2,712 research outputs found
High order finite element calculations for the deterministic Cahn-Hilliard equation
In this work, we propose a numerical method based on high degree continuous
nodal elements for the Cahn-Hilliard evolution. The use of the p-version of the
finite element method proves to be very efficient and favorably compares with
other existing strategies (C^1 elements, adaptive mesh refinement, multigrid
resolution, etc). Beyond the classical benchmarks, a numerical study has been
carried out to investigate the influence of a polynomial approximation of the
logarithmic free energy and the bifurcations near the first eigenvalue of the
Laplace operator
Linear orbits of arbitrary plane curves
The `linear orbit' of a plane curve of degree is its orbit in
under the natural action of \PGL(3). In this paper we obtain
an algorithm computing the degree of the closure of the linear orbit of an
arbitrary plane curve, and give explicit formulas for plane curves with
irreducible singularities. The main tool is an intersection@-theoretic study of
the projective normal cone of a scheme determined by the curve in the
projective space of matrices; this expresses the degree of
the orbit closure in terms of the degrees of suitable loci related to the
limits of the curve. These limits, and the degrees of the corresponding loci,
have been established in previous work.Comment: 33 pages, AmS-TeX 2.
Stationary problems for equation of the KdV type and dynamical -matrices.
We study a quite general family of dynamical -matrices for an auxiliary
loop algebra related to restricted flows for equations of
the KdV type. This underlying -matrix structure allows to reconstruct Lax
representations and to find variables of separation for a wide set of the
integrable natural Hamiltonian systems. As an example, we discuss the
Henon-Heiles system and a quartic system of two degrees of freedom in detail.Comment: 25pp, LaTe
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