A discontinuous finite element approximation of quasi-static growth of brittle fractures

We propose a discontinuous finite element approximation for a model of quasi-static growth of brittle fractures in linearly elastic bodies formulated by Francfort and Marigo, and based on the classical Griffith's criterion. We restrict our analysis to the case of anti-planar shear and we consider discontinuous displacements which are piecewise affine with respect to a regular triangulation.Comment: 34 pages, 4 figure

Medical implantable devices for the controlled release of anti-TGF-beta1 in the repair of peripheral nerve injuries

The development of novel bioartificial nerve grafts which release soluble therapeutic agents, shows great promises guiding the extension of the injured axons and optimizing and improving the degree and specificity of neural outgrowth. The TGF-â family cytokines are polypeptides involved in pathogenesis of neuropathies during nerve lesion. In particular, studies carried out on TGF-â1 have demonstrated its key-role as a humoral stimulus in scar formation. The use of neutralising antibodies to this pro-fibrotic factor, incorporated and released by medical devices, could be potentially useful to get improved results in nerve repair. The aim of this study was to characterise the uptake and release of antibodies, structurally no different from the anti-TGFâ1 specific ones, by innovative constructs based on the use of biodegradable and biocompatible compounds with which to support and improve peripheral nerve repair

Sufficient conditions for the existence of a center in polynomial systems of arbitrary degree

In this paper, we consider polynomial systems of the form $\dot x=y+P (x,y)$, $\dot y=-x+Q(x,y)$, where $P$ and $Q$ are polynomials of degree $n$ wihout linear part. For the case $n=3$, we have found new sufficient conditions for a center at the origin, by proposing a first integral linear in certain coefficient of the system. The resulting first integral is in the general case of Darboux type. By induction, we have been able to generalize these results for polynomial systems of arbitrary degree

Experimental achievement of the entanglement assisted capacity for the depolarizing channel

We experimentally demonstrate the achievement of the entanglement assisted capacity for classical information transmission over a depolarizing channel. The implementation is based on the generation and local manipulation of 2-qubit Bell states, which are finally measured at the receiver by a complete Bell state analysis. The depolarizing channel is realized by introducing quantum noise in a controlled way on one of the two qubits. This work demonstrates the achievement of the maximum allowed amount of information that can be shared in the presence of noise and the highest reported value in the noiseless case.Comment: 4 pages, 3 figure

New sufficient conditions for a center and global phase portraits for polynomial systems

In this paper we consider cubic polynomial systems of the form: $\dot x=y+P(x,y)$, $\dot y=-x+Q(x,y)$, where $P$ and $Q$ are polynomials of degree 3 without linear part. If $M(x,y)$ is an integrating factor of the system, we propose its reciprocal $V(x,y)=\frac{1}{M(x,y)}$ as a linear function of certain coefficients of the system. We find in this way several new sets of sufficient conditions for a center. The resulting integrating factors are of Darboux type and the first integrals are in the Liouville form. By induction, we have generalized these results for polynomials systems of arbitrary degree. Moreover, for the cubic case, we have constructed all the phase portraits for each new family with a center

Information Content of the Gravitational Field of a Quantum Superposition

When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no ``gravitons'' are emitted during the experiment.Comment: 4 pages, 1 figure. First prize essay in the Gravity Research Foundation 2019 Essays on Gravitation. To appear in IJMPD. arXiv admin note: substantial text overlap with arXiv:1807.0701

Quantum Superposition of Massive Objects and the Quantization of Gravity

We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies ("particles") under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice's particle) and vacuum fluctuations of the electromagnetic field (which limits Bob's ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We correct an error in the analysis of Mari et al. and of Baym and Ozawa, who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.Comment: 9 pages, 1 figure. Version accepted for publication in Phys.Rev.

Vacuum static compactified wormholes in eight-dimensional Lovelock theory

In this paper new exact solutions in eight dimensional Lovelock theory will be presented. These solutions are vacuum static wormhole, black hole and generalized Bertotti-Robinson space-times with nontrivial torsion. All the solutions have a cross product structure of the type $M_{5}\times \Sigma_{3}$ where $M_{5}$ is a five dimensional manifold and $\Sigma_{3}$ a compact constant curvature manifold. The wormhole is the first example of a smooth vacuum static Lovelock wormhole which is neither Chern-Simons nor Born-Infeld. It will be also discussed how the presence of torsion affects the "navigableness" of the wormhole for scalar and spinning particles. It will be shown that the wormhole with torsion may act as "geometrical filter": a very large torsion may "increase the traversability" for scalars while acting as a "polarizator" on spinning particles. This may have interesting phenomenological consequences.Comment: LaTeX, 27 pages, no figures, some comments added. Version accepted for publication in Physical Review

Using non-smooth multi-domain dynamics to improve the safety on haul roads in surface mining

The paper presents a preliminary numerical study aimed to improve the safety on haul roads in surface mining. The interaction and collision between granular berms and ultra-class haul trucks are investigated by using non-smooth multi-domain dynamics. The haul truck is modelled as a rigid multibody system and the granular berm as a distribution of rigid particles using the discrete element method. A non-smooth dynamics approach is applied to enable stable and time-efficient simulation of the full system with strong coupling. The numerical model is first calibrated using full-scale data from experimental tests and then applied to investigate the collision between the haul truck and granular berms of different geometry under various approach conditions