Mathematical models and analysis of liquid crystals and gels
نویسندگان
چکیده
In this series of lectures, we address mathematical models of materials systems that, in recent decades, have inspired many developments in partial differential equations. From physical point of view, such problems arise in soft condensed matter and are also linked to relevant applications in optics and mechanics. Liquid crystal phases found in organic and synthetic compounds are intermediate between solids and liquids. Gels consist of solids that can hold solvent. Both types of properties are often encountered as coexisting in physical and biological systems. Mathematically, such problems span many topics from calculus of variations, homogenization, nonlinear elasticity, to diffusive and hyperbolic dynamics.
منابع مشابه
Nano-sized AlPO4-5 Crystals: Synthesis and characterization
Molecular sieves and zeolites are materials whose crystalline frameworks form nanometer or subnanometer pores. A variety of different crystal structures are known having a range of pore sizes. Because the pore sizes are usually smaller than 2 nm, they are classified as microporous materials. Synthesis of microporous materials is usually conducted by the high temperature treatment (80-200 °C) of...
متن کاملNano-sized AlPO4-5 Crystals: Synthesis and characterization
Molecular sieves and zeolites are materials whose crystalline frameworks form nanometer or subnanometer pores. A variety of different crystal structures are known having a range of pore sizes. Because the pore sizes are usually smaller than 2 nm, they are classified as microporous materials. Synthesis of microporous materials is usually conducted by the high temperature treatment (80-200 °C) of...
متن کاملGelation Time of Hexamethylenetetramine Polymer Gels Used in Water Shutoff Treatment
Among the methods available to reduce water production, injecting a gelling system composed of a polymer and a crosslinker has been widely used. In this work, a hydrogel was prepared by crosslinking of an aqueous solution containing hexamethylenetetramine (HMTA) as crosslinker, hydrochloric acid (HCl) as an activator, and the co-polymer of 2-acrylamido-2methyl-propanesulfonic-acid sodium salt (...
متن کاملSelf-assembled liquid-crystalline gels designed from the bottom up.
Liquid crystals are often combined with polymers to influence the liquid crystals' orientation and mechanical properties, but at the expense of reorientation speed or uniformity of alignment. We introduce a new method to create self-assembled nematic liquid-crystal gels using an ABA triblock copolymer with a side-group liquid-crystalline midblock and liquid-crystal-phobic endblocks. In contrast...
متن کاملElectrically switchable cylindrical Fresnel lens based on holographic polymer-dispersed liquid crystals using a Michelson interferometer
Fabricating an electrically switchable cylindrical Fresnel lens based on holographic polymer-dispersed liquid crystals (H-PDLC) using a Michelson interferometer is reported. Simplicity of the method and possibility of fabricating different focal length lenses in a single set up are among the advantages of the method. It is demonstrated that the Fresnel structured zone plate acts as a cylindrica...
متن کامل