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  • 1
    Electronic Resource
    Electronic Resource
    On the theory and solar application of inductive grids (1977)
    Springer
    Applied physics 14 (1977), S. 1-20 
    Details
    ISSN: 1432-0630
    Keywords: 42.80 ; 78.20 ; 41
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A brief description is given of the rigorous formulism of Chen, which describes the diffraction by perfectly-conducting inductive grids. The formulism is used to prove several general properties of grids, including the relevant form of the Reciprocity Theorem. The theory is used to investigate the equivalent circuit model proposed by other authors for thin grids, and also to derive a monomodal model of the type first proposed by Chen. The latter model is shown to be useful even in the region where more than one spectral order propagates. The accuracy of the formulism is established by the comparison of calculated results with a number of far-infrared measurements on grids. The use of grids as solar-selective elements is investigated. They are shown to be capable of providinga/e ratios of the order of 30–40, provided that they are always pointed towards the sun, and that the diffuse content of the illumination is low.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00882627
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  • 2
    Electronic Resource
    Electronic Resource
    Extraction of structural information from measured transport properties of composites (1982)
    Springer
    Applied physics 29 (1982), S. 19-27 
    Details
    ISSN: 1432-0630
    Keywords: 72.90+y ; 42.70 Fh ; 44.30+v ; 46.30 Cn
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract We describe clearly Milton's bounds on the scalar transport properties of composite materials in the case when no geometrical information is known about the composite, but when a set of measured values of a transport property is available. We consider how the measured values may be used when they are subject to known errors. In this case, a statistical analysis is employed. We illustrate the various conclusions which may result from this analysis by considering six cases involving both two-and three-dimensional composites. In four of the six cases, estimates of the volume fraction of the composite in agreement with the known value are obtained. In the fifth case, the analysis pointed out a possible error in the experimental data, while in the sixth it revealed a critical dependence of transport properties on composite geometry due to filamentary linking between particles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00618111
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  • 3
    Electronic Resource
    Electronic Resource
    Lattice sums for gratings and arrays (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 7808-7816 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Lattice sums arising in quasiperiodic Green's functions for the Helmholtz equation, over general two-dimensional arrays are investigated. The array sums are related to those over a single quasiperiodic line of sources, and their difference is be expressed in terms of exponentially convergent series. It is shown that our expressions can be used to generate the sums pertaining to the case of photonic gap states, associated with complex quasiperiodicity (Bloch) vectors. The accuracy and computational speed of our expressions are illustrated. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1310361
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  • 4
    Electronic Resource
    Electronic Resource
    Analytical results for a class of sums involving Bessel functions and square arrays (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2043-2052 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a class of sums involving Bessel functions summed over the square array. The sums involve the length (ξ) of an arbitrary vector lying within the central unit cell. We establish conditions under which the sums reduce to polynomial forms in ξ (possibly with a single logarithmic term in addition), and show how these polynomials may be conveniently evaluated. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531492
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  • 5
    Electronic Resource
    Electronic Resource
    Static Bloch sums for the square array (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2802-2813 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider sums arising in doubly quasiperiodic Green's functions for the Laplace equation, over the square array. The sums are represented as Fourier series, and it is shown that the coefficients in the series can be obtained as polynomials. We give expressions from which the first six array sums can be evaluated efficiently, and accurate to better than one part in 107, over most of the Brillouin zone. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1467968
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  • 6
    Electronic Resource
    Electronic Resource
    Exact modelling of cubic lattice permittivity and conductivity (1977)
    [s.l.] : Nature Publishing Group
    Nature 265 (1977), S. 128-129 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The first order (dipole) solution to the problem is known as the Lorentz-Lorenz equation or the Maxwell Garnett equation e = 1 - 3f/[(2 + e1)/(1 - e1)] + f where e, e1 are, respectively, the permittivities of the resultant medium and of the spherical particles (both measured relative to the ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/265128a0
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  • 7
    Electronic Resource
    Electronic Resource
    On a bessel function integral (1992)
    Springer
    Applicable algebra in engineering, communication and computing 2 (1992), S. 207-216 
    Details
    ISSN: 1432-0622
    Keywords: Integration ; Symbolic Computation ; MAPLE ; Special Functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract We consider the integral $$\int\limits_0^\infty {xe^{ - \eta x^2 } } J_b (Kx)Y_b (kx)dx$$ whereη, K, k andb are all positive real numbers. We reduce this integral to a linear combination of two integrals. The first of these is an exponential integral, which can be expressed as a difference of two Shkarofsky functions, or can easily be evaluated numerically. The second is the original integral, but withk andK both replaced by √kK. We express this as a MeijerG function, and then reduce it to the sum of an associated Bessel function and a modified Bessel function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01294334
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  • 8
    Electronic Resource
    Electronic Resource
    Crossed gratings: A theory and its applications (1979)
    Springer
    Applied physics 18 (1979), S. 39-52 
    Details
    ISSN: 1432-0630
    Keywords: 42.80 ; 78.20 ; 41
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract We introduce a rigorous formulation for the problem of the diffraction by a finitely-conducting, bi-periodic surface. The formationon is based on a coordinate transformation which maps the grating surface onto a plane. The transformed Maxwell equations are resolved using an iterative technique. The numerical implementation is tested against a number of criteria, including a comparison with two recently developed formalisms. As well, it is shown to give results in agreement with the Reciprocity Theorem, which is derived for efficiencies of crossed gratings in unpolarized light. The method has been shown to work throughout the whole range of values of surface conductivity. We investigate the effect of a surface-corrugation on the solar absorptance of a metallic mirror. We discuss a useful equivalence property linking the behaviour of crossed gratings with that of classical gratings. We exhibit for the first time a grating in a highly-reflecting metal capable of totally absorbing unpolarized incident light.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935902
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  • 9
    Electronic Resource
    Electronic Resource
    Electrostatic and optical resonances of arrays of cylinders (1980)
    Springer
    Applied physics 23 (1980), S. 223-235 
    Details
    ISSN: 1432-0630
    Keywords: 41 ; 66 ; 84.60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The solutions of the electrostatic potential problem for the square and hexagonal arrays of circular cylinders with zero applied field (homogeneous or resonant solutions) are studied. We show that for non-touching cylinders, the set of resonances is discrete except in the neighbourhood of one point, at which the dielectric constant of the array has an essential singularity. For arrays of touching cylinders, the set is well represented by a continuous distribution. This representation enables the derivation of the asymptotic form of the expansion for the dielectric constant of the array when the dielectric constant of the cylinders is large. The known value of the first term in the expansion enables us to derive the second term. The physical characteristics of the resonant solutions are studied. Metals achieve values of dielectric constant which are close to the resonant values (real and negative) for certain wavelengths. Curves are given which enable the prediction of those wavelengths at which the optical resonances of both arrays occur, for any area fraction and composition of a columnar cerment film.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00914904
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  • 10
    Electronic Resource
    Electronic Resource
    Electrostatic and optical resonances of cylinder pairs (1981)
    Springer
    Applied physics 24 (1981), S. 311-318 
    Details
    ISSN: 1432-0630
    Keywords: 41 ; 66 ; 84.60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract We study the polarizability α(σ) of a pair of identical cylinders, each of dielectric constant σ and immersed in a medium of unit dielectric constant. In the case of non-touching cylinders, the spectrum of resonant solutions is shown to be discrete, whereas when the cylinders touch it is continuous, and corresponds to a branch-cut of α(σ). This behaviour is compared with that of the spectrum of ε(σ), the dielectric constant of an infinite array of cylinders. We derive a simple expression for α(σ), and use it to obtain ε(σ) for a dilute array of touching cylinder pairs. The resulting formula is shown to have properties differing from those of the widely-used Maxwell-Garnett and effective medium theories, and consequently it may prove useful in studies of solar-selective columnar cermets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00899728
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