Augmented Lagrangian preconditioners for the Oseen-Frank model of nematic and cholesteric liquid crystals

We propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen-Frank model arising in cholesteric liquid crystals. By applying the augmented Lagrangian method, the Schur complement of the director block can be better approximated by the weighted mass matrix of the Lagrange multiplier, at the cost of making the augmented director block harder to solve. In order to solve the augmented director block, we develop a robust multigrid algorithm which includes an additive Schwarz relaxation that captures a pointwise version of the kernel of the semi-definite term. Furthermore, we prove that the augmented Lagrangian term improves the discrete enforcement of the unit-length constraint. Numerical experiments verify the efficiency of the algorithm and its robustness with respect to problem-related parameters (Frank constants and cholesteric pitch) and the mesh size

Large-Scale Patterning and Dynamics of Topological Solitons In Chiral Nematic Liquid Crystals

The coexistence of order and fluidity in soft condensed matter often mimics that found in biological cells, which allows for complex collective dynamics and for highly technological applications, like displays and sensors. In active soft matter, different forms of emergent order can even arise because of this out-of-equilibrium dynamic behavior, powered by local energy conversion. We show that this emergent ordering can mimic behavior of familiar living systems with coherent motion, like crowds of people and schools of fish. Most active matter systems are biological in origin, although the discovery of inanimate, purely synthetic particles capable of such emergent behavior would enable new breeds of materials and nanomachines. Such examples are limited, typically with chemical or mechanical agitation sources of energy. We show that thousands of particle-like topological solitons can exhibit collective dynamics while either (1) each converting macroscopically-supplied electric energy into motion along spontaneously-selected directions uncorrelated with the direction of electric field, (2) responding to photo-manipulation of the material&rsquo;s elastic free energy landscape by changing shape or moving away from the light, or (3) a combination of the two. We demonstrate that these soliton dynamics occur in the absence of backflows, have the ability to carry cargo, display tunable dynamic self-assembly with their neighbors, possess long-range repulsive interactions, and exhibit emergent order and giant-number fluctuation scaling consistent with active systems such as schooling fish. We uncover how these topological solitons react to changes in the local and global elastic free energy, both in samples with flat geometries and spherical liquid crystal shells. We further show that skyrmions in motion can pack together as dense quasi-hexagonal crystallites and exhibit crowding and jamming behavior similar to crowds of people moving around obstacles. Uniquely to our system, this plethora of emergent active behavior occurs in the absence of physical or biological particles and material flows, revealing the defining characteristics of the new field of solitonic active matter and promising many technological uses.</p

Flowing matter

This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena.Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents.Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter.This book is the legacy of the COST Action MP1305 “Flowing Matter”

Microscopic characterization of mesoscopic magnetic textures in Fe3Sn2

The itinerant ferromagnet Fe3Sn2 displays a plethora of spin textures due to competing magnetic interactions. Dendrites, stripes, topologically trivial and skyrmionics bubbles can be realized by applying magnetic field, or geometric confinement using focused ion beam (FIB). Magnetic force microscopy (MFM) and Lorentz transmission electron microscopy (LTEM) are used to image these spin textures, while micromagnetic simulations elucidate the obtained contrast. Fe3Sn2 serves as a model system for similar intermediate Q materials, where the shape anisotropy and the uniaxial magnetocrystalline anisotropy compete on comparable scales. Thus, the presented results pave the way towards spintronics applications.Die itinerante, ferromagnetische Verbindung Fe3Sn2 weist infolge konkurrierender magnetischer Interaktionen eine Vielzahl von Spin-Texturen auf. Dendriten, Streifen-, sowie topologisch geschützte und triviale Bubble-Domänen können durch externes magnetisches Feld, beziehungsweise geometrische Beschränkungen mittels Focused Ion Beam (FIB) stabilisiert werden. Magnetic Force Microscopy (MFM) und Lorentz Transmission Electron Microscopy (LTEM) dienen zur Abbildung der magnetischen Strukturen, deren Kontrast durch micromagnetische Simulationen erklärt wird. Fe3Sn2, stellt ein Modellsystem für viele „intermediate Q“ Materialien dar. Diese zeichnen sich durch ausgeglichene Form- und magnetokristalline Anisotropie aus. Die präsentierten Resultate weisen den Weg hin zu Spintronic basierten Anwendungen

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

Research Reports: 1997 NASA/ASEE Summer Faculty Fellowship Program

For the 33rd consecutive year, a NASA/ASEE Summer Faculty Fellowship Program was conducted at the Marshall Space Flight Center (MSFC). The program was conducted by the University of Alabama in Huntsville and MSFC during the period June 2, 1997 through August 8, 1997. Operated under the auspices of the American Society for Engineering Education, the MSFC program was sponsored by the Higher Education Branch, Education Division, NASA Headquarters, Washington, D.C. The basic objectives of the program, which are in the 34th year of operation nationally, are: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate an exchange of ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA centers. The Faculty Fellows spent 10 weeks at MSFC engaged in a research project compatible with their interests and background and worked in collaboration with a NASA/MSFC colleague. This document is a compilation of Fellows' reports on their research during the summer of 1997. The University of Alabama in Huntsville presents the Co-Directors' report on the administrative operations of the program. Further information can be obtained by contacting any of the editors

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students