Indentation of ellipsoidal and cylindrical elastic shells

Thin shells are found in nature at scales ranging from viruses to hens’ eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus et al. [Phys. Rev. Lett. (submitted)] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells

The indentation of pressurized elastic shells: From polymeric capsules to yeast cells

Pressurized elastic capsules arise at scales ranging from the 10 m diameter pressure vessels used to store propane at oil refineries to the microscopic polymeric capsules that may be used in drug delivery. Nature also makes extensive use of pressurized elastic capsules: plant cells, bacteria and fungi have stiff walls, which are subject to an internal turgor pressure. Here we present theoretical, numerical and experimental investigations of the indentation of a linearly elastic shell subject to a constant internal pressure. We show that, unlike unpressurized shells, the relationship between force and displacement demonstrates two linear regimes. We determine analytical expressions for the effective stiffness in each of these regimes in terms of the material properties of the shell and the pressure difference. As a consequence, a single indentation experiment over a range of displacements may be used as a simple assay to determine both the internal pressure and elastic properties of capsules. Our results are relevant for determining the internal pressure in bacterial, fungal or plant cells. As an illustration of this, we apply our results to recent measurements of the stiffness of baker’s yeast and infer from these experiments that the internal osmotic pressure of yeast cells may be regulated in response to changes in the osmotic pressure of the external medium

Wrinkling of pressurized elastic shells

We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We present scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells

Robust Multi-Partite Multi-Level Quantum Protocols

We present a tripartite three-level state that allows a secret sharing protocol among the three parties, or a quantum key distribution protocol between any two parties. The state used in this scheme contains entanglement even after one system is traced out. We show how to utilize this residual entanglement for quantum key distribution purposes, and propose a realization of the scheme using entanglement of orbital angular momentum states of photons.Comment: 9 pages, 2 figure

Triggered qutrits for Quantum Communication protocols

A general protocol in Quantum Information and Communication relies in the ability of producing, transmitting and reconstructing, in general, qunits. In this letter we show for the first time the experimental implementation of these three basic steps on a pure state in a three dimensional space, by means of the orbital angular momentum of the photons. The reconstruction of the qutrit is performed with tomographic techniques and a Maximum-Likelihood estimation method. In this way we also demonstrate that we can perform any transformation in the three dimensional space

A Cretaceous foraminiferal assemblage from West of Kerman area (Iran)

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Experimental Quantum Coin Tossing

In this letter we present the first implementation of a quantum coin tossing protocol. This protocol belongs to a class of ``two-party'' cryptographic problems, where the communication partners distrust each other. As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits. In this way, we have also performed the first complete quantum communication protocol with qutrits. In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum. We also show the experimental bounds of a possible cheater and the ways of detecting him

Angular Schmidt Modes in Spontaneous Parametric Down-Conversion

We report a proof-of-principle experiment demonstrating that appropriately chosen set of Hermite-Gaussian modes constitutes a Schmidt decomposition for transverse momentum states of biphotons generated in the process of spontaneous parametric down conversion. We experimentally realize projective measurements in Schmidt basis and observe correlations between appropriate pairs of modes. We perform tomographical state reconstruction in the Schmidt basis, by direct measurement of single-photon density matrix eigenvalues.Comment: 5 pages, 4 figure

Superpositions of the Orbital Angular Momentum for Applications in Quantum Experiments

Two different experimental techniques for preparation and analyzing superpositions of the Gaussian and Laguerre-Gassian modes are presented. This is done exploiting an interferometric method on the one hand and using computer generated holograms on the other hand. It is shown that by shifting the hologram with respect to an incoming Gaussian beam different superpositions of the Gaussian and the Laguerre-Gaussian beam can be produced. An analytical expression between the relative phase and the amplitudes of the modes and the displacement of the hologram is given. The application of such orbital angular momenta superpositions in quantum experiments such as quantum cryptography is discussed.Comment: 18 pages, 4 figures. to appear in Journal of Optics