This book explores the diverse types of Schroedinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose-Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schroedinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose-Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schroedinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose-Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.

This book discusses the tribological, rheological and optical properties of liquid-crystal nanomaterials as well as lubricant media. It also describes the formation of liquid-crystal materials and the application of cholesteric liquid-crystal compounds in technical friction units and in human and animal joints. Further, it shows the connection between the tribological and other physical properties of liquid-crystal cholesterol compounds and develops a lubricity conceptual model of cholesteric-nematic, liquid-crystalline nanostructures on the basis of physical and energetic interpretations. This general model is valid for all surfaces and friction pairs, including biopolymers, and could lead to applications of cholesteric liquid-crystalline nanomaterials in different friction units and tribosystems as well as in the treatment of joint diseases.

This book presents an overview of fundamental aspects of surface-based biosensors and techniques for enhancing their detection sensitivity and speed. It focuses on rapid detection using miniaturized sensors and describes the physical principles of nanoscale transducers, surface modifications, microfluidics and reaction engineering, diffusion and kinetics. A key challenge in the field of bioanalytical sensors is the rapid delivery of target biomolecules to the sensing surface. While various nanostructures have shown great promise in sensitive detection, diffusion-limited binding of analyte molecules remains a fundamental problem. Recently, many researchers have put forward novel schemes to overcome this challenge, such as nanopore channels, electrokinetics, and dielectrophoresis, to name but a few. This book provides the readers an up-to-date account on these technological advances.

This book presents the topology optimization theory for laminar flows with low and moderate Reynolds numbers, based on the density method and level-set method, respectively. The density-method-based theory offers efficient convergence, while the level-set-method-based theory can provide anaccurate mathematical expression of the structural boundary. Unsteady, body-force-driven and two-phase properties are basic characteristics of the laminar flows. The book discusses these properties, which are typical of microfluidics and one of the research hotspots in the area of Micro-Electro-Mechanical Systems (MEMS), providing an efficient inverse design approach for microfluidic structures. To demonstrate the applications of this topology optimization theory in the context of microfluidics, it also investigates inverse design for the micromixer, microvalve and micropump, which are key elements in lab-on-chip devices.

This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugene and Francois Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented "rigid particles" with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises.

This book introduces and discusses both the fundamental aspects and the measurability of applications of time-symmetric kinetic quantities, outlining the features that constitute the non-dissipative branch of non-equilibrium physics. These specific features of non-equilibrium dynamics have largely been ignored in standard statistical mechanics texts. This introductory-level book offers novel material that does not take the traditional line of extending standard thermodynamics to the irreversible domain. It shows that although stationary dissipation is essentially equivalent with steady non-equilibrium and ubiquitous in complex phenomena, non-equilibrium is not determined solely by the time-antisymmetric sector of energy-entropy considerations. While this should not be very surprising, this book provides timely, simple reminders of the role of time-symmetric and kinetic aspects in the construction of non-equilibrium statistical mechanics.

This book presents a detailed overview of the design, formatting, application, and development of microfluidic chips in the context of cell biology research, enumerating each element involved in microfluidics-based cell analysis, discussing its history, status quo, and future prospects, It also offers an extensive review of the research completed in the past decade, including numerous color figures. The individual chapters are based on the respective authors' studies and experiences, providing tips from the frontline to help researchers overcome bottlenecks in their own work. It highlights a number of cutting-edge techniques, such as 3D cell culture, microfluidic droplet technique, and microfluidic chip-mass spectrometry interfaces, offering a first-hand impression of the latest trends in the field and suggesting new research directions. Serving as both an elementary introduction and advanced guidebook, the book interests and inspires scholars and students who are currently studying microfluidics-based cell analysis methods as well as those who wish to do so.

This thesis both broadens and deepens our understanding of the Brownian world. It addresses new problems in diffusion theory that have recently attracted considerable attention, both from the side of nanotechnology and from the viewpoint of pure academic research. The author focusses on the difussion of interacting particles in restricted geometries and under externally controlled forces. These geometries serve, for example, to model ion transport through narrow channels in cell membranes or a Brownian particle diffusing in an optical trap, now a paradigm for both theory and experiment. The work is exceptional in obtaining explicit analytically formulated answers to such realistic, experimentally relevant questions. At the same time, with its detailed exposition of the problems and a complete set of references, it presents a clear and broadly accessible introduction to the domain. Many of the problem settings and the corresponding exact asymptotic laws are completely new in diffusion theory.

Magnetic perovskite with multi functional properties (magneto-resistive, magneto-dielectric, multiferroics, spintronics, etc.) have attracted increasing attention due to their possible applications towards storage materials and intriguing fundamental Physics. Despite the numerous investigations on multi functional materials in the past few years, a very few magnetic perovskites have been known to realize as ferromagnetic-insulators. In perovskites centred transition metal oxides strong interplay between lattice, charge, spin and/or orbital degrees of freedom provide a fantastic playground to tune their physical properties. The main purpose of this book is to introduce the phenomenon and physics of complex magnetism (phase separation, spin glass, frustrations, etc.) in perovskite manganites and cobaltites via an experimental approach. The book is organized into four chapters; Chap. 1 gives a brief introduction of various interesting phenomena in magnetic perovskites. Chapter 2 describes the results of the investigations on electronic phase separation and glassy ferromagnetism of the hole-doped perovskite manganites and cobaltites. Ordered and disordered effects and related aspects in hole-doped perovskite cobaltites are described in Chap. 3. Finally, in Chap. 4 the bismuth based magnetic perovskite is discussed.

This book focuses on droplets and sprays and their applications. It discusses how droplet level transport is central to a multitude of applications and how droplet level manipulation and control can enhance the efficiency and design of multiphase systems. Droplets and sprays are ubiquitous in a variety of multiphase and multiscale applications in surface patterning, oil recovery, combustion, atomization, spray drying, thermal barrier coating, renewable energy, and electronic cooling, to name but a few. This book provides two levels of details pertaining to such applications. Each chapter delves into a specific application and provides not only an overview but also detailed physical insights into the application mechanism from the point of view of droplets and sprays. All chapters provide a mix of cutting-edge applications, new diagnostic techniques and modern computational methodologies, as well as the fundamental physical mechanism involved in each application. Taken together, the chapters provide a translational perspective on these applications, from basic transport processes to optimization, and from design to implementation using droplets or sprays as fundamental building blocks. Given its breadth of coverage, the book will be of interest to students, researchers, and industry professionals alike.

This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Moebius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure-property-function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.

This book investigates the common nature of granular and active systems, which is rooted in their intrinsic out-of-equilibrium behavior, with the aim of finding minimal models able to reproduce and predict the complex collective behavior observed in experiments and simulations. Granular and active matter are among the most studied systems in out-of-equilibrium statistical physics. The book guides readers through the derivation of a fluctuating hydrodynamic description of granular and active matter by means of controlled and transparent mathematical assumptions made on a lattice model. It also shows how a macroscopic description can be provided from microscopic requirements, leading to the prediction of collective states such as cooling, swarming, clustering and the transitions among them. The analytical and numerical results shed new light on the physical connection between the local, microscopic properties of few particles and the macroscopic collective motion of the whole system.

This book presents a comprehensive and unifying approach to analytical identification of material properties of biological materials. Focusing on depth-sensing indentation testing, pipette aspiration testing, and torsion of soft tissues, it discusses the following important aspects in detail: damping, adhesion, thickness effect, substrate effect, elastic inhomogeneity effect, and biphasic effect. This book is intended for advanced undergraduate and graduate students, researchers in the area of biomechanics as well as for biomedical engineers interested in contact problems and involved in inverse materials parameters prediction analysis.

This book focuses on the widely used experimental techniques available for the structural, morphological, and spectroscopic characterization of materials. Recent developments in a wide range of experimental techniques and their application to the quantification of materials properties are an essential side of this book. Moreover, it provides concise but thorough coverage of the practical and theoretical aspects of the analytical techniques used to characterize a wide variety of functional nanomaterials. The book provides an overview of widely used characterization techniques for a broad audience: from beginners and graduate students, to advanced specialists in both academia and industry.

Pressure is one of the essential thermodynamic variables that, due to some former experimental difficulties, was long known as the forgotten variable. But this has changed over the last decade. This book includes the most essential first experiments from the 1960s and reviews the progress made in understanding glass formation with the application of pressure in the last ten years. The systems include amorphous polymers and glass-forming liquids, polypeptides and polymers blends. The thermodynamics of these systems, the relation of the structural relaxation to the chemical specificity, and their present and future potential applications are discussed in detail. The book provides (a) an overview of systems exhibiting glassy behavior in relation to their molecular structure and provides readers with the current state of knowledge on the liquid-to-glass transformation, (b) emphasizes the relation between thermodynamic state and dynamic response and (c) shows that the information on the pressure effects on dynamics can be employed in the design of materials for particular applications. It is meant to serve as an advanced introductory book for scientists and graduate students working or planning to work with dynamics. Several scientific papers dealing with the effects of pressure on dynamics have appeared in leading journals in the fields of physics in the last ten years. The book provides researchers and students new to the field with an overview of the knowledge that has been gained in a coherent and comprehensive way.

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The 3rd edition of this important dictionary offers more than 12,000 entries with expanded encyclopaedic-style definitions making this major reference work invaluable to practitioners, researchers and students working in the area of polymer science and technology. This new edition now includes entries on computer simulation and modeling, surface and interfacial properties and their characterization, functional and smart polymers. New and controlled architectures of polymers, especially dendrimers and controlled radical polymerization are also covered.

This monograph contains expert knowledge on complex fluid-flows in microfluidic devices. The topical spectrum includes, but is not limited to, aspects such as the analysis, experimental characterization, numerical simulations and numerical optimization. The target audience primarily comprises researchers who intend to embark on activities in microfluidics. The book can also be beneficial as supplementary reading in graduate courses.

This book brings together the many concepts and discoveries in liquid crystal colloids contributed over the last twenty years and scattered across numerous articles and book chapters. It provides both a historical overview of the development of the field and a clear perspective on the future applications in photonics. The book covers all phenomena observed in liquid crystal colloids with an emphasis on experimental tools and applications of topology in condensed matter, as well as practical micro-photonics applications. It includes a number of spectacular manifestations of new topological phenomena not found or difficult to observe in other systems. Starting from the early works on nematic colloids, it explains the basics of topological defects in ordered media, charge and winding, and the elastic forces between colloidal particles in nematics. Following a detailed description of experimental methods, such as optical tweezing and particle tracking, the book eases the reader into the theoretical part, which deals with elastic deformation of nematic liquid crystals due to inclusions and surface alignment. This is discussed in the context of basic mean field Landau-de Gennes Q-tensor theory, with a brief explanation of the free-energy minimization numerical methods. There then follows an excursion into the topology of complex nematic colloidal structures, colloidal entanglement, knotting and linking. Nematic droplets, shells, handlebodies and chiral topological structures are addressed in separate chapters. The book concludes with an extensive chapter on the photonic properties of nematic dispersions, presenting the concept of integrated soft matter photonics and discussing the concepts of nematic and chiral nematic microlasers, surface-sensitive photonic devices and smectic microfibers. The text is complemented by a large bibliography, explanatory sketches and beautiful micrographs.

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other materials than graphene, collectively known as "Dirac matter", and offer a thorough description of the merging transition of Dirac cones that occurs in the energy spectrum, in various experiments involving stretching of the microscopic hexagonal lattice; the third contribution, entitled "Quantum Transport in Graphene: Impurity Scattering as a Probe of the Dirac Spectrum", given by Helene Bouchiat, a leading experimentalist in mesoscopic physics, with Sophie Gueron and Chuan Li, shows how measuring electrical transport, in particular magneto-transport in real graphene devices - contaminated by impurities and hence exhibiting a diffusive regime - allows one to deeply probe the Dirac nature of electrons. The last two contributions focus on topological insulators; in the authoritative "Experimental Signatures of Topological Insulators", Laurent Levy reviews recent experimental progress in the physics of mercury-telluride samples under strain, which demonstrates that the surface of a three-dimensional topological insulator hosts a two-dimensional massless Dirac metal; the illuminating final contribution by David Carpentier, entitled "Topology of Bands in Solids: From Insulators to Dirac Matter", provides a geometric description of Bloch wave functions in terms of Berry phases and parallel transport, and of their topological classification in terms of invariants such as Chern numbers, and ends with a perspective on three-dimensional semi-metals as described by the Weyl equation. This book will be of broad general interest to physicists, mathematicians, and historians of science.

This thesis describes lyotropic chromonic liquid crystals (LCLCs) with exotic elastic and viscous properties. The first part of the thesis presents a thorough analysis of the elastic and viscous properties of LCLCs as functions of concentration, temperature and ionic contents, while the second part explores an active nematic system: living liquid crystals, which represent a combination of LCLC and living bacteria. LCLCs are an emerging class of liquid crystals that have shown profound connections to biological systems in two aspects. First, the assembly process of the chromonic aggregates is essentially the same as DNA oligomers and other super-molecular assemblies of biological origin. LCLCs thus provide an excellent model system for studying physical properties such as the elasticity and viscosity of these supramolecular assemblies. Second, LCLCs are biocompatible, thus serving as a unique anisotropic matrix to interface with living systems such as bacteria. This thesis deepens our understanding of both aspects. The noncovalent nature of chromonic aggregation produces the unique viscoelasticity to be found in LCLCs, which differs dramatically from that of traditional LCs. Anisotropic interactions between LCLCs and bacteria lead to fascinating phenomena such as the deformation of LCLCs with a characteristic wavelength determined by the elasticity of the LCLCs and the activity of the bacteria, orientationally controlled trajectories of bacteria and visualization of 24 nm flagella motion.

The research and its outcomes presented here is devoted to the use of x-ray scattering to study correlated electron systems and magnetism. Different x-ray based methods are provided to analyze three dimensional electron systems and the structure of transition-metal oxides. Finally the observation of multipole orderings with x-ray diffraction is shown.

This book provides the state-of-the art of the present understanding of avalanche phenomena in both functional materials and geophysics. The main emphasis of the book is analyzing these apparently different problems within the common perspective of out-of-equilibrium phenomena displaying spatial and temporal complexity that occur in a broad range of scales. Many systems, when subjected to an external force, respond intermittently in the form of avalanches that often span over a wide range of sizes, energies and durations. This is often related to a class of critical behavior characterized by the absence of characteristic scales. Typical examples are magnetization processes, plastic deformation and failure occuring in functional materials. These phenomena share many similarities with seismicity arising from the earth crust failure due to stresses that originate from plate tectonics.

This book describes in great detail the semi-solid processing of aluminum alloys. The authors examine the fundamentals of semi-solid metal processing, provide guidelines for research, illustrate the tools that are employed, and explain the measured parameters for semi-solid processing characterization.

This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.