B. Allen, S. Rogers, J. Ghilardi, P. Menning, M. Kuskovsky, I. Baubaum, D. Simone, P. Manyth, Noxious cutaneous thermal stimuli induce a graded release of endogenous substance P in the spinal cord: Imaging peptide action in vivo. J. Neurosci 17, 5221–5227 (1997) R. Bar-Ziv, E. Moses, Instability and pearling states produced in tubular membranes by competition of curvature and tension phys. Rev. Lett. 73, 1392–1395 (1994) D. Bratsun, A. DeWit, Buoyancy-driven pattern formation in reactive immiscible two-layer systems. Chem. Eng. Sci. 66, 5723–5734 (2011) P. Byrd, M. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists, 2nd edn. (Springer, Berlin, 1971) R. Capovilla, C. Chryssomalakos, J. Guven, Elastica hypoarealis. Eur. Phys. J. B 29, 163–166 (2002)MathSciNet K. Cole, Surface forces of the arbacia egg. J. Cell. Comp. Physiol. 1, 1–9 (1932) C. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante. J. Math. Pures et Appliques 6, 309–320 (1841) P. Djondjorov, M. Hadzhilazova, I. Mladenov, V. Vassilev, Beyond Delaunay surfaces. J. Geom. Symmetry Phys. 18, 1–11 (2010) P. Djondjorov, V. Vassilev, I. Mladenov, Deformation of injected vesicles adhering onto flat rigid substrates. Comput. Math. Appl. 64, 214–220 (2012) P. Djondjorov, V. Vassilev, M. Hadzhilazova, I. Mladenov, Analytic description of the viscous fingering interface in a Hele-Shaw cell. Geom. Integr. Quant. 13, 107–113 (2012a) L. dos Reis, A. Miranda, Controlling fingering instabilities in nonflat Hele-Shaw geometries. Phys. Rev. E 84, 066313 (2011) J. Eells, The surfaces of Delaunay. Math. Intell. 9, 53–57 (1987) M. Hadzhilazova, J.-F. Ganghoffer, I. Mladenov, Analytical description of the shapes of beaded nerve fibres. CRAS (Sofia) 63, 1155–1162 (2010) M. Hadzhilazova, I. Mladenov, Surface tension via Cole’s experiment, in Proceedings of the Tenth International Summer School of Chemical Engineering, (Sofia, 2004) pp. 195–200 M. Hadzhilazova, I. Mladenov, A mathematical examination of squeezing and stretching of spherical vesicles. Geom. Integr. Quant. 6, 231–239 (2005) M. Hadzhilazova, I. Mladenov, J. Oprea, Unduloids and their geometry. Archivum Mathematicum 43, 417–429 (2007) K. Kenmotsu, Surfaces of revolution with prescribed mean curvature. Tohoku Math. J. 32, 147–153 (1980) K. Kenmotsu, Surfaces of revolution with periodic mean curvature. Osaka J. Math. 40, 687–696 (2003) M. Kozlov, V. Markin, Possible mechanism of membrane fusion. Biofizika 28, 242–247 (1983) P. Kuzmin, J. Zimmerberg, Y. Chizmadzhev, F. Cohen, A quantitative model for membrane fusion based on low-energy intermediates. Proc. Natl. Acad. Sci. 98, 7235–7240 (2001) E. Leandro, R. Oliveira, J. Miranda, Geometric approach to stationary shapes in rotating Hele-Shaw flows. Phys. D Nonlinear Phenom. 237, 652–664 (2008) P. Manthy, C. Allen, J. Ghilardi, Rapid endocytosis of a G protein-coupled receptor: Substance P-Evoked internalization of its receptor in the rats triatum in vivo. Proc. Natl. Acad. Sci. USA 92, 2622–2626 (1995) V. Markin, D. Tanellian, R. Jersild, S. Ochs, Biomechanics of stretch-induced beading. Biophys. J. 78, 2852–2860 (1999) V. Markin, J. Albanesi, Membrane fusion: Stalk model revisited. Biophys. J. 82, 693–712 (2002) I. Mladenov, Delaunay surfaces revisited. CRAS (Sofia) 55, 19–24 (2002a) I. Mladenov, New solutions of the shape equation. Eur. Phys. J. B 29, 327–330 (2002) H. Naito, M. Okuda, Z.-C. Ou-Yang, New solutions to the Helfrich variation problem for the shapes of lipid bilayer vesicles: Beyond Delaunay’s surfaces. Phys. Rev. Lett. 74, 4345–4348 (1995) J. Nye, H. Lean, A. Wright, Interfaces and falling drops in a Hele-Shaw cell. Eur. J. Phys. 5, 73–80 (1984) S. Ochs, R. Jersild, Myelin intrusions in beaded nerve fibers. Neuroscience 36, 553–567 (1990) S. Ochs, R. Pourmand, R. Jersild Jr., Origin of beading constrictions at the axolemma: Presence in unmyelinated axons and after ί,ί' -Iminodipropionitrile(IDPN) degradation of the cytoskeleton. Neuroscience 70, 1081–1096 (1996) S. Ochs, R. Pourmand, R. Jersild Jr., R. Friedman, The origin and nature of beading: A reversible transformation of the shape of nerve fibers. Neurobiol 52, 391–426 (1997) R. Oliveira, J. Miranda, E. Leandro, Ferrofluid patterns in a radial magnetic field: Linear stability, nonlinear dynamics, and exact solutions. Neuroscience 77, 016304 (2008) J. Oprea, Differential Geometry and Its Applications, 3rd edn. (Mathematical Association of America, Washington D. C, 2007) Z.-C. Ou-Yang, J.-X. Liu, Y.-Z. Xie, Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases (World Scientific, Hong Kong, 1999) P. Saffman, G. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid. Proc. Roy. Soc. A 245, 312–329 (1958) K. Schwarzenberger, K. Eckert, S. Odenbach, Relaxation oscillations between Marangoni cells and double diffusive fingers in a reactive liquid-liquid system. Chem. Eng. Sci. 68, 530–540 (2012) D. Tanelian, V. Markin, Biophysical and functional consequences of receptor-mediated nerve fiber transformation. Biophys. J. 72, 1092–1108 (1997) V. Vassilev, P. Djonjorov, I. Mladenov, Cylindrical equilibrium shapes of fluid membranes. J. Phys. A: Math. Theor. 41, 435201–16 (2008) V. Vassilev, P. Djonjorov, I. Mladenov, Symmetry groups, conservation laws and group-invariant solutions of the membrane shape equation. Geom. Integr. Quant. 7, 265–279 (2006) V. Vassilev, P. Djonjorov, I. Mladenov, On the translationally-invariant solutions of the membrane shape equation. Geom. Integr. Quant. 8, 312–321 (2007) E. Whittaker, G. Watson, A Course of Modern Analysis, (Cambridge University Press, Cambridge, 1922) M. Yoneda, Tension at the surface of sea-urchin egg: A critical examination of Cole’s experiment. J. Exp. Biol. 41, 893–906 (1964) H. Zhu, S. Wu, S. Schachter, Site-specific and sensory neuron-dependent increases in postsynaptic glutamate sensitivity accompany serotonin-induced long-term facilitation at aplysia sensomotor synapses. J. Neurosci. 17, 4976–4985 (1997)