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In the last two centuries and more particularly in the last decades, the geometry of foams has become an important research domain, in mathematics, physics, material sciences and biology. Most of the simplest geometrical observations of bubble clusters have long resisted rigorous mathematical proofs. Geometries can even get more complicated if immiscible fluids are considered. Although they have to fulfill Plateau's laws like soap bubble clusters if the surface tensions are close to unity, this is not the case in general. In 1996, Frederick J. Almgren asked whether there is "any stable cluster of bubbles in $\mathbb{R}^3$ with some bubble being topologically a torus". We propose to answer the latter numerically with simple numerical examples. We build stable soap bubble clusters with a triple torus bubble, a fivefold torus bubble or an elevenfold torus bubble. The construction uses the geometry of a simple immiscible fluids cluster with a torus bubble.

The interaction of multiple bubbles is a complex physical problem. A simplified case of multiple bubbles is studied theoretically with a bubble located at the center of a circular bubble cluster. All bubbles in the cluster are equally spaced and own the same initial conditions as the central bubble. The unified theory for bubble dynamics (Zhang et al. arXiv:2301.13698) is applied to model the interaction between the central bubble and the circular bubble cluster. To account for the effect of the propagation time of pressure waves, the emission source of the wave is obtained by interpolating the physical information on the time axis. An underwater explosion experiment with two bubbles of different scales is used to validate the theoretical model. The effect of the bubble cluster with a variation in scale on the pulsation characteristics of the central bubble is studied.

We propose a low-dimensional modeling approach to simulate the dynamics, acoustic emissions and interactions of cavitation bubbles, based on a quasi-acoustic assumption. This quasi-acoustic assumption accounts for the compressibility of the medium surrounding the bubble and its finite speed of sound, whereby the potential of the acoustic wave emitted by the bubble propagates along outgoing characteristics. With these ingredients, a consistent set of equations describing the radial bubble dynamics as well as the resulting acoustic emissions and bubble-bubble interactions is obtained, which is accurate to the first order of the Mach number. This model is tested by considering several representative test cases, including the resonance behavior of multiple interacting bubbles and the response of dense mono- and polydisperse bubble clusters to a change in ambient pressure. The results are shown to be in excellent agreement with results reported in the literature. The differences associated with the finite propagation speed of the acoustic waves are observed to be most pronounced for the pressure-driven bubble dynamics in dense bubble clusters and the onset of cavitation in response to a

This paper introduces a new approach for bubble detection based on mixed causal and noncausal autoregressive processes and their tail process representation during an explosive episode. Departing from traditional definitions of bubbles as nonstationary and temporarily explosive processes, we adopt a perspective in which prices are assumed to follow a strictly stationary process, with the bubble considered an intrinsic component of its nonlinear dynamics. The proposed approach provides a bubble indicator for detecting bubbles and measuring their duration. We implement our strategy to investigate the phenomenon called the "green bubble" in the field of renewable energy investment.

The study of gas bubble dynamics in liquids is justified by the numerous applications and natural phenomena where this two-phase flow is encountered. Gas bubbles move as forces are applied to them; their dynamics are full of nuances that need to be addressed carefully. Since the mass of gas bubbles is practically negligible, in comparison to that of the surrounding liquid, their reaction to the fluid is controlled by the added mass acceleration and is thus impacted by all the forces arising from the fluid action. Furthermore, since their surface can be deformed by the same forces acting on them, their shape may change leading to changes in their resistance to move, the drag force, and therefore affecting their speed and their interaction with the surrounding flow which is often turbulent. The liquid rheology, as well as its surfactant content can also affect the bubble shape and motion as well. Understanding these issues, in addition to the effect of interactions with other bubbles, walls, and non-uniform flows, provides sufficient elements to model and predict bubble behavior through the solution of dynamic equations. In this review, we cover the key aspects of non-condensable gas

Presented here are experiments clarifying how the deformation of cavitation bubbles affects their rebound. Rebound bubbles carry the remaining energy of a bubble following its initial collapse, which dissipates energy mainly through shock waves, jets, and heat. The rebound bubble undergoes its own collapse, generating such violent events anew, which can be even more damaging or effective than at first bubble collapse. However, modeling rebound bubbles is an ongoing challenge because of the lack of knowledge on the exact factors affecting their formation. Here we use single-laser-induced cavitation bubbles and deform them by variable gravity or by a neighboring free surface to quantify the effect of bubble deformation on the rebound bubbles. Within a wide range of deformations, the energy of the rebound bubble follows a logarithmic increase with the bubble's initial dipole deformation, regardless of the origin of this deformation.

An exact and analytical solution, in four-dimensional general relativity, describing a collinear array of an arbitrary number of Kerr black holes inside an expanding bubble of nothing is built, thanks to the inverse scattering technique. Physical properties and thermodynamics of the single Kerr in the bubble are studied. No cosmic strings or struts are present. The binary black hole system displays equilibrium configurations, because the expanding bubble surrounding the black holes balances the mutual gravitational attraction of the two constituents.

Cosmological first-order phase transitions (FOPTs) serve as comprehensive probes into our early Universe with associated generations of stochastic gravitational waves and superhorizon curvature perturbations or even primordial black holes. In characterizing the FOPT, phenomenological parameters like transition temperatures, strength factors, bubble separations, and energy budgets can be easily extracted from the macroscopic equilibrium features of the underlying particle physics models except for the terminal wall velocity of the bubble expansion, making it the last key parameter to be determined most difficultly due to the non-equilibrium nature of the microscopic transition model. In this paper, we propose a new model-independent approach to calculate the bubble wall velocity by virtue of an extra junction condition from the conservation and violation of the total number density current across the shock front (if any) and bubble wall, respectively.

Electrofuels (e-fuels) produced from renewable electricity and carbon sources have gained significant attention in recent years as promising alternatives to fossil fuels for the transportation sector. However, the highly volatile e-fuels, such as short-chain oxymethylene ethers are prone to flash vaporization phenomena, which is associated with the formation and growth of vapor bubbles, followed by explosive bursting of the liquid jet. The simulation of a flash boiling spray of such highly volatile liquid fuels in the context of automotive or cryogenic engines is numerically challenging due to several reasons, including (1) the complexity of the bubble growth process in the presence of multiple vapor bubbles and (2) the need to use an extremely small time step size to accurately capture the underlying physics associated with the flash boiling process. In this paper, we first present a bubble growth model in flash boiling microdroplets considering bubble interactions along with the finite droplet size effects. Based on the dimensional analysis of the newly derived Rayleigh Plesset equation, a simplified semi-analytical solution for bubble growth, which also includes the bubble inter

In the maritime industry, the injection of air bubbles into the turbulent boundary layer under the ship hull is seen as one of the most promising techniques to reduce the overall fuel consumption. However, the exact mechanism behind bubble drag reduction is unknown. Here we show that bubble drag reduction in turbulent flow dramatically depends on the bubble size. By adding minute concentrations (6 ppm) of the surfactant Triton X-100 into otherwise completely unchanged strongly turbulent Taylor-Couette flow containing bubbles, we dramatically reduce the drag reduction from more than 40% to about 4%, corresponding to the trivial effect of the bubbles on the density and viscosity of the liquid. The reason for this striking behavior is that the addition of surfactants prevents bubble coalescence, leading to much smaller bubbles. Our result demonstrates that bubble deformability is crucial for bubble drag reduction in turbulent flow and opens the door for an optimization of the process.

We carry out a series of experiments with a special interest on growing and condensing processes of vapor bubble(s) injected into a subcooled pool. We examine effects of the degree of subcooling of the bulk in the pool and injection rate of the vapor into the pool. We pay their special attention to (i) abrupt collapse of the injected vapor bubble to form micrometer-scale bubbles, and (ii) interaction of adjacent vapor bubbles laterally injected to the pool through the orifices. We have found that a fine disturbance does arise on the surface of the vapor bubble just prior to its abrupt collapse. The bubble never exhibits an abrupt collapse without such instability over the free surface. In the case of the injection of a pair of vapor bubbles through the neighboring orifices, the interaction between the bubbles and the effects of the induced flows by the bubble behaviors control the surface dynamics. This fluid dynamics video introduces those phenomena.

A longstanding prediction in interstellar theory posits that significant quantities of molecular gas, crucial for star formation, may be undetected due to being ``dark" in commonly used molecular gas tracers, such as carbon monoxide. We report the discovery of Eos, the closest dark molecular cloud, located just 94 parsecs from the Sun. This cloud is the first molecular cloud ever to be identified using H$_2$ far ultra-violet (FUV) fluorescent line emission, which traces molecular gas at the boundary layers of star-forming and supernova remnant regions. The cloud edge is outlined along the high-latitude side of the North Polar Spur, a prominent x-ray/radio structure. Our distance estimate utilizes 3D dust maps, the absorption of the soft X-ray background, and hot gas tracers such as O\,{\sc vi}; these place the cloud at a distance consistent with the Local Bubble's surface. Using high-latitude CO maps we note a small amount (M$_{\rm{H}_2}\approx$20-40\,M$_\odot$) of CO-bright cold molecular gas, in contrast with the much larger estimate of the cloud's true molecular mass (M$_{\rm{H}_2}\approx3.4\times 10^3$\,M$_\odot$), indicating most of the cloud is CO-dark. Combining observationa

Some of the peculiar electrodynamical effects associated with gauged ``dimension bubbles'' are presented. Such bubbles, which effectively enclose a region of 5d spacetime, can arise from a 5d theory with a compact extra dimension. Bubbles with thin domain walls can be stabilized against total collapse by the entrapment of light charged scalar bosons inside the bubble, extending the idea of a neutral dimension bubble to accommodate the case of a gauged U(1) symmetry. Using a dielectric approach to the 4d dilaton-Maxwell theory, it is seen that the bubble wall is almost totally opaque to photons, leading to a new stabilization mechanism due to trapped photons. Photon dominated bubbles very slowly shrink, resulting in a temperature increase inside the bubble. At some critical temperature, however, these bubbles explode, with a release of radiation.

Bubble segmentation and size detection algorithms have been developed in recent years for their high efficiency and accuracy in measuring bubbly two-phase flows. In this work, we proposed an architecture called bubble generative adversarial networks (BubGAN) for the generation of realistic synthetic images which could be further used as training or benchmarking data for the development of advanced image processing algorithms. The BubGAN is trained initially on a labeled bubble dataset consisting of ten thousand images. By learning the distribution of these bubbles, the BubGAN can generate more realistic bubbles compared to the conventional models used in the literature. The trained BubGAN is conditioned on bubble feature parameters and has full control of bubble properties in terms of aspect ratio, rotation angle, circularity and edge ratio. A million bubble dataset is pre-generated using the trained BubGAN. One can then assemble realistic bubbly flow images using this dataset and associated image processing tool. These images contain detailed bubble information, therefore do not require additional manual labeling. This is more useful compared with the conventional GAN which genera

We use computational methods to determine the minimal yield-stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension ($γ$) and the ratio of the yield-stress to the buoyancy stress ($Y$). For a given geometry, bubbles are static for $Y > Y_c$, which we determine for a range of shapes. Given that surface tension is negligible, long prolate bubbles require larger yield-stress to hold static compared to oblate bubbles. Non-zero $γ$ increases $Y_c$ and for large $γ$ the yield-capillary number ($Y/γ$) determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. 2D planar and axisymmetric bubbles are studied.

Primordial black holes (PBHs) may form before cosmological first-order phase transitions, leading to inevitable collisions between PBHs and bubble walls. In this Letter, we have simulated for the first time the co-evolution of an expanding scalar wall passing through a black hole with full numerical relativity. This black hole-bubble wall collision yields multiple far-reaching phenomena, including the PBH mass growth, gravitational wave radiations, and momentum recoil that endows PBHs with additional velocities, approximately doubling the formation rate for PBH binaries and hence strengthening the observational constraints on the PBH abundances.

We argue that expanding bubbles of nothing are a widespread feature of systems of black holes with multiple or non-spherical horizons, appearing as a limit of regions that are narrowly enclosed by the horizons. The bubble is a minimal cycle that links the Einstein-Rosen bridges in the system, and its expansion occurs through the familiar stretching of space in black hole interiors. We demonstrate this idea (which does not involve any Wick rotations) with explicit constructions in four and five dimensions. The geometries of expanding bubbles in these dimensions arise as a limit of, respectively, static black hole binaries and black rings. The limit is such that the separation between the two black holes, or the inner hole of the black ring, becomes very small, and the horizons of the black holes correspond to acceleration horizons of the bubbles. We also explain how a five-dimensional black hole binary gives rise to a different type of expanding bubble. We then show that bubble spacetimes can host black hole binaries and black rings in static equilibrium, with their gravitational attraction being balanced against the background spacetime expansion. Similar constructions are expected

For decades we have known that the Sun lies within the Local Bubble, a cavity of low-density, high-temperature plasma surrounded by a shell of cold, neutral gas and dust. However, the precise shape and extent of this shell, the impetus and timescale for its formation, and its relationship to nearby star formation have remained uncertain, largely due to low-resolution models of the local interstellar medium. Leveraging new spatial and dynamical constraints from the Gaia space mission, here we report an analysis of the 3D positions, shapes, and motions of dense gas and young stars within 200 pc of the Sun. We find that nearly all the star-forming complexes in the solar vicinity lie on the surface of the Local Bubble and that their young stars show outward expansion mainly perpendicular to the bubble's surface. Tracebacks of these young stars' motions support a scenario where the origin of the Local Bubble was a burst of stellar birth and then death (supernovae) taking place near the bubble's center beginning 14 Myr ago. The expansion of the Local Bubble created by the supernovae swept up the ambient interstellar medium into an extended shell that has now fragmented and collapsed into

We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the melting temperature on the GC content of the DNA sequence. Using these thresholds for base pair openings, we obtain bubble lifetime distributions for bubbles of lengths up to ten base pairs as the GC content of the sequences is varied, which are accurately fitted with stretched exponential functions. We find that for both models the average bubble lifetime decreases with increasing either the bubble length or the GC content. In addition, the obtained bubble length distributions are also fitted by appropriate stretched exponential functions and our results show that short bubbles have similar likelih