The structure of isoperimetric bubbles on $\mathbb{R}^n$ and $\mathbb{S}^n$

The shape of a nucleus is one of fundamental nuclear properties. We perform a\nsystematic investigation of bubble nuclei that also exhibit shape coexistence\nin Hf, W, Os, Pt and Hg even-even isotopes using the deformed relativistic\nHartree-Bogoliubov theory in continuum. For a systematic study, we first\nconsider nuclear bubble structures and shape coexistence separately. We confirm\nthat deformations and pairing correlations hinder bubble structures by\ncomparing our results with those from relativistic continuum Hartree-Bogoliubov\ntheory that assumes spherical symmetry in nuclei. We then predict candidate\nisotopes with both bubble structure and shape coexistence. We observe that the\ndepletion fraction factor that characterizes bubble structure is mostly smaller\nin oblate deformation than in prolate, while some isotopes such as $^{206}$Os\nhave bubble structures both in oblate and prolate deformations. We compare the\nproton single-particle energy levels for the candidates of shape coexistence\nboth with only prolate bubble structure and with prolate and oblate bubble\nstructures.\n

Acoustic cavitation is a process by which small bubbles are formed in a liquid that is exposed to sound waves such as ultrasound. These bubbles are peculiar because they expand and collapse violently on themselves resulting in high temperatures (>5000C) and pressures (>100 atm) inside them. This process happens repeatedly and at the frequency of the ultrasound. Furthermore, these bubbles occur in large ensembles of thousands often forming larger structures far greater than the bubbles themselves. Acoustic cavitation has many industrial applications from cleaning of delicate electronic components to sonochemistry (the use of ultrasound to enhance chemical reactions in solution). Sonochemistry has gained attention because of its high energy efficiency, low waste production and synergistic capabilities with other green technologies like microwaves. Therefore, precise understanding of cavitation inside sonoreactors (chemical reactors with the capability to apply ultrasound to the reactants) is important to up-scale this technology. Despite its benefits, upscaling sonoreactors has been a major industrial challenge due to technical challenges as well as difficulties in predicting their behaviour due to the extremely complex nature of cavitation. Numerical methods can be used to predict the behaviour of cavitation, but it has been a numerical challenge for decades. These bubbles interact with each other by coalescing and breaking up and they effect the applied ultrasound as well by scattering on coming waves. The problem is highly non-linear. Early simulations focused on single bubble dynamics but over decades of computational advancements larger ensembles of bubbles could be simulated. However, dimensions of sonoreactors can range between a few millimeters to meters - which is much larger than the bubbles or bubble structures. Furthermore, the time scales on which bubble oscillation, translation, structure formation, and chemical reactions occur are spread between microseconds to seconds. Thus, modelling of the full n-body problem of cavitation and it’s non-linear coupling with the soundfield is nearly impossible. However averaging methods exist to simplify the problem and can be used in the design and development of sonoreactors. The work here tries to use existing models as well as develop them to find a middle ground in the complexity of modeling the dynamics inside sonoreactors. To this extent, experimental measurements of the soundfield of sonoreactors were compared to numerical simulations to verify and optimize the model.

The interface area between the bubble and emulsion phases in a fluidized catalyst bed is one of the important parameters used to analyze and design the fluidized bed reactor. We used a fast-scanning X-ray CT system to observe the bubble shape and structure. We then obtained the transient 2-dimensional cross sectional gas-phase distribution in a fluidized catalyst bed. Using image-processing techniques, pseudo 3-dimensional images of the bubbles were reconstructed. The bubble structure was studied based on the 3-dimensional images and the previously obtained results in a 2-dimensional fluidized bed. It was found that the bubble shape was not spherical but complicated, and that the bubbles ascending in a fluidized catalyst bed consisted of some smaller bubbles.

Morphological selections and dynamical evolutions of buckling patterns in SiAlNx films: From straight-sided to telephone cord or bubble structures

An analysis has been made of the bubble and crystal structure and of the isotopic composition of a hailstone from a severe storm which occurred near Cardiff on 1 July 1968. A trajectory for the stone has been deduced from the isotopic data which is consistent with its crystal and bubble structures. Updraught profiles have been calculated also and are in reasonable agreement with those inferred from the extended parcel theory.

Plasma bubbles in the ionosphere have a significant effect on radio wave communication and navigation. Under the worst condition, it will fail to function the systems relying on the ionosphere. On the other hand, the physical mechanisms of evolution and diurnal variations of the plasma bubbles in the ionosphere are still unclear. Therefore, it is still worthy to simulate the plasma bubbles in the ionosphere for radio wave propagation and science. In this study, the equatorial plasma bubbles induced by one- and two- dimensional disturbance in the ionosphere are simulated, where traveling ionospheric disturbance (TID) is used to produce the two-dimensional disturbance in the ionosphere. The dispersion relationship of gravity wave is used to represent the corresponding wavelength of TID in this study. More importantly, we investigate the effect of recombination rate on the development of plasma bubbles by numerical simulation. The simulation results show that the recombination rate of the plasma in the ionosphere has a significant effect on the development of plasma bubbles. The greater the recombination rate, the more time it takes to produce the plasma bubbles. For one-dimensional disturbance in the ionosphere, there is no significant effect in the structure of plasma bubbles for the recombination rate of the plasma. However, the recombination rate plays a significant effect on the structure of plasma bubbles induced by TID. When the recombination rate is less in numerical simulation, the complex structure including bifurcation, plume-like structures, and pinching of plasma bubbles can occur in the development of bubbles. In contrast, the structure of plasma bubbles is simpler when the recombination rate is greater in simulation. As a result, the recombination rate of the plasma is a significant factor for simulating the plasma bubbles in the ionosphere. The greater recombination rate can result in the slowing down of equatorial plasma bubbles and the simplifying the structure of the bubbles as well. In addition, it is found that not all of plasma bubbles at the bottom of the ionosphere can grow to the top of the ionosphere when many bubbles occur on the bottom side. The direction of the polarization electric field near the bubbles can be changed in the non-linear development of the bubbles. Therefore, only the bubbles where the polarization electric field is always eastward can develop to the topside.

Summary form only given. In recent years, several novel structures of amplifying random media have been reported for controlling the spectrum and efficiency of random laser emission [1-3]. For example, monodisperse scattering particles have shown to allow us to control the emission spectrum [1], and when there is a defect in the distribution of monodisperse particles, light is found to be concentrated and enhanced in the defect region [2]. These two studies have revealed that the laser emission can be controlled by adding some regularity to the random structure. Another variation in the structure is the shape of the scatterers, which has been found to affect the efficiency of random lasing [3]. In this study, we investigate the random laser emission from random media with a “bubble structure” which has non-scattering regions distributed randomly. Although this structure seems to be similar to superdiffusive media [4], the non-scattering regions are not controlled to realize a Levy flight for light.Figure 1 shows a schematic of the random structures we used. Random media with a bubble structure are fabricated by using pulverized photopolymer (Gluelabo GLX19-117) doped with rhodamine 6G (R6G) laser dye as spacer particles (SPs). The size of SPs ranges from 53 to 300 μm. TiO2 scattering particles with a diameter of 180 nm and the SPs are dispersed in light curable photopolymer (Adell K40) which is doped with R6G with a density of 6.7 × 103 mol/l. The volume filling fraction of scattering particles is 10%. K40 and GLX polymers have the same refractive index of 1.5, and are doped with the same density of R6G. The liquid polymer medium is then put on a slide glass with a cover glass on top and cured by illuminating it with ultraviolet and visible light for 10 min. The thickness of the fabricated random media is 0.2 mm. A typical emission spectrum obtained from a bubble structure is shown in Fig. 2, together with one for a homogeneous medium for comparison. The bubble medium is seen to exhibit higher peak intensity than the homogeneous medium. We performed experiments with various ranges of the size of SPs: 53-300 μm, 53-106 μm, 106-180 μm, and 180-300 μm. Results show that bubble structures present up to 1.5 times higher emission intensities than the homogeneous one for the SPs of 53-300 μm. The filling fraction of SPs in which strong light emission occurs was found to be 5 to 10%. It is interesting to note that amplifying random media with R6G doped GLX as a host medium show no laser emission so that the emission efficiency of R6G in GLX is much lower than R6G in K40.We investigated the mode properties of the bubble medium to examine the reason for the strong emission. The intensity correlation between different pairs of spikes in the emission spectrum was evaluated [5] for a homogeneous medium and a bubble medium containing 5% of the SPs with sizes of 53-300 μm. The average number of independent resonant modes was found to be about 2.7 for both cases, whereas the average number of spikes per mode was about 1.5 for the bubble medium and 2 for the homogeneous medium. The result shows that addition of SPs in an amplifying random medium leads to a reduction in the number of resonant frequency in each random lasing mode. Numerical simulations are being planned to elucidate this phenomenon.

An investigation was made of the gases evolved during the firing of porcelain enamels. The investigation included (1) examination of gas evolution with a microscope while specimens were being fired, (2) examination of fired specimens for changes in bubble structure with firing time, (3) examination of the changes in the normal gas evolution when water‐free enamels were used, (4) analysis with the mass spectrometer of the gases trapped in the bubble structure after varying firing times, (5) determination of the source of the carbon gases in the bubble structure using radioactive C14 as a tracer, and (6) determination of the effect of various pretreatments of the clay used for suspending the coating slip on the resulting bubble structure of the fired specimens. The results showed that the principal gases evolved during the firing were carbon monoxide, carbon dioxide, and hydrogen. The blistering that is often observed in the early stage of firing when porcelain enamels are applied to low‐carbon steel was found to be caused by evolution of the carbon gases formed by the oxidation of the carbon in the steel. Evidence was obtained that the hydrogen formed from the reaction between the dissolved water in the coating and the hot‐iron base slowly diffuses into the coating as the firing continues. Some of the hydrogen also diffuses into the metal. On fast cooling this hydrogen is expelled, causing bubbles to form in the coating at the interface. It was found that a considerable portion of the bubble structure in an enamel fired for a normal time is due to some impurity in the clay mill addition. The impurity is probably organic matter adsorbed on the clay particles.

The comparative effect of several clays on the physical characteristics of typical ground‐coat and cover enamels was investigated. In the ground‐coat enamels, the effect of the clays on the firing characteristics, the development of the bubble structure, reboiling, and the set characteristics were studied. Suitable amounts of each of the clays were used as mill additions to the following cover enamels: (1) superopaque antimony frit, (2) zirconium frit, (3) a clear frit as used for colors, and (4) fluoride frit. The effect on reflectance, gloss, and the resistance to gouging was noted on these samples. Spectrophotometer curves were run on selected cover‐enamel surfaces. The clays showed a widely varying effect on the set characteristics and the bubble structure of the ground‐coat enamels. The different clays with the antimony frit caused a wide variation in the gouging characteristics while, with the zirconium frit, the clays had less effect, the gouging values being uniformly high.SummaryThe general effect of the various clays in sheet‐iron ground‐coat and cover enamels may be summarized in the following manner:(1) In the clays tested, the chemical analysis and the physical data, such as particle size, hydrogen‐ion concentration, or pyrometric cone equivalent, do not give a satisfactory basis for predicting the general usability of clays in porcelain enamels.(2) When the various clays were milled in the same ground‐coat frit and then fired, photomicrographs showed a widely varying bubble structure in the fired enamel.(3) Some of the clays brought about an earlier development of adherence or bond between the metal and the ground‐coat enamel.(4) The clays which gave a large bubble structure in the ground‐coat layer, when impacted with the falling‐weight test, gave a large fracture area, while those giving a small bubble structure caused a small fracture area.(5) The freshly milled ground‐coat enamel containing the various clays was adjusted to give (a) a pickup of 40 gm. per sq. ft., thus yielding a variable solids‐to‐liquid ratio and (b) a specific gravity of 1.65, yielding a constant solids‐to‐liquid ratio in the slips. The enamel slips were tested for the weight picked up after specific aging periods; the various clays were found to cause an increase in the weight picked up in some cases, in others a decrease, while others gave practically no change in the weight‐pickup value after various aging periods.(6) At an application weight of 60 gm. per sq. ft. the different clays caused a maximum variation of about 6% reflectance in the antimony, 12% in the zirconium, and 25% in the clear frit.(7) The spectrophotometric curves of the various clay and frit combinations showed that the clays gave uniform spectral values in the antimony and clear frits; in the zirconium frit, a greater variation in reflectance was found in the red portion of the spectrum than in the blue or green portions.(8) The various clays in the antimony frit showed a marked difference in the gouging characteristics of the surfaces, while in the zirconium frit the clays caused only a slight variation in gouging as all of the values were uniformly high.

In this work, we propose the SPR fiber sensor based on a bubble structure. Conventional SPR optical fiber sensors have an anomalous broadening of the resonance dip in the near-infrared band. Therefore, we propose to utilize a bubble structure to improve the FWHM of the spectrum. The sensor utilizes no-core fiber as the sensing platform and multimode fiber as the transmission fiber, and fabricates a bubble at the fusion of the two fibers. The effect of bubble size on the SPR effect is investigated experimentally, and the results show that bubbles can improve the sensitivity and reduce the FWHM of SPR sensor. The refractive index sensing test was implemented on the proposed SPR bubble sensor. The experimental results showed that the bubble structure enhanced the maximum sensitivity of the SPR sensor by 927.7 nm/RIU. Finally, the effect of the bubble on the response time of the sensor is discussed. The method of using a bubble structure to improve sensor performance is simple to operate and easy to implement.

Introduction Applications of acoustic cavitation gain in importance and become more widespread recently. While its utilization in traditional fields persists and is subject to optimization, new types and areas of application emerge as well. In many cases, however, it is realized that not all physical processes involved are well enough understood yet. In particular the link between process parameters like acoustic field geometry, frequency or intensity, and the observed or desired effects, might not be sufficiently clear. This is sometimes true even qualitatively, and then a quantitative analysis is naturally out of the scope anyway. An important aspect of this link in acoustic cavitation is the formation of bubble structures: The applied sound field generates certain bubble distributions in space and time with specific bubble size populations, which in turn mediate the microscopic effects via their oscillation and/or collapse properties. A systematic characterization and comprehension of different bubble structures has started only recently [1], and here we want to give a further contribution to advance the knowledge with respect to the process chain in acoustic cavitation. A distinct bubble structure at 230 kHz has been observed and investigated by means of high-speed recordings, sonoluminescence measurements, and cleaning tests. We speculate that the observed phenomena are universal for a class of acoustic field geometries over a broader frequency range.

We study the effects of deformation, tensor and pairing correlation on the evolution of bubble structure in 46Ar, 22O and Cl isotopes using a deformed Skyrme-Hartree-Fock model with BCS and Lipkin-Nogami number projection approximation. The parameter SLy5 of the Skyrme energy functionals is adopted together with various kinds of density-dependent pairing interaction and various kinds of tensor interaction. In the spherical case, considering pairing correlation (IS + IV) or switch off pairing, there is a clear bubble structure in 46Ar with interaction SLy5 + Tw, respectively. For 46Ar, we find that deformation weakens the bubble structure strongly, and pairing correlation also weakens the bubble in 46Ar and 22O , respectively. On the other hand, the SLy5 + Tw + IS + IV interaction evolves the bubble structure of neutron-rich Cl isotopes 43-47Cl in deformed cases because the occupation probability of states $ 2s_{1/2}$ decreases from 1 to 0.5.

In the framework of the Skyrme–Hartree–Fock–Bogoliubov approach with the SkT interaction, the pairing effects on the proton bubble structures of 46Ar and 206Hg are discussed. In calculations, three kinds of pairing forces (volume, surface and mixed pairing interactions) are used. For 46Ar, it is shown that the bubble structure with the volume pairing is almost the same as that with the mixed pairing. The bubble with the surface pairing is less pronounced than those with the volume and mixed pairings. Analyzing the density distributions and occupation probabilities of the proton s states and the quasi-degeneracy between the proton 2s1/2 and 1d3/2 orbitals, we explain the difference between the bubble structure with the surface pairing and those with the volume and mixed pairings. For 206Hg, it is seen that the proton density distribution with the surface pairing is different from those with the volume and mixed pairings in the whole region of the radial distance. In addition, it is found that the bubbles with the three pairing forces are different from each other and the least pronounced bubble is obtained with the surface pairing. Thus the selection of the pairing force is important for the study of the nuclear bubble structure.

This study investigated the effect of hot water on the rheological properties of the batter, bubble structure, and sensory properties of the bread. We focused on the thickening effect of starch gelatinization and developed a method to produce gluten‐free rice flour bread without additives by increasing the temperature of the water used in the production of gluten‐free rice flour bread. Hot water at 50–80°C was more effective than 5°C in improving bubble number and bubble size. In batters prepared using water at 68 and 70°C, which had excellent bubble structure, the frequency‐dependent fluctuations of the storage and loss moduli were smaller, while the loss coefficient values were larger. The batters showed more favorable sensory qualities at higher temperatures than the cold‐water batters. Appropriate temperature control of the water added during batter preparation can enable easier and cost‐effective preparation of high‐quality gluten‐free rice flour bread.Novelty impact statement Appropriate temperature control of the water added during batter preparation improved the quality of gluten‐free rice flour bread. Batter prepared with water at 68 and 70°C improved rheological properties, bubble structure, and sensory properties significantly.

In view of insufficient insulation of the typical plastic greenhouses in alpine regions, the study, with Numercial software, designed a plastic film with bubble structure and carried out five sets of comparative simulation experiments by changing the diameter of bubbles. The results of experiments show that in the visible light range (wavelength range from 300nm to 1100 nm), the transmittance increases with increasing wavelength, and it can be maximized when the diameter of the bubble is gradually changed. When the wavelength is less than 600 nm, the transmittance of the film is less than 60%. However, in the case of a film with a bubble structure, the transmittance of the film is significantly enhanced in the range of 300 to 600 nm, and it is also obviously improved at 600 to 1100 nm, especially at 700 to 1100 nm, it can still increase by about 10% and thereby exceeds 80%. The reflectivity is overall lower than that of the bubble-free structure, which further demonstrates that the structure proposed in this paper can further increase the utilization of solar energy from the aspects of increasing transmittance and reducing reflectivity.