Multilayer Theory Research Articles

Evaluation of Melter Slag as a Base Course Material

The demand for quality natural aggregates for use in pavement construction is approaching a critical state in some parts of New Zealand and other countries around the world. The search for alternative sources of aggregate to minimize the utilization of natural aggregates and provide a high quality substitute has led to slag. The purpose of this study was primarily to examine the engineering, environmental and economical issues relating to the utilization of melter slag as a base course material. New Zealand pavements are predominantly thin-surfaced unbound granular flexible pavements where the main design criterion is the vertical compressive strain at the top of the subgrade imposed by each axle load. Laboratory testing used Repeat Load Triaxial apparatus to determine the resilient modulus and permanent deformation characteristics of the melter slag aggregate and two traditional aggregate materials. The principles of multi-layer elastic theory were then used in a pavement design exercise to determine the engineering and economic benefits of the slag. Additives were also attempted in the laboratory testing to investigate the effect they would have on the melter slag aggregate. Results showed the performance of the slag exceeds that of the natural aggregates in terms of both resilient modulus and permanent deformation characteristics, and the addition of lime and cement binders enhanced these characteristics even further. The study also investigated various environmental and economic factors associated with the use of the slag and concluded that melter slag should be considered as an adequate substitute for traditional premium aggregates in road construction.

On the use of the Murakami's zig-zag function in the modeling of layered plates and shells

This paper discusses the use of the Murakami zig-zag function (MZZF) in the two-dimensional modeling of multilayered plates and shells. A literature overview of the available works is first presented. A `simple use' of the MZZF is discussed: the MZZF is used to introduce the zig-zag effect in classical and higher order theories which are formulated with only displacement unknowns. An `advanced use' of the MZZF is then considered to introduce the zig-zag effect in those theories which are formulated on the basis of both displacement and transverse stress assumptions. A number of new plate/shell theories has been considered. Numerical results encompassing, static, dynamic and thermally loaded orthotropic, simply supported plates and shells are presented to show both the effectiveness and limitations of the MZZF in the modeling of layered structures. Linear up to forth-order expansions for the in-plane and the out-of-plane displacements, in the thickness plate/shell direction, have been compared. It has been concluded that the MZZF is a valuable tool to enhance the performances of both classical and advanced theories. The conducted numerical evaluations have shown in particular that multilayered plate and shell theories can be greatly improved by the use of MZZF.

熱サイクルを受けるCSP実装体のたわみと応力の解析(J01-3 熱変形と衝撃,J01 エレクトロニクス実装における熱制御および信頼性評価)

In the present paper, a deformation induced in a new bonding technology of Chip Size Package (CSP) using resin encapsulation sheets is examined numerically and experimentally. Deflections after cooling from a bonding temperature are measured experimentally for various kinds of substrate and the thickness of an integrated circuit using a laser beam. In particular, a simple theory on the basis of a multilayered plate theory considering a viscoelastic property in the substrate and encapsulation are presented, arid the thermo-viscoelastic analysis for the deflection of CSP is performed. We could show that the simple formula for multilayered plates based on the thermo-viscoelastic theory can estimate fairly well the deflection of CSP in experiment.

Thermo-Viscoelastic Analysis of Deflection in CSP Electronic Device Packages

In the present paper, a deformation induced in a new bonding technology of chip-scale package (CSP) using resin encapsulation sheets is examined numerically and experimentally. Deflections after cooling from a bonding temperature are measured experimentally for various kinds of substrate and the thickness of an integrated circuit using a laser beam. In particular, a simple theory on the basis of a multilayered plate theory considering a viscoelastic property in the substrate is presented, and the thermo-viscoelastic analysis for the deflection of CSP is performed. Furthermore, the thermo-elastoplastic finite element method analysis is performed under the same temperature history. We could show that the simple formula for multilayered plates based on the thermo-viscoelatic theory can estimate fairly well the deflection of CSP in experiment.

Conformal field theory approach to bulk wave functions in the fractional quantum Hall effect

We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of non-unitary b/c-spin systems. These yield a promising conformal field theory analogon of the composite fermion picture of Jain. Fractional statistics is described by twist fields which naturally appear in the b/c-spin systems. We provide a geometrical interpretation of our approach in which bulk wave functions are seen as holomorphic functions over a ramified covering of the complex plane, where the ramification precisely resembles the fractional statistics of the quasi-particle excitations in terms of branch points on the complex plane. To extend Jain's main series, we use the concept of composite fermions pairing to spin singlets, which enjoys a natural description in terms of the particular c=-2 b/c-spin system as known from the Haldane-Rezayi state. In this way we derive conformal field theory proposals for lowest Landau level bulk wave functions for more general filling fractions. We obtain a natural classification of the experimentally confirmed filling fractions which does not contain prominent unobserved fillings. Furthermore, our scheme fits together with classifications in terms of K-matrices of effective multilayer theories leading to striking restrictions of these coupling matrices.

Historical review of Zig-Zag theories for multilayered plates and shells

This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1) Lekhnitskii (1935) was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2) Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian (1958), who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner (1984), who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3) On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, (LMT), Ambartsumian Multilayered Theory (AMT), and Reissner Multilayered Theory (RMT). As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4) LMT although very promising, has almost been ignored in the open literature. 5) Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6) RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references.

Theoretical determination of first adsorbed layer of water in methylcellulose

Analytical predictions for first adsorption layer of water as a function of relative humidity in hydrophilic materials were developed using multilayer adsorption theories (BET and GAB). These predictions were compared with experimental values of bound water adsorbed by methylcellulose reported in a previous paper. A proper analysis method is proposed that improves the determination of the physical parameters employed by the GAB theory. The applicability of the GAB and BET adsorption models employed in the study of condensable vapors or gas condensation is discussed.

Intermodulation in the spectrophotometric cell

Multiple reflections at cell walls give rise to modulation terms in the transmission coefficient of the beam passing through a spectrophotometric cell. Considering the cell as a planar layered system, these intrinsic modulation terms are subjected to numerical simulation according to a multilayer structure theory, assuming the system behaves as an infinitely thick medium contained between two layers that act as multilayered systems, which is approximated by a three layer system with a thicker second layer for simplicity. A frequency modulation is used to correct for lack of parallelism in cell walls. The degree of coherence of the incident beam is taken into account in the squared magnitude of the Fresnel transmission coefficient. The modulation pseudoperiod and an inner pseudoperiod are estimated, and noise in the average transmission signal due to intermodulation is explored.

Vibration and Damping Prediction of Laminates with Constrained Viscoelastic Layers--Numerical Analysis by a Multilayer Higher-Order-Deformable Finite Element and Experimental Observations

In this article, a multilayered and higher-order-deformable finite element is developed for free vibration analysis of multilayer-deformable laminates such as laminated plates with constrained viscoelastic interlayers. The developed finite element (FE) is based both on the multilayer theory and on the higher-order theory, in which the cubic variations of the in-plane displacements and the quadratic of the out-of-plane displacements are assumed for each discrete layer. In the present multilayer FE, the displacement continuity constrains at the layer interfaces are enforced through the penalty function method. For numerically predicting modal loss factors as damping effectiveness of laminates, the modal strain energy method is also implemented into the present FE analysis. In addition to the FE development, well-devised experimental measurements are conducted to obtain dynamic properties of several actually fabricated laminated coupons and sandwich panels, which contain some viscoelastic layers for improving damping performance. Comparisons of the numerical results by the present and the conventional FEs with the experimental results obtained are made to investigate the accuracy and validity of both the present FE and the experiment itself for dynamic characterization of such special-purpose, multilayer-deformable laminates and sandwiches as are dealt with in this study.

Traffic-Load-Induced Permanent Deformation of Road on Soft Subsoil

A method for predicting the traffic-load-induced settlement of road on soft subsoil with a low embankment is proposed. The traffic-load-induced dynamic stress in subsoil is calculated by the multilayer elastic theory (not covered in this paper). Then the plastic vertical strain in subsoil is calculated by an empirical equation, in which constants are related to the physical and mechanical properties of subsoil. The method was applied to analyze three different cases in Saga, Japan. Comparisons of the calculated values with field data indicate that the proposed method can provide a reasonable prediction of traffic-load-induced permanent settlement of the road on soft subsoil with a low embankment. The method is useful for designing the road with a low embankment on soft subsoil. For the cases studied with embankment thickness of 0.75 to 2.7 m, the depth significantly influenced by traffic load is about 6 m below the base of the embankments.

Anomalous dispersion and superluminal group velocity in a coaxial photonic crystal: Theory and experiment

We demonstrate that coaxial cables with a periodic impedance exhibit dispersion properties specific to photonic crystals, albeit on a much lower frequency scale. Highly superluminal (>2c) pulse propagation is observed near the photonic band gap at 10 MHz. The influence of group velocity dispersion and crystal length on the traveling speed and shape of a Gaussian pulse are discussed. Results compare favorably with a simple multilayer theory and a coupled-mass model of the structure.

OVERLAY DESIGN WITH CTAM FOR AIRPORT ASPHALT PAVEMENTS

Design method of overlay using cement treated asphalt material (CTAM) was developed for airport asphalt pavements, not only to reduce the time during which the facility is closed for pavement rehabilitation but to have high durability against heavy duty aircraft loadings. First, mechanical properties of CTAM are investigated in laboratory tests, and an in situ construction test was conducted. Based on these, the structural design method of overlay construction was finally developed by the use of multi-layered elastic theory in consideration of joints in CTAM.

Georgina Born and David Hesmondhalgh, eds. Western Music and Its Others: Difference, Representation, and Appropriation in Music. Berkeley: University of California Press, 2000. xi, 360 pp. ISBN 0-520-22083-8 (hardcover), ISBN 0-520-22084-6 (paperback) Pirkko Moisala and Beverley Diamond, eds. Music and Gender. Urbana and Chicago: University of Illinois Press, 2000. ix, 376 pp. ISBN 0-252-02544-X (hardcover), ISBN 0-252-06865-3 (paperback)

Georgina Born and David Hesmondhalgh, eds. Western Music and Its Others: Difference, Representation, and Appropriation in Music. Berkeley: University of California Press, 2000. xi, 360 pp. ISBN 0-520-22083-8 (hardcover), ISBN 0-520-22084-6 (paperback). Pirkko Moisala and Beverley Diamond, eds. Music and Gender. Urbana and Chicago: University of Illinois Press, 2000. ix, 376 pp. ISBN 0-252-02544-X (hardcover), ISBN 0-252-06865-3 (paperback). Over the last decade of the 20th century, music scholarship inched its way towards the kind of engagement with critical theory long embraced by the other arts.1 With the two books under review here, Western Music and Its Others: Difference, Representation, and Appropriation in Music and Music and Gender, music scholarship has achieved a sophisticated marriage of music and critical theory. Gone is the sometimes tiresome confessional tone of early musicology, largely absent is the glossing of musical materials too often found in sociological books on popular music. The hallmark of both volumes is their conscientious effort to map out explicit methodological and theoretical territory. Both books are rigorous, adventurous, and carefully considered collections of essays that serve as important models for the training of young scholars. My motivation for writing this review comes from my use of essays from these books in two different courses on music and identity in recent years. Interestingly, the first course was a cultural studies seminar, while the second was taught to upper-year music students.2 I was much struck by the fact that the material could be useful in such different contexts. My cultural studies students had uneven competence in music theory and history, while my music students were largely unfamiliar with critical theory. Both groups engaged in ongoing, lively debate generated by the ideas raised in these books. This review will not attempt a comprehensive description of each essay contained in both volumes. Rather, I will address particular pieces for their relevance as pedagogical material, giving greater attention to Western Music and Its Others, as a full review of Music and Gender will appear in a forthcoming issue of CUMR.3 I want to argue that if a critical and interdisciplinary approach to musical scholarship is to be useful in the academy, we must integrate it into the training of undergraduates, rather than waiting to deprogram our graduate students. MAPPING A CRITICAL THEORY OF MUSIC Of particular value in both books are the detailed introductory essays, which go beyond describing their distinct projects by advancing exciting theoretical possibilities for musical scholarship. In Western Music and Its Others, Georgina Born and David Hesmondhalgh map a complex terrain marked by working across musical sub-disciplines (musicology, ethnomusicology, popular music studies and film music studies), in order to think through a range of cultural issues. These are expressed as a number of relationships (between Orientalism/Postcolonialism, Modernism/Postmodernism, and Fusion/Hybridity) through which issues of identity, representation, and appropriation may be examined. The authors skillfully negotiate this potentially unwieldy combination of attitudes and lenses, identifying a number of core conceptual problems present in any critical approach to the study of music. At the centre is the need for a multi-layered theory that is both processual and homological, understanding that music can both construct new identities and reflect existing ones (p. 31). I found this weighty (fifty-eight page) essay most useful near the end of my courses on music and identity. Once familiar with the specific essays in the book, students were better able to track its dense argument and range of theoretical terms. In their introduction to Music and Gender, Beverley Diamond and Pirkko Moisala reveal a more closely defined project: that of articulating a feminist ethnomusicology, expressed within a postcolonial frame that recognizes the fluid and relational nature of culture (p. …

Measurement of coatings' elastic properties by mechanical methods: Part 1. Consideration on experimental errors

A critical analysis of some mechanical methods employed for measuring the elastic properties of coatings is presented. A rational basis for properly choosing test methods, transducers and layer thicknesses is provided. The analyzed methods, usually applied to relatively thick coatings, include four-point bending tests and the resonance technique. General relationships for the evaluation of coatings' elastic properties, derived from the multilayer beam and plate theories, are discussed. On the basis of the error propagation theory, for different combinations of materials and layer thicknesses, the influence of typical experimental errors, test setup parameters and material properties is analyzed, and sensitivity coefficients for relative errors are discussed. The critical experimental variables and their effect on measurement accuracy are highlighted, suggesting suitable conditions for selecting specimen geometry and testing conditions. A procedure for measurement at high temperature is outlined.

General theory of sub-quarterwave multilayers with highly absorbing materials.

A general theory of multilayers with enhanced reflectance has been developed based on the superposition of sub-quarterwave layers of various highly radiation-absorbing materials. The theory has been developed by second-order expansion of the multilayer reflectance with respect to the optical-constant differences between the materials in the multilayer. The current paper completes and improves the theory that was developed in a previous paper [J. Opt. Soc. Am. A 18, 1406 (2001)] by including the case of nonnormal incidence and general radiation polarization and by providing more-accurate film thickness values of the optimized multilayer than with the previous theory. The theory provides an accurate approach to the design of a new concept of multilayer coatings with more than two materials. The new multilayers are adequate to enhance the reflectance of the materials particularly in the far and the extreme ultraviolet.

Optical Characteristics of Self-Assembled Ultrathin Films of Tetra-Copperphthalocyanine by Attenuated Total Reflection

Multilayer thin films consisting of alternate layer-pairs of cationic macrocycles (tetra-copperphthalocyanine) and anionic macromolecules (polyethylenimine) were fabricated on thin silver film using alternate electrostatic self-assembly technique. The optical properties of the film were characterized by uv-vis absorption spectra and attenuated total reflection measurements. From the data analysis based on the multilayer reflection theory, it was shown that the ultra thin films were successfully fabricated by self-assembly technique with the mean layer-pairs thickness of 25 Å. Moreover, especially for tetra-copperphthalocyanine layer, we obtained the anisotropy in dielectric constants with respect to the surface normal, indicating anisotropic orientation of the tetra-copperphthalocyanine molecules on the polyethylenimine layer.

Reflectance enhancement with sub-quarterwave multilayers of highly absorbing materials.

A new theory of multilayers with enhanced normal reflectance has been developed based on the superposition of a few layers of various different radiation-absorbing materials. Every layer in the multilayer had a subquarterwave optical thickness. The theory was developed for materials with small refractive-index differences, although it is also valid in some cases for materials with large refractive-index differences. Reflectance enhancements were obtained in a very broad band and over a wide range of incidence angles. The theory is particularly suited to designing multilayers with enhanced reflectance in the extreme ultraviolet for wavelengths above 50 nm. In this spectral region the reflectance of single layers of all materials is relatively low, and standard multilayers are not possible because of the high absorption of materials.

Scattering and radiation from a fluid-loaded coated cylindrical shell

A common question when dealing with fluid-loaded coated structures is how well a normally reacting coating layer models the radiation and scattering from a fluid-loaded coated cylindrical. Modeling with a normally reacting layer simplifies the model which therefore allows more complex conditions to be analyzed. To explore this question analytic solutions are obtained for the scattering from a fluid-loaded cylindrical shell with a compliant coating using both multilayer shell theory [L. Flax and W. G. Neubauer, J. Acoust. Soc. Am. 61, 307 (1977)], and a normally reacting coating solution [J. M. Cuschieri and D. Feit, J. Acoust. Soc. Am. 107, 3196 (2000)]. The similarities and differences in the scattering results that are obtained using either of these two approaches are presented for different coating thicknesses and characteristics.

Pavement Design in Takalimakan Desert

The design method for pavements in the Takalimakan desert was proposed through the investigation of test roads and theoretical analysis. The function of geotextile in pavement structures is analyzed by the shear lag model, with a result that the shear bearing capacity of geotextile is proportional to its tensile modulus and the second derivative of its tensile deformation. Combining the layer-peeling method, a bearing plate method, and modulus back—calculation, the modulus of resilience of each layer in the pavement structure is determined. By means of multilayer elastic theory, the influence of contact conditions in the pavement on the tensile stresses and displacement is quantitatively analyzed. Stresses for unbonded wearing course and gravel-base course increase by more than four times. Change of contact conditions has little effect on the surface deflection. Therefore, the variation of surface deflection cannot reflect the shear instability between subbase and subgrade. Direct shear testing must be ut...

Homeotropic polar anchoring energy of a nematic liquid crystal using the fully leaky waveguide technique

Optical excitation of a series of fully leaky guided modes has been used to explore the director distortion of a hybrid-aligned nematic liquid crystal with a negative dielectric anisotropy (Merck-BDH, MLC 6608) under application of an ac electric field. Hybrid alignment is realized by the use of a lecithin film on the top glass plate and rubbed polyimide on the bottom plate, both plates having indium–tin–oxide coatings. Continuum theory is used to model the director profile through the cell. Fitting the fully leaky guided mode data both in transmission and reflection using optical multilayer theory together with continuum modeling gives the director profile both with and without applied fields. From this fitting the changes in the surface tilt angle and its gradient are obtained. Using this information the polar anchoring coefficient of the homeotropic surface Wθ is deduced. At 23.1 °C we find Wθ=(4.6±0.2)×10−4 J m−2.