東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Anisotropic isoperimetric problems a...

Franceschi, Valentina.

Linked to FindBook

Google Book

Amazon

博客來

Anisotropic isoperimetric problems and related topics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Anisotropic isoperimetric problems and related topics/ edited by Valentina Franceschi, Alessandra Pluda, Giorgio Saracco.
other author:	Franceschi, Valentina.
Published:	Singapore :Springer Nature Singapore : : 2024.,
Description:	vii, 213 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Calculus of variations - Congresses. -
Online resource:	https://doi.org/10.1007/978-981-97-6984-1
ISBN:	9789819769841

Anisotropic isoperimetric problems and related topics
Anisotropic isoperimetric problems and related topics[electronic resource] /edited by Valentina Franceschi, Alessandra Pluda, Giorgio Saracco. - Singapore :Springer Nature Singapore :2024. - vii, 213 p. :ill. (some col.), digital ;24 cm. - Springer INdAM series,v. 622281-5198 ;. - Springer INdAM series ;v. 62..

This 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.

ISBN: 9789819769841

Standard No.: 10.1007/978-981-97-6984-1doiSubjects--Topical Terms:

658515
Calculus of variations
--Congresses.

LC Class. No.: QA316 / .A55 2024

Dewey Class. No.: 515.64

Anisotropic isoperimetric problems and related topics
LDR:03067nmm a2200325 a 4500 001 2389173
003 DE-He213
005 20241219115248.0
006 m d
007 cr nn 008maaau
008 250916s2024 si s 0 eng d
020 $a 9789819769841 $q (electronic bk.)
020 $a 9789819769834 $q (paper)
024 7 $a 10.1007/978-981-97-6984-1 $2 doi
035 $a 978-981-97-6984-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA316 $b .A55 2024
072 7 $a PBW $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBW $2 thema
082 0 4 $a 515.64 $2 23
090 $a QA316 $b .A599 2024
245 0 0 $a Anisotropic isoperimetric problems and related topics $h [electronic resource] / $c edited by Valentina Franceschi, Alessandra Pluda, Giorgio Saracco.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2024.
300 $a vii, 213 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Springer INdAM series, $x 2281-5198 ; $v v. 62
520 $a This 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 $a Calculus of variations $x Congresses. $3 658515
650 1 4 $a Applications of Mathematics. $3 890893
650 2 4 $a Analysis. $3 891106
650 2 4 $a Applications of Discrete Mathematics. $3 3599507
700 1 $a Franceschi, Valentina. $3 3754740
700 1 $a Pluda, Alessandra. $3 3754741
700 1 $a Saracco, Giorgio. $3 3754742
710 2 $a SpringerLink (Online service) $3 836513
711 2 $a Anisotropic Isoperimetric Problems & Related Topics (Conference) $d (2022 : $c Rome, Italy) $3 3754744
773 0 $t Springer Nature eBook
830 0 $a Springer INdAM series ; $v v. 62. $3 3754743
856 4 0 $u https://doi.org/10.1007/978-981-97-6984-1
950 $a Mathematics and Statistics (SpringerNature-11649)