74,421 research outputs found
Preroughening transitions in a model for Si and Ge (001) type crystal surfaces
The uniaxial structure of Si and Ge (001) facets leads to nontrivial
topological properties of steps and hence to interesting equilibrium phase
transitions. The disordered flat phase and the preroughening transition can be
stabilized without the need for step-step interactions. A model describing this
is studied numerically by transfer matrix type finite-size-scaling of interface
free energies. Its phase diagram contains a flat, rough, and disordered flat
phase, separated by roughening and preroughening transition lines. Our estimate
for the location of the multicritical point where the preroughening line merges
with the roughening line, predicts that Si and Ge (001) undergo preroughening
induced simultaneous deconstruction transitions.Comment: 13 pages, RevTex, 7 Postscript Figures, submitted to J. Phys.
The Mass of the Centaurus A Group of Galaxies
The mass M, and the radius R_h, of the Centaurus A group are estimated from
the positions and radial velocities of 30 probable cluster members. For an
assumed distance of 3.9 Mpc it is found that R_h \sim 640 kpc. The velocity
dispersion in the Cen A group is 114 \pm 21 km/s. From this value, and R_h =
640 kpc, the virial theorem yields a total mass of 1.4 \times 10^{13} M_{\sun}
for the Cen A group. The projected mass method gives a mass of 1.8 \times
10^{13} M_{\sun}. These values suggest that the Cen A group is about seven
times as massive as the Local Group. The Cen A mass-to-light ratio is found to
be M/L_B = 155-200 in solar units. The cluster has a zero-velocity radius R_0 =
2.3 Mpc.Comment: 8 pages, 1 figure, in LaTeX format; to appear in the Astronomical
Journal in January 200
Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity
We present some open problems and obtain some partial results for spectral
optimization problems involving measure, torsional rigidity and first Dirichlet
eigenvalue.Comment: 18 pages, 4 figure
Are the Luminosities of RR Lyrae Stars Affected by Second Parameter Effects?
There is a serious discrepancy between the distance to the LMC derived from
the Cepheid Period-Luminosity relation and that obtained by using the Galactic
calibration for the luminosity of RR Lyrae stars. It is suggested that this
problem might be due to the fact that second parameter effects make it
inappropriate to apply Galactic calibrations to RR Lyrae variables in the
Magellanic Clouds, i.e. Mv(RR) could depend on both [Fe/H] and on one or more
second parameters.Comment: 10 pages as uuencoded compressed Postscript. Also available at
http://www.dao.nrc.ca/DAO/SCIENCE/science.htm
On the torsion function with Robin or Dirichlet boundary conditions
For and the -torsion function with
Robin boundary conditions associated to an arbitrary open set \Om \subset
\R^m satisfies formally the equation in \Om and on \partial \Om. We
obtain bounds of the norm of {\it only} in terms of the bottom
of the spectrum (of the Robin -Laplacian), and the dimension of the
space in the following two extremal cases: the linear framework (corresponding
to ) and arbitrary , and the non-linear framework (corresponding to
arbitrary ) and Dirichlet boundary conditions (). In the
general case, and our bounds involve also
the Lebesgue measure of \Om.Comment: 19 page
A monomial matrix formalism to describe quantum many-body states
We propose a framework to describe and simulate a class of many-body quantum
states. We do so by considering joint eigenspaces of sets of monomial unitary
matrices, called here "M-spaces"; a unitary matrix is monomial if precisely one
entry per row and column is nonzero. We show that M-spaces encompass various
important state families, such as all Pauli stabilizer states and codes, the
AKLT model, Kitaev's (abelian and non-abelian) anyon models, group coset
states, W states and the locally maximally entanglable states. We furthermore
show how basic properties of M-spaces can transparently be understood by
manipulating their monomial stabilizer groups. In particular we derive a
unified procedure to construct an eigenbasis of any M-space, yielding an
explicit formula for each of the eigenstates. We also discuss the computational
complexity of M-spaces and show that basic problems, such as estimating local
expectation values, are NP-hard. Finally we prove that a large subclass of
M-spaces---containing in particular most of the aforementioned examples---can
be simulated efficiently classically with a unified method.Comment: 11 pages + appendice
Killing spinor space-times and constant-eigenvalue Killing tensors
A class of Petrov type D Killing spinor space-times is presented, having the
peculiar property that their conformal representants can only admit Killing
tensors with constant eigenvalues.Comment: 11 pages, submitted to CQ
Robust Counterparts of Inequalities Containing Sums of Maxima of Linear Functions
This paper adresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box uncertainty, and affine in a parameter with general uncertainty. In the literature, often the reformulation that is exact when there is no uncertainty is used. However, in robust optimization this reformulation gives an inferior solution and provides a pessimistic view. We observe that in many papers this conservatism is not mentioned. Some papers have recognized this problem, but existing solutions are either too conservative or their performance for different uncertainty regions is not known, a comparison between them is not available, and they are restricted to specific problems. We provide techniques for general problems and compare them with numerical examples in inventory management, regression and brachytherapy. Based on these examples, we give tractable recommendations for reducing the conservatism.robust optimization;sum of maxima of linear functions;biaffine uncertainty;robust conic quadratic constraints
Kriging Models That Are Robust With Respect to Simulation Errors
In the field of the Design and Analysis of Computer Experiments (DACE) meta-models are used to approximate time-consuming simulations. These simulations often contain simulation-model errors in the output variables. In the construction of meta-models, these errors are often ignored. Simulation-model errors may be magnified by the meta-model. Therefore, in this paper, we study the construction of Kriging models that are robust with respect to simulation-model errors. We introduce a robustness criterion, to quantify the robustness of a Kriging model. Based on this robustness criterion, two new methods to find robust Kriging models are introduced. We illustrate these methods with the approximation of the Six-hump camel back function and a real life example. Furthermore, we validate the two methods by simulating artificial perturbations. Finally, we consider the influence of the Design of Computer Experiments (DoCE) on the robustness of Kriging models.Kriging;robustness;simulation-model error
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