As predicted by classical macroscopic theory, the lifetime for nanoscale gas bubbles is extremely short. However, stable gas nanobubbles have been experimentally observed in recent years. In this report, we theoretically show that, if the inner density of gas bubbles is sufficiently high, the lifetime of nanobubbles can increase by at least 4 orders of magnitude, and even approaches the timescale for experimental observations. nanobubble, stability, long lifetime, inner density Interfaces of solid surfaces against liquids are of broad interest. If nanoscale gas nucleates at the liquid/solid interface, interfacial properties and dynamics of the system might significantly change, for example, by the occurrence of long-ranged interactions between hydrophobic interfaces immersed in water [1][2][3] , stability of colloidal systems [4] , flotation of minerals [5][6][7] , rupture of wetting films [8] , and reduction of friction and drag in microfluidic transportation [9][10][11][12][13] .There are many experiments supporting the existence of surface nanobubbles at the solid-liquid interface by atomic force microscopy (AFM) measurements [14][15][16][17][18][19][20][21][22] , and also other techniques [23,24] . However, the Laplace equationpredicts that nanoscale bubbles have a very high inner gas pressure. In the equation,ΔP is the pressure difference of bubble between its inner and outer, γ is the surface tension at the interface between bubble and liquid, and R is the radius of bubble. For example, a nanobubble with a radius of 10 nm would have an inner pressure of 144 atm. Consequently, the gas in the nanobubble would rapidly dissolve in ambient liquid. It should be noted that the validity of the Laplace equation on the nanometer dimension is questionable, and the surface tension on the nanometer dimension may be

No abstract

In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In this paper, we show that the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: Given a geometric representation of a Coxeter group in a Lorentz space, the set of limit directions of weights equals the set of limit roots. Additionally, we use Coxeter complexes to describe tangency graphs of the corresponding Boyd-Maxwell ball packings. Finally, we enumerate all the Coxeter systems that generate Boyd-Maxwell ball packings.2010 Mathematics Subject Classification. Primary 52C17, 20F55; Secondary 05C30.

Osteogenic glue that reproduces the natural bone composition represents the final frontier of orthopedic adhesives with the potential to revolutionize surgical strategies against comminuted fractures. However, it is difficult to achieve an all-in-one formula, which could provide flexible and reliable adhesiveness while avoiding interfering with or even promoting the healing of glued fractures. Herein, an osteogenic glue characterized by inorganic-in-organic integration between amine-modified mesoporous bioactive glass nanoparticles (AMBGN) and bioadhesive gelatin-dextran network (GelDex) is introduced as an all-in-one tool to flexibly adhere and splice bone fragments and subsequently guide fracture healing during degradation. Relying on such integration, a 4-fold improvement in cohesiveness is presented, followed by a nearly 5-fold enhancement in adhesive strength in ex vivo porcine bone samples. The reversible and re-adjustable adhesiveness also enables glue to effectively splice intricate fragments from highly comminuted fractures in the rabbit radius in an in vivo environment. Moreover, well-preserved organic-inorganic integrity during degradation of the glue guides sustained interfacial osteogenesis and achieve satisfying healing outcomes in glued fractures, as observed by the 2-fold improvement in biomechanical and radiological performance compared with commercially available cyanoacrylate adhesives. The current findings propose an all-in-one solution for the fixation of bone fragments during surgery.