Seismic Radiation From Simple Models of Earthquakes

We review some basic features of shear wave generation and energy balance for a 2D anti plane rupture. We first study the energy balance for a flat fault, and for a fault that contains a single localized kink. We determine an exact expression for the partition between strain energy flow released from the elastic medium surrounding the fault, radiated energy flow and energy release rate. This balance depends only on the rupture speed and the residual stress intensity factor. When the fault contains a kink, the energy available for fracture is reduced so that the rupture speed is reduced. When rupture speed changes abruptly, the radiated energy flow also changes abruptly. As rupture propagates across the kink, a shear wave is emitted that has a displacement spectral content that decreases like ω^(-2) at high frequencies. We then use spectral elements to model the propagation of an antiplane crack with a slip-weakening friction law. Since the rupture front in this case has a finite length scale, the wave emitted by the kink is smoothed at very high frequencies but its general behavior is similar to that predicted by the simple sharp crack model. A model of a crack that has several kinks and wanders around a mean rupture directions, shows that kinks reduce the rupture speed along the average rupture direction of the fault. Contrary to flat fault models, a fault with kinks produces high frequency waves that are emitted every time the rupture front turns at a kink. Finally, we discuss the applicability of the present results to a 3D rupture model

Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that diverge from or converge to the initial path, a feature that may be tested in future experiments. The model rests on a scenario of crack branching with some reasonable assumptions based on general considerations and in exact dynamic results for anti-plane branching. It is argued that it is possible to use a static analysis of the crack bifurcation for plane loading as a good approximation to the dynamical case. The results are interesting since they explain within a continuum mechanics approach the main features of the branching instabilities of fast cracks in brittle materials, i.e. critical speeds, branching angle and the geometry of subsequent branches paths.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur

Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure

Synthesis of noble metal-decorated NH2-MIL-125 titanium MOF for the photocatalytic degradation of acetaminophen under solar irradiation

This work reports the solvothermal synthesis of a titanium-based metal organic framework (NH2-MIL-125(Ti)) and the further deposition of palladium, platinum and silver nanoparticles on its framework, with the aim to obtain visible light-driven photocatalysts. The structure of the NH2-MIL-125 was not affected by the incorporation of the metal nanoparticles, while the textural properties changed depending on the metal used. All M/NH2-MIL-125 (M = Pd, Pt, Ag) synthesized materials showed enhanced light absorption in the visible region due to the effect of the metal nanoparticles, which were mainly in reduced state as confirmed by XPS analyses. The metal nanoparticles were between 1.8 and 3.8 nm in size depending of the metal. They were responsible for the reduction in the recombination process, as suggested by photoluminescence measurements. The photocatalytic performance of M/NH2-MIL-125 was tested for the degradation of acetaminophen (ACE) under simulated solar irradiation. Pt/NH2-MIL-125 achieved the highest conversion rate (rate constant of 0.0165 min−1), with complete conversion of the contaminant in less than three hours. Scavengers studies confirmed that O.-2[rad]− radicals play a main role in the degradation process, followed by .OH radicals. The catalytic stability of Pt/NH2-MIL-125 was confirmed upon three successive reaction cycles. Different water matrices were tested to understand the effect of common inorganic ions, being the presence of bicarbonates the most detrimental to the performance of the photocatalytic processThis research was funded by the State Research Agency (PID2019-106186RB-I00/AEI/10.13039/501100011033). V. Muelas-Ramos thanks to MCIU for BES-2017-082613 gran

Dynamic stability of crack fronts: Out-of-plane corrugations

The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar crack fronts in the framework of linear elastic fracture mechanics. We discuss a minimal scenario in which linearly unstable crack front corrugations might emerge above a critical front propagation speed. We calculate this speed as a function of Poisson's ratio and show that corrugations propagate along the crack front at nearly the Rayleigh wave-speed. Finally, we hypothesize about a possible relation between such corrugations and the long-standing problem of crack branching.Comment: 5 pages, 2 figures + supplementary informatio

Roughness of tensile crack fronts in heterogenous materials

The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent $\zeta=1/2$, is found. The rough phase becomes possible due to the destabilization of the linear modes by the nonlinear terms. Taking into account the irreversibility of the crack propagation, we infer that the roughness exponent found in experiments might become history-dependent, and so our result gives a lower bound for $\zeta$.Comment: 7 page

First Order Phase Transition of a Long Polymer Chain

We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\mu$ and $\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\beta$-$\mu$ plane.Comment: 11 pages, 7 figure

Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

Equilibrium, kinetics and breakthrough curves of acetaminophen adsorption onto activated carbons from microwave-assisted FeCl3-activation of lignin

Activated carbons have been prepared by chemical activation of lignin with FeCl3 using microwave (MW) heating. The use of MW significantly reduced the activation time compared to conventional heating. Microwave power, impregnation ratio (R: mass ratio of FeCl3 to lignin precursor) and MW holding time have been studied as variables affecting the development of porous texture. The optimum conditions were found at 800 W, R = 5 and 30 min MW heating time. Under those conditions an essentially microporous activated carbon was obtained, with BET surface area higher than 1150 m2·g−1 and acidic surface, whose pH at the point of zero charge was 4.2. This activated carbon was tested for the adsorption of acetaminophen, as model emerging contaminant, from aqueous phase. The adsorption isotherms, obtained at 20, 40 and 60 °C, fitted well to Redlich–Peterson model. The maximum acetaminophen adsorption reached about 300 mg·g−1 at 60 °C. Values of 35.5 kJ·mol−1 and 238.3 J·mol−1·K−1 were obtained for the enthalpy and entropy of adsorption, respectively. Those positive values are indicative of an endothermic process and increased randomness at the solid/solution interface upon adsorption. The adsorption kinetics was better described by pseudo-second order driving force model. Breakthrough curves were also obtained at different adsorption temperatures, flow rates and acetaminophen inlet concentrations. They fitted well to a logistic-type equation representative of the Bohart-Adams, Thomas and Yoon-Nelson models. Adsorbent regeneration with hot water (80 °C) revealed easy and complete desorption thus providing a promising view of the potential application of this activated carbonThe authors acknowledge the financial support from the State Research Agency (PID2019-106186RB-I00/AEI/10.13039/501100011033, Spain). M. Penas-Garzón thanks Spanish MECD for FPU16/00576 gran

Modeling flocks with perceptual agents from a dynamicist perspective

Computational simulations of flocks and crowds have typically been processed by a set of logic or syntactic rules. In recent decades, a new generation of systems has emerged from dynamicist approaches in which the agents and the environment are treated as a pair of dynamical systems coupled informationally and mechanically. Their spontaneous interactions allow them to achieve the desired behavior. The main proposition assumes that the agent does not need a full model or to make inferences before taking actions; rather, the information necessary for any action can be derived from the environment with simple computations and very little internal state. In this paper, we present a simulation framework in which the agents are endowed with a sensing device, an oscillator network as controller and actuators to interact with the environment. The perception device is designed as an optic array emulating the principles of the animal retina, which assimilates stimuli resembling optic flow to be captured from the environment. The controller modulates informational variables to action variables in a sensory-motor flow. Our approach is based on the Kuramoto model that describes mathematically a network of coupled phase oscillators and the use of evolutionary algorithms, which is proved to be capable of synthesizing minimal synchronization strategies based on the dynamical coupling between agents and environment. We carry out a comparative analysis with classical implementations taking into account several criteria. It is concluded that we should consider replacing the metaphor of symbolic information processing by that of sensory-motor coordination in problems of multi-agent organizations