Inelastic deformation during sill and laccolith emplacement: Insights from an analytic elastoplastic model

Numerous geological observations evidence that inelastic deformation occurs during sills and laccoliths emplacement. However, most models of sill and laccolith emplacement neglect inelastic processes by assuming purely elastic deformation of the host rock. This assumption has never been tested, so that the role of inelastic deformation on the growth dynamics of magma intrusions remains poorly understood. In this paper, we introduce the first analytical model of shallow sill and laccolith emplacement that accounts for elasto-plastic deformation of the host rock. It considers the intrusion's overburden as a thin elastic bending plate attached to an elastic-perfectly-plastic foundation. We find that, for geologically realistic values of the model parameters, the horizontal extent of the plastic zone lp is much smaller than the radius of the intrusion a. By modeling the quasi-static growth of a sill, we find that the ratio lp/a decreases during propagation, as 1/ \sqrt a 4 $\Delta$P , with $\Delta$P the magma overpressure. The model also shows that the extent of the plastic zone decreases with the intrusion's depth, while it increases if the host rock is weaker. Comparison between our elasto-plastic model and existing purely elastic models shows that plasticity can have a significant effect on intrusion propagation dynamics, with e.g. up to a doubling of the overpressure necessary for the sill to grow. Our results suggest that plasticity effects might be small for large sills, but conversely that they might be substantial for early sill propagation.

Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space

We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. This is in contrast to the noncommutative configuration space where the time reversal symmetry of the harmonic oscillator is always broken.Comment: 7 pages Late

Formulation, Interpretation and Application of non-Commutative Quantum Mechanics

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non commutativity are identified.Comment: 11 page

Supersymmetry breaking in noncommutative quantum mechanics

Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the number of supercharges are conserved. It is argued that this breaking is closely related to the breaking of time reversal symmetry arising from noncommutativity

Drainage fracture networks in elastic solids with internal fluid generation

Experiments in which CO2 gas was generated by the yeast fermentation of sugar in an elastic layer of gelatine gel confined between two glass plates are described and analyzed theoretically. The CO2 gas pressure causes the gel layer to fracture. The gas produced is drained on short length scales by diffusion and on long length scales by flow in a fracture network, which has topological properties that are intermediate between river networks and hierarchical-fracture networks. A simple model for the experimental system with two parameters that characterize the disorder and the intermediate (river-fracture) topology of the network was developed and the results of the model were compared with the experimental results