Differential Geometry

Read e-book online Differential Geometry and Continuum Mechanics PDF

By Gui-Qiang G. Chen, Michael Grinfeld, R. J. Knops

ISBN-10: 3319185721

ISBN-13: 9783319185729

ISBN-10: 331918573X

ISBN-13: 9783319185736

This booklet examines the intriguing interface among differential geometry and continuum mechanics, now regarded as being of accelerating technological importance. subject matters mentioned comprise isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, using manifolds within the description of microstructure in continuum mechanics, experimental dimension of microstructure, defects, dislocations, floor energies, and nematic liquid crystals. Compensated compactness in partial differential equations can be treated.

The quantity is meant for experts and non-specialists in natural and utilized geometry, continuum mechanics, theoretical physics, fabrics and engineering sciences, and partial differential equations. it's going to even be of curiosity to postdoctoral scientists and complicated postgraduate study students.

These court cases contain revised written models of the vast majority of papers offered by means of prime specialists on the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers were peer reviewed.

Show description

Read or Download Differential Geometry and Continuum Mechanics PDF

Similar differential geometry books

Download e-book for iPad: Variational principles for second-order differential by Joseph Grifone, Zoltan Muzsnay

During this booklet the writer has attempted to use "a little mind's eye and pondering" to modelling dynamical phenomena from a classical atomic and molecular viewpoint. Nonlinearity is emphasised, as are phenomena that are elusive from the continuum mechanics perspective. FORTRAN programmes are supplied within the appendices An creation to formal integrability concept of partial differential platforms; Frolicher-Nijenhuis conception of derivations; differential algebraic formalism of connections; important stipulations for variational sprays; obstructions to the integrability of the Euler-Lagrange process; the category of in the neighborhood variational sprays on two-dimensional manifolds; Euler-Lagrange structures within the isotropic case

Download e-book for iPad: An Introduction to Dirac Operators on Manifolds by Jan Cnops

Dirac operators play a major function in numerous domain names of arithmetic and physics, for instance: index thought, elliptic pseudodifferential operators, electromagnetism, particle physics, and the illustration thought of Lie teams. during this primarily self-contained paintings, the elemental rules underlying the idea that of Dirac operators are explored.

Read e-book online L’Hôpital's Analyse des infiniments petits: An Annotated PDF

This monograph is an annotated translation of what's thought of to be the world’s first calculus textbook, initially released in French in 1696. That anonymously released textbook on differential calculus was once in line with lectures given to the Marquis de l’Hôpital in 1691-2 by means of the good Swiss mathematician, Johann Bernoulli.

Extra info for Differential Geometry and Continuum Mechanics

Example text

Superficially, this situation resembles the problem of Ginzburg-Landau vortices studied by Bethuel et al. [BBH94] and others. ) In this case, however, the analogy is not good and we need completely different tools. For this choice of the potential function, we expect needle-shaped surfaces. We analyse surfaces of revolution in particular and we determine a limiting energy for this special case. Furthermore, we have some estimates for more general surfaces. In contrast to the first problem, it is not clear how to generalise the theory to similar potential functions.

Step 2. The second derivatives of r may be bounded in terms of a bound for the mean curvature H of the surface r as follows. The expression of H implies g11 H = 1 1 2 2 − 2h 12 g11 g12 + h 11 g12 ) + h 11 . (h 22 g11 2|g| 2 Since the surface is convex and the unit normal n was chosen to be an inner normal, the quadratic form on the right-hand side is positive definite so that we have h 11 < 2g11 H. Similarly, we have h 22 < 2g22 H. Then we get √ |h 12 | < 2H g11 g22 , since (h ij ) is positive definite.

He also pointed out that a reasonable sufficient condition might be the decay rate of the Gauss curvature at infinity. In 1993, Hong [Hon93] gave an affirmative answer and showed that a correct sufficient condition is that the Gauss curvature decays at infinity faster than the inverse square of the geodesic distance. 4 Let (M, g) be a complete simply connected smooth surface with Gauss curvature K < 0 and (ρ, θ) be a (global) geodesic polar coordinate. Assume, for some constant δ > 0, (H1 ) (H2 ) ρ2+δ |K | is decreasing in ρ outside a compact set; ∂θi ln |K |, (i = 1, 2), ρ∂ρ ∂θ ln |K | are bounded.

Download PDF sample

Differential Geometry and Continuum Mechanics by Gui-Qiang G. Chen, Michael Grinfeld, R. J. Knops

by Mark

Rated 4.38 of 5 – based on 14 votes