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Liquid crystals (LCs) were discovered more than a century ago, and were, for a long time, treated as a physical curiosity, until the development of flat panel screens and display devices caused a revolution in the information display industry, and in fact in society. There would be no mobile phones without liquid crystals, no flat screen TVs or computer monitors, no virtual reality, just to name a few of the applications that have changed our whole world of vision and perception. All of these inventions are based on liquid crystals that are formed through a change in temperature, thermotropic LCs. However, there is another form of liquid crystals, described even earlier, yet much less talked about; the lyotropic liquid crystals that occur through the change of concentration of some molecules in a solvent. These are found in abundance in nature, making up the cell membranes, and are used extensively in the food, detergents and cosmetics industries. In this collection of articles by experts in their respective research areas, we bring together some of the most recent and innovative aspects of lyotropic liquid crystals, which we believe will drive future research and set novel trends in this field.

Lyotropic liquid crystals --- uniaxial nematic phase --- biaxial nematic phase --- stabilization of nematic phases --- micelle --- surfactants --- chromonics --- structure --- physico-chemical properties --- rods --- curved surface --- Potts --- liquid crystal --- graphene oxide --- lyotropic --- colloid --- nematic --- lyotropic liquid crystals --- SmC* phase --- chirality --- ferroelectricity --- hydrogen bonds --- hydration forces --- cellulose nanocrystals --- hydroxypropyl cellulose --- chiral nematic --- cholesteric liquid crystals --- colloidal suspensions --- kinetic arrest --- gelation --- glass formation --- coffee-ring effect --- bragg reflection --- chromonic --- amphiphilic --- colloidal --- application --- biaxial nematic transition --- field behavior --- diluted nematic systems --- lyotropic liquid crystal --- nanomaterial --- mesogen --- phase behavior

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This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems.

conservation laws --- feedback stabilization --- input-to-state stability --- numerical approximations --- nonlocal velocity --- macroscopic models --- traffic data --- gap analysis --- multi-phase models --- Volterra integral equations --- asymptotic-preserving --- numerical stability --- Cellular Potts model --- cell migration --- nucleus deformation --- microchannel device --- regularization theory --- multivariate stochastic processes --- cross-power spectrum --- magnetoencephalography --- MEG --- functional connectivity --- spectral complexity --- soil organic carbon --- RothC --- non-standard integrators --- Exponential Rosenbrock–Euler --- langevin equation --- Mean Field Games system --- kinetic Fokker–Planck equation --- hypoelliptic operators --- Caputo fractional derivative --- Allee effect --- existence and stability --- Hopf bifurcation --- implicit schemes --- optimal design --- soft tissue mechanics --- mutual information --- biaxial experiment --- inverse problems --- information theory --- LWR model --- follow-the-leader model --- phase transition --- creeping --- seepage --- fundamental diagram --- lane discipline --- networks --- aggregation equation --- relaxation limit --- scalar conservation law --- finite volume scheme --- differential equations --- mathematical biology --- microfluidic chip --- applied mathematics --- numerical methods --- computational mathematics --- differential and integro-differential models