107,931 research outputs found
Projection and ground state correlations made simple
We develop and test efficient approximations to estimate ground state
correlations associated with low- and zero-energy modes. The scheme is an
extension of the generator-coordinate-method (GCM) within Gaussian overlap
approximation (GOA). We show that GOA fails in non-Cartesian topologies and
present a topologically correct generalization of GOA (topGOA). An RPA-like
correction is derived as the small amplitude limit of topGOA, called topRPA.
Using exactly solvable models, the topGOA and topRPA schemes are compared with
conventional approaches (GCM-GOA, RPA, Lipkin-Nogami projection) for
rotational-vibrational motion and for particle number projection. The results
shows that the new schemes perform very well in all regimes of coupling.Comment: RevTex, 12 pages, 7 eps figure
Consequences of the center-of-mass correction in nuclear mean-field models
We study the influence of the scheme for the correction for spurious
center-of-mass motion on the fit of effective interactions for self-consistent
nuclear mean-field calculations. We find that interactions with very simple
center-of-mass correction have significantly larger surface coefficients than
interactions for which the center-of-mass correction was calculated for the
actual many-body state during the fit. The reason for that is that the
effective interaction has to counteract the wrong trends with nucleon number of
all simplified schemes for center-of-mass correction which puts a wrong trend
with mass number into the effective interaction itself. The effect becomes
clearly visible when looking at the deformation energy of largely deformed
systems, e.g. superdeformed states or fission barriers of heavy nuclei.Comment: 12 pages LATeX, needs EPJ style files, 5 eps figures, accepted for
publication in Eur. Phys. J.
An Unsplit, Cell-Centered Godunov Method for Ideal MHD
We present a second-order Godunov algorithm for multidimensional, ideal MHD.
Our algorithm is based on the unsplit formulation of Colella (J. Comput. Phys.
vol. 87, 1990), with all of the primary dependent variables centered at the
same location. To properly represent the divergence-free condition of the
magnetic fields, we apply a discrete projection to the intermediate values of
the field at cell faces, and apply a filter to the primary dependent variables
at the end of each time step. We test the method against a suite of linear and
nonlinear tests to ascertain accuracy and stability of the scheme under a
variety of conditions. The test suite includes rotated planar linear waves, MHD
shock tube problems, low-beta flux tubes, and a magnetized rotor problem. For
all of these cases, we observe that the algorithm is second-order accurate for
smooth solutions, converges to the correct weak solution for problems involving
shocks, and exhibits no evidence of instability or loss of accuracy due to the
possible presence of non-solenoidal fields.Comment: 37 Pages, 9 Figures, submitted to Journal of Computational Physic
A new steplength selection for scaled gradient methods with application to image deblurring
Gradient methods are frequently used in large scale image deblurring problems
since they avoid the onerous computation of the Hessian matrix of the objective
function. Second order information is typically sought by a clever choice of
the steplength parameter defining the descent direction, as in the case of the
well-known Barzilai and Borwein rules. In a recent paper, a strategy for the
steplength selection approximating the inverse of some eigenvalues of the
Hessian matrix has been proposed for gradient methods applied to unconstrained
minimization problems. In the quadratic case, this approach is based on a
Lanczos process applied every m iterations to the matrix of the most recent m
back gradients but the idea can be extended to a general objective function. In
this paper we extend this rule to the case of scaled gradient projection
methods applied to non-negatively constrained minimization problems, and we
test the effectiveness of the proposed strategy in image deblurring problems in
both the presence and the absence of an explicit edge-preserving regularization
term
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