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