Non-isothermal propagation and arrest of km-sized km-deep sills at calderas

<p>Caldera unrest is often attributed to magma intrusion into a sill. In several cases, like Fernandina and Sierra Negra, Kilauea south caldera, and Campi Flegrei, the sill is km-sized and km-deep. A few questions related to sill emplacement at calderas seem still unanswered: how do sills form and spread, why can magma propagate for kilometers without solidifying, and why do ground deformation data rarely, if ever, detect sill propagation.<br>When considering isoviscous incompressible magma intruding at a constant rate into a homogeneous half-space under non-isothermal conditions and forming a circular sill, mathematical modeling includes: a fluid-dynamic equation (relying on lubrication theory), a fracture propagation criterion, an elasticity equation (link between fluid overpressure and sill opening), and a heat-transfer magma-solidification equation. As already known, a small lag must exist between the fluid (magma) and fracture fronts, because of the large pressure gradients required to drive a viscous liquid into a narrow opening.<br>We show that the free-surface effects on the elasticity equation are negligible, provided that depth-to-radius is smaller than one, as at the above-mentioned calderas; thus, spreading occurs like in an infinite medium. Taking advantage of published studies on hydraulic fracture propagation, first we consider isothermal spreading, as governing equations admit approximate analytical solutions for sill radius, sill opening, fluid overpressure and lag size.  Next we consider non-isothermal spreading of an isoviscous incompressible single-component magma, which is initially at its solidification temperature.<br>We show that if the sill is at least a couple of kilometers deep and the product of viscosity and injection rate is sufficiently small, then the lag between the magma and fracture fronts is much smaller than the sill radius during most of the propagation process; as a consequence, propagation velocity is practically unaffected by the lag, except for the initial phase. Because of the way solidified magma thickness and sill opening grow with distance from the tip in the near-tip region, zero-lag non-isothermal spreading would stop after travelling unrealistically short distances, unless magma intrudes rocks that are as hot as the solidification temperature or has unrealistic overpressures. Thus, we consider how the lag might affect the sill maximum size, by preventing solidification at the tip. We compute non-isothermal propagation velocity and the solidified magma thickness by adapting the approach originally developed by Dontsov (2016) for the zero-lag propagation of penny-shaped hydraulic fractures with leak-off; then we relate the lag size to the propagation velocity using the isothermal solutions.<br>We find that the lag plays a fundamental role in postponing the sill arrest by magma solidification, because heat exchange between the magma and the hosting rock is effective only behind the lag, where the magma has some finite thickness and sill opening grows with distance from the tip faster than thickness of solidified magma.<br>As for ground deformation, we show that its pattern does not change appreciably over time if the final sill radius is smaller than 2 to 3 km: this explains why it is usually attributed to the inflation of a stationary source.</p>

Integrated improvement of the elasticity-based mesh deformation method based on robust parameters and mesh quality

Highly robust mesh deformation methods are key techniques for solving unsteady flow field problems with moving or deforming boundaries. Because it is imperative to reduce the remeshing times, these methods are important in engineering applications, especially for complex geometric boundaries and large displacements. We introduce three classical elasticity-based mesh deformation methods and determine the limitations of the two nonlinear classical methods. Two steps were taken to achieve an integrated improvement: first, the robust power parameters a and b and the weighted parameter x are introduced to enhance the robustness of the basic elasticity equation. Second, a mesh quality parameter is implemented to prevent the large distortion of the poor elements and this parameter is added to the elasticity equation as a constraint. To validate the validity of the integrated improvement approach, several test cases of a moving or deforming two-dimensional flat plate are used. Additionally, two simulated engineering examples are used to demonstrate the application of the integrated improvement for practical problems, including the pitching oscillation of a National Advisory Committee for Aeronautics (NACA) 0012 airfoil and the ONERA M6 wing. The results show that the integrated improvement approach does not only allow for the selection of suitable robust parameters to achieve more robust deformed meshes but also reduces the distortion of the poor elements near the moving boundary, even when the deformation is severe.

The use of nanoindentation for determining internal lengths and the constitutive response of monument materials: models and experiments

An alternative interpretation of nanoindentation experimental data and the associated phenomenon of indentation size effect (ISE) is proposed on the basis of a simple gradient elasticity equation, used to account for the development of elastic gradients generated by the geometry characterizing the indenter-specimen system. An application is considered for marble, i.e. a construction/restoration material.

Study on Strength Calculation and Bend Stress Test of Face Gear

Based on normal elasticity equation, this paper has developed the calculation formula of face gear’s contact strength, bend strength and scuffing strength. This work put forward an analytical calculation method of face gear’s bend strength and constructed the analytical model. The result of bend strength of face gear was obtained by computer simulation. Based on the research, we designed and manufactured a suit of face gearbox. According to the tooth space trait, a method was represented to test bending stress of tooth by arrangement of sensing device in the tip end of the tooth of face gear. A test-bed has been set up with which the bending stress of tooth of face gear was carried out. The results showed that the maximal bending stress of test is similar to the simulation results by ANSYS.

Duality and compactness results in high-contrast homogenization of incompressible two-dimensional elasticity problems

Some of the proofs in the above paper are incomplete.The pressure term in the incompressible elasticity equation needs to be considered and estimated in order to pass to the limit in the homogenization process. This will require Sections 2.2 and 3.2 to be rewritten.A corrected version will be submitted in due course.