Mechanics of motility initiation and motility arrest in crawling cells

Motility initiation in crawling cells requires transformation of a symmetric state into a polarized state. In contrast, motility arrest is associated with re-symmetrization of the internal configuration of a cell. Experiments on keratocytes suggest that polarization is triggered by the increased contractility of motor proteins but the conditions of re-symmetrization remain unknown. In this paper we show that if adhesion with the extra-cellular substrate is sufficiently low, the progressive intensification of motor-induced contraction may be responsible for both transitions: from static (symmetric) to motile (polarized) at a lower contractility threshold and from motile (polarized) back to static (symmetric) at a higher contractility threshold. Our model of lamellipodial cell motility is based on a 1D projection of the complex intra-cellular dynamics on the direction of locomotion. In the interest of analytical transparency we also neglect active protrusion and view adhesion as passive. Despite the unavoidable oversimplifications associated with these assumptions, the model reproduces quantitatively the motility initiation pattern in fish keratocytes and reveals a crucial role played in cell motility by the nonlocal feedback between the mechanics and the transport of active agents. A prediction of the model that a crawling cell can stop and re-symmetrize when contractility increases sufficiently far beyond the motility initiation threshold still awaits experimental verification

Boundary effects on non-equilibrium localized structures in spatially extended systems

A study of the effects of system boundaries on bistable front propagation in nonequilibrium reaction-diffusion systems is presented. Two model partial differential equations displaying bistable fronts, with distinct experimental motivations and mathematical structure, are examined in detail utilizing simulations and perturbation techniques. We see that propagating fronts in both models bounce, trap, pin, or oscillate at the boundary, contingent on the imposed boundary condition, initial front speed and distance from the boundary. The similarities in front boundary interactions in these two models is traced to the fact that they display the same front instability (Ising-Bloch bifurcation) that controls the speed of propagation. A simplified dynamical picture based on ordinary differential equations that captures the essential features of front motion described by the original partial differential equations, is derived and analyzed for both models. In addition to addressing experimentally important boundary effects, we establish the universality of the Ising-Bloch bifurcation. Useful analytical insights into perturbative analysis of reaction diffusion systems are also presented

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Spatiotemporal dynamics of continuum neural fields

We survey recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields. Neural fields model the large-scale dynamics of spatially structured biological neural networks in terms of nonlinear integrodifferential equations whose associated integral kernels represent the spatial distribution of neuronal synaptic connections. They provide an important example of spatially extended excitable systems with nonlocal interactions and exhibit a wide range of spatially coherent dynamics including traveling waves oscillations and Turing-like patterns

A numerical study on the viscous fingering instability of immiscible displacement in Hele-Shaw cells

In this thesis, the viscous fingering instability of radial immiscible displacement is analysed numerically using novel mesh-reduction and interface tracking techniques. Using a reduced Hele-Shaw model for the depth averaged lateral flow, viscous fingering instabilities are explored in flow regimes typical of subsurface carbon sequestration involving supercritical CO2 - brine displacements, i.e. with high capillary numbers, low mobility ratios and inhomogeneous permeability/temperature fields. A high accuracy boundary element method (BEM) is implemented for the solution of homogeneous, finite mobility ratio immiscible displacements. Through efficient, explicit tracking of the sharp fluid-fluid interface, classical fingering processes such as spreading, shielding and splitting are analysed in the late stages of finger growth at low mobility ratios and high capillary numbers. Under these conditions, large differences are found compared with previous high or infinite mobility ratio models and critical events such as plume break-off and coalescence are analysed in much greater detail than has previously been attempted. For the solution of inhomogeneous mobility problems, a novel meshless radial basis function-finite collocation method is developed that utilises a dynamic quadtree dataset and local enforcement of interface matching conditions. When coupled with the BEM, the numerical scheme allows the analysis of variable permeability effects and the transition in (de)stabilising mechanisms that occurs when the capillary number is increased with a fixed, spatially varying permeability. Finally, thermo-viscous fingering is explored in the context of immiscible flows, with a detailed mechanistic study presented to explain, for the first time, the immiscible thermo-viscous fingering process

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities—both at the microstructural scale in materials and at the macroscopic, structural level—lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials

1980 summer study program in geophysical fluid dynamics : coherent features in geophysical flows

Four principal lecturers shored the task of presenting the subject "Coherent Features in Geophysical Flows" to the participants of the twenty-second geophysical fluid dynamics summer program. Glenn Flierl introduced the topic and the Kortweg-de Vries equation via a model of finite amplitude motions on the beta plane. He extended the analysis to more complex flows in the ocean and the atmosphere and in the process treated motions of very large amplitude. Larry Redekopp's three lectures summarized an extensive body of the mathematical literature on coherent features. Andrew Ingersoll focussed on the many fascinating features in Jupiter's atmosphere. Joseph Keller supplemented an interesting summary of laboratory observations with suggestive models for treating the flows.Office of Naval Research under Contract N00014-79-C-067

A numerical study on the viscous fingering instability of immiscible displacement in Hele-Shaw cells

In this thesis, the viscous fingering instability of radial immiscible displacement is analysed numerically using novel mesh-reduction and interface tracking techniques. Using a reduced Hele-Shaw model for the depth averaged lateral flow, viscous fingering instabilities are explored in flow regimes typical of subsurface carbon sequestration involving supercritical CO2 - brine displacements, i.e. with high capillary numbers, low mobility ratios and inhomogeneous permeability/temperature fields. A high accuracy boundary element method (BEM) is implemented for the solution of homogeneous, finite mobility ratio immiscible displacements. Through efficient, explicit tracking of the sharp fluid-fluid interface, classical fingering processes such as spreading, shielding and splitting are analysed in the late stages of finger growth at low mobility ratios and high capillary numbers. Under these conditions, large differences are found compared with previous high or infinite mobility ratio models and critical events such as plume break-off and coalescence are analysed in much greater detail than has previously been attempted. For the solution of inhomogeneous mobility problems, a novel meshless radial basis function-finite collocation method is developed that utilises a dynamic quadtree dataset and local enforcement of interface matching conditions. When coupled with the BEM, the numerical scheme allows the analysis of variable permeability effects and the transition in (de)stabilising mechanisms that occurs when the capillary number is increased with a fixed, spatially varying permeability. Finally, thermo-viscous fingering is explored in the context of immiscible flows, with a detailed mechanistic study presented to explain, for the first time, the immiscible thermo-viscous fingering process

Modelling of Phase Separation in Alloys with Coherent Elastic Misfit

Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can form regular precipitate superlattices. Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) `macroscopic' models treating the two phases as elastic media separated by a sharp interface (ii) `mesoscopic' models in which the concentration varies continuously across the interface (iii) `microscopic' models which use the positions of individual atoms.Comment: 106 pages, in Latex, figures available upon request, e-mail addresses: [email protected], [email protected], [email protected], submitted to the Journal of Statistical Physic