1,037 research outputs found
Dual methods and approximation concepts in structural synthesis
Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins
ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide
A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included
Experimental vs. Numerical Eigenvalues of a Bunimovich Stadium Billiard -- A Comparison
We compare the statistical properties of eigenvalue sequences for a gamma=1
Bunimovich stadium billiard. The eigenvalues have been obtained by two ways:
one set results from a measurement of the eigenfrequencies of a superconducting
microwave resonator (real system) and the other set is calculated numerically
(ideal system). The influence of the mechanical imperfections of the real
system in the analysis of the spectral fluctuations and in the length spectra
compared to the exact data of the ideal system are shown. We also discuss the
influence of a family of marginally stable orbits, the bouncing ball orbits, in
two microwave stadium billiards with different geometrical dimensions.Comment: RevTex, 8 pages, 8 figures (postscript), to be published in Phys.
Rev.
Circular dielectric cavity and its deformations
The construction of perturbation series for slightly deformed dielectric
circular cavity is discussed in details. The obtained formulae are checked on
the example of cut disks. A good agreement is found with direct numerical
simulations and far-field experiments.Comment: 17 pages, 12 figure
First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard
With a perturbation body technique intensity distributions of the electric
field strength in a flat microwave billiard with a barrier inside up to mode
numbers as large as about 700 were measured. A method for the reconstruction of
the amplitudes and phases of the electric field strength from those intensity
distributions has been developed. Recently predicted superscars have been
identified experimentally and - using the well known analogy between the
electric field strength and the quantum mechanical wave function in a
two-dimensional microwave billiard - their properties determined.Comment: 4 pages, 5 .eps figure
Inferring periodic orbits from spectra of simple shaped micro-lasers
Dielectric micro-cavities are widely used as laser resonators and
characterizations of their spectra are of interest for various applications. We
experimentally investigate micro-lasers of simple shapes (Fabry-Perot, square,
pentagon, and disk). Their lasing spectra consist mainly of almost equidistant
peaks and the distance between peaks reveals the length of a quantized periodic
orbit. To measure this length with a good precision, it is necessary to take
into account different sources of refractive index dispersion. Our experimental
and numerical results agree with the superscar model describing the formation
of long-lived states in polygonal cavities. The limitations of the
two-dimensional approximation are briefly discussed in connection with
micro-disks.Comment: 13 pages, 19 figures, accepted for publication in Physical Review
Biofilms on glacial surfaces: hotspots for biological activity
Glaciers are important constituents in the Earth’s hydrological and carbon cycles, with predicted warming leading to increases in glacial melt and the transport of nutrients to adjacent and downstream aquatic ecosystems. Microbial activity on glacial surfaces has been linked to the biological darkening of cryoconite particles, affecting albedo and increased melt. This phenomenon, however, has only been demonstrated for alpine glaciers and the Greenland Ice Sheet, excluding Antarctica. In this study, we show via confocal laser scanning microscopy that microbial communities on glacial surfaces in Antarctica persist in biofilms. Overall, ~35% of the cryoconite sediment surfaces were covered by biofilm. Nanoscale scale secondary ion mass spectrometry measured significant enrichment of 13C and 15N above background in both Bacteroidetes and filamentous cyanobacteria (i.e., Oscillatoria) when incubated in the presence of 13C–NaHCO3 and 15NH4. This transfer of newly synthesised organic compounds was dependent on the distance of heterotrophic Bacteroidetes from filamentous Oscillatoria. We conclude that the spatial organisation within these biofilms promotes efficient transfer and cycling of nutrients. Further, these results support the hypothesis that biofilm formation leads to the accumulation of organic matter on cryoconite minerals, which could influence the surface albedo of glaciers
Asymptotic behaviour of multiple scattering on infinite number of parallel demi-planes
The exact solution for the scattering of electromagnetic waves on an infinite
number of parallel demi-planes has been obtained by J.F. Carlson and A.E. Heins
in 1947 using the Wiener-Hopf method. We analyze their solution in the
semiclassical limit of small wavelength and find the asymptotic behaviour of
the reflection and transmission coefficients. The results are compared with the
ones obtained within the Kirchhoff approximation
Random wave functions and percolation
Recently it was conjectured that nodal domains of random wave functions are
adequately described by critical percolation theory. In this paper we
strengthen this conjecture in two respects. First, we show that, though wave
function correlations decay slowly, a careful use of Harris' criterion confirms
that these correlations are unessential and nodal domains of random wave
functions belong to the same universality class as non critical percolation.
Second, we argue that level domains of random wave functions are described by
the non-critical percolation model.Comment: 13 page
Spectral properties of distance matrices
Distance matrices are matrices whose elements are the relative distances
between points located on a certain manifold. In all cases considered here all
their eigenvalues except one are non-positive. When the points are uncorrelated
and randomly distributed we investigate the average density of their
eigenvalues and the structure of their eigenfunctions. The spectrum exhibits
delocalized and strongly localized states which possess different power-law
average behaviour. The exponents depend only on the dimensionality of the
manifold.Comment: 31 pages, 9 figure
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