Symmetry, invariance and the structure of matter

Richard D. James

Symmetry, invariance and the structure of matter

Richard D. James

Aerospace Engineering and Mechanics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

We present a mathematical view of the structure of matter based on the invariance of the classical equations of physics.

Original language	English (US)
Title of host publication	Invited Lectures
Editors	Boyan Sirakov, Paulo Ney de Souza, Marcelo Viana
Publisher	World Scientific Publishing Co. Pte Ltd
Pages	3985-4012
Number of pages	28
ISBN (Electronic)	9789813272934
State	Published - 2018
Event	2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil Duration: Aug 1 2018 → Aug 9 2018

Publication series

Name	Proceedings of the International Congress of Mathematicians, ICM 2018
Volume	4

Conference

Conference	2018 International Congress of Mathematicians, ICM 2018
Country/Territory	Brazil
City	Rio de Janeiro
Period	8/1/18 → 8/9/18

Bibliographical note

Funding Information:
This work was supported by AFOSR (FA9550-15-1-0207), NSF (DMREF-1629026), ONR (N00014-14-1-0714), and the MURI program (FA9550-12-1-0458, FA9550-16-1-0566). MSC2010: primary 82-02; secondary 20H15, 35Q60, 51F25, 70H33, 78A45. Keywords: Atomic structure, symmetry, objective structures, isometry groups, molecular dynamics, invariant manifold, Boltzmann equation, homoenergetic solutions, Maxwell’s equations, non-equilibrium statistical mechanics, X-ray methods.

Publisher Copyright:
© ICM 2018.All rights reserved.

Keywords

Atomic structure
Boltzmann equation
Homoenergetic solutions
Invariant manifold
Isometry groups
Maxwell’s equations
Molecular dynamics
Non-equilibrium statistical mechanics
Objective structures
Symmetry
X-ray methods

OpenUrl availability

Full text

Cite this

Symmetry, invariance and the structure of matter. / James, Richard D.
Invited Lectures. ed. / Boyan Sirakov; Paulo Ney de Souza; Marcelo Viana. World Scientific Publishing Co. Pte Ltd, 2018. p. 3985-4012 (Proceedings of the International Congress of Mathematicians, ICM 2018; Vol. 4).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

@inproceedings{0a782989debb4ee4b038543973c0a903,

title = "Symmetry, invariance and the structure of matter",

abstract = "We present a mathematical view of the structure of matter based on the invariance of the classical equations of physics.",

keywords = "Atomic structure, Boltzmann equation, Homoenergetic solutions, Invariant manifold, Isometry groups, Maxwell{\textquoteright}s equations, Molecular dynamics, Non-equilibrium statistical mechanics, Objective structures, Symmetry, X-ray methods",

author = "James, {Richard D.}",

note = "Funding Information: This work was supported by AFOSR (FA9550-15-1-0207), NSF (DMREF-1629026), ONR (N00014-14-1-0714), and the MURI program (FA9550-12-1-0458, FA9550-16-1-0566). MSC2010: primary 82-02; secondary 20H15, 35Q60, 51F25, 70H33, 78A45. Keywords: Atomic structure, symmetry, objective structures, isometry groups, molecular dynamics, invariant manifold, Boltzmann equation, homoenergetic solutions, Maxwell{\textquoteright}s equations, non-equilibrium statistical mechanics, X-ray methods. Publisher Copyright: {\textcopyright} ICM 2018.All rights reserved.; 2018 International Congress of Mathematicians, ICM 2018 ; Conference date: 01-08-2018 Through 09-08-2018",

year = "2018",

language = "English (US)",

series = "Proceedings of the International Congress of Mathematicians, ICM 2018",

publisher = "World Scientific Publishing Co. Pte Ltd",

pages = "3985--4012",

editor = "Boyan Sirakov and {de Souza}, {Paulo Ney} and Marcelo Viana",

booktitle = "Invited Lectures",

address = "Singapore",

}

TY - GEN

T1 - Symmetry, invariance and the structure of matter

AU - James, Richard D.

N1 - Funding Information: This work was supported by AFOSR (FA9550-15-1-0207), NSF (DMREF-1629026), ONR (N00014-14-1-0714), and the MURI program (FA9550-12-1-0458, FA9550-16-1-0566). MSC2010: primary 82-02; secondary 20H15, 35Q60, 51F25, 70H33, 78A45. Keywords: Atomic structure, symmetry, objective structures, isometry groups, molecular dynamics, invariant manifold, Boltzmann equation, homoenergetic solutions, Maxwell’s equations, non-equilibrium statistical mechanics, X-ray methods. Publisher Copyright: © ICM 2018.All rights reserved.

PY - 2018

Y1 - 2018

N2 - We present a mathematical view of the structure of matter based on the invariance of the classical equations of physics.

AB - We present a mathematical view of the structure of matter based on the invariance of the classical equations of physics.

KW - Atomic structure

KW - Boltzmann equation

KW - Homoenergetic solutions

KW - Invariant manifold

KW - Isometry groups

KW - Maxwell’s equations

KW - Molecular dynamics

KW - Non-equilibrium statistical mechanics

KW - Objective structures

KW - Symmetry

KW - X-ray methods

UR - http://www.scopus.com/inward/record.url?scp=85086404585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086404585&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85086404585

T3 - Proceedings of the International Congress of Mathematicians, ICM 2018

SP - 3985

EP - 4012

BT - Invited Lectures

A2 - Sirakov, Boyan

A2 - de Souza, Paulo Ney

A2 - Viana, Marcelo

PB - World Scientific Publishing Co. Pte Ltd

T2 - 2018 International Congress of Mathematicians, ICM 2018

Y2 - 1 August 2018 through 9 August 2018

ER -

Symmetry, invariance and the structure of matter

Abstract

Publication series

Conference

Bibliographical note

Keywords

OpenUrl availability

Other files and links

Fingerprint

Cite this