General neck condition for the limit shape of budding vesicles

The shape equation and linking conditions for a vesicle with two-phase domains are derived. We refine the conjecture on the general neck condition for the limit shape of a budding vesicle proposed by J\"{u}licher and Lipowsky [Phys. Rev. Lett. \textbf{70}, 2964 (1993); Phys. Rev. E \textbf{53}, 2670 (1996)], and then we use the shape equation and linking conditions to prove that this conjecture holds not only for axisymmetric budding vesicles, but also for asymmetric ones. Our study reveals that the mean curvature at any point on the membrane segments adjacent to the neck satisfies the general neck condition for the limit shape of a budding vesicle when the length scale of the membrane segments is much larger than the characteristic size of the neck but still much smaller than the characteristic size of the vesicle.Comment: 11 pages, 4 figure

The hydrostatic equilibrium and Tsallis equilibrium for self-gravitating systems

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium of self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions and Tsallis equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.Comment: 7 pages, 9 Reference

The role of phosphorylation and dephosphorylation of shell matrix proteins in shell formation : an in vivo and in vitro study

Protein phosphorylation is a fundamental mechanism regulating many aspects of cellular processes. Shell matrix proteins (SMPs) control crystal nucleation, polymorphism, morphology, and organization of calcium carbonate crystallites during shell formation. SMPs phosphorylation is suggested to be important in shell formation but the mechanism is largely unknown. Here, to investigate the mechanism of phosphorylation of SMPs in biomineralization, we performed in vivo and in vitro experiment. By injection of antibody against the anti-phosphoserine/threonine /tyrosine into the extrapallial fluid of the pearl oyster Pinctada fucata, phosphorylation of matrix proteins were significantly reduced after 6 days. Newly formed prismatic layers and nacre tablet were found to grow abnormally with reduced crystallinity and possibly changed crystal orientation shown by Raman spectroscopy. In addition, regeneration of shells is also inhibited in vivo. Then, protein phosphatase was used to dephosphorylate SMPs extracted from the shells. After dephosphorylation, the ability of SMPs to inhibiting calcium carbonate formation have been reduced. Surprisingly, the ability of SMPs to modulate crystal morphology have been largely compromised although phosphorylation extent remained to be at least half of the control. Furthermore, dephosphorylation of SMPs changed the distribution of protein occlusions and decreased the amount of protein occlusions inside crystals shown by confocal imaging, indicating interaction between phosphorylated SMPs and crystals. Taken together, this study provides insight into the mechanism of phosphorylation of SMPs during shell formation

Paradoxes of causal loops in spacetime

There is, among some scientists and philosophers, the idea that any theory that would allow the time travel would introduce causal issues. These types of temporal paradoxes can be avoided by the Novikov self-consistency principle or by a variation in the interpretation of many worlds with interacting worlds. The world in which we live has, according to David Lewis, a Parmenidean ontology: "a manifold of events in four dimensions," and the occupants of the world are the 4-dimensional aggregates of the stages - "temporal lines". The causal loops in backwards time travel involve events that appear to "come from nowhere," paradoxical "self-existent" objects or information, resulting in a bootstrap paradox. Many believe that causality loops are not impossible or unacceptable, but only inexplicable. DOI: 10.13140/RG.2.2.28792.7040

Semiclassical Green Function in Mixed Spaces

A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations of Green functions as two special cases of the form.Comment: 8 pages, typeset by Scientific Wor