56 research outputs found
Critical Susceptibility Exponent Measured from Fe/W(110) Bilayers
The critical phase transition in ferromagnetic ultrathin Fe/W(110) films has
been studied using the magnetic ac susceptibility. A statistically objective,
unconstrained fitting of the susceptibility is used to extract values for the
critical exponent (gamma), the critical temperature Tc, the critical amplitude
(chi_o) and the range of temperature that exhibits power-law behaviour. A
fitting algorithm was used to simultaneously minimize the statistical variance
of a power law fit to individual experimental measurements of chi(T). This
avoids systematic errors and generates objective fitting results. An ensemble
of 25 measurements on many different films are analyzed. Those which permit an
extended fitting range in reduced temperature lower than approximately .00475
give an average value gamma=1.76+-0.01. Bilayer films give a weighted average
value of gamma = 1.75+-0.02. These results are in agreement with the
-dimensional Ising exponent gamma= 7/4. Measurements that do not exhibit
power-law scaling as close to Tc (especially films of thickness 1.75ML) show a
value of gamma higher than the Ising value. Several possibilities are
considered to account for this behaviour.Comment: -Submitted to Phys. Rev. B -Revtex4 Format -6 postscript figure
An integral method for solving nonlinear eigenvalue problems
We propose a numerical method for computing all eigenvalues (and the
corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that
lie within a given contour in the complex plane. The method uses complex
integrals of the resolvent operator, applied to at least column vectors,
where is the number of eigenvalues inside the contour. The theorem of
Keldysh is employed to show that the original nonlinear eigenvalue problem
reduces to a linear eigenvalue problem of dimension .
No initial approximations of eigenvalues and eigenvectors are needed. The
method is particularly suitable for moderately large eigenvalue problems where
is much smaller than the matrix dimension. We also give an extension of the
method to the case where is larger than the matrix dimension. The
quadrature errors caused by the trapezoid sum are discussed for the case of
analytic closed contours. Using well known techniques it is shown that the
error decays exponentially with an exponent given by the product of the number
of quadrature points and the minimal distance of the eigenvalues to the
contour
Semidefinite Characterization and Computation of Real Radical Ideals
For an ideal given by a set of generators, a new
semidefinite characterization of its real radical is
presented, provided it is zero-dimensional (even if is not). Moreover we
propose an algorithm using numerical linear algebra and semidefinite
optimization techniques, to compute all (finitely many) points of the real
variety as well as a set of generators of the real radical
ideal. The latter is obtained in the form of a border or Gr\"obner basis. The
algorithm is based on moment relaxations and, in contrast to other existing
methods, it exploits the real algebraic nature of the problem right from the
beginning and avoids the computation of complex components.Comment: 41 page
- …