21,950 research outputs found
Distance-two labelings of digraphs
For positive integers , an -labeling of a digraph is a
function from into the set of nonnegative integers such that
if is adjacent to in and if
is of distant two to in . Elements of the image of are called
labels. The -labeling problem is to determine the
-number of a digraph , which
is the minimum of the maximum label used in an -labeling of . This
paper studies - numbers of digraphs. In particular, we
determine - numbers of digraphs whose longest dipath is of
length at most 2, and -numbers of ditrees having dipaths
of length 4. We also give bounds for -numbers of bipartite
digraphs whose longest dipath is of length 3. Finally, we present a linear-time
algorithm for determining -numbers of ditrees whose
longest dipath is of length 3.Comment: 12 pages; presented in SIAM Coference on Discrete Mathematics, June
13-16, 2004, Loews Vanderbilt Plaza Hotel, Nashville, TN, US
Microscopic Restoration of Proton-Neutron Mixed Symmetry in Weakly Collective Nuclei
Starting from the microscopic low-momentum nucleon-nucleon interaction V{low
k}, we present the first systematic shell model study of magnetic moments and
magnetic dipole transition strengths of the basic low-energy one-quadrupole
phonon excitations in nearly-spherical nuclei. Studying in particular the
even-even N=52 isotones from 92Zr to 100Cd, we find the predicted evolution of
the predominantly proton-neutron non-symmetric state reveals a restoration of
collective proton-neutron mixed-symmetry structure near mid-shell. This
provides the first explanation for the existence of pronounced collective
mixed-symmetry structures in weakly-collective nuclei.Comment: 5 Pages, 3 figure
Successive Coordinate Search and Component-by-Component Construction of Rank-1 Lattice Rules
The (fast) component-by-component (CBC) algorithm is an efficient tool for
the construction of generating vectors for quasi-Monte Carlo rank-1 lattice
rules in weighted reproducing kernel Hilbert spaces. We consider product
weights, which assigns a weight to each dimension. These weights encode the
effect a certain variable (or a group of variables by the product of the
individual weights) has. Smaller weights indicate less importance. Kuo (2003)
proved that the CBC algorithm achieves the optimal rate of convergence in the
respective function spaces, but this does not imply the algorithm will find the
generating vector with the smallest worst-case error. In fact it does not. We
investigate a generalization of the component-by-component construction that
allows for a general successive coordinate search (SCS), based on an initial
generating vector, and with the aim of getting closer to the smallest
worst-case error. The proposed method admits the same type of worst-case error
bounds as the CBC algorithm, independent of the choice of the initial vector.
Under the same summability conditions on the weights as in [Kuo,2003] the error
bound of the algorithm can be made independent of the dimension and we
achieve the same optimal order of convergence for the function spaces from
[Kuo,2003]. Moreover, a fast version of our method, based on the fast CBC
algorithm by Nuyens and Cools, is available, reducing the computational cost of
the algorithm to operations, where denotes the number
of function evaluations. Numerical experiments seeded by a Korobov-type
generating vector show that the new SCS algorithm will find better choices than
the CBC algorithm and the effect is better when the weights decay slower.Comment: 13 pages, 1 figure, MCQMC2016 conference (Stanford
Shell model description of the 14C dating beta decay with Brown-Rho-scaled NN interactions
We present shell model calculations for the beta-decay of the 14C ground
state to the 14N ground state, treating the states of the A=14 multiplet as two
0p holes in an 16O core. We employ low-momentum nucleon-nucleon (NN)
interactions derived from the realistic Bonn-B potential and find that the
Gamow-Teller matrix element is too large to describe the known lifetime. By
using a modified version of this potential that incorporates the effects of
Brown-Rho scaling medium modifications, we find that the GT matrix element
vanishes for a nuclear density around 85% that of nuclear matter. We find that
the splitting between the (J,T)=(1+,0) and (J,T)=(0+,1) states in 14N is
improved using the medium-modified Bonn-B potential and that the transition
strengths from excited states of 14C to the 14N ground state are compatible
with recent experiments.Comment: 4 pages, 5 figures Updated to include referee comments/suggestion
Hot new directions for quasi-Monte Carlo research in step with applications
This article provides an overview of some interfaces between the theory of
quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC
theoretical settings: first order QMC methods in the unit cube and in
, and higher order QMC methods in the unit cube. One important
feature is that their error bounds can be independent of the dimension
under appropriate conditions on the function spaces. Another important feature
is that good parameters for these QMC methods can be obtained by fast efficient
algorithms even when is large. We outline three different applications and
explain how they can tap into the different QMC theory. We also discuss three
cost saving strategies that can be combined with QMC in these applications.
Many of these recent QMC theory and methods are developed not in isolation, but
in close connection with applications
Rigorous treatment of electrostatics for spatially varying dielectrics based on energy minimization
A novel energy minimization formulation of electrostatics that allows
computation of the electrostatic energy and forces to any desired accuracy in a
system with arbitrary dielectric properties is presented. An integral equation
for the scalar charge density is derived from an energy functional of the
polarization vector field. This energy functional represents the true energy of
the system even in non-equilibrium states. Arbitrary accuracy is achieved by
solving the integral equation for the charge density via a series expansion in
terms of the equation's kernel, which depends only on the geometry of the
dielectrics. The streamlined formalism operates with volume charge
distributions only, not resorting to introducing surface charges by hand.
Therefore, it can be applied to any spatial variation of the dielectric
susceptibility, which is of particular importance in applications to
biomolecular systems. The simplicity of application of the formalism to real
problems is shown with analytical and numerical examples.Comment: 27 pages, 5 figure
Ginzburg-Landau theory of crystalline anisotropy for bcc-liquid interfaces
The weak anisotropy of the interfacial free-energy is a crucial
parameter influencing dendritic crystal growth morphologies in systems with
atomically rough solid-liquid interfaces. The physical origin and quantitative
prediction of this anisotropy are investigated for body-centered-cubic (bcc)
forming systems using a Ginzburg-Landau theory where the order parameters are
the amplitudes of density waves corresponding to principal reciprocal lattice
vectors. We find that this theory predicts the correct sign,
, and magnitude, , of this anisotropy in good agreement
with the results of MD simulations for Fe. The results show that the
directional dependence of the rate of spatial decay of solid density waves into
the liquid, imposed by the crystal structure, is a main determinant of
anisotropy. This directional dependence is validated by MD computations of
density wave profiles for different reciprocal lattice vectors for
crystal faces. Our results are contrasted with the prediction of the reverse
ordering from an earlier formulation of
Ginzburg-Landau theory [Shih \emph{et al.}, Phys. Rev. A {\bf 35}, 2611
(1987)].Comment: 9 pages, 5 figure
Experimental investigation of the deformation behavior of aluminium-bicrystals
This Max-Planck project report discusses the deformation behaviour of an aluminium-bicrystal with a symmetrical tilt boundary and an initial misorientation of 8.7 Degrees. The specimen was compressed in a channel die to 30% engineering thickness reduction at room temperature. Afterwards the crystal orientations were determined by electron backscatter diffraction (EBSD) and the plastic strain distribution was measured by photogrametry. It was found that the two abutting crystals close to the grain boundary rotate towards each other, whereas the grain interiors increase their mutual misorientation during plastic loading
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