04111nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050002100153072001700174072002300191072001600214100008300230245015800313250001800471264006900489300006600558336002600624337002600650338003600676347002400712490004900736505059600785520174301381650002203124650002703146650002603173650002803199650003003227650002203257650002003279650003703299650002603336650002803362710003403390773002603424776003603450776003603486830004903522856004603571978-3-031-70200-6DE-He21320251030113141.0cr nn 008mamaa241014s2024    sz |    s    |||| 0|eng d  a97830317020067 a10.1007/978-3-031-70200-62doi 4aQC173.45-173.458 7aPHFC2bicssc 7aSCI0770002bisacsh 7aPHFC2thema1 aSelinger, Jonathan V.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aIntroduction to Topological Defects and Solitonsh[electronic resource] :bIn Liquid Crystals, Magnets, and Related Materials /cby Jonathan V. Selinger.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIII, 213 p. 80 illus., 77 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Physics,x1616-6361 ;v10320 aChapter 1. Introduction to Defects -- Chapter 2. Introduction to Solitons -- Chapter 3. Free Energy -- Chapter 4. Dynamics and Statistical Mechanics -- Chapter 5. Prequel to Defects: Variable Magnitude of Order -- Chapter 6. Further Issues: Defect Phase/Orientation, Charge Density, Curvature -- Chapter 7. 2D Nematic Order, Active Liquid Crystals -- Chapter 8. 3D Polar or Nematic Order -- Chapter 9. Defects in Crystals -- Chapter 10. 2D Measuring Surface: Hedgehogs, Skyrmions -- Chapter 11. 3D Measuring Surface: Hopfions -- Chapter 12. Phases With Regular Arrays of Defects or Solitons.  aThis textbook introduces topological defects and solitons at a level suitable for advanced undergraduates and beginning graduate students in physics and materials science. It avoids the formal mathematics of topology, and instead concentrates on the physical properties of these topological structures. The first half of the book concentrates on fundamental principles of defects and solitons, and illustrates these principles with a single example—the xy model for 2D magnetic order. It begins by defining the concept of a winding number, and uses this concept to describe the topology of defects (vortices or disclinations) and solitons (domain walls), carefully identifying the similarities and differences between these two types of topological structures. It then goes on to discuss physical properties of defects and solitons, including free energy, dynamics, statistical mechanics, and coupling with curvature. It shows how these concepts emerge from a theory with variable magnitude of order, and hence how topology can be viewed as an approximation to physics. The second half goes on to explore a wider range of topological defects and solitons. First, it considers more complex types of order—2D nematic liquid crystals, 3D magnetic or liquid-crystal order, 2D or 3D crystalline solids—and shows how each type of order leads to specific topological structures. Next, it discusses defects and solitons that are characterized by 2D or 3D measuring surfaces, not just 1D loops, including hedgehogs, skyrmions, and hopfions. These structures are more complex, but they can still be understood using the same fundamental principles. A final chapter describes the formation of phases with regular arrays of defects or solitons. 0aCondensed matter. 0aSoft condensed matter. 0aMathematical physics. 0aDifferential equations.14aCondensed Matter Physics.24aCondensed Matter.24aSoft Materials.24aMathematical Methods in Physics.24aMathematical Physics.24aDifferential Equations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303170199308iPrinted edition:z9783031702013 0aLecture Notes in Physics,x1616-6361 ;v103240uhttps://doi.org/10.1007/978-3-031-70200-6