Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Heat Kernel Measure on Central Extension of Current Groups in any Dimension
2006
We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.
Integration of finite displacement interface element in reference and current configurations
2017
In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two i…
Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type
2014
Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.
Analysis of a slow–fast system near a cusp singularity
2016
This paper studies a slow fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking advantage of this normal form, we investigate the transition near the cusp singularity by means of the blow up technique. Our contribution relies heavily in the usage of normal form theory, allowing us to refine previous results. (C) 2015 Elsevier Inc. All rights reserved.
Bifurcations of cuspidal loops
1997
A cuspidal loop for a planar vector field X consists of a homoclinic orbit through a singular point p, at which X has a nilpotent cusp. This is the simplest non-elementary singular cycle (or graphic) in the sense that its singularities are not elementary (i.e. hyperbolic or semihyperbolic). Cuspidal loops appear persistently in three-parameter families of planar vector fields. The bifurcation diagrams of unfoldings of cuspidal loops are studied here under mild genericity hypotheses: the singular point p is of Bogdanov - Takens type and the derivative of the first return map along the orbit is different from 1. An analytic and geometric method based on the blowing up for unfoldings is propos…
Mappings of finite distortion: Formation of cusps II
2007
For s > 0 s>0 given, we consider a planar domain Ω s \Omega _s with a rectifiable boundary but containing a cusp of degree s s , and show that there is no homeomorphism f : R 2 → R 2 f\colon \mathbb {R}^2\to \mathbb {R}^2 of finite distortion with exp ( λ K ) ∈ L l o c 1 ( R 2 ) \exp (\lambda K)\in L^1_{\mathrm {loc}}(\mathbb {R}^2) so that f ( B ) = Ω s f(B)=\Omega _s when λ > 4 / s \lambda >4/s and B B is the unit disc. On the other hand, for λ > 2 / s \lambda >2/s such an f f exists. The critical value for λ \lambda remains open.
A note to “Mappings of finite distortion: formation of cusps II”
2010
We consider planar homeomorphisms f : R 2 → R 2 f\colon \mathbb {R}^2\to \mathbb {R}^2 that are of finite distortion and map the unit disk onto a specific cusp domain Ω s \Omega _s . We study the relation between the degree s s of the cusp and the integrability of the distortion function K f K_f by sharpening a previous result where K f K_f is assumed to be locally exponentially integrable.
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
1987
AbstractA cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate toWe define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent toOur main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to
Variational methods for the steady state response of elastic–plastic solids subjected to cyclic loads
2003
Abstract Solids (or structures) of elastic–plastic internal variable material models and subjected to cyclic loads are considered. A minimum net resistant power theorem, direct consequence of the classical maximum intrinsic dissipation theorem of plasticity theory, is envisioned which describes the material behavior by determining the plastic flow mechanism (if any) corresponding to a given stress/hardening state. A maximum principle is provided which characterizes the optimal initial stress/hardening state of a cyclically loaded structure as the one such that the plastic strain and kinematic internal variable increments produced over a cycle are kinematically admissible. A steady cycle min…
Statistical Properties of Generalized Strain Criterion for Multiaxial Random Fatigue
1989
ABSTRACT Statistical properties of generalized criterion of the maximum shear and normal strains on the fracture plane have been presented, Functions of probability distribution and spectral density of the equivalent strain have been analysed on the assumption that a random tensor of strain state is a six-dimensional stationary and ergodic Gaussian process. The expected value and variance of the equivalent strain have been determined as well. From spectral analysis a new limitation has been derived for extension of some multiaxial cyclic fatigue criteria to random loadings. It is connected with the fact that in some cases the frequency band of the equivalent strain is greater than that for …