Earthquake ruptures modulated by waves in damaged fault zones

Faults are usually surrounded by damaged zones of lower elastic moduli and seismic wave velocities than their host rocks. If the interface between the damaged rocks and host rocks is sharp enough, earthquakes happening inside the fault zone generate reflected waves and head waves, which can interact with earthquake ruptures and modulate rupture properties such as rupture speed, slip rate, and rise time. We find through 2–D dynamic rupture simulations the following: (1) Reflected waves can induce multiple slip pulses. The rise time of the primary pulse is controlled by fault zone properties, rather than by frictional properties. (2) Head waves can cause oscillations of rupture speed and, in a certain range of fault zone widths, a permanent transition to supershear rupture with speeds that would be unstable in homogeneous media. (3) Large attenuation smears the slip rate function and delays the initial acceleration of rupture speed but does not affect significantly the rise time or the period of rupture speed oscillations. (4) Fault zones cause a rotation of the background stress field and can induce plastic deformations on both extensional and compressional sides of the fault. The plastic deformations are accumulated both inside and outside the fault zone, which indicates a correlation between fault zone development and repeating ruptures. Spatially periodic patterns of plastic deformations are formed due to oscillating rupture speed, which may leave a permanent signature in the geological record. Our results indicate that damaged fault zones with sharp boundaries promote multiple slip pulses and supershear ruptures

Moulding hydrodynamic 2D-crystals upon parametric Faraday waves in shear-functionalized water surfaces.

Faraday waves, or surface waves oscillating at half of the natural frequency when a liquid is vertically vibrated, are archetypes of ordering transitions on liquid surfaces. Although unbounded Faraday waves patterns sustained upon bulk frictional stresses have been reported in highly viscous fluids, the role of surface rigidity has not been investigated so far. Here, we demonstrate that dynamically frozen Faraday waves—that we call 2D-hydrodynamic crystals—do appear as ordered patterns of nonlinear gravity-capillary modes in water surfaces functionalized with soluble (bio)surfactants endowing in-plane shear stiffness. The phase coherence in conjunction with the increased surface rigidity bears the Faraday waves ordering transition, upon which the hydrodynamic crystals were reversibly molded under parametric control of their degree of order, unit cell size and symmetry. The hydrodynamic crystals here discovered could be exploited in touchless strategies of soft matter and biological scaffolding ameliorated under external control of Faraday waves coherence.post-print3461 K

Numerical simulation of reaction fronts in dissipative media

Fronts of reaction in certain systems (such as so-called solid flames and detonation fronts) can be simulated by a single-equation phenomenological model of Strunin (1999, 2009). This is a high-order nonlinear partial differential equation describing the shape of the front as a function of spatial coordinates and time. The equation is of active-dissipative type, with 6th-order spatial derivative. For one-dimensional case, the equation was previously solved using the Galerkin method, but only one numerical experiment with limited information on the dynamics was obtained. For two-dimensional case only two numerical ex- periments were reported so far, in which a low-accuracy infinite difference scheme was used. In this thesis, we use a more recent and sophisticated method, namely the one-dimensional integrated radial basis function networks (1D-IRBFN). The method had been developed by Tran-Cong and May-Duy (2001, 2003) and successfully applied to several problems such as structural analysis, viscoelastic flows and fluid-structure interaction. In contrast to commonly used approaches, where a function of interest is differentiated to give approximate derivatives, leading to a reduction in convergence rate for derivatives (and this reduction increases with derivative order, which magnifes errors), the 1D-IRBFN method uses the integral formulation. It utilizes spectral approximants to represent highest-order derivatives under consideration. They are then integrated analytically to yield approximate expressions for lower-order derivatives and the function itself. In this thesis the following main results are obtained. A numerical program implementing the 1D-IRBFN method is developed in Matlab to solve the equation of interest. The program is tested by (a) constructing a forced version of the equation, which allows analytical solution, and verifying the numerical solution against the analytical solution; (b) reproducing one-dimensional spinning waves obtained from the model previously. A modified version of the program is successfully applied to similar high-order equations modelling auto-pulses in fluid flows with elastic walls. We obtained numerically and analyzed a far richer variety of one-dimensional dynamics of the reaction fronts. Two kinds of boundary conditions were used: homogeneous conditions on the edges of the domain, and periodic conditions corresponding to periodicity of the front on a cylinder. The dependence of the dynamics on the size of the domain is explored showing how larger space accommodates multiple spinning waves. We determined the critical domain size (bifurcation point) at which non-trivial settled regimes become possible. We found a regime where the front is shaped as a pair of kinks separated by a relatively short distance. Interestingly, the pair moves in a stable joint formation far from the boundaries. A similar regime for three connected kinks is obtained. We demonstrated that the initial condition determines the direction of motion of the kinks, but not their size and velocity. This is typical for active-dissipative systems. The settled character of these regimes is demonstrated. We also applied the 1D-IRBFN method to two-dimensional topology corresponding to a solid cylinder. Stable spinning wave solutions are obtained for this case

Pattern selection models: From normal to anomalous diffusion

“Pattern formation and selection is an important topic in many physical, chemical, and biological fields. In 1952, Alan Turing showed that a system of chemical substances could produce spatially stable patterns by the interplay of diffusion and reactions. Since then, pattern formations have been widely studied via the reaction-diffusion models. So far, patterns in the single-component system with normal diffusion have been well understood. Motivated by the experimental observations, more recent attention has been focused on the reaction-diffusion systems with anomalous diffusion as well as coupled multi-component systems. The objectives of this dissertation are to study the effects of superdiffusion on pattern formations and to compare them with the effects of normal diffusion in one-, and multi-component reaction-diffusion systems. Our studies show that the model parameters, including diffusion coefficients, ratio of diffusion powers, and coupling strength between components play an important role on the pattern formation. Both theoretical analysis and numerical simulations are carried out to understand the pattern formation in different parameter regimes. Starting with the linear stability analysis, the theoretical studies predict the space of Turing instability. To further study pattern selection in this space, weakly nonlinear analysis is carried out to obtain the regimes for different patterns. On the other hand, numerical simulations are carried out to fully investigate the interplay of diffusion and nonlinear reactions on pattern formations. To this end, the reaction-diffusion systems are solved by the Fourier pseudo-spectral method. Numerical results show that superdiffusion may substantially change the patterns in a reaction-diffusion system. Different superdiffusive exponents of the activator and inhibitor could cause both qualitative and quantitative changes in emergent spatial patterns. Comparing to single-component systems, the patterns observed in multi-component systems are more complex”--Abstract, page iv

Biomechanics of pressure ulcer in body tissues interacting with external forces during locomotion

2009-2010 > Academic research: refereed > Publication in refereed journalAuthor’s OriginalPublishe

Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems

International audienceThis paper is an extension of the previous review Nonlinear Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments done by the authors, and it is devoted to applications of nonlinear normal modes (NNMs) theory. NNMs are typical regimes of motions in wide classes of nonlinear mechanical systems. The significance of NNMs for mechanical engineering is determined by several important properties of these motions. Forced resonances motions of nonlinear systems occur close to NNMs. Nonlinear phenomena, such as nonlinear localization and transfer of energy, can be analyzed using NNMs. The NNMs analysis is an important step to study more complicated behavior of nonlinear mechanical systems. This review focuses on applications of Kauderer–Rosenberg and Shaw–Pierre concepts of nonlinear normal modes. The Kauderer–Rosenberg NNMs are applied for analysis of large amplitude dynamics of finite-degree-of-freedom nonlinear mechanical systems. Systems with cyclic symmetry, impact systems, mechanical systems with essentially nonlinear absorbers, and systems with nonlinear vibration isolation are studied using this concept. Applications of the Kauderer–Rosenberg NNMs for discretized structures are also discussed. The Shaw–Pierre NNMs are applied to analyze dynamics of finite-degree-of-freedom mechanical systems, such as floating offshore platforms, rotors, piece-wise linear systems. Studies of the Shaw–Pierre NNMs of beams, plates, and shallow shells are reviewed, too. Applications of Shaw–Pierre and King–Vakakis continuous nonlinear modes for beam structures are considered. Target energy transfer and localization of structures motions in light of NNMs theory are treated. Application of different asymptotic methods for NNMs analysis and NNMs based model reduction are reviewed

Flow Behavior And Instabilities In Viscoelastic Fluids: Physical And Biological Systems

The flow of complex fluids, especially those containing polymers, is ubiquitous in nature and industry. From blood, plastic melts, to airway mucus, the presence of microstructures such as particles, proteins, and polymers, can impart nonlinear material properties not found in simple fluids like water. These rheological behaviors, in particular viscoelasticity, can give rise to flow anomalies found in industrial settings and intriguing transport dynamics in biological systems. The first part of my work focuses on the flow of viscoelastic fluids in physical systems. Here, I investigate the flow instabilities of viscoelastic fluids in three different geometries and configurations. Realized in microfluidic channels, these experiments mimic flows encountered in technology spanning the oil extraction, pharmaceutical, and chemical industries. In particular, by conducting high-speed velocimetry on the flow of polymeric fluid in a micro-channel, we report evidence of elastic turbulence in a parallel shear flow where the streamline is without curvature. These turbulent-like characteristics include activation of the flow at many time scales, anomalous increase in flow resistance, and enhanced mixing associated with the polymeric flow. Moreover, the spectral characteristics and spatial structures of the velocity fluctuations are different from that in a curved geometry. Measured using novel holographic particle tracking, Lagrangian trajectories show spanwise dispersion and modulations, akin to the traveling waves in the turbulent pipe flow of Newtonian fluids. These curvature perturbations far downstream can generate sufficient hoop stresses to sustain the flow instabilities in the parallel shear flow. The second part of the thesis focuses on the motility and transport of active swimmers in viscoelastic fluids that are relevant to biological systems and human health. In particular, by analyzing the swimming of the bi-flagellated green algae {\it Chlamydomonas reinhardtii} in viscoelastic fluid, we show that fluid elasticity enhances the flagellar beating frequency and the wave speed. Yet the net swimming speed of the alga is hindered for fluids that are sufficiently elastic. The origin of this complex response lies in the non-trivial change in flagellar gait due to elasticity. Numerical simulations show that such change in gait reduces elastic stress build up in the fluid and increases efficiency. These results further illustrate the complex coupling between fluid rheology and swimming gait in the motility of micro-organisms and other biological processes such as mucociliary clearance in mammalian airways

A study of poststenotic shear layer instabilities

Imperial Users onl

Assessment and control of transition to turbulence in plane Couette flow

Transition to turbulence in shear flows is a puzzling problem regarding the motion of fluids flowing, for example, through the pipe (pipe flow), as in oil pipelines or blood vessels, or confined between two counter-moving walls (plane Couette flow). In this kind of flows, the initially laminar (ordered and layered) state of fluid motion is linearly stable, but turbulent (disordered and swirling) flows can also be observed if a suitable perturbation is imposed. This thesis concerns the assessment of transitional properties of such flows in the uncontrolled and controlled environments allowing for the quantitative comparisons of control strategies aimed at suppressing or trigerring transition to turbulence. Efficient finite-amplitude perturbations typically take the form of small patches of turbulence embedded in the laminar flow and called turbulent spots. Using direct numerical simulations, the nonlinear dynamics of turbulent spots, modelled as exact solutions, is investigated in the transitional regime of plane Couette flow and a detailed map of dynamics encompassing the main features found in transitional shear flows (self-sustained cycles, front propagation and spot splitting) is built. The map represents a quantitative assessment of transient dynamics of turbulent spots as a dependence of the relaminarisation time, i.e. the time it takes for a finite-amplitude perturbation, added to the laminar flow, to decay, on the Reynolds number and the width of a localised perturbation. By applying a simple passive control strategy, sinusoidal wall oscillations, the change in the spot dynamics with respect to the amplitude and frequency of the wall oscillations is assessed by the re-evaluation of the relaminarisation time for few selected localised initial conditions. Finally, a probabilistic protocol for the assessment of transition to turbulence and its control is suggested. The protocol is based on the calculation of the laminarisation probability, i.e. the probability that a random perturbation decays as a function of its energy. It is used to assess the robustness of the laminar flow to finite-amplitude perturbations in transitional plane Couette flow in a small computational domain in the absence of control and under the action of sinusoidal wall oscillations. The protocol is expected to be useful for a wide range of nonlinear systems exhibiting finite-amplitude instability