Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Reliable TDC position determination: a comparison of different thermodynamic methods through experimental data and simulations
2008
It is known to internal combustion researcher that the correct determination of the crank position when the piston is at Top Dead Centre (TDC) is very important, since an error of 1 crank angle degree (CAD) can cause up to a 10% evaluation error on indicated mean effective pressure (IMEP) and a 25% error on the heat released by the combustion: the TDC position should be then known within a precision of 0.1 CAD. This task can be accomplished by means of a dedicated capacitive sensor, which allows a measurement within the required 0.1 degrees precision. Such a sensor has a substantial cost and its use is not really fast; a different approach can be followed using a thermodynamic method, whose…
Multiplicity of fixed points and growth of ε-neighborhoods of orbits
2012
We study the relationship between the multiplicity of a fixed point of a function g, and the dependence on epsilon of the length of epsilon-neighborhood of any orbit of g, tending to the fixed point. The relationship between these two notions was discovered before (Elezovic, Zubrinic, Zupanovic) in the differentiable case, and related to the box dimension of the orbit. Here, we generalize these results to non-differentiable cases introducing a new notion of critical Minkowski order. We study the space of functions having a development in a Chebyshev scale and use multiplicity with respect to this space of functions. With the new definition, we recover the relationship between multiplicity o…
Non-accumulation of critical points of the Poincaré time on hyperbolic polycycles
2007
We call Poincare time the time associated to the Poincar6 (or first return) map of a vector field. In this paper we prove the non-accumulation of isolated critical points of the Poincare time T on hyperbolic polycycles of polynomial vector fields. The result is obtained by proving that the Poincare time of a hyperbolic polycycle either has an unbounded principal part or is an almost regular function. The result relies heavily on the proof of Il'yashenko's theorem on non-accumulation of limit cycles on hyperbolic polycycles.
Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
2014
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…
Computational stability of an initially radial solution of a growth/dissolution problem in a nonradial implementation
1991
We consider a free boundary problem modelling the growth/dissolution of a crystal. The aim is to investigate the following question: Does the solution to the crystal growth problem posed in two dimensions with radially symmetric initial and boundary condition evolve as a radially symmetric solution?
Guaranteed Error Bounds for Conforming Approximations of a Maxwell Type Problem
2009
This paper is concerned with computable error estimates for approximations to a boundary-value problem $$\mathrm{curl}\ {\mu }^{-1}\mathrm{curl}\ u + {\kappa }^{2}u = j\quad \textrm{ in }\Omega ,$$ where μ > 0 and κ are bounded functions. We derive a posteriori error estimates valid for any conforming approximations of the considered problems. For this purpose, we apply a new approach that is based on certain transformations of the basic integral identity. The consistency of the derived a posteriori error estimates is proved and the corresponding computational strategies are discussed.
Minimal unit vector fields
2002
We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.
A WAVELET OPERATOR ON THE INTERVAL IN SOLVING MAXWELL'S EQUATIONS
2011
In this paper, a differential wavelet-based operator defined on an interval is presented and used in evaluating the electromagnetic field described by Maxwell's curl equations, in time domain. The wavelet operator has been generated by using Daubechies wavelets with boundary functions. A spatial differential scheme has been performed and it has been applied in studying electromagnetic phenomena in a lossless medium. The proposed approach has been successfully tested on a bounded axial-symmetric cylindrical domain.
The exterior derivative as a Killing vector field
1996
Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded Laplacian operator that annihilates the whole algebra of differential forms.
Volume, energy and generalized energy of unit vector fields on Berger spheres: stability of Hopf vector fields
2005
We study to what extent the known results concerning the behaviour of Hopf vector fields, with respect to volume, energy and generalized energy functionals, on the round sphere are still valid for the metrics obtained by performing the canonical variation of the Hopf fibration.