Results 281 to 290 of about 1,342,909 (347)

Theory of the Critical Point of 4He

1990
We do not have yet a microscopic global theory of the thermodynamic properties of 4He in the normal phase, inclusive of the region of the critical point. At a very simple level the effect of the attractive part of the interatomic forces has been considered1 in a perturbative way starting from the properties of quantum hard spheres.
K. J. Runge, L. Reatto, A. Meroni
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Duality and Perturbation Methods in Critical Point Theory

, 1993
1. Lipschitz and smooth perturbed minimization principles 2. Linear and plurisubharmonic perturbed minimization principles 3. The classical min-max theorem 4. A strong form of the min-max principle 5. Relaxed boundary conditions in the presence of a dual
N. Ghoussoub
semanticscholar   +1 more source

Nonsmooth Critical Point Theory

1999
The aim of this chapter is to present general results, many of them belonging to the authors, that can be applied to locally Lipschitz functionals, possibly invariant under a compact Lie group of linear isometries. The nonsmooth critical point theory in the locally Lipschitz case originates in the work of Chang [4].
Dumitru Motreanu, Panagiotis D. Panagiotopoulos   +1 more
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Critical Points and Morse Theory

1997
In this chapter we introduce Morse theory, a systematic way of studying certain features of smooth functions on manifolds. We will primarily consider surfaces and three-manifolds, because the main applications of Morse theory in computer geometry are concentrated in these dimensions.
Tosiyasu L. Kinii, Anatolij T. Fomenko
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Variational Principles and Critical Point Theory [PDF]

, 2013
This chapter addresses variational principles and critical point theory that will be applied later in the book for setting up variational methods in the case of nonlinear elliptic boundary value problems. The first section of the chapter illustrates the connection between the variational principles of Ekeland and Zhong and compactness-type conditions ...
Dumitru Motreanu, Nikolaos S. Papageorgiou, Viorica Venera Motreanu   +2 more
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The critical point and scaling theory

Physica, 1974
Abstract The origin and physical meaning of the scaling and homogeneity hypotheses in the theory of equilibrium critical phenomena are discussed. The purely thermodynamic critical-point exponent relations, and those that also involve the coherence length, are first derived from separate and apparently unrelated hypotheses.
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Topics in Critical Point Theory

, 2012
Preface 1. Morse theory 2. Linking 3. Applications to semilinear problems 4. Fucik spectrum 5. Jumping nonlinearities 6. Sandwich pairs Appendix: Sobolev spaces Bibliography Index.
K. Perera, M. Schechter
semanticscholar   +1 more source

Critical Point Theory

1993
In the study of nonminimum critical points, a basic method is the so-called minimax principle. In this chapter we study the connections between Morse theory and a variety of concrete versions of the minimax principle. We point out that the minimax principle for relative homology classes is particularly suitable for Morse theory because certain critical
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Topics on critical point theory [PDF]

, 1993
Many questions in mathematics and physics can be reduced to the problem of finding and classifying the critical points of a suitable functional on an appropriate manifold. In this thesis, we will be concerned with the problems of existence, location and structure of critical points by building upon the well known min-max methods that are presently used
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Critical points with discrete Morse theory

ACM SIGGRAPH 2015 Posters, 2015
In this work, we present some of the unexpected observations resulted from our recent research. We, recently, needed to identify a small number of important critical points, i.e. minimum, maximum and saddle points, on a given manifold mesh surface. All critical points on a manifold triangular mesh can be identified using discrete Gaussian curvature ...
Xiaoning Wang, He Ying, Peihong Guo, Ergun Akleman, Wei Liu   +4 more
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