Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

Shear-induced transitions and instabilities in surfactant wormlike micelles

In this review, we report recent developments on the shear-induced transitions and instabilities found in surfactant wormlike micelles. The survey focuses on the non-linear shear rheology and covers a broad range of surfactant concentrations, from the dilute to the liquid-crystalline states and including the semi-dilute and concentrated regimes. Based on a systematic analysis of many surfactant systems, the present approach aims to identify the essential features of the transitions. It is suggested that these features define classes of behaviors. The review describes three types of transitions and/or instabilities : the shear-thickening found in the dilute regime, the shear-banding which is linked in some systems to the isotropic-to-nematic transition, and the flow-aligning and tumbling instabilities characteristic of nematic structures. In these three classes of behaviors, the shear-induced transitions are the result of a coupling between the internal structure of the fluid and the flow, resulting in a new mesoscopic organization under shear. This survey finally highlights the potential use of wormlike micelles as model systems for complex fluids and for applications.Comment: 64 pages, 31 figures, 2 table

Thermalization in QCD: theoretical approaches, phenomenological applications, and interdisciplinary connections

Heavy-ion collisions at BNL's Relativistic Heavy-Ion Collider (RHIC) and CERN's Large Hadron Collider (LHC) provide strong evidence for the formation of a quark-gluon plasma, with temperatures extracted from relativistic viscous hydrodynamic simulations shown to be well above the transition temperature from hadron matter. How the strongly correlated quark-gluon matter forms in a heavy-ion collision, its properties off-equilibrium, and the thermalization process in the plasma, are outstanding problems in QCD. We review here the theoretical progress in this field in weak coupling QCD effective field theories and in strong coupling holographic approaches based on gauge-gravity duality. We outline the interdisciplinary connections of different stages of the thermalization process to non-equilibrium dynamics in other systems across energy scales ranging from inflationary cosmology, to strong field QED, to ultracold atomic gases, with emphasis on the universal dynamics of non-thermal and of hydrodynamic attractors. We survey measurements in heavy-ion collisions that are sensitive to the early non-equilibrium stages of the collision and discuss the potential for future measurements. We summarize the current state-of-the art in thermalization studies and identify promising avenues for further progress.Comment: 79 pages, 34 figures, prepared for Reviews of Modern Physics; version 2: small improvements and additions, submitted versio

Probing transitions and phase-ordering of charge-density waves

Due to their reduced dimensionality, surfaces and quasi two-dimensional materials exhibit numerous intriguing physical phenomena that drastically differ from the bulk. To resolve these effects and the associated dynamics at their intrinsic timescales requires experimental methodologies combining a high surface sensitivity with the essential temporal resolution. However, to date, there are still very few methods that facilitate investigation of the structural degrees of freedom of surfaces on the atomic scale along with a temporal resolution of femtoseconds or picoseconds. Addressing these challenges, this thesis covers the development and application of ultrafast low-energy electron diffraction in a backscattering geometry to study structural dynamics at surfaces. In this context, a central aspect is the development of a miniaturized and laser-driven electron source based on a nanometric needle photocathode. Using such a sharp metal tip, the photoemitted electron bunches offer a particularly high coherence and remarkably short pulse durations, which were also successfully implemented recently in ultrafast transmission electron microscopy, as well as in time-resolved transmission low-energy electron diffraction. Employing the capabilities of this novel technique, so-called transition metal dichalcogenides constitute an ideal prototype system. Specifically, in the present work, the transient structural disorder of charge-density waves at the surface of 1T-TaS2 has been examined. Following the optically induced transition between two temperature-dependent charge-density wave phases, this method enables the observation of a highly disordered transient state and the subsequent phase-ordering kinetics. More precisely, the temporal evolution of the growing charge-density correlation length is traced over several hundreds of picoseconds and found to obey a power-law scaling behavior. Due to the particular properties of the charge-density wave system at hand, the observed transient disorder can be explained by the ultrafast formation of topological defects and their subsequent annihilation. These results are complemented by a numerical modeling using a timedependent Ginzburg-Landau approach. Finally, two different excitation schemes demonstrating the possibility to study the relaxation of the investigated sample on the nanosecond and microsecond timescale are presented, as well as future prospects of ultrafast low-energy electron diffraction, including other promising surface sample systems

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy

Investigation of Dynamic Behavior of Brittle Solids by Discrete Systems

With the remarkably rapid growth of computer capabilities and corresponding advance of numerical algorithms as background, the landscape of the engineering and scientific research is continually changing. In the pre-computer era, the physical sciences were characterized by interplay between theory and experiment, both necessarily simplified to eliminate the complexities that rendered the phisical phenomena impossible to tackle. In the last two-three decades, the computer technology surge altered substantially this relationship by enriching the research by a new element: the computer experiment. The change is far reaching indeed. The computer simulations significantly pushed the envelope of “solvable” problems. When they, by constantly demanding more accurate inputs from both theorists and experimentalists, manage to come very close to capturing the reality of a phenomenon, they become an extremely powerful tool indispensible in interpretation of the experimental results at the spatial and temporal scales beyond the reach of everdeveloping experimental techniques. More than that: the virtual laboratory enables us to perform experiments that are beyond imagination in the actual laboratory, with practically unlimited level of control. The objective of the research efforts reviewed in this monograph was threefold. First, to identify patterns and dominant aspects of dynamic response of idealized brittle solids subjected to high strain rates. Second, to propose simple, approximate, design oriented models needed to capture some of those salient features. Third, to investigate universal trends in which disorder and strain rate influence that dynamic response. The outlined approach leads to rational estimates of the radial tractions required to expand dynamically a cylindrical cavity and, consequently, the forces on the projectile nose resisting penetration; and eventually, the corresponding penetration depth of the superior-strength projectile through the infinite brittle medium. The models are based on the micromechanics of deformation and damage evolution in the generic brittle material with random microstructure and inferior tensile strength. The considered problems are, in addition to ballistics, also frequently encountered in mining, metalworking, transportation, etc. The proposed models accounts for the prominent properties of brittle materials: a random microstructure, pressure-dependent shear strength, inferior tensile strength and presence of process induced micro-defects; and the characteristic deformation features such as the rate-dependent fracture pattern, granular flow, and deterioration of the effective material properties. The effect of “pre-existing” material imperfections on the material properties and their change in the course of deformation is an indication that a rational model should be sought within the scope of damage mechanics. The strategy selected in this study is to use the virtual laboratory experiments to reduce the dependence on actual tests (often too difficult and/or expensive, if not impossible, to perform) and provide a reasonably detailed picture of the state of material and mechanical fields in the infinite brittle target. Due to the extreme loading conditions, the concepts of strain, stiffness tensor, damage and temperature are, at best, conditionally acceptable since the corresponding deformation process is nonlocal, non-linear and non-equilibrated. To eliminate large spatial and temporal fluctuations the “local” values of these fields are determined by volume averaging. As a consequence, the model resolution is rather coarse and the results are primarily directed to the estimates of the global parameters of the problem which are, fortunately, most important for engineering purposes. The approximation of a solid by an ensemble of interacting particles (so called, lattice, spring-network, or discrete models) is selected for at least three reasons. First, the introduction of morphological and structural disorder is straightforward. Second, the selection of the constitutive relations is not arbitrary since it can be, in principle, inferred from the molecular dynamics simulations on the sub-meso scales. Finally, there is no need for developing time-consuming numerical techniques to track the material interfaces. The rationale for the selected strategy is fully supported by the simulation results. This monograph grew out of my dissertation “Dynamic Loading of Brittle Materials with Random Microstructure” presented at Arizona State University (1997) in partial fulfillement of the requirements for the degree Doctor of Philosophy. The offsprings of that dissertation were numerous research papers prepared in collaboration with the late Professor Dusan Krajcinovic. The monograph is organized in five chapters describing the major subject areas; the chapters are divided into sections and the sections into thematic subsections. It is important to note that this book is not a review monograph of the discrete numerical methods, but a brief treatise on a narrow multidisciplinary research area. Thus, many valuable references in the topical areas are surely inadverantly left out. The material in Section 2.1 is a brief survey of standard background information on conventional molecular dynamics. The introduction to particle dynamics models presented in Section 2.2 is based mostly on Krajcinovic and Mastilovic (1999) and Mastilovic and Krajcinovic (1999a). The core of the monograph, which comprises Chapters 3 and 4 describing the numerical simulations and the corresponding analytical modelling, is founded primarily on the following publications: Mastilovic and Krajcinovic (1999b) (Sections 3.1 through 3.3); Mastilovic and Krajcinovic (1999a) (Section 3.4 and 4.1); Krajcinovic and Mastilovic (2001a) (Section 3.4); and Mastilovic et al. (2008) (Subsection 3.3.1). Section 4.2, concerned with the penetration depth modelling, follows closely analysis in Mastilovic and Krajcinovic (1999c). The topics covered in Appendices A and D are originally published in Mastilovic (2008) and Mastilovic (accepted). Finally, the mentioned advent of high productivity computing takes its toll on many results presented in this study. Many numerical models that pushed the envelope of PC performace 10-15 years ago are orders of magnitude behind the current state-ofthe- art, which is an unavoidable drawback of postponed publication in rapidly developing research areas. Therefore, as I prepared the manuscript, I had to resist a strong urge to re-do many simulations presented herein; successfully, I am happy to admit. Last but not least, I am indepted to many for help and support during the years of work shaped in this monograph; no one is named here but no one is forgotten

Characterization, modeling, and simulation of multiscale directed-assembly systems

Nanoscience is a rapidly developing field at the nexus of all physical sciences which holds the potential for mankind to gain a new level of control of matter over matter and energy altogether. Directed-assembly is an emerging field within nanoscience in which non-equilibrium system dynamics are controlled to produce scalable, arbitrarily complex and interconnected multi-layered structures with custom chemical, biologically or environmentally-responsive, electronic, or optical properties. We construct mathematical models and interpret data from direct-assembly experiments via application and augmentation of classical and contemporary physics, biology, and chemistry methods. Crystal growth, protein pathway mapping, LASER tweezers optical trapping, and colloid processing are areas of directed-assembly with established experimental techniques. We apply a custom set of characterization, modeling, and simulation techniques to experiments to each of these four areas. Many of these techniques can be applied across several experimental areas within directed-assembly and to systems featuring multiscale system dynamics in general. We pay special attention to mathematical methods for bridging models of system dynamics across scale regimes, as they are particularly applicable and relevant to directed-assembly. We employ massively parallel simulations, enabled by custom software, to establish underlying system dynamics and develop new device production methods

Prédétermination des hauteurs de départ d'avalanches. Modélisation combinée statistique-mécanique

La prédétermination de la hauteur de départ des avalanches représente un défi majeur pour l'évaluation du risque en montagne. Cette hauteur constitue en effet un ingrédient d'entrée important des procédures de zonage et de cartographie du risque. Dans cette thèse, nous présentons un formalisme rigoureux dans lequel les distributions de hauteur de départ d'avalanche sont exprimées à travers un couplage des facteurs mécaniques et météorologiques. Le critère de stabilité du système plaque - couche fragile est étudié en utilisant une analyse mécanique par éléments finis prenant en compte l'hétérogénéité spatiale des propriétés mécaniques. Considérant qu'une avalanche ne peut se produire que si la hauteur de chute de neige dépasse une hauteur critique correspondant au critère de stabilité, les distributions de hauteur de départ obtenues à partir du modèle mécanique sont couplées avec la distribution des chutes de neige extrêmes sur 3 jours. Nous montrons que ce modèle couplé est capable de reproduire des données de terrain de 369 avalanches naturelles de plaque à La Plagne (France). Non seulement la queue de la distribution en loi puissance, correspondant à des épaisseurs de plaque élevées, mais aussi le corps de la distribution pour les plaques moins épaisses, sont bien reproduits par le modèle. Les avalanches petites à moyennes semblent être essentiellement contrôlées par la mécanique, tandis que les grosses avalanches et l'exposant de la loi puissance associé, sont influencés par un couplage mécanique - météorologique fort. Par ailleurs, nous démontrons que la distribution obtenue est fortement dépendante de l'espace, et, en utilisant les processus max-stables permettant une interpolation spatiale rigoureuse, notre modèle couplé est utilisé pour obtenir des cartes de hauteur de départ d'avalanche pour différentes périodes de retour sur l'ensemble des Alpes françaises.The evaluation of avalanche release depth distributions represents a major challenge for hazard management in mountaineous regions. This depth constitutes an important input ingredient of hazard mapping procedures. This PhD thesis presents a rigorous formalism in which these distributions are expressed through a coupling of mechanical and meteorological factors. The stability criterion of a layered snowpack is investigated using a finite-element analysis accounting for the spatial heterogeneity of weak-layer mechanical properties. Considering that an avalanche can occur only if the snowfall depth exceeds a critical value corresponding to a stability criterion, release depth distributions obtained from the mechanical model are coupled with the distribution of 3-day extreme snowfalls. We show that this coupled model is able to reproduce field data from 369 natural slab avalanches in La Plagne (France). Not only the power-law tail of the distribution, corresponding to large slab depths, but also the core of the distribution for shallow slab depths, are well represented. Small to medium-sized avalanches appear to be controlled mainly by mechanics, whereas large avalanches and the associated power-law exponent, are influenced by a strong mechanical-meteorological coupling. Finally, we demonstrate that the obtained distribution is strongly space dependent, and, using max-stables processes allowing a rigorous spatial interpolation, our coupled model is used to obtain release depth maps for given return periods in the whole French Alps.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF