An effective-medium approach to the optical properties of heterogeneous materials with nonlinear properties

Abstract

We have derived an analytic approach, based on the hypothesis of the effective-medium theory, to evaluate the effective dielectric magnitudes, including the effective third order nonlinear optical susceptibility α(χ⁽³⁾), of a heterogeneous two-component medium in which one of the components (the host matrix or the embedded particle respectively) presents nonlinear behaviour. Our formulation allows us to solve the full nonlinear problem in the whole range of concentrations without treating the nonlinear effects as a small perturbation to the linear behaviour. Therefore, it can be considered as an upper limit of the commonly used low-field nonlinear approximations for heterogeneous materials. Under certain conditions, these composites can exhibit a bistable regime that the present theory properly describes in wide ranges of the concentration, shape, wavelength, dielectric contants and intrinsic nonlinear optical susceptibility of the nonlinear component as well as in terms of the intensity of the external electric field. The present approach has been used to calculate the nonlinear optical response of Cu—Al₂O₃ nanocomposites.     

A multiscale analytical approach to evaluate osseointegration

Osseointegrated implants are frequently used in reconstructive surgery, both in the dental and orthopedic field, restoring physical function and improving the quality of life for the patients. The bone anchorage is typically evaluated at micrometer resolution, while bone tissue is a dynamic composite material composed of nanoscale collagen fibrils and apatite crystals, with defined hierarchical levels at different length scales. In order to understand the bone formation and the ultrastructure of the interfacial tissue, analytical strategies needs to be implemented enabling multiscale and multimodal analyses of the intact interface. This paper describes a sample preparation route for successive analyses allowing assessment of the different hierarchical levels of interest, going from macro to nano scale and could be implemented on single samples. Examples of resulting analyses of different techniques on one type of implant surface is given, with emphasis on correlating the length scale between the different techniques. The bone-implant interface shows an intimate contact between mineralized collagen bundles and the outermost surface of the oxide layer, while bone mineral is found in the nanoscale surface features creating a functionally graded interface. Osteocytes exhibit a direct contact with the implant surface via canaliculi that house their dendritic processes. Blood vessels are frequently found in close proximity to the implant surface either within the mineralized bone matrix or at regions of remodeling.     

A digital microfluidic approach to homogeneous enzyme assays

A digital microfluidic device was applied to a variety of enzymatic analyses. The digital approach to microfluidics manipulates samples and reagents in the form of discrete droplets, as opposed to the streams of fluid used in channel microfluidics. This approach is more easily reconfigured than a channel device, and the flexibility of these devices makes them suitable for a wide variety of applications. Alkaline phosphatase was chosen as a model enzyme and used to convert fluorescein diphosphate into fluorescein. Droplets of alkaline phosphatase and fluorescein diphosphate were merged and mixed on the device, resulting in a 140-nL, stopped-flow reaction chamber in which the fluorescent product was detected by a fluorescence plate reader. Substrate quantitation was achieved with a linear range of 2 orders of magnitude and a detection limit of approximately 7.0 x 10-20 mol. Addition of a small amount of a nonionic surfactant to the reaction buffer was shown to reduce the adsorption of enzyme to the device surface and extend the lifetime of the device without affecting the enzyme activity. Analyses of the enzyme kinetics and the effects of inhibition with inorganic phosphate were performed, and Km and kcat values of 1.35 microM and 120 s-1, respectively, agreed with those obtained in a conventional 384-well plate under the same conditions (1.85 microM and 155 s-1). A phototype device was also developed to perform multiplexed enzyme analyses. It was concluded that the digital microfluidic format is able to perform detailed and reproducible assays of substrate concentrations and enzyme activity in much smaller reaction volumes and with higher sensitivity than conventional methods.     

A differential approach to microstructure-dependent bounds for multiphase heterogeneous media

We present a new method of deriving microstructure-dependent bounds on the effective properties of general heterogeneous media. The microstructure is specified by the average Eshelby tensors. In the small contrast limit, we introduce and calculate the expansion coefficient tensors. We then show that the effective tensor satisfies a differential inequality with the initial condition given by the expansion coefficient tensors in the small contrast limit. Using the comparison theorem, we obtain rigorous bounds on the effective tensors of multiphase composites. These new bounds, taking into account the average Eshelby tensors for homogeneous problems, are much tighter than the microstructure-independent Hashin–Shtrikman bounds. Also, these bounds are applicable to non-well-ordered composites and multifunctional composites. We anticipate that this new approach will be useful for the modeling and optimal design of multiphase multifunctional composites.     

Elastic properties of RCC under flexural loading-experimental and analytical approach

In structural analysis, especially in indeterminate structures, it becomes essential to know material and geometrical properties of members. The codal provisions recommend elastic properties of concrete and steel and these are fairly accurate enough. The stress–strain curve for concrete cylinder or a cube specimen is plotted. The slope of this curve is modulus of elasticity of plain concrete. Another method of determining modulus of elasticity of concrete is by flexural test of a beam specimen. The modulus of elasticity most commonly used for concrete is secant modulus. The modulus of elasticity of steel is obtained by performing a tension test of steel bar. While performing analysis by any software for high rise building, cross area of plain concrete is taken into consideration whereas effects of reinforcement bars and concrete confined by stirrups are neglected. The aim of study is to determine elastic properties of reinforced cement concrete material. Two important stiffness properties such as AE and EI play important role in analysis of high rise RCC building idealized as plane frame. The experimental programme consists of testing of beams (model size 150 × 150 × 700 mm) with percentage of reinforcement varying from 0.54 to 1.63%. The experimental results are verified by using 3D finite element techniques. This study refers to the effect of variation of percentage of main longitudinal reinforcement and concrete grade. Effect of confinement is not considered and it appears in a separate study.     

An analytical approach for calculating vacuum properties of outgassing tubing systems

A method has been investigated to calculate vacuum properties, such as flow conductance and pressure drop, for complex tubing systems, taking into account the outgassing of the tube walls. The procedure is based on the determination of the pressure drop, Δp_i, of each tube element, starting at the chamber with a given mass flow rate, q_b1. The flow conductance, G, of the system follows from the overall pressure drop, ΔpΣⁿ_i Δp_i as $\text{G\&z.dbnd;q}{}_{\mathrm{b1}}\text{/Δp}$. The results are applied to analysing a vacuum system of the First Spacelab Payload.     

An approach to micro-macro modeling of heterogeneous materials

 A micro-macro strategy suitable for modeling the mechanical response of heterogeneous materials at large deformations and non-linear history dependent material behaviour is presented. When using this micro-macro approach within the context of finite element implementation there is no need to specify the homogenized constitutive behaviour at the macroscopic integration points. Instead, this behaviour is determined through the detailed modeling of the microstructure. The performance of the method is illustrated by the simulation of pure bending of porous aluminum. The influence of the spatial distribution of heterogeneities on the overall macroscopic behaviour is discussed by comparing the results of micro-macro modeling for regular and random structures. Received 9 July 2000     

A cleaner enzymatic approach for producing non-phthalate plasticiser to replace toxic-based phthalates

Clean Technologies and Environmental Policy - Dioctyl phthalate (DOP) is industrially commonly used as a polyvinyl chloride (PVC) plasticiser. As DOP does not form a chemical link with PVC, it...     

A nonholonomic approach to isoparallel problems and some applications

Isoparallel problems are a class of optimal control problems on principal fibre bundles endowed with a connection and a Riemannian metric on the base space. These problems consist of finding the shortest curve on the base among those with a given parallel transport operator. It has been shown that when the structure group of the principal bundle admits a bi-invariant metric, the normal solutions are precisely the projections of the geodesics (relative to an appropriate Riemannian metric) on the bundle. In this work we obtain a generalization of this result that holds true for any structure group, by transforming the isoparallel problem into a nonholonomic problem of a generalized type. The latter reduces to the geodesic problem if the structure group has a bi-invariant metric. We illustrate the theory with an application to the optimal control of an elastic rolling ball (the plate-ball system), relating some aspects of this problem to the dynamics of a simple pendulum. Finally, we indicate how the study of locomotion of microorganisms can benefit from this approach. This work shows how optimal control and generalized nonholonomic mechanics are related within the context of Lagrangian reduction.     

A powerful approach to develop nitrogen-doped graphene sheets: theoretical and experimental framework

Journal of Materials Science - We have reported a novel route to develop highly conductive graphene sheets using camphor as a natural precursor followed by nitrogen doping via low-temperature...     

Estimating shear properties of walnut wood: a combined experimental and theoretical approach

In this study, several theoretical models to numerically estimate shear properties of orthotropic materials are introduced. These approaches are based on the combination of Hankinson’s empirically derived formula with other empirical and analytical calculations. Next to shear moduli, which are estimated from the elastic moduli and Poisson’s ratios, shear strengths are also estimated from the in-axis strengths. The models are validated by mechanical tests on walnut wood (Juglans regia L.), for which a sufficient data set can be found in literature. The Arcan test is used to estimate the shear moduli, while the shear block test is used to estimate the shear strengths. The results show that the model, which is based on a combined use of Hankinson’s formula and tensor rotation, gives the best estimation of shear moduli as evaluated by the minimum differences to the experimentally obtained results. For the shear strengths, a combination of Hankinson’s formula and Norris’ failure criterion shows the best agreement in comparison to the experimental data. The theoretical calculations may be used for a time efficient estimation of shear modulus and strength in comparison to the very time-consuming experimental estimation.     

Axisymmetric analytical solutions for a heterogeneous multi-ferroic circular plate subjected to electric loading

In the present article, responses of an electrically loaded heterogeneous circular plate of transversely isotropic multi-ferroic materials are investigated. The axisymmetric problem is solved by adopting the direct displacement method developed by the second author. The corresponding generalized displacement functions are obtained through a step-by-step integration procedure. The coupling magneto-electro-elastic fields in the plate, which exactly satisfy the upper and lower boundary conditions and approximately meet the cylindrical boundary condition, are explicitly expressed. Numerical calculations are performed for two particular plates to investigate the influence of material heterogeneity.     

Structural stability of oligomeric proteins: A mean-field theoretical approach

We present a mean-field approach for calculating thermodynamic properties(free energies) of protein–solvent systems. We apply this method to thetumor suppressor protein p53, where we study the stability of itstetramerization domain when subjected to site-directed mutagenesis. Acomparison with experimental results is included.     

A continuum mechanics approach to some problems in subcritical crack propagation

The results of the so-called energetic approach to fracture for the cases of a sharp crack without and with a cohesive zone are briefly reviewed with particular attention to the crack tip singularity analysis and to the issue of energy dissipation due to crack propagation. The case of a crack with a cohesive zone removing all thermomechanical singularities is then further analyzed, focusing the attention on the question of the thermodynamic admissibility of subcritical crack growth, and on some of the hypotheses that lead to the derivation of subcritical crack growth laws. A two-phase cohesive zone model for discontinuous crack growth is presented and its thermodynamics analyzed, followed by an example of its possible application.     

A boundary element approach to some nonlinear equations from fluid mechanics

We consider a boundary integral approach to some nonlinear partial differential equations from fluid dynamics. The nonlinear equations are replaced by a sequence of linear equations, each of which is solved by the boundary element method. In order to avoid body integral contributions to the boundary integral equations, an approximate particular solution is first derived. This is achieved by replacing the body terms with an approximation for which there is a known solution. The present paper considers an approximation in terms of Gaussian distributions, a representation that has several desirable features.     

Depolarization of surface-enhanced fluorescence: an approach to fluorescence polarization assays

Localized surface plasmons of metallic particles of subwavelength sizes strongly modify the spectral properties of nearby fluorophores. The enhanced radiative decay rate leads to high fluorescence efficiencies and decreased fluorescence lifetimes. In this report we show that metal-enhanced fluorescence generated by the presence of the silver islands on the glass substrate displays high depolarization. Intensities, lifetimes, and emission anisotropies of several fluorophore protein conjugates have been studied in the absence and presence of metallic nanostructures. Despite highly decreased lifetimes of about 10-fold and immobilization of conjugates on the solid substrate, the observed emission anisotropies for all fluorophores on the metal-enhanced substrate decreased 300-500% compared to that in solution. This observation implies a new generation of fluorescence polarization immunoassays with broad applications because of no restrictions to the lifetime of the probe and the size of labeled biomolecules. The changes in polarization are due to binding that occur on the bioactive surface localized near the metal particles.     

An empirical approach to compare the performance of heterogeneous academic fields

In this paper, we propose a ‘scaling’ approach to compare the scientific performance of Italian heterogeneous academic disciplines. This method is based on the idea that, after eliminating the percentages of ‘silent’ researchers, the distribution of bibliometric parameters of the different academic fields can be superimposed and collapse into a unique master curve by a single scaling parameter. By using data on the scientific production of around 2,500 scholars of the university of Rome ‘La Sapienza’ from the Web of Science from 2004 to 2008, we (i) demonstrate the existence of a master curve, (ii) determine the scaling factors that work like rates of substitution to compare the scientific production across different academic fields on a common ground, (iii) show that the master bibliometric distribution follows a log-normal law and (iv) illustrate the relevance of the proposed approach for research assessment and allocation of competitive funding at the university level.     

Effective mechanical properties of EM composite conductors: an analytical and finite element modeling approach

An analytical model and numerical approach to predict the effective mechanical properties of a composite conductor consisting of metallic core and insulation layers are presented in this paper. The analytical model was developed based on a two-step homogenizations and mechanics analysis for composite unit cell. The Step 1 homogenization derives the effective properties of the out-wrapped composite insulation layers. The Step 2 homogenization further smears the metallic core and the effective composite insulation layers to develop homogenized mechanical properties for composite conductor according to appropriate homogenization sequences. The procedure of using numerical approach and finite element method to determine the unit cell effective constants were also described and the results of the FEA prediction were presented. The analytical predictions were compared well to the numerical results for the nine material constants that characterize the effective mechanical properties of the composite conductor.