Liquid Crystals. Pawel Pieranski

structures in f...Figure 1.13. (a) Refractive optics from localized defect structures in frustrate...Figure 1.14. (a) Natural white light imaging of the four types of cholesteric fi...Figure 1.15. (a) Left: XPOL image of a spontaneous 1D phase grating made of CF1s...Figure 1.16. (a) Simulated director field of a CF2 structure. Inset: transverse ...Figure 1.17. (a) Simulated director field of a structure that corresponds to a C...Figure 1.18. Simulated lensing effect experienced by light propagating on-axis a...Figure 1.19. (a) Simulated waveguiding of an azimuthally polarized beam with a d...Figure 1.20. (a) Top: concentric lamellar structure of a smectic A filament ende...Figure 1.21. (a) TM lasing illustration in an optically pumped radial nematic dr...Figure 1.22. (a) Left: illustration of the 3D director field associated with the...Figure 1.23. (a) Elastic multipoles from spherical particles. From left to right...Figure 1.24. XPOL images of self-assembled packing of localized defect structure...Figure 1.25. (a) Calculated intensity and phase of the random superposition of 4...Figure 1.26. (a) Map of lines of equal degree of polarization in the atmosphere ...Figure 1.27. (a) Polarization ellipses around generic C points, whose naming was...Figure 1.28. Illustration of singularity removal of nematic disclination lines w...Figure 1.29. (a) Maps of intensity (top) and phase (bottom) of Laguerre–Gauss mo...Figure 1.30. Main kinds of vortex beam shaping strategies. (a) Optical profilome...Figure 1.31. Two distinct experimental situations leading to the spontaneous gen...Figure 1.32. (a) Optical vortex generation from a radial nematic droplet trapped...Figure 1.33. Experimental demonstrations of singular diffraction gratings produc...Figure 1.34. (a) Calculated meridional (left panel) and transverse (at z = L/2, ...Figure 1.35. (a) Experimental voltage-tunable vortex purity of an isolated umbil...Figure 1.36. (a) Typical XPOL observation of a random distribution of disclinati...Figure 1.37. Illustration of several approaches to generate localized umbilics i...Figure 1.38. Main self-induced optical vortex generation processes based on ligh...Figure 1.39. (a–d) Field-induced arrays of umbilics in nematic films with perpen...Figure 1.40. (a) Lyot’s Drawing of his coronagraph. Copyright: Observatoire de P...Figure 1.41. Laboratory demonstration of optical vortex coronagraphy using liqui...Figure 1.42. (a,b) Evolution of the core and transverse swirl of localized magne...Figure 1.43. (a) Binary star sunset image from the movie Star Wars: A New Hope. ...Figure 1.44. (a) Principle of multispectral modulation of the orbital angular mo...

      2 Chapter 2Figure 2.1. Director configurations around a colloidal sphere in a uniform nemat...Figure 2.2. Nonlinear LCEP of a glass sphere powered by an AC electric field (La...Figure 2.3. Mechanism of charge separation and electro-osmotic flows of nematic ...Figure 2.4. Sign reversal of the LCEP velocity by changing anisotropic permittiv...Figure 2.5. LCEO flows in the pre-designed photo-patterned surface alignment (Pe...Figure 2.6. LCEK applications in microreactions. (a) PolScope image of the direc...Figure 2.7. Sorting of droplets with different surface properties by LCEK flows ...Figure 2.8. Living liquid crystal comprised of swimming bacteria (extensile micr...Figure 2.9. Controlled dynamics of bacteria by the patterned LCLC. (a) Designed ...Figure 2.10. Transition from individual to collective motion caused by the incre...Figure 2.11. Bacteria swarming in the patterned 2D lattice of spiraling vortices...Figure 2.12. Bacteria polar jets in the alternating splay-bend strips and transp...

      3 Chapter 3Figure 3.1. Direct and crossed effects in nematic and cholesteric liquid crystal...Figure 3.2. Gay–Berne ellipsoids illustrating the notations of equation [3.33]Figure 3.3. Rigid twisted string of six oblate Gay–Berne ellipsoids featuring a ...Figure 3.4. (a) Phase diagram of the mixture EM + CC. Along the dashed line, the...Figure 3.5. Photo taken between crossed polarizers of a homeotropic sample subje...Figure 3.6. (a) Phase shift as a function of the temperature gradient when d = 1...Figure 3.7. Geometry proposed by Poursamad to measure the Akopyan and Zel’dovich...Figure 3.8. Transmitted intensity between crossed polarizers. Crosses are experi...Figure 3.9. (a) Angular velocity as a function of the sample temperature measure...Figure 3.10. (a) Effective Leslie coefficient | as a function of temperature (δT...Figure 3.11. Typical texture observed between crossed polarizers with the mixtur...Figure 3.12. (a) Nine photographs taken at the compensation temperature showing ...Figure 3.13. Numerical simulation of the deformation of the extinction branches ...Figure 3.14. (a) Typical texture observed between crossed polarizers in the pres...Figure 3.15. (a) Schematic of the cell used to impose an electric field. (b–d) T...Figure 3.16. π-walls propagating when E/Estop ≈ 1.6. The intensity of the backgr...Figure 3.17. Angular velocity as a function of temperature measured in the Lesli...Figure 3.18. Director field inside of a CF1 when q0 > 0 (right-handed cholesteri...Figure 3.19. Nature of the frustration transition in the plane of the anisotropy...Figure 3.20. Drift direction of CF1 segments observed in homeotropic samples of ...Figure 3.21. (a) Drift velocity as a function of the temperature difference ΔT ,...Figure 3.22. Drift velocity of the CF1s and coexistence voltage V2 as a function...Figure 3.23. (a-b) Two single spirals rotating in the same direction observed in...Figure 3.24. Spiral of CF1 observed between crossed polarizers close to the smec...Figure 3.25. Growth of a CF1 in the homeotropic nematic. The dashed lines show t...Figure 3.26. Circular (a) and radial (b) configurations and system of polar coor...Figure 3.27. (a, b) vθ-amplitude in the radial plane (r, z) and (c,d) vθ-profile...Figure 3.28. Mixed planar-homeotropic geometry. In (a), the anchoring is planar ...Figure 3.29. Velocity field in the planar-circular/homeotropic geometry. (a) |-a...Figure 3.30. Orthoradial component of the velocity vθ as a function of r at z = ...

      4 Chapter 4Figure 4.1. Classification of topological defects in systems with an order param...Figure 4.2. Spontaneous shrinking and collapse of disclination loops in a nemati...Figure 4.3. Stable systems of disclinations. (a) Disclination loop threaded on a...Figure 4.4. Occurrence of nematic monopoles: (a) as companions of inclusions wit...Figure 4.5. Topology of disclinations and monopolesFigure 4.6. The dowser texture. (a) Coexistence of the dowser and homeotropic te...Figure 4.7. Generic experiment paving the way to the dowser texture. (a) Perspec...Figure 4.8. Collapse of the peripheral disclination into a monopoleFigure 4.9. Three-stage road to the dowser texture. (a–d) Schematic representati...Figure 4.10. Defects in systems with complex order parameters: (a) vortices in a...Figure 4.11. Nematic layers with degenerated anchoring conditions. (a) Film of 5...Figure 4.12. Monopole–antimonopole pair generated in a dowsons collider. (a) Vie...Figure 4.13. Collisions of monopole/antimonopole pairs in a dowsons collider. Su...Figure 4.14. Tropisms of the dowser texture. (a) Symmetry of the dowser texture ...Figure 4.15. Generic setup called Double Dowsons Collider 1 (DDC1). (a) General ...Figure 4.16. Shortening of preparation of the dowser texture by a transitory app...Figure 4.17. Generation of a unique homeotropic-in-dowser domain by the reductio...Figure 4.18. Stability of homeotropic-in-dowser domains in Poiseuille flows. (a)...Figure 4.19. Flow-assisted bowser-dowser transformation in a capillary. (a,a’) F...Figure 4.20. Flow-assisted hemeotropic-dowser transition in the circular geometr...Figure 4.21. Alignment of the dowser field by a radial Poiseuille flow directed ...Figure 4.22. The origin of the rheotropism. (a) Hydrodynamic torque Γz exerted b...Figure 4.23. Evolution of the dowser texture during one period of the up and dow...Figure 4.24. Winding of the dowser texture by harmonic motion of the glass slide...Figure 4.25. Mechanical analogies of the wound up dowser texture. (a) Detailed v...Figure 4.26. Flows inside a nematic droplet driven by a harmonic up and down mot...Figure 4.27. Setups tailored for the asynchronous winding of the dowser field. (...Figure 4.28. Circular Dowsons Collider 2. (a) Perspective view of the glass slid...Figure 4.29. Asynchronous winding of the dowser field with the Circular Dowsons ...Figure 4.30. Hybrid winding of the dowser field with the Circular Dowsons Collid...Figure 4.31. Action of an alternating Poiseuille flow on a wound up dowser field...Figure 4.32. Simulation of the spatiotemporal cross-section. (a) Definition of t...Figure 4.33. Winding of the dowser field by the magnetic field. (a) Initial radi...Figure 4.34. Slow elastic collapse of the circular 2π-wall. (a) Spatiotemporal c...Figure 4.35. Viscoelastic unwinding of the dowser field in a circular droplet ca...Figure 4.36. Origin of the cuneitropism. (a and b) When h = constant, the distor...Figure 4.37. Spontaneous flexo-electric polarization of the dowser textureFigure 4.38. Setup. (a) General perspective view. (b) Cross-section of the sampl...Figure 4.39. The first evidence of the flexo-electric polarization in MBBA (a–c)...Figure 4.40. Measurements of the flexo-electric polarization in MBBA and 5CB. (a...Figure 4.41. Evidence of electro-osmotic flows. (a) General view of a quasi-equi...Figure 4.42. Poiseuille flows driven by electrosmosis in the one-gap system of e...Figure 4.43. Electro-osmotic flows in the two-gap system of electrodes. (a) Gaps...Figure 4.44. Convection of the dowser field. Spatiotemporal cross-sections