Extraction of structural information from measured transport properties of composites

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.     

Concerning bounds on the transport and mechanical properties of multicomponent composite materials

The Hashin-Shtrikman and Walpole bounds for the transport properties and bulk modulus of multicomponent composite materials are shown to be attained in a wide range of cases. Thus in these cases the bounds are the best possible bounds that can be given in terms of the properties of the components and the volume fractions. For three-component materials new bounds are conjectured. The conjectured bounds are presumed to apply in the cases where the Hashin-Shtrikman and Walpole bounds are not attained.     

Electrostatic and optical resonances of arrays of cylinders

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.     

Investigation of L1_0 FePt-based soft/hard composite bit-patterned media by micromagnetic simulation

The soft/hard composite patterned media have potential to be the next generation of magnetic recording,but the composing modes of soft and hard materials have not been investigated systematically.L10 Fe Pt-based soft/hard composite patterned media with an anisotropic constant distribution are studied by micromagnetic simulation.Square arrays and hexagonal arrays with various pitch sizes are simulated for two composing types:the soft layer that encloses the hard dots and the soft layer that covers the whole surface.It is found that the soft material can reduce the switching fields of bits effectively for all models.Compared with the first type,the second type of models possess low switching fields,narrow switching field distributions,and high gain factors due to the introduction of inter-bit exchange coupling.Furthermore,the readout waveforms of the second type are not deteriorated by the inter-bit soft layers.Since the recording density of hexagonal arrays are higher than that of square arrays with the same center-to-center distances,the readout waveforms of hexagonal arrays are a little worse,although other simulation results are similar for these two arrays.     

Interferometric array generation

We report the formation of square, rectangular as well as hexagonal arrays of small light spots in one single setup using Michelson and Mach–Zehnder interferometers in tandem. The geometry of arrays can be altered easily online, by changing the relative orientations of the mirrors. The arrays could be scanned over large longitudinal distances and could be compressed to give large spot density. The expression for the resultant intensity distribution for the arrays has been worked out and the computed pattern is compared with the experimental data.     

Point defect states in two-dimensional phononic crystals

The point defect states of acoustic wave in the two-dimensional arrays of water cylinders with circular (square) cross section in mercury host are studied. The influence of the defect geometry on the defect band modes is investigated.     

Transport properties of arrays of intersecting cylinders

Formalisms are presented which enable the accurate calculation of the polarizability of an isolated square prism, and of the transport properties of square arrays of both circular cylinders and square prisms, over the entire range of volume fractions. For volume fractions close to zero and to unity, the results are shown to agree with dipolar formulae based on the appropriate polarizability. For volume fractions close to touching, the transport property varies rapidly but smoothly through the multipolar region. The results are shown to be in good qualitative agreement with experimental curves.     

Magnetotransport properties in magnetic nanotubes studied using Monte Carlo simulations

The dependences of the magnetoelectric transport properties of nanotubes on the temperature, diameter and anisotropy were simulated using the Monte Carlo method, the Heisenberg model and the Drude formula. The simulations included the effects of an external magnetic field, magnetocrystalline anisotropy and nearest neighbor interactions. Two types of nanotubes with different unit cells (square and hexagonal) were implemented. The influence of the nanotube geometry was also analyzed. A smaller dependence of the resistivity on the nanotube diameter and magnetocrystalline anisotropy was observed for the square unit cell nanotubes compared to the results obtained for the hexagonal unit cell nanotubes. Furthermore, lower fluctuations in the resistivity were observed in the former. In contrast, an external magnetic field had a greater influence on the resistivity of the square unit cell nanotubes than for the hexagonal unit cell nanotubes.     

Coercivity reduction in a two-dimensional array of nano-particles

We report on theoretical investigation of the magnetization reversal in two-dimensional arrays of ferromagnetic nano-particles with parameters of cobalt. The system was optimized for achieving the lowest coercivity in an array of particles located in the nodes of triangular, hexagonal and square grids. Based on the numerical solution of the non-stochastic Landau-Lifshitz-Gilbert equation we show that each particle distribution type is characterized with a proper optimal distance, allowing to lower the coercivity values for approximately 30% compared with the reference value obtained for a single nano-particle. It was shown that the reduction of coercivity occurs even if the particle position in the array is not very precise. In particular, the triangular particle arrangement maintained the same optimal distance between the particles under up to 20% random displacements of their position within the array.     

Two-dimensional phased arrays for application in surgery: Scanning by several focuses

Numerical simulation and comparative analysis of acoustic fields formed by two-dimensional phased arrays designed for ultrasonic surgery are conducted for the case of scanning by several focuses (in particular, by nine focuses arranged in a line and also by an array of nine focuses forming a 3×3 square grid). Calculations are performed for arrays with elements positioned at the surface both regularly (in square, ring, or hexagonal patterns) and randomly. Criteria for evaluating the “quality” of the intensity distributions in the field formed by the array in the case of scanning by several focuses are proposed. The quality of the intensity distributions for arrays containing 255 and 256 elements 5 mm in diameter arranged in regular patterns on the array’s surface (in square, ring, or hexagonal patterns) is inferior to that for arrays containing 256 randomly positioned elements. Among the regular arrays, the highest quality of intensity distributions is obtained for ring arrays, and the lowest quality is obtained for arrays with elements arranged in square or hexagonal patterns. The irregularity in the element positioning the array’s surface improves the quality of intensity distributions by reducing the secondary intensity peaks in the field formed by the array and, primarily, in the focal plane.     

Electronic and hole minibands in quantum wire arrays of different crystallographic structure

We consider semiconductor heterostructures consisting of GaAs rods embedded in Al_xGa_1 − xAs and disposed in sites of a square or triangular lattice. The electronic and hole spectra around the conduction band bottom and the valence band top are examined for electrons and holes propagating in plane of periodicity, versus geometry of the lattice formed by the rods, concentration of Al in the matrix material, and structural parameters including the filling fraction and the lattice constant. Our calculations use the envelope function and are based on the effective-mass approximation. We show that the electronic and hole spectra resulting from the periodicity of the heterostructure, depend on the factors considered and that the effect of lattice geometry varies substantially with lattice constant. For low lattice constant values the minigaps are significantly wider in the case of triangular lattice, while for high lattice constant values only slightly thiner minigaps occur in the square lattice-based arrays. We discuss the consequences of our findings for the efficiency of solar cells.     

Modification of laser gain properties through local-field effects and nanostructuring

We have recently developed a simple phenomenological model that allows one to account for the modifications of the gain characteristics of nanocomposite optical materials with specific geometries. Here we give a generalized formulation of our model to show that it can be applied to a broad variety of composite geometries. We demonstrate the application of our model using the Maxwell Garnett composite geometry with the resonant molecules in its host, which represent a practically important case that has not been treated earlier. We also give numerical examples for the Maxwell Garnett composite geometry with the resonances in either host or inclusions, and find the conditions under which it is possible to achieve an enhancement or suppression of the small-signal gain coefficient compared to its value in a bulk material. Using our simple model, one can identify the set of parameters, exhibiting the desired changes to the gain characteristics, prior to or instead of performing a more precise computationally intensive analysis.     

两相复合材料有效热导率的理论推导

复合材料有效热导率的解析表达式一直是传热问题中人们想要解决的问题.本文选用合适的单元体,采用热阻模型和积分平均方法,分别对分散相为球体和圆柱体的两相复合材料的有效热导率进行了推导.对于多孔复合材料,当孔隙率较大或温度较高时辐射换热的影响不能忽略,本文分析了气孔为球体或圆柱体时辐射换热对其有效热导率的影响.将计算所得有效热导率与相关实验数据进行了比较,结果表明两者吻合较好,证明了公式的准确性.     

Bounds for the complex dielectric constant of a two-phase composite

We study the effective dielectric constant of a two-phase composite for the case where the dielectric constants of the two components are complex. Milton has derived a sequence of narrowing bounds in the complex plane limiting the possible values of the effective dielectric constant, assuming that certain geometrical coefficients characterizing the medium are known. We cast Milton's bounds in a different form, making use of auxiliary functions introduced by Bergman. We derive explicit expressions for the bounds up to third order and compare values for the corresponding geometrical coefficient derived for different geometries.     

Whispering gallery mode propagation in photonic crystals in front of subwavelength slit arrays: Interplay with extraordinary transmission

We numerically study the propagation of light in 2D photonic crystals (PC) made of infinite cylinders of high refractive index, via the excitation of their morphological dependent resonances, in the presence of metallic arrays of subwavelength slits, either corrugated or not, that may produce extraordinary transmission. In this way, we confirm and illustrate previous theoretical findings on PCs and show new effects when combined with slits. Among them, we show that the whispering gallery mode excitation in the PC couples dominates the transmission of the slit arrays alone. Appropriate design of the system parameters and the illumination conditions, selects the transport and confinement of energy.     

Calculation of the interface exchange coupling constants between Fe and FeF2-like fluorides

The interface exchange coupling between ferromagnetic (F) and antiferromagnetic (AF) materials is interesting in itself and has also attracted recent attention in relation to the exchange bias phenomenon. A major difficulty in developing a reliable exchange bias theory lies in the fact that both the F and AF interface characteristics (geometry and physical parameters) are hard to determine experimentally and complicated to estimate theoretically. We adopt in this paper two alternative interface configurations to obtain upper and lower bounds for the computed values of the exchange coupling across the interface between metallic Fe and insulating FeF₂, derived on the basis of ab initio calculations implemented for a periodic supercell. Electronic structures and total energies were computed within density functional theory using the generalized gradient approximation for the exchange correlation potential. We expect the results obtained to be useful in model simulations with larger unit cells and non-collinear spins.     

Negative refractive index, perfect lenses and checkerboards: Trapping and imaging effects in folded optical spaces

Newly discovered metamaterials have opened new vistas for better control of light via negative refraction, whereby light refracts in the “wrong” manner. These are dielectric and metallic composite materials structured at subwavelength lengthscales. Their building blocks consist of local resonators such as conducting thin bars and split rings driving the material parameters such as the dielectric permittivity and magnetic permeability to negative (complex) values. Combined together, these structural elements can bring about a (complex valued) negative effective refractive index for the Snell–Descartes law and result in negative refraction of radiation. Negative refractive index materials can support a host of surface plasmon states for both polarizations of light. This makes possible unique effects such as imaging with subwavelength image resolution through the Pendry–Veselago slab lens. Other geometries have also been investigated, such as cylindrical or spherical lenses that enable a magnification of images with subwavelength resolution. Superlenses of three-fold (equilateral triangle), four-fold (square) and six-fold (hexagonal) geometry allow for multiple images, respectively two, three, and five. Generalization to rectangular and triangular checkerboards consisting of alternating cells of positive and negative refractive index represents a very singular situation in which the density of modes diverges at the corners, with an infinity of images. Sine-cosecant anisotropic heterogeneous square and triangular checkerboards can be respectively mapped onto three-dimensional cubic and icosahedral corner lenses consisting of alternating positive and negative refractive regions. All such systems with corners between negative and positive refractive media display very singular behavior with the local density of states becoming infinitely large at the corner, in the limit of no dissipation. We investigate all of these, using the unifying viewpoint of transformation optics. To cite this article: S. Guenneau, S.A. Ramakrishna, C. R. Physique 10 (2009).     

Improvement of Image Spatial Resolution in Optoacoustic Tomography with the Use of a Confocal Array

The spatial resolution and size of the sensitivity area of tomographic systems are estimated by calculating sensitivity maps and spatial resolution maps in the image plane of complex arrays. The relation between the size of areas of high sensitivity and high spatial resolution for real-time oriented tomographic systems with confocal arrays is studied. It is shown that arrays with toroidal geometry significantly improve the diagnostic capabilities of optoacoustic and laser-ultrasound structural analysis of biological objects, rocks, and composite materials.     

高浓度纤维增强材料介电特性计算方法

针对复合材料的微观结构非均匀和各向异性特点带来的数值方法计算慢、内存消耗大的问题,利用均匀化方法计算纤维增强复合材料的等效电磁参数.采用了纤维低体积添加比至高体积添加比的迭代方法,同时提出了一个描述材料微观结构的修正的特征长度,将现有的均匀化方法推广至非准静态(微波频段)条件下高纤维浓度情况.提出的修正的均匀化模型可直接用于反射系数、屏蔽效能等计算,其屏蔽效能与实际微观结构复合材料的数值仿真结果进行了对比,验证了提出的等效电磁参数计算公式的有效性和频率适用范围.     

On the Bergman-Milton bounds for the homogenization of dielectric composite materials

The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider the Bergman-Milton bounds in light of the recent emergence of metamaterials, in which unconventional parameter regimes for relative permittivities are encountered. Specifically, it is demonstrated that: (a) for nondissipative materials the bounds may be unlimited if the constituent materials have relative permittivities of opposite signs; (b) for weakly dissipative materials characterized by relative permittivities with real parts of opposite signs, the bounds may be exceedingly large.