Random tensor models in the large N limit: Uncoloring the colored tensor models

Tensor models generalize random matrix models in yielding a theory of dynamical triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a 1/N expansion and a continuum limit accessible analytically. In this paper we prove that these results extend to the most general tensor model for a single generic, i.e. non-symmetric, complex tensor. Colors appear in this setting as a canonical book-keeping device and not as a fundamental feature. In the large N limit, we exhibit a set of Virasoro constraints satisfied by the free energy and an infinite family of multicritical behaviors with entropy exponents \gamma_m=1-1/m.Comment: 15 page

Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems

In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincar\'e equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant r\'egime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.Comment: 4 pages, 5 fi

Rapid extraction of genomic DNA from small plant leaf samples

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Measurements of Extended Magnetic Fields in Laser-Solid Interaction

Magnetic fields generated from a laser-foil interaction are measured with high fidelity using a proton radiography scheme with in situ x-ray fiducials. In contrast to prior findings under similar experimental conditions, this technique reveals the self-generated, Biermann-battery fields extend beyond the edge of the expanding plasma plume to a radius of over 3.5 mm by t=+1.4 ns, a result not captured in state-of-the-art magneto-hydrodynamics simulations. An analysis of two mono-energetic proton populations confirms that proton deflection is dominated by magnetic fields far from the interaction (>2 mm) and electric fields are insignificant. Comparisons to prior work suggest a new physics mechanism for the magnetic field generation and transport in laser-solid interactions.Comment: 9 pages, 8 figure

Molecular mechanistic origin of the toughness of natural adhesives, fibres and composites

Natural materials are renowned for their strength and toughness(1-5). Spider dragline silk has a breakage energy per unit weight two orders of magnitude greater than high tensile steel(1,6), and is representative of many other strong natural fibres(3,7,8). The abalone shell, a composite of calcium carbonate plates sandwiched between organic material, is 3,000 times more fracture resistant than a single crystal of the pure mineral(4,5). The organic component, comprising just a few per cent of the composite by weight(9), is thought to hold the key to nacre's fracture toughness(10,11). Ceramics laminated with organic material are more fracture resistant than non-laminated ceramics(11,12), but synthetic materials made of interlocking ceramic tablets bound by a few weight per cent of ordinary adhesives do not have a toughness comparable to nacre(13). We believe that the key to nacre's fracture resistance resides in the polymer adhesive, and here we reveal the properties of this adhesive by using the atomic force microscope(14) to stretch the organic molecules exposed on the surface of freshly cleaved nacre. The adhesive fibres elongate in a stepwise manner as folded domains or loops are pulled open. The elongation events occur for forces of a few hundred piconewtons, which are smaller than the forces of over a nanonewton required to break the polymer backbone in the threads. We suggest that this 'modular' elongation mechanism might prove to be quite general for conveying toughness to natural fibres and adhesives, and we predict that it might be found also in dragline silk