10,685 research outputs found
Fast computation of effective diffusivities using a semi-analytical solution of the homogenization boundary value problem for block locally-isotropic heterogeneous media
Direct numerical simulation of diffusion through heterogeneous media can be
difficult due to the computational cost of resolving fine-scale
heterogeneities. One method to overcome this difficulty is to homogenize the
model by replacing the spatially-varying fine-scale diffusivity with an
effective diffusivity calculated from the solution of an appropriate boundary
value problem. In this paper, we present a new semi-analytical method for
solving this boundary value problem and computing the effective diffusivity for
pixellated, locally-isotropic, heterogeneous media. We compare our new solution
method to a standard finite volume method and show that equivalent accuracy can
be achieved in less computational time for several standard test cases. We also
demonstrate how the new solution method can be applied to complex heterogeneous
geometries represented by a grid of blocks. These results indicate that our new
semi-analytical method has the potential to significantly speed up simulations
of diffusion in heterogeneous media.Comment: 29 pages, 4 figures, 5 table
Vorticity cutoff in nonlinear photonic crystals
Using group theory arguments, we demonstrate that, unlike in homogeneous
media, no symmetric vortices of arbitrary order can be generated in
two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry.
The only condition needed is that the non-linearity term exclusively depends on
the modulus of the field. In the particular case of 2D periodic systems, such
as nonlinear photonic crystals or Bose-Einstein condensates in periodic
potentials, it is shown that the realization of discrete symmetry forbids the
existence of symmetric vortex solutions with vorticity higher than two.Comment: 4 pages, 5 figures; minor changes in address and reference
The Torsion of Members Having Sections Common in Aircraft Construction
Within recent years a great variety of approximate torsion formulas and drafting-room processes have been advocated. In some of these, especially where mathematical considerations are involved, the results are extremely complex and are not generally intelligible to engineers. The principal object of this investigation was to determine by experiment and theoretical investigation how accurate the more common of these formulas are and on what assumptions they are founded and, if none of the proposed methods proved to be reasonable accurate in practice, to produce simple, practical formulas from reasonably correct assumptions, backed by experiment. A second object was to collect in readily accessible form the most useful of known results for the more common sections. Formulas for all the important solid sections that have yielded to mathematical treatment are listed. Then follows a discussion of the torsion of tubular rods with formulas both rigorous and approximate
Elastic Instability of Members Having Sections Common in Aircraft Construction
Two fundamental problems of elastic stability are discussed in this report. In part one formulas are given for calculating the critical stress at which a thin, outstanding flange of a compression member will either wrinkle into several waves or form into a single half wave and twist the member about its longitudinal axis. A mathematical study of the problem, which together with experimental work has led to these formulas, is given in an appendix. Results of test substantiating the recommended formulas are also presented. In part two the lateral buckling of beams is discussed. The results of a number of mathematical studies of this phenomenon have been published prior to this writing, but very little experimentally determined information relating to the problem has been available heretofore. Experimental verification of the mathematical deductions is supplied
Preferred orientation of n-hexane crystallized in silicon nanochannels: A combined x-ray diffraction and sorption isotherm study
We present an x-ray diffraction study on n-hexane in tubular silicon channels
of approximately 10 nm diameter both as a function of the filling fraction f of
the channels and as a function of temperature. Upon cooling, confined n-hexane
crystallizes in a triclinic phase typical of the bulk crystalline state.
However, the anisotropic spatial confinement leads to a preferred orientation
of the confined crystallites, where the crystallographic direction
coincides with the long axis of the channels. The magnitude of this preferred
orientation increases with the filling fraction, which corroborates the
assumption of a Bridgman-type crystallization process being responsible for the
peculiar crystalline texture. This growth process predicts for a channel-like
confinement an alignment of the fastest crystallization direction parallel to
the long channel axis. It is expected to be increasingly effective with the
length of solidifying liquid parcels and thus with increasing f. In fact, the
fastest solidification front is expected to sweep over the full silicon
nanochannel for f=1, in agreement with our observation of a practically perfect
texture for entirely filled nanochannels
Kinetic Energy Density Study of Some Representative Semilocal Kinetic Energy Functionals
There is a number of explicit kinetic energy density functionals for
non-interacting electron systems that are obtained in terms of the electron
density and its derivatives. These semilocal functionals have been widely used
in the literature. In this work we present a comparative study of the kinetic
energy density of these semilocal functionals, stressing the importance of the
local behavior to assess the quality of the functionals. We propose a quality
factor that measures the local differences between the usual orbital-based
kinetic energy density distributions and the approximated ones, allowing to
ensure if the good results obtained for the total kinetic energies with these
semilocal functionals are due to their correct local performance or to error
cancellations. We have also included contributions coming from the laplacian of
the electron density to work with an infinite set of kinetic energy densities.
For all the functionals but one we have found that their success in the
evaluation of the total kinetic energy are due to global error cancellations,
whereas the local behavior of their kinetic energy density becomes worse than
that corresponding to the Thomas-Fermi functional.Comment: 12 pages, 3 figure
Spatial fluctuations in an optical parametric oscillator below threshold with an intracavity photonic crystal
We show how to control spatial quantum correlations in a multimode degenerate
optical parametric oscillator type I below threshold by introducing a spatially
inhomogeneous medium, such as a photonic crystal, in the plane perpendicular to
light propagation. We obtain the analytical expressions for all the
correlations in terms of the relevant parameters of the problem and study the
number of photons, entanglement, squeezing, and twin beams. Considering
different regimes and configurations we show the possibility to tune the
instability thresholds as well as the quantumness of correlations by breaking
the translational invariance of the system through a photonic crystal
modulation.Comment: 12 pages, 7 figure
Ab initio wavefunction based methods for excited states in solids: correlation corrections to the band structure of ionic oxides
Ab initio wavefunction based methods are applied to the study of electron
correlation effects on the band structure of oxide systems. We choose MgO as a
prototype closed-shell ionic oxide. Our analysis is based on a local
Hamiltonian approach and performed on finite fragments cut from the infinite
solid. Localized Wannier functions and embedding potentials are obtained from
prior periodic Hartree-Fock (HF) calculations. We investigate the role of
various electron correlation effects in reducing the HF band gap and modifying
the band widths. On-site and nearest-neighbor charge relaxation as well as
long-range polarization effects are calculated. Whereas correlation effects are
essential for computing accurate band gaps, we found that they produce smaller
changes on the HF band widths, at least for this material. Surprisingly, a
broadening effect is obtained for the O 2p valence bands. The ab initio data
are in good agreement with the energy gap and band width derived from
thermoreflectance and x-ray photoemission experiments. The results show that
the wavefunction based approach applied here allows for well controlled
approximations and a transparent identification of the microscopic processes
which determine the electronic band structure
A topological charge selection rule for phase singularities
We present an study of the dynamics and decay pattern of phase singularities
due to the action of a system with a discrete rotational symmetry of finite
order. A topological charge conservation rule is identified. The role played by
the underlying symmetry is emphasized. An effective model describing the short
range dynamics of the vortex clusters has been designed. A method to engineer
any desired configuration of clusters of phase singularities is proposed. Its
flexibility to create and control clusters of vortices is discussed.Comment: 4 pages, 3 figure
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