Effective complex permittivity tensor of a periodic array of cylinders

We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, and whose dielectric properties are complex-valued. Efficient formulas are provided to determine the effective complex permittivity tensor which are in excellent agreement with numerical calculations. We also show that in contrast to the real-valued case, the real and imaginary parts of the effective complex-valued tensor can exhibit non-monotonic behavior as functions of volume fraction of cylinders, and can be either greater or less than that of the constituents.Comment: 13 pages, 14 figure

On the determination of the boundary impedance from the far field pattern

We consider the Helmholtz equation in the half space and suggest two methods for determining the boundary impedance from knowledge of the far field pattern of the time-harmonic incident wave. We introduce a potential for which the far field patterns in specially selected directions represent its Fourier coefficients. The boundary impedance is then calculated from the potential by an explicit formula or from the WKB approximation. Numerical examples are given to demonstrate efficiency of the approaches. We also discuss the validity of the WKB approximation in determining the impedance of an obstacle.Comment: 10 pages, 4 figure

The effect of disorder on the wave propagation in one-dimensional periodic optical systems

The influence of disorder on the transmission through periodic waveguides is studied. Using a canonical form of the transfer matrix we investigate dependence of the Lyapunov exponent $\gamma$ on the frequency $\nu$ and magnitude of the disorder $\sigma$. It is shown that in the bulk of the bands $\gamma \sim \sigma^2$, while near the band edges it has the order $\gamma \sim \sigma^{2/3}$. This dependence is illustrated by numerical simulations.Comment: 15 pages, 4 figure

Clusters of Bloch waves in three-dimensional periodic media

We consider acoustic wave propagation through a periodic array of the inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength is fixed. We derive and rigorously justify the dispersion relation for general frequencies and show that there are exceptional frequencies for which the solution is a cluster of waves propagating in different directions with different frequencies so that the dispersion relation cannot be defined uniquely. Examples are provided for the spherical inclusions.Comment: 28 pages, 1 figur

The effective conductivity of a periodic lattice of circular inclusions

We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain an exact analytic expression for the effective conductivity tensor as well as its expansion in terms of volume fraction of the cylinders. Results are illustrated by examples.Comment: 21 pages, 5 figure

Dietary intake based on physical activity level in Korean elementary school students

Prevalence of childhood obesity is increasing significantly worldwide due to energy imbalance perhaps stemming from undesirable dietary behavior and physical activity level. The objective of the study was to examine the effects of physical activity level on nutritional status in elementary school students. The subjects were comprised of 287 elementary school students between 4th and 6th grades in Seoul, Korea. The level of physical activity was scored with a modified Godin leisure-time exercise questionnaire and was categorized as active, moderately active, and sedentary. Dietary intakes were obtained using a 24-hour food recall method. An analysis of variance (ANOVA) was conducted to test for global significant differences of nutrient intakes by physical activity level. Boys were more active than girls. Daily intakes of energy in moderately active boys were significantly higher than in the sedentary group, but intakes of calcium and iron in moderately active boys were lower than active boys. For girls, physical activity level did not affect nutrient density at all. Intakes of calcium, vitamin C, and folate for both boys and girls were below 50% of recommended intake. Physical activity did not affect nutrient density and our participants were exposed to nutritional imbalance. Therefore, the results suggest that nutrition education regarding balanced diet and optimum physical activity is required for children's health and growth