Bending Elasticity Measurements for Fluctuating Vesicles (Alex)

The mechanical properties of lipid membranes have been extensively studied over the past few decades [1]. Their ability to bend under very low stress is one of the main mechanical properties of such soft materials. This softness is characterised by a very small value of the bending modulus (on the order of 10 kBT). As a result, a flaccid vesicle can attain many thermally allowed shapes at constant volume, which leads the thin-walled vesicles to fluctuate (the so-called flicker phenomenon) [1]. Measurements of these thermal excitations have been used to estimate the bending modulus of red blood cells and artificial vesicles [2][3][4]. Here, we re-examine this methodology and discuss some of its limitations; e.g., video-microscopy gives only partial information in the sense that it provides a two-dimensional view of the three-dimensionally fluctuating vesicle. In order to overcome this technical limitation, we develop two new possible methods for inferring mechanical information about membranes from the projected intensity of fluorescent quasi-spherical vesicles.

[1] U. Seifert, Adv. Phys. 46, 13 (1997), [2] J. F. Faucon et al., J. Phys. (Paris) 50, 2389 (1989), [3] J. Pécréaux et al., Eur. Phys. J. E 13, 277 (2004), [4] P. Méléard et al., Eur. Phys. J. E 34, 116 (2011)

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The Strong Disorder Renormalisation Group in the age of Tensor Networks (Andrew)

We have developed a tensor network method of performing the numerical strong disorder renormalisation group (SDRG) approach [1] to the random 1D spin-1/2 Heisenberg model. The numerical SDRG can be reformulated as a randomly branching binary tree tensor network (TTN). This knowledge then enables us to perform a variational update to the network to improve accuracy as well as efficiently calculate expectation values and entanglement entropy. Furthermore, I will discuss how the geometry of the network is related to the physical properties that the network can model.

[1] T. Hikihara, A. Furusaki, and M. Sigrist, Phys. Rev. B, vol. 60, p. 12116, 1999.