Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations

The technique of applying form-invariant, spatial coordinate transformations of Maxwell’s equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.     

Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Given a subset E of convex functions from into which satisfy growth conditions of order p>1 and an open bounded subset of , we establish the continuity of a map μΦ_μ from the set of all Young measures on equipped with the narrow topology into a set of suitable functionals defined in and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization.     

Multiquadratic Extensions, Rigid Fields and Pythagorean Fields

Let F be a field of characteristic other than 2. Let F⁽²⁾ denotethe compositum over F of all quadratic extensions of F, letF⁽³⁾ denote the compositum over F⁽²⁾ of all quadratic extensionsof F⁽²⁾ that are Galois over F, and let F^{3} denote the compositumover F⁽²⁾ of all quadratic extensions of F⁽²⁾. This paper showsthat F⁽³⁾ = F^{3} if and only if F is a rigid field, and thatF⁽³⁾ = K⁽³⁾ for some extension K of F if and only if F is Pythagoreanand . The proofs depend mainly on the behavior of quadratic forms over quadratic extensions,and the corresponding norm maps.     

Multiplication Modules and a Theorem of P. F. Smith

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stable Exponents in Discrete Groups

It is known that in a word hyperbolic group the stable exponent of every nontorsion element is an integer. We prove that this is also true in finitely generated nilpotent groups. On the other hand, we show that for any rational number 1 there exists a torsionfree CAT(0) group containing an element whose stable exponent is equal to .     

Modal decomposition method for modeling the interaction of Lamb waves with cracks

The interaction of the low-order antisymmetric (a0) and symmetric (s0) Lamb waves with vertical cracks in aluminum plates is studied. Two types of slots are considered: (a) internal crack symmetrical with respect to the middle plane of the plate and (b) opening crack. The modal decomposition method is used to predict the reflection and transmission coefficients and also the through-thickness displacement fields on both sides of slots of various heights. The model assumes strip plates and cracks, thus considering two-dimensional plane strain conditions. However, mode conversion (a0 into s0 and vice versa) that occurs for single opening cracks is considered. The energy balance is always calculated from the reflection and transmission coefficients, in order to check the validity of the results. These coefficients together with the through-thickness displacement fields are also compared to those predicted using a finite element code widely used in the past for modeling Lamb mode diffraction problems. Experiments are also made for measuring the reflection and transmission coefficients for incident a0 or s0 lamb modes on opening cracks, and compared to the numerical predictions.     

A High-Resolution Analysis of the ν3 Absorption Band of Trifluoromethane

A high-resolution (up to 0.0018 cm⁻¹ unapodized) room temperature mid-infrared (650 to 750 cm⁻¹, 13.3 to 15.4 μm) absorption measurement of the ν₃ vibrational band of trifluoromethane (fluoroform, CHF₃, HFC-23) vapor was made with a Fourier transform spectrometer. A rovibrational analysis of over 1400 infrared transitions of the ν₃ band has yielded rotational constants, including sextic centrifugal distortion constants. The results are compared with two previous analyses of microwave and infrared spectra. The line positions of the lower J parts of the ν₃+ν₆−ν₆ and 2ν₃−ν₃ hot bands have been identified and constants obtained for the 2ν₃ state. The central Q branch and a few unblended transitions of the ν₃ band of ¹³CF₃H have been identified and the band origin has been determined. The relative intensities of the ν₃ band together with the 2ν₃−ν₃ hot band and ν₃ band of ¹³CF₃H have been calculated using the constants derived from this work.     

Characterisation of core-shell latexes by flow field-flow fractionation with multi-angle light scattering detection

Flat channel asymmetrical flow field-flow fractionation with multi-angle light scattering (MALS) detection was used to study the swelling behaviour of core-shell particles with either carboxylated or hydroxylated shells as a function of pH and ionic strength. The equilibration time of the most heavily carboxylated core-shells appeared to be of the order of several hours. At low ionic strength (5 mM), the carboxylated core-shells showed a definite swelling response to a change in pH in the range from 5 to 10, ranging from a hydrodynamic radius increase of 24 to 118%, depending on the degree of carboxylation. A much milder response was found for the change of the root mean square (r.m.s.) radius as measured with MALS, indicating that the scattering plane is moving inwards during the swelling process due to a decreasing density of the shell. The hydroxylated core-shells appeared to be inert to a change in pH. Also the response of two expanded (pH 10) carboxylated core-shells on increasing ionic strength was studied. Comparison of the results of these ionic strength experiments with theoretical predictions based on Donnan equilibrium led us to the conclusion that a significant amount of counter-ion condensation may take place in the shells.     

A simple Maxwell-Wagner-Butler-Volmer approach to the impedance of the hydrogen electrode in a nafion fuel cell

A simple one-dimensional model of the impedance of a hydrogen/Nafion electrode is set up combining the usual Maxwell-Wagner approach for linear, homogeneous, and isotropic media with the linearized Butler-Volmer equation for the interfacial, electrochemical reaction. Only one relaxation semicircle is normally seen in the Nyquist diagram, but a low-frequency arc may appear at high overvoltages. The model is described by only two dimensionless parameters (in addition to the dimensionless frequency). These parameters are related to the double-layer capacitance and to the interfacial electrochemical reaction rate, respectively. With some adjustments, the model can be used to explain the observed equilibrium impedance from 40 to 70 degrees C of a symmetric cell of the type C/Pt/H(2)|Nafion 117/H(2)/Pt/C. The hydrogen electrodes in this cell were built up as a disperse multiphase region (carbon, platinum grains, Nafion 117, and hydrogen gas) as commonly done in solid polymer fuel cells.