and deposition, and total organic carbon (TOC), are influenced by complex interactions between several physical environmental factors including water depth, sediment grain size, wave orbital velocity, current speed, current direction, and the extent of the infralittoral zone around depositional areas. Extrapolation of the optimised model was used to predict spatial patterns of macroalgal deposition and TOC across the coastline and to identify potentially important carbon sinks. This study builds on recent studies providing empirical evidence for macroalgal biomass deposits in near-shore sediments, and a framework for predicting the spatial distribution of potential carbon sinks and informing future surveys aimed at determining the potential for long-term macroalgal carbon sequestration in marine sediments.

The dark side of FIRE: predicting the population of dark matter subhaloes around Milky Way-mass galaxies

ABSTRACT A variety of observational campaigns seek to test dark matter models by measuring dark matter subhaloes at low masses. Despite their predicted lack of stars, these subhaloes may be detectable through gravitational lensing or via their gravitational perturbations on stellar streams. To set measurable expectations for subhalo populations within Lambda cold dark matter, we examine 11 Milky Way (MW)-mass haloes from the FIRE-2 baryonic simulations, quantifying the counts and orbital fluxes for subhaloes with properties relevant to stellar stream interactions: masses down to $10^{6}\, \text{M}_\odot$, distances ≲50 kpc of the galactic centre, across z = 0 − 1 (tlookback = 0–8 Gyr). We provide fits to our results and their dependence on subhalo mass, distance, and lookback time, for use in (semi)analytical models. A typical MW-mass halo contains ≈16 subhaloes $\gt 10^{7}\, \text{M}_\odot$ (≈1 subhalo $\gt 10^{8}\, \text{M}_\odot$) within 50 kpc at z ≈ 0. We compare our results with dark matter-only versions of the same simulations: because they lack a central galaxy potential, they overpredict subhalo counts by 2–10×, more so at smaller distances. Subhalo counts around a given MW-mass galaxy declined over time, being ≈10× higher at z = 1 than at z ≈ 0. Subhaloes have nearly isotropic orbital velocity distributions at z ≈ 0. Across our simulations, we also identified 4 analogues of Large Magellanic Cloud satellite passages; these analogues enhance subhalo counts by 1.4–2.1 times, significantly increasing the expected subhalo population around the MW today. Our results imply an interaction rate of ∼5 per Gyr for a stream like GD-1, sufficient to make subhalo–stream interactions a promising method of measuring dark subhaloes.

Dynamic response of water flow and sediment transport off the Yellow River mouth to tides and waves in winter

Freshwater and sediments are transported from the Yellow River mouth downstream along the coast into Laizhou Bay under the northeasterly wind in winter. Numerical experiments indicate that sediment transport shows the tendency of convergence in the river mouth, divergence in the downstream area, and convergence in the north of Laizhou Bay. Tides and waves are the two main forcings affecting the transport of water and sediments off river mouths. For the high-turbidity Yellow River mouth and the adjacent sea, tidal forcing enhances the subtidal downstream transport of water and sediments off the river mouth into Laizhou Bay, whereas wave forcing has little effect on the advection of water and sediments. Sediment resuspension is controlled by the bottom shear stress induced by tides and waves. The tide-induced bottom shear stress is higher in the north of Laizhou Bay and south of Bohai Bay due to the stronger bottom tidal current. The wave-induced bottom shear stress plays a more important role in sediment resuspension, which is higher in the nearshore region along the Yellow River Delta away from the coast to some extent on account of the maximum near-bottom wave orbital velocity. Tidal mixing strengthens the upward diffusion of the bottom suspended sediments. Without tidal forcing, there is an interesting phenomenon along the Yellow River Delta. In the nearshore region, the decreased bottom shear stress suspends less sediment above the bed. However, in the offshore region, the enhanced stratification hinders the upward diffusion of the bottom sediment due to the lack of tidal mixing, resulting in higher suspended sediment concentration (SSC) in the bottom layer.

First Open-Coast HF Radar Observations of a 2-Phase Volcanic Tsunami, Tonga 2022

We describe results from coastal radar systems that observed anomalous current flows generated by the volcanic eruption in the Tongan archipelago on 15 January 2022 UTC, reporting the first radar detection of a volcanic tsunami. The eruption caused small tsunamis along the western U.S. Coast, generating some damage in a few harbors. The highest tsunami signal in U.S. tide gauge data from the California coast occurred at Arena Cove, with significant heights detected at Port San Luis and Crescent City. We analyze correlated wave orbital velocity detections by High Frequency (HF) radars along the coast between Gerstle Cove and Santa Barbara. Signals observed by the radars indicate that the event had two phases, each with its own distinct genesis: an initial weak surface disturbance, most likely generated by the wave of atmospheric pressure that moved outward from the blast source at just below the speed of sound, followed by a stronger disturbance that arrived approximately 3.5 h later, matching the arrival time for a wave moving entirely through the water from the volcano to the U.S. West Coast. We conclude that this phase consists of a conventional water wave tsunami and weaker waves generated by the pulse. We also report the detection of a small pulse-generated event off the west coast of Florida. Radar observations are compared with water level measurements at nearby tide gauges and a DART buoy, and with observations of barometric pressure. We point out that a Proudman near-resonance at the Tonga Trench is unlikely to explain the second phase observations. Comparison with tide gauge signals at San Francisco, generated by the Krakatoa eruption in 1883, support our conclusions.

Time-optimal maneuvers of a spacecraft between two arbitrary states in proximity of a circular reference orbit

The problem is considered to find the time-optimal control that transfers a fourth-order system that consists of a double integrator and a harmonic oscillator, coupled by one control channel, between two arbitrary states. That fourth-order system is equivalent to the Hill-Clohessy-Wiltshire model of the relative dynamics of an orbiting spacecraft in proximity of a second spacecraft on a circular reference orbit, subjected to a thrust parallel to the orbital velocity vector and having time-continuous amplitude. A new method is here introduced to determine the time-optimal control problem stated above. This method combines two previously discovered optimal control synthesis methods: the method by Romano and Curti (2020), that enables to find (analytically, in some case) the optimal control transferring a general Linear Time Invariant Normal system between two arbitrary states; and, the method by Belousova and Zarkh (1996), that enables to find the optimal control transferring a fourth-order system consisting of a double integrator and a harmonic oscillator, coupled by one control channel, from an arbitrary initial state to the origin of the state space, if the optimal control is a priori known, that transfers the same system from a reference state to the origin. The here proposed combined method utilizes two phases. During the first phase, a number of reference minimum-time controls are obtained that transfer the system from specific reference states to the state space origin; this is achieved by exploiting Pontryagin’s principle together with back-propagation from the origin of the state space. During the second phase, a search is run along a particular curve in the state space (named extremal search path) that depends on the boundary states of the problem at hand. In particular, a minimum-time control problem is iteratively solved to find the optimal control history that steers the system from a state on that curve to the origin, by exploiting Belousova and Zarkh method, until a particular state is found which satisfies an equivalency condition that, as demonstrated by Romano and Curti, guarantees that the optimal control history pertaining to the problem of transferring the system from that state to the origin is the same optimal control history that transfers the system between the arbitrarily set initial and final states. The new results, substantiated by numerical experiments, have both a theoretical and a practical value, as they could be applied for the optimal guidance of spacecraft performing autonomous proximity maneuvers.

Gravothermal collapse of self-interacting dark matter halos as the origin of intermediate mass black holes in Milky Way satellites

Milky Way (MW) satellites exhibit a diverse range of internal kinematics, reflecting in turn a diverse set of subhalo density profiles. These profiles include large cores and dense cusps, which any successful dark matter model must explain simultaneously. A plausible driver of such diversity is self-interactions between dark matter particles (SIDM) if the cross section passes the threshold for the gravothermal collapse phase at the characteristic velocities of the MW satellites. In this case, some of the satellites are expected to be hosted by subhalos that are still in the classical SIDM core phase, while those in the collapse phase would have cuspy inner profiles, with a SIDM-driven intermediate mass black hole (IMBH) in the centre as a consequence of the runaway collapse. We develop an analytical framework that takes into account the cosmological assembly of halos and is calibrated to previous simulations; we then predict the timescales and mass scales ($M_{\rm BH}$) for the formation of IMBHs in velocity-dependent SIDM (vdSIDM) models as a function of the present-day halo mass, $M_0$. Finally, we estimate the region in the parameter space of the effective cross section and $M_0$ for a subclass of vdSIDM models that result in a diverse MW satellite population, as well as their corresponding fraction of SIDM-collapsed halos and those halos' inferred IMBH masses. We predict the latter to be in the range $0.1-1000~ {\rm M_\odot}$ with a $M_{\rm BH}-M_0$ relation that has a similar slope, but lower normalization, than the extrapolated empirical relation of super-massive black holes found in massive galaxies.

Weighing the Darkness. II. Astrometric Measurement of Partial Orbits with Gaia

Over the course of several years, stars trace helical trajectories as they traverse across the sky due to the combined effects of proper motion and parallax. It is well known that the gravitational pull of an unseen companion can cause deviations to these tracks. Several studies have pointed out that the astrometric mission Gaia will be able to identify a slew of new exoplanets, stellar binaries, and compact object companions with orbital periods as short as tens of days to as long as Gaia's lifetime. Here, we use mock astrometric observations to demonstrate that Gaia can identify and characterize black hole companions to luminous stars with orbital periods longer than Gaia's lifetime. Such astrometric binaries have orbital periods too long to exhibit complete orbits, and instead are identified through curvature in their characteristic helical paths. By simultaneously measuring the radius of this curvature and the orbital velocity, constraints can be placed on the underlying orbit. We quantify the precision with which Gaia can measure orbital accelerations and apply that to model predictions for the population of black holes orbiting stars in the stellar neighborhood. Although orbital degeneracies imply that many of the accelerations induced by hidden black holes could also be explained by faint low-mass stars, we discuss how the nature of certain putative black hole companions can be confirmed with high confidence using Gaia data alone.

Estimation of the main parameters of wave action on the gentle slopes of the banks of large water bodies

When designing coastal protection measures, special attention is paid to the creation and expansion of a natural beach slope on the coast of a water body. To assign geometric dimensions to relatively stable beach slopes, it is necessary to evaluate the relationship of waves, taking into account the level regime characteristic of a given section of the coast. The aim of the research is to explore the features of the transformation of the wave profile in shallow water and to conduct a comparative analysis of theory and experiment. The studies were carried out in a wave tray, where the waves were reproduced by a swinging shield. The features of the transformation of the wave profile at decreasing depths of the shallow water of a large water body are considered. An assessment is given of the change in the kinematic characteristics of a wave incident in a shallow water zone on an unfortified beach slope with a depth of 10, 20 and 30. The results of experimental studies are presented and analyzed, as a result of which the influence of the wave steepness on the kinematic characteristics and features of wave transformation in shallow water is revealed. A comparative analysis of theoretical solutions and experimental data with an assessment of the area of their applicability is carried out. On the whole, the wave profile and the horizontal component of the orbital velocity during the passage of the wave crest are in satisfactory agreement with the calculations according to the Stokes theory at relative depths of more than 0.07. It has been established that for shallow water conditions the relative height of the wave crest affecting the beach slope of the near-shore zone of the coast of a large water body is most noticeably affected by the slope, with an increase from 10 to 30 the magnitude of the wave steepness can increase by 1.2 times.

Empirical formulas for near-bed wave orbital velocity parameters involved in maximum wave load in random wave trains

This paper presents empirical methods utilizing recently developed formulas (Kawamata and Kobayashi., 2022; Kawamata et al., 2018) to predict the maximum wave forces on near-bed structures and wave-induced movement ratios of isolated rocks in random wave trains. The methods assume that the maximum wave load occurs when the velocity semi-amplitude defined as half the difference between successive negative and positive peaks of the near-bed wave orbital velocity is maximized. The empirical formulas for the velocity-waveform parameters at the maximum velocity semi-amplitude in a random wave train were derived from the near-bed velocities and surface elevations measured in laboratory wave flumes. The laboratory formula for the maximum velocity semi-amplitude was reviewed and improved with near-bed wave orbital velocities and surface elevations estimated from pressure measurements under a wider range of wave conditions in the field. The newly developed formulas for the velocity-waveform parameters at velocity semi-amplitude maxima, combined with the previously developed formulas, showed reasonable agreement with the maximum wave forces measured on the artificial reef models under random waves in a laboratory wave flume as well as with the movement ratio of quarry rocks (median mass = 0.40 t) observed in a field test.

Back Cover: Predestined Steady‐State Entanglement under Pure Vacuum Noise (Adv. Quantum Technol. 3/2023)

For a pair of rotating qubits under pure vacuum noise with appropriate orbital radius and angular velocity, entanglement is not only resilient against vacuum noise for initially entangled states, but is also predestined to be created and be preserved for arbitrary initially separable states. More details can be found in article number 2200159 by Yuebing Zhou, Jiawei Hu, and Hongwei Yu.

Momentum transfer from the DART mission kinetic impact on asteroid Dimorphos

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on 26 September 2022 as a planetary defence test1. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defence, intended to validate kinetic impact as a means of asteroid deflection. Here we report a determination of the momentum transferred to an asteroid by kinetic impact. On the basis of the change in the binary orbit period2, we find an instantaneous reduction in Dimorphos’s along-track orbital velocity component of 2.70 ± 0.10 mm s−1, indicating enhanced momentum transfer due to recoil from ejecta streams produced by the impact3,4. For a Dimorphos bulk density range of 1,500 to 3,300 kg m−3, we find that the expected value of the momentum enhancement factor, β, ranges between 2.2 and 4.9, depending on the mass of Dimorphos. If Dimorphos and Didymos are assumed to have equal densities of 2,400 kg m−3, {beta =3.61}_{-0.25}^{+0.19}(1sigma ). These β values indicate that substantially more momentum was transferred to Dimorphos from the escaping impact ejecta than was incident with DART. Therefore, the DART kinetic impact was highly effective in deflecting the asteroid Dimorphos.

Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications

In this paper, we discuss the design and feasibility of a multifunctional laser instrument capable of precision ranging, time transfer, and wideband communications over interplanetary distances throughout our solar system. To simplify the communications discussion, On-Off Keying (OOK) is assumed for the high bandwidth (MHz to GHz) modulation format, and the required laser powers and transmit and receive apertures are determined for each Earth–planet link as a function of data rate. Optimization of the transmitter and receiver antenna gains is reviewed. It is further assumed that the spacecraft is in orbit about the planet of interest in order to justify the need for large data downloads rates and that single-photon sensitive detector arrays can be utilized to aid in the acquisition, detection, and tracking of the opposite terminal. Satellite acquisition and tracking is complicated by the long one-way propagation distances (up to 40 AU), the finite speed of light, the orbital and rotational velocities of the two planets, and, if applicable, the spacecraft orbital speed about the planet. Taking advantage of the highly circular and coplanar planetary orbits within our solar system, point ahead angles are estimated for all combinations of possible Earth–planet positions revealing solar orbital geometries where planetary motion does not introduce a need for point ahead angles. Finally, possible methods for simplifying the initial mutual acquisition of the planetary and Earth terminals and maintaining the coalignment of their respective optical systems is discussed.

On the Incompleteness of Birkhoff’s Theorem: A New Approach to the Central Symmetric Gravitational Field in Vacuum Space

Birkhoff’s theorem (1923) states that in the framework of General Relativity the only solution to the central symmetric gravitational field in vacuum is the Schwarzschild metric. This result has crucial consequences in the resolution of the dark matter problem. This problem can only be solved through the discovery of a new type of matter particles, or by the introduction of a new theory of gravitation which supplants General Relativity. After reviewing Birkhoff’s theorem, it was discovered that by starting the calculation of the metric from an indeterminate metric whose coefficients are locally defined, we obtain a solution containing two arbitrary functions. In general, these functions do not induce any difference between this solution and the Schwarzschild metric. However, it can be seen that if we choose a triangular signal for these functions, the situation changes dramatically: (1) the metric is broken down into four distinct metrics that replace each other cyclically over time, (2) for two of these four metrics, the coordinate differentials dr and dt switch their spatial/temporal role cyclically, (3) the four metrics are not separable: they form a single logical set that we call a 4-metric and (4) this 4-metric cannot be transformed into the Schwarzschild metric by any coordinate change. According to these findings, there is a second solution in the spherical space, in addition to the Schwarzschild metric, and thus, Birkhoff’s theorem is incomplete. In the 4-metric, the orbital velocity of a massive particle does not depend on the radial distance. This 4-metric is thus in agreement with the baryonic Tully–Fisher relation (BTFR), (consequently BTFR is in agreement with a solution of General Relativity without presence of dark matter and without hypothesis on the distribution of stars in galaxies). By combining the 4-metric with the Schwarzschild metric, another 4-metric in agreement with the observed galaxy rotation curve can been obtained. The calculation of the light deflection in this space is also exposed in this paper. According to these findings: (1) it is not necessary to introduce the notion of dark matter or the notion of distribution of stars in galaxies in order to find the observed galaxy rotation curve in the framework of General Relativity, (2) the modification of the metric with respect to the Schwarzschild metric appears to be due to the existence of a lower bound of the space-time curvature in galaxies (without external field effect), this phenomenon leading to a temporal oscillation of the space-time curvature, (3) an analysis of the external field effect for the Milky Way-Andromeda couple allows to model the rotation curve of the two galaxies beyond the plateau zone. The validation of these findings would be the first step toward challenging the standard model of cosmology ([Formula: see text]CDM), as the [Formula: see text]CDM model cannot be in agreement with the observed galaxy rotation curve without presence of dark matter. The second step would be the demonstration that there is no dark matter in intergalactic spaces (not included in this paper).

A simple approach for wave absorbing control of plunger wavemakers using machine learning: Numerical study

Due to the complex geometry, the research for theoretical methods on wave absorption with plunger-type wavemakers is not easy. Therefore, this paper proposes a simple approach for wave absorbing control of plunger wavemakers using machine learning. The main contribution of this approach is to control plunger wavemakers to absorb waves in the time domain, and no theoretical derivation is required. The neural networks are trained to map the time-independent relationship between the wavemaker velocity and recorded wave variables (i.e. wave period, water depth, free-surface elevation along the wavemaker, velocities of the free-surface elevation along the wavemaker and position of the wavemaker). A penalty term is proposed to avoid the overfitting of neural networks. A numerical wave flume is applied to generate training data and simulate wave absorption. Taking a wedge plunger wavemaker as an example, the regular wave absorption with full reflection is tested. The simulated wave profiles and wave orbital velocities are validated with analytical solutions, showing that the proposed approach is effective at eliminating the reflected wave. A cylinder plunger wavemaker is also performed to absorb the solitary and irregular waves. The irregular wave can be absorbed stably in a long-term simulation. The solitary wave with a small height can also be absorbed well, illustrating the potential of the proposed approach in different plunger shapes and wave conditions. • This paper proposes a simple approach for wave absorbing control of plunger wavemakers using machine learning, and no complex theoretical derivation is required. • Penalty term based on wave mechanisms is introduced to prevent neural networks from overfitting. • Once the target wave profiles in front of the wavemaker are given, it can realize generating waves and absorbing reflected waves at the same time. • The proposed approach is suitable for different plunger shapes and wave conditions.