A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering The form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator A comprehensive presentation of the inverse scattering method is given and general features of the solution are discussed The relationship of the scattering theory and Backlund transformations is brought out In view of the role of the dispersion relation, the comparatively simple asymptotic states, and the similarity of the method itself to Fourier transforms, this theory can be considered a natural extension of Fourier analysis to nonlinear problems

The Inverse scattering transform fourier analysis for nonlinear problems

The term soliton has recently been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed. To date at least seven distinct wave systems, representing a wide range of applications in applied science, have been found to exhibit such solutions. This review paper covers the current status of soliton research, paying particular attention to the very important "inverse method" whereby the initial value problem for a nonlinear wave system can be solved exactly through a succession of linear calculations.

The soliton: A new concept in applied science

The hierarchical self-assembly of disc-shaped molecules leads to the formation of discotic liquid crystals. These materials are of fundamental importance not only as models for the study of energy and charge migration in self-organized systems but also as functional materials for device applications such as, one-dimensional conductors, photoconductors, light emitting diodes, photovoltaic solar cells, field-effect transistors and gas sensors. The negative birefringence films formed by polymerized nematic discotic liquid crystals have been commercialized as compensation foils to enlarge the viewing angle of commonly used twisted nematic liquid crystal displays. To date the number of discotic liquid crystals derived from more than 50 different cores comes to about 3000. This critical review describes, after an in-depth introduction, recent advances in basic design principles and synthetic approaches towards the preparation of most frequently encountered discotic liquid crystals.

Self-organization of disc-like molecules: chemical aspects

Theory of Flow Phenomena in Liquid Crystals

In this review we introduce recent advances in the development of cellulose nanomaterials and the construction of high order structures by applying some principles of colloid and interface science. These efforts take advantage of natural assemblies in the form of fibers that nature constructs by a biogenetic bottom-up process that results in hierarchical systems encompassing a wide range of characteristic sizes. Following the reverse process, a top-down deconstruction, cellulose materials can be cleaved from fiber cell walls. The resulting nanocelluloses, mainly cellulose nanofibrils (CNF) and cellulose nanocrystals (CNC, i.e., defect-free, rod-like crystalline residues after acid hydrolysis of fibers), have been the subject of recent interest. This originates from the appealing intrinsic properties of nanocelluloses: nanoscale dimensions, high surface area, morphology, low density, chirality and thermo-mechanical performance. Directing their assembly into multiphase structures is a quest that can yield useful outcomes in many revolutionary applications. As such, we discuss the use of non-specific forces to create thin films of nanocellulose at the air–solid interface for applications in nano-coatings, sensors, etc. Assemblies at the liquid–liquid and air–liquid interfaces will be highlighted as means to produce Pickering emulsions, foams and aerogels. Finally, the prospects of a wide range of hybrid materials and other systems that can be manufactured via self and directed assembly will be introduced in light of the unique properties of nanocelluloses.

Nanocellulose properties and applications in colloids and interfaces

Liquid Crystals and Biological Structures

Most lipids do not pass, on heating, directly from a crystalline structure to an isotropic structure. They are often characterized by a number of intermediate phases, ranging from the plastic crystal, where the center of gravity of the molecule may rotate about one or more axes while the three-dimensional order of the crystal remains, to nematic liquid crystals, which have birefrigent properties of crystals and yet are characterized by completely random ordering of the molecular centers. The smectic and cholesteric liquid crystalline structures are most commonly encountered in lipids. The structural characteristics of these systems are discussed. Of particular interest in living systems are liquid crystals, which are formed by cholesteric esters and many protein materials, and the two-dimensional crystals (smectic structure), which are formed by fatty acid derivatives. The mechanisms of energy transfer and the mechanical alignment in these liquid crystalline systems are unique and require different considerations from those found adaptable to liquids or solids. The properties of liquid crystals which might best be associated with living systems will be discussed, including surface properties and diffusivity.

Liquid crystals and living systems.

Thermodynamic study of solutions with liquid crystal solvents by gas-liquid partition chromatography

Chapter 12 – Liquid Crystals in Medicine

Liquid crystals may be classified in two major categories, namely, thermotropic and lyotropic. Thermotropic liquid crystals are commonly prepared by heating organic compounds, whereas lyotropic liquid crystals are made by mixing two or more components. Thermotropic liquid crystals are mainly of interest in this paper. They have been classified as nematic (threadlike) and smectic (soapy). Most commercial applications have focused on thermotropic liquid crystals; however, lyotropic liquid crystals are important in the detergent industry and in living systems. Thermotropic and lyotropic liquid crystals show polymorphism. The properties and structure of the different polymorphic forms are discussed. The two most-active areas of applications of liquid crystals are nondestructive testing and display media; both are considered. Liquid crystals have been used as solvents in structure determination (nmr) in chromatography and in study of chemical kinetics.

Glenn H. Brown

Papers

Liquid Crystals and Biological Structures

Liquid crystals and living systems.

Thermodynamic study of solutions with liquid crystal solvents by gas-liquid partition chromatography

Chapter 12 – Liquid Crystals in Medicine

Structure, properties, and some applications of liquid crystals*