000 05027nam a22005655i 4500
001 978-981-97-6984-1
003 DE-He213
005 20251030114628.0
007 cr nn 008mamaa
008 241219s2024 si | s |||| 0|eng d
020 _a9789819769841
_9978-981-97-6984-1
024 7 _a10.1007/978-981-97-6984-1
_2doi
050 4 _aT57-57.97
072 7 _aPBW
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPBW
_2thema
245 1 0 _aAnisotropic Isoperimetric Problems and Related Topics
_h[electronic resource] /
_cedited by Valentina Franceschi, Alessandra Pluda, Giorgio Saracco.
250 _a1st ed. 2024.
264 1 _aSingapore :
_bSpringer Nature Singapore :
_bImprint: Springer,
_c2024.
300 _aVII, 213 p. 11 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer INdAM Series,
_x2281-5198 ;
_v62
505 0 _a -- Geometric invariants of non-smooth framed curves (by Bevilacqua, Lussardi, and Marzocchi) -- Minimal periodic foams with equal cells (by Cesaroni and Novaga) -- On a Cheeger--Kohler-Jobin inequality (by Lucardesi, Mazzoleni, and Ruffini) -- Isoperimetry on manifolds with Ricci bounded below: overview of recent results and methods (by Pozzetta) -- Stochastic homogenization of functionals defined on finite partitions (by Bach and Ruf) -- On sets with finite distributional fractional perimeter (by Comi and Stefani) -- On a Free-Endpoint Isoperimetric Problem in R^2 (by Alama, Bronsard, and Vriend) -- Isoperimetric sets in nonnegative scalar curvature and their role through various concepts of mass (by Benatti and Fogagnolo) -- A crystallization result in two dimensions for a soft disc affine potential (by Del Nin and De Luca).
520 _aThis book contains contributions from speakers at the "Anisotropic Isoperimetric Problems & Related Topics" conference in Rome, held from Sep 5 to 9, 2022. The classic isoperimetric problem has fascinated mathematicians of all eras, starting from the ancient Greeks, due to its simple statement: what are the sets of a given volume with minimal perimeter? The problem is mathematically well understood, and it plays a crucial role in explaining physical phenomena such as soap bubble shapes. Variations of the problem, including weighted counterparts with density dependencies, representing inhomogeneity and anisotropy of the medium, broaden its applicability, even in non-Euclidean environments, and they allow for descriptions, e.g., of crystal shapes. At large, the perimeter's physical interpretation is that of an attractive force; hence, it also appears in describing systems of particles where a balance between attractive and repulsive forces appears. A prominent example is that of Gamow's liquid drop model for atomic nuclei, where protons are subject to the strong nuclear attractive force (represented by the perimeter) and the electromagnetic repulsive force (represented by a nonlocal term). Such a model has been shown to be sound, as it explains the basic characteristics of the nuclei, and it successfully predicts nuclear fission for nuclei with a large atomic number. Similar energy functionals model various physical and biological systems, showcasing the competition between short-range interfacial and long-range nonlocal terms, leading to pattern formation. The authors mention, e.g., the Ohta–Kawasaki model for microphase separation of diblock copolymers and the Yukawa potential for colloidal systems. Despite diverse systems, the emergence of microphases follows similar patterns, although rigorously proving this phenomenon remains a challenge. The book collects several contributions within these topics, shedding light on the current state of the art.
650 0 _aMathematics.
_965523
650 0 _aMathematical analysis.
_964178
650 0 _aDiscrete mathematics.
650 1 4 _aApplications of Mathematics.
_965529
650 2 4 _aAnalysis.
650 2 4 _aApplications of Discrete Mathematics.
_967427
700 1 _aFranceschi, Valentina.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_989210
700 1 _aPluda, Alessandra.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_989211
700 1 _aSaracco, Giorgio.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_989212
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9789819769834
776 0 8 _iPrinted edition:
_z9789819769858
776 0 8 _iPrinted edition:
_z9789819769865
830 0 _aSpringer INdAM Series,
_x2281-5198 ;
_v62
_977740
856 4 0 _uhttps://doi.org/10.1007/978-981-97-6984-1
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c65862
_d65862