Explore the vast range of titles available.

The increasing penetration of renewable energy leads to a continuous reduction in system inertia, for which conventional synchronization criteria based solely on frequency consistency can no longer accurately capture the coupled dynamics of frequency and voltage during transients. To address this issue, this paper employs the concept of complex frequency and develops an analysis framework that integrates theory, indices, and simulation for assessing synchronization stability in low-inertia power systems. Firstly, the basic concepts and mathematical formulation of complex frequency and complex frequency synchronization are introduced. Then, dynamic criteria for local and global complex synchronization are established, upon which a complex inertia index is proposed. This index unifies the supporting role of traditional frequency inertia and the voltage support capability associated with voltage inertia, enabling the quantitative evaluation of the strength of coordinated frequency–voltage support and disturbance rejection within a region. Finally, transient simulations on a modified WSCC nine-bus system are carried out to validate the proposed method. The results show that the method can clearly reveal the synchronization relationships between subnetworks and the overall system, providing a useful theoretical reference for stability analysis and control strategy design in low-inertia power systems.

Unsteady, wall-bounded sedimentation of spheres at low particle Reynolds numbers, Re P ≲ 0.1 , under the influence of small elastic deformation was investigated experimentally. The complete kinematics of elastic and rigid spheres sedimenting from rest at various initial distances from a rigid plane wall in a rectangular duct were measured. Several previously unrecognized phenomena arising from fluid inertia and superimposed elastohydrodynamic effects were identified and analyzed. Among these is an inertial wall attraction , whereby particles migrate toward the wall during the initial acceleration phase. After this initial phase, rigid spheres sedimenting at Re P ≈ O ( 10 - 1 ) followed behavior consistent with classic wall-lift models, including approximately linear migration away from the wall. In contrast, at smaller Reynolds numbers, Re P ≈ O ( 10 - 2 ) , both rigid and elastic spheres exhibited persistently unsteady sedimentation, characterized by deceleration despite increasing wall distance. These results enable the formulation of a conceptual framework that classifies near-wall sedimentation regimes according to particle Reynolds number and the position of boundaries relative to the Stokes length scale. For increasing deformability, the unsteady behavior was further modulated by nonlinearities. The observations suggest the presence of an elastohydrodynamic memory effect arising from the coupling of fluid inertial forces with particle deformability. The experimental findings are supported by computational fluid dynamics simulations that provide qualitative insight into the evolving flow field. Overall, the results demonstrate that classic assumptions commonly applied to particle sedimentation in creeping flows break down in the presence of nearby boundaries and reveal a counterintuitive trend: as the particle Reynolds number decreases, fluid inertia can play an increasingly important role in governing particle motion near walls. The proposed conceptual framework may therefore aid the interpretation of the near-wall dynamics of deformable microplastic particles, for which comparable material properties and flow regimes are encountered in environmental and wastewater flows. Graphical abstract

Collective decision-making in biological systems requires all individuals in the group to go through a behavioural change of state. During this transition fast and robust transfer of information is essential to prevent cohesion loss. The mechanism by which natural groups achieve such robustness, however, is not clear. Here we present an experimental study of starling flocks performing collective turns. We find that information about direction changes propagates across the flock with a linear dispersion law and negligible attenuation, hence minimizing group decoherence. These results contrast starkly with present models of collective motion, which predict diffusive transport of information. Building on spontaneous symmetry breaking and conservation-law arguments, we formulate a theory that correctly reproduces linear and undamped propagation. Essential to this framework is the inclusion of the birds’ behavioural inertia. The theory not only explains the data, but also predicts that information transfer must be faster the stronger the group’s orientational order, a prediction accurately verified by the data. Our results suggest that swift decision-making may be the adaptive drive for the strong behavioural polarization observed in many living groups. How do flocks of birds remain cohesive while dodging predators? A study tracking up to 400 starlings reveals that information propagates in a linear fashion and with no attenuation, meaning that the language of phase transitions in correlated materials can be used to describe flocking behaviour.

Understanding the motion of magnetic skyrmions is essential if they are to be used as information carriers in devices. It is now shown that topological confinement endows the skyrmions with an unexpectedly large mass, which plays a key role in their dynamics. Skyrmions are topologically protected winding vector fields characterized by a spherical topology 1 . Magnetic skyrmions can arise as the result of the interplay of various interactions, including exchange, dipolar and anisotropy energy in the case of magnetic bubbles 2 , 3 , 4 and an additional Dzyaloshinskii–Moriya interaction in the case of chiral skyrmions 5 . Whereas the static and low-frequency dynamics of skyrmions are already well under control 6 , 7 , 8 , 9 , their gigahertz dynamical behaviour 2 has not been directly observed in real space. Here, we image the gigahertz gyrotropic eigenmode dynamics of a single magnetic bubble and use its trajectory to experimentally confirm its skyrmion topology. The particular trajectory points to the presence of strong inertia, with a mass much larger than predicted by existing theories. This mass is endowed by the topological confinement of the skyrmion and the energy associated with its size change. It is thereby expected to be found in all skyrmionic structures in magnetic systems and beyond. Our experiments demonstrate that the mass term plays a key role in describing skyrmion dynamics.

The renormalization group is a key set of ideas and quantitative tools of statistical physics that allow for the calculation of universal quantities that encompass the behaviour of different kinds of collective systems. Extension of the predictive power of the renormalization group to collective biological systems would greatly strengthen the effort to put physical biology on a firm basis. Here we present a step in that direction by calculating the dynamical critical exponent z of natural swarms of insects using the renormalization group to order ϵ = 4 − d. We report the emergence of a novel fixed point, where both activity and inertia are relevant. In three dimensions, the critical exponent at the new fixed point is z = 1.35, in agreement with both experiments (1.37 ± 0.11) and numerical simulations (1.35 ± 0.04). Our results probe the power of the renormalization group for the quantitative description of collective behaviour, and suggest that universality may also play a decisive role in strongly correlated biological systems.Tests of the predictions of the renormalization group in biological experiments have not yet been decisive. Now, a study on the collective dynamics of insect swarms provides a long-sought match between experiment and theory.

The effects of fluid inertia on a self-propelling inextensible waving sheet in an Oldroyd-B fluid are examined. The swimming velocity of the sheet is calculated in the limit in which the amplitude of the waves propagating along the sheet is small relative to the wavelength of the waves. The rate of work done by the sheet is also calculated. It is found that the swimming speed decreases monotonically approaching a limiting value with increasing Reynolds number ( R ) for a Newtonian fluid. For an Oldroyd-B fluid, the swimming speed increases to a maximum and then decreases asymptotically to a limiting value with increasing R . In contrast, it increases monotonically to a limiting value with increasing R for a Maxwell fluid. The limiting value is highest for the Maxwell fluid and lowest for the Oldroyd-B fluid. The corresponding value for the Newtonian fluid lies in between. The rate of work done by the sheet increases with increasing Reynolds number for all Deborah numbers. However, the energy consumed at a fixed swimming speed is lesser for an Oldroyd-B fluid than that of a Newtonian fluid. These results suggest that contrary to the Newtonian case, the fluid inertia supports the swimming sheet motion in a complex fluid. At a particular Deborah number, the oscillation frequency of the sheet could be adjusted to achieve the maximum speed. Similarly, at a particular frequency of oscillation, the Deborah numbers could be adjusted to achieve the maximum speed. These observations are in sharp contrast with the previous results reported for Newtonian and second-order fluids. Graphical abstract

The impact of fluid inertia on fracture flow dynamics, particularly under high-velocity conditions, has emerged as a critical consideration in petroleum engineering and related fields. This review paper investigates the profound effects of inertia-dominated nonlinear flow, a phenomenon increasingly recognised for its significant influence on fluid dynamics in rock fractures. Given the prevalence and importance of such flows in field applications, neglecting fluid inertial effects is no longer justifiable. A comprehensive investigation into these effects is essential for advancing our understanding of fracture flow mechanisms and optimising engineering practices. This review aims to thoroughly analyse the impact of fluid inertia on applications in hydraulic fracturing. It offers an in-depth discussion of how fluid inertia affects critical aspects of crack propagation, fracture diagnostics, proppant transport and settlement, and fines migration. Additionally, this paper identifies and explores four main factors that influence the fluid inertia effect in fracture flows: fracture roughness, intersections and dead ends within the fracture network, variations in contact area and fracture aperture, and the role of shear displacement. The review provides valuable insights into the complex interplay between fluid inertia and fracture flow dynamics by elucidating these factors.

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research. Graphical abstract

Cosmic-ray interactions with the atmosphere produce a flux of neutrinos in all directions with energies extending above the TeV scale1. The Earth is not a fully transparent medium for neutrinos with energies above a few TeV, as the neutrino–nucleon cross-section is large enough to make the absorption probability non-negligible2. Since absorption depends on energy and distance travelled, studying the distribution of the TeV atmospheric neutrinos passing through the Earth offers an opportunity to infer its density profile3–7. This has never been done, however, due to the lack of relevant data. Here we perform a neutrino-based tomography of the Earth using actual data—one-year of through-going muon atmospheric neutrino data collected by the IceCube telescope8. Using only weak interactions, in a way that is completely independent of gravitational measurements, we are able to determine the mass of the Earth and its core, its moment of inertia, and to establish that the core is denser than the mantle. Our results demonstrate the feasibility of this approach to study the Earth’s internal structure, which is complementary to traditional geophysics methods. Neutrino tomography could become more competitive as soon as more statistics is available, provided that the sources of systematic uncertainties are fully under control.

The Leidenfrost effect—the levitation and hovering of liquid droplets on hot solid surfaces—generally requires a sufficiently high substrate temperature to activate liquid vaporization. Here we report the modulation of Leidenfrost-like jumping of sessile water microdroplets on micropillared surfaces at a relatively low temperature. Compared to traditional Leidenfrost effect occurring above 230 °C, the fin-array-like micropillars enable water microdroplets to levitate and jump off the surface within milliseconds at a temperature of 130 °C by triggering the inertia-controlled growth of individual vapour bubbles at the droplet base. We demonstrate that droplet jumping, resulting from momentum interactions between the expanding vapour bubble and the droplet, can be modulated by tailoring of the thermal boundary layer thickness through pillar height. This enables regulation of the bubble expansion between the inertia-controlled mode and the heat-transfer-limited mode. The two bubble-growth modes give rise to distinct droplet jumping behaviours characterized by constant velocity and constant energy regimes, respectively. This heating strategy allows the straightforward purging of wetting liquid droplets on rough or structured surfaces in a controlled manner, with potential applications including the rapid removal of fouling media, even when located in surface cavities. The Leidenfrost effect—a droplet hovering on a hot surface due to vapour in between—requires a surface temperature of about 230 °C. Now a tailored microstructured surface is shown to enable quick hovering of water droplets at 130 °C.