Cylinder Arrangement Research Articles

Homogenization of Dissipative Photonic Crystals

We consider propagation of the H- and E-modes in a periodic arrangement of dissipative dielectric cylinders. Using the plane-wave expansion method, we derive analytical formulas for the imaginary part of the low-frequency efiective dielectric constants. The formula for the anti-Hermitian part of the efiective dielectric tensor is valid for arbitrary Bravais lattice and arbitrary fllling fractions.

Self-Assembly of Cylinder-Forming Block Copolymers on Ultrananocrystalline Diamond (UNCD) Thin Films for Lithographic Applications

AbstractBlock copolymers (BCPs) consist of two or more chemically distinct and incompatible polymer chains (or blocks) covalently bonded. Due to the incompatibility and connectivity constraints between the two blocks, diblock copolymers spontaneously self-assemble into microphase-separated nanoscale domains that exhibit ordered 0, 1, 2 or 3 dimensional morphologies at equilibrium. Commonly observed microdomain morphologies in bulk samples are periodic arrangements of lamellae, cylinders, or spheres. Block copolymer lithography refers to the use of these ordered structures in the form of thin films as templates for patterning through selective etching or deposition. The self-assembly and domain orientation of block copolymers on a given substrate is critical to realize block copolymer lithography as a tool for large throughput nanolithography applications. In this work, we survey the morphology of cylinder-forming block copolymers by atomic force microscopy (AFM). Three kind of block copolymers were studied: a) poly(styrene-block-ferrocenyldimethylsilane), PS-b-PFS b) poly(styrene-block-methylmethacrylate), PS-b-PMMA and c) poly(styrene-block-dimethylsiloxane) PS-b-PDMS. Block copolymers were dissolved in a neutral solvent for both blocks (toluene) in order to obtain solutions of various concentrations (1 and 1.5 wt %). From these solutions, films were prepared by spin casting on ultrananocrystalline diamond (UNCD) thin film substrates. Results indicate that PS-b-PFS exhibits chemical and morphological compatibility to the UNCD surface in terms of wetting and domain control. A systematic comparison of self-assembly of these polymers on silicon nitride substrates demonstrates that UNCD thin films would require pre-treatment to be considered as a substrate for BCP lithography.

Numerical Investigation of Laminar Unsteady Wakes Behind Two Inline Square Cylinders Confined in a Channel

Two-dimensional numerical investigations have been carried out to study the behavior of unsteady wake for flow past an inline arrangement of square cylinders confined in a channel. The present work aims to study the influence of the relative size and arrangement of the two cylinders on vortex shedding characteristics in their wakes. A computational code has been developed using finite difference approach based on modified MAC algorithm for solution of governing flow equations. Effect of size ratio of the two cylinders, the cylinder spacing in streamwise direction and flow Reynolds number on the wake flow characteristics of the two cylinders have been presented. The temporal characteristics of the wake are analyzed using time series analysis. Results indicate that for a given Reynolds number, there exist a range of values of size ratio and cylinder spacing for which vortex shedding can occur in the wake of the upstream cylinder.

A simple formula for the effective complex conductivity of periodic fibrous composites with interfacial impedance and applications to biological tissues

This paper presents a simple analytical expression for the effective complex conductivity of a periodic hexagonal arrangement of conductive circular cylinders embedded in a conductive matrix, with interfaces exhibiting a capacitive impedance. This composite material may be regarded as an idealized model of a biological tissue comprising tubular cells, such as skeletal muscle. The asymptotic homogenization method is adopted, and the corresponding local problem is solved by resorting to Weierstrass elliptic functions. The effectiveness of the present analytical result is proved by convergence analysis and comparison with finite-element solutions and existing models.

Acoustic cloaking by two-dimensional sonic crystals

It has been previously shown that a two dimensional sonic crystal made of a periodic arrangement of solid cylinders in air behaves in the low frequency limit (homogenization) like an acoustic metamaterials with anisotropic effective density and isotropic effective bulk modulus [D. Torrent and J. Sanchez-Dehesa, New J. Phys. February 2008]. Here, the homogenization method is extended to the case of sonic crystals with two types of cylinders in the unit cell, and analytical expressions for the anisotropic effective density are then obtained. Moreover, it will be shown how these new acoustic metamaterials can be used to physically realize the solution for the acoustic cloaking proposed by Cummer and Schurig [New. J. Phys., vol. 9, 45, 2007] [Work supported by MEC of Spain.]

Anisotropic mass density by two-dimensional acoustic metamaterials

We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define (in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.

Crystalline phases in chiral ferromagnets: Destabilization of helical order

In chiral ferromagnets, weak spin-orbit interactions twist the ferromagnetic order into spirals, leading to helical order. We investigate an extended Ginzburg-Landau theory of such systems where the helical order is destabilized in favor of crystalline phases. These crystalline phases are based on periodic arrangements of double-twist cylinders and are strongly reminiscent of blue phases in liquid crystals. We discuss the relevance of such blue phases for the phase diagram of the chiral ferromagnet MnSi.

An Experimental Study on Forced Convection Heat Transfer From An Embedded Horizontal Cylinders Array in A Porous Medium in Cross Flow

An experimental study on forced convection heat transfer from an embedded horizontal cylinders array in a porous medium in cross flow was carried out under constant heated cylinder surface temperature condition. The study included the effect of Peclet number, heated cylinder location in array, and the spaces between cylinders on the heat loss ability from this cylinder, as well as the enhancement in heat transfer rate due to embedding the cylinders array in a porous medium. An experimental set-up was used for this purpose which consists of a blower, air duct, test section, and heating element which is represented by a copper cylinder with a diameter of (12.7 mm) heated internally by an electrical source, which represents transfer and heat loss element through this set-up. The experiments were done at the range of spacing ratios between (1.2 ≤ S / D ≤ 2 ) for the cylinders array consisting of five embedded horizontal cylinders in a porous medium consisted of Alumina granules with a particle diameter rate of (3.938 mm) in a turbulent flow at Peclet numbers between (15 < Pe < 56 ). The study showed that the ability of heated cylinder to heat loss is a function of Peclet number, its location in array, and the spaces between cylinders. This ability is increased by increasing Peclet number, and it was shown that this ability reaches maximum value at the third cylinder in array at a spacing ratio of (S/D=1.6) and also at the fourth cylinder in array at a spacing ratio of (S/D=1.4). Also, it was shown that the heated cylinder at any location in array for almost spacing ratios, there was an increase in the heat transfer as maximum (21%) in comparison with a single embedded cylinder in a porous medium. It was noticed that the maximum enhancement value of heat transfer from a heated cylinder in cylinders array (due to embedding it in a porous medium) was nearly five times the heat that transferred from the same free cylinders array or arrangement at the same flow velocity depending on available data from preceding experimental study.

Combined Forced- and Natural-Convection Heat Transfer in Horizontally CounterRotating Eccentric and Concentric Cylinders

The present investigation focuses on the numerical simulation of mixed-convection heat transfer in a horizontal annulus configuration. The flow is set to operate in the laminar regime under steady-state condition. A counterrotating cylinder arrangement is considered while the inner cylinder is heated. A nonuniform grid size is employed in the radial direction to capture the velocity and temperature distributions near the walls. Furthermore, discretization of the governing equations is achieved using a finite-element scheme based on the Galerkin method of weighted residuals. The flow and thermal characteristics are explored for a pertinent range of dimensionless velocity ratio, gap-width ratio, and Rayleigh number given by 0 ≤ κ ≤ 5, 0.5 ≤ σ ≤ 5.0, and 103 ≤ Ra ≤ 105 while eccentricity factor ϵ(r, φ) is varied over various radial and angular positions. The local Nusselt number distributions along the cylinders are documented over a range of operating conditions.

Effect of interface on thermodynamic behavior of liquid crystalline type amphiphilic di‐block copolymers

AbstractIn PEOm‐b‐PMA(Az)n amphiphilic diblock copolymers, nanoscale structures exhibit an hexagonal‐packed PEOm cylinders arrangement. To precisely investigate the role of interfacial interactions between hydrophilic PEOm and hydrophobic PMA(Az)n including mesogene sequences in the side chains, at the isotropic transition, polymer systems are submitted to thermal and barometric effects under hydrostatic pressure. The thermodynamic investigation is based on the original coupled calorimetric‐PVT technique, yielding scanning transitiometry. Three phase diagrams can be represented versus pressure: (1) isotropic temperature described by Clapeyron equation (Tiso vs. P), (2) change of volume of the system (ΔViso vs. P), (3) entropy of the system (ΔSiso vs. P). In presence of mercury as pressure transmitting fluid, (dTiso/dP) as well as ΔViso and ΔSiso are larger for a PMA(Az)n homopolymer compared to those for the investigated copolymer. Additional calculations of ΔSiso using thermal and mechanical effects give consistent results. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1354–1364, 2007

Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T

First and second normal stress differences of a 50 vol.% magnetorheological fluid (MRF) are investigated by using a commercial plate–plate magneto-rheometer (Anton Paar GmbH) with plate–plate and cone–plate geometry. The manufacturer modified the instrument to achieve higher normal force (60 N) and torque (295 mNm) capacity. An additional modification by us allows an online determination of the true magnetic flux density B in the MRF by means of a Hall probe. FEM Maxwell 2D simulations quantitatively verify the Hall probe results and give detailed insight into the radial flux density profile within the MRF sample. Without shear, the static normal force F N for plate–plate increases as a power law: F N ∝ B 2.4. A similar magnitude is found for cone–plate geometry, in contrast to the expectation. For steady shear at 10 s −1, the plate–plate normal force built-up limits the experiments at high flux densities rather than the torque generated. The normal forces increase linearly with the shear stress at high flux density. The first normal stress difference N 1 is positive and about five times larger than the shear stress. The second normal stress difference N 2 is also positive. The experimentally derived N 2/ N 1 ratio of 1/4 distinctly deviates from theoretical predictions ( N 2/ N 1 = −1) for a semi-dilute MRF. Improvements of the radial flux density profiles are required to verify the normal stress difference ratio and to support the conjecture that the positive but small N 2 is a consequence of the densely packed MRF, which does not allow to create extended chain-like structures. As shown in the appendix, the experimentally determined N 2/ N 1 ratio is favorable to stabilize concentricity in concentric cylinder arrangements, relevant for the MRF application in clutches.

Low-frequency index of refraction for a two-dimensional metallodielectric photonic crystal

We calculate analytically the effective index of refraction ${n}_{eff}$ of a periodic arrangement of nonmagnetic metallic cylinders in the low-frequency limit. At $\ensuremath{\omega}\ensuremath{\rightarrow}0$ the dielectric constant of the cylinders is singular, ${ϵ}_{m}(\ensuremath{\omega})\ensuremath{\approx}\ensuremath{-}({\ensuremath{\omega}}_{p}∕\ensuremath{\omega}{)}^{2}$, allowing propagation in the plane of periodicity of a mode with the magnetic field parallel to the cylinders ($H$ polarization). The in-plane electric field induces eddy currents, which are localized in a narrow skin layer. We show that the magnetic moment of the eddy currents leads to diamagnetic response if the radius of the cylinders is larger than the skin depth $\ensuremath{\delta}\ensuremath{\sim}{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\mathrm{cm}$. Otherwise, the cylinders are transparent for the electromagnetic field and their magnetic moment can be neglected. Magnetization of the cylinders gives rise to distinct values of the quasistatic and static indices of refraction and explains a paradox with noncommuting limits ${ϵ}_{m}\ensuremath{\rightarrow}\ensuremath{\infty}$ and $\ensuremath{\omega}\ensuremath{\rightarrow}0$.

Anisotropic dynamical mass density by two-dimensional arrays of solid cylinders in air

The long wavelength limit (homogenization) of two‐dimensional (2‐D) periodic arrangements of elastic cylinders in a fluid or a gas (i.e., sonic crystals) is analyzed through the linear part of their band structure. It is found that sonic crystals behave (in the homogenization limit) as effective metamaterials with anisotropic dynamical mass density and fluidlike speed of sound. The special case of rigid cylinders embedded in several 2‐D lattices is studied here. It is shown that these systems are suitable to build 2‐D anisotropic fluidlike metamaterials. Finally, the reflection and transmission through an anisotropic‐elastic medium will be discussed. [Work supported by MEC of Spain and GVA of Valencia.]

A gradient index sonic lens based on acoustic metamaterials

We report a method to design and characterize broadband gradient index lenses. The lenses are based on two‐dimensional sonic crystals, which are periodic arrangements of elastic cylinders embedded in air. It will be shown that gradient index sonic lenses built with rigid cylinders are more powerful than conventionally curved lenses. We also demonstrate that the designing possibilities increased by considering the mixture of two types of cylinders in the sonic crystal. So, a gradient index lens with zero reflectance at the surface is proposed by employing a mixture of aerogel and rigid cylinders. Finally, a multiple scattering theory has been employed to compare the performance of conventionally curved lenses and gradient index lenses. [Work supported by MEC of Spain and GVA of Valencia.]

Numerical simulation for aerodynamic characteristics of two circular cylinders in staggered arrangement by a third-order upwind finite element method

We present numerical results for flow patterns around two circular cylinders in a staggered arrangement, and fluid forces of the cylinders which are placed in a uniform flow. The numerical results for flow around two circular cylinders are obtained by two- and three-dimensional computations. The distances of the in-line and transverse directions between the centers of two circular cylinders are taken into consideration as the parameters of the computation. Stabilization of numerical solutions is achieved by using a third-order upwind finite element method. In the case of tandem arrangement of the circular cylinders, it is well known from experimental data that, when two circular cylinders are placed at a distance of approximately diameters between the centers of cylinders, the fluid forces of both cylinders vary suddenly. Therefore, in this paper, the circular cylinders are put at two kinds of distances of 3- and 4-diameters to the in-line direction and are also put at distances of diameters to the transverse direction. The obtained results for two circular cylinders in the staggered arrangement are qualitatively compared with experimental data.

Correlation between single-cylinder properties and bandgap formation in photonic structures

The origin of frequency gaps in the dispersion relation of periodic, quasi-periodic, and random photonic structures consisting of different arrangements of dielectric cylinders has been investigated. For TM polarization it was found that the formation and properties of gaps are strongly affected by Mie resonances of a single cylinder. Both the spectral position and size depend on the properties of this single scatterer. In contrast, for TE polarization no correlation between the scattering properties and bandgap formation was found, as Mie resonances are spectrally not well separated. For the inverted structure consisting of air cylinders in a dielectric material, the frequency gaps depend on the spatial arrangement of the cylinders because no pronounced Mie resonances exist in this case.

Numerical research on heat transfer enhancement for high Prandtl-number fluid

The molten salt, Flibe, has been recommended as a candidate coolant material in the blanket system of the FFHR fusion reactor though it is high Prnadtl-number ( Pr) fluid that leads to low heat transfer performance. This paper, describes the results of numerical simulations performed in order to estimate the effects of cylinders as obstructions for heat-transfer enhancement in high- Pr fluid duct flow. Two-dimensional thermofluid simulations were performed for cases with 44, 24 and 48 cylinders, respectively, inserted perpendicularly to the fluid flow, and acting as heat transfer enhancers between parallel plates. From these analyses, the flow contraction created by the cylinders causes a high-vorticity around the heated wall. This high-vorticity plays an important role in the heat-transfer enhancement. In the high-vorticity region, the momentum perpendicular to a wall has a large gradient along the stream direction. In fact, the fluid flows down while rotating and “washing” the heated wall. This effect is also governed by the arrangement of cylinders. A staggered arrangement is adopted in the case with 44 cylinders, while square arrangement is employed in the cases with 24 and 48 cylinders. The enhancement of perpendicular flow is very effective when using a staggered arrangement, procuring a higher heat transfer downstream of the cylinders. The estimated pressure drop for high- Pr fluid flow was larger for the with 44 cylinders than for the cases with 24 and 48 cylinders. This result indicates that the heat transfer of high- Pr fluid flow strongly depends on the effect of flow stirring caused by obstructions.

Template Cross-Linking Effects on Morphologies of Swellable Block Copolymer and Mesostructured Silica Thin Films

Mesostructured silica films were formed from cross-linked poly(d8-styrene-block-2-vinylpyridine) (dPS-b-P2VP) diblock copolymer template films by swelling with silica precursor solutions. The mesoscopic and macroscopic morphologies of the resulting materials depended strongly on the extent of P2VP cross-linking. Without cross-linking, extensive rearrangement of the initial 2D hexagonal arrangement of dPS cylinders took place during swelling, leading to wormlike mesostructures. At low extents of template cross-linking, osmotic stresses led to a surface-wrinkling instability with a morphology directed by the anisotropic mechanical properties of the swelled block copolymer mesostructure. At higher degrees of P2VP cross-linking, wrinkling was suppressed, and the composite silica/polymer mesostructures corresponded to essentially affine expansions of the initial template structures normal to the film plane. At low extents of P2VP cross-linking, the mesostructures of the hybrid block copolymer/silica films were preserved during oxidation and removal of the block copolymer template species, leading to stable mesoporous silica films. At high extents of P2VP cross-linking, however, insufficient amounts of silica were incorporated to form stable porous inorganic materials, leading to mesostructural collapse. An intermediate level of cross-linking allowed the preparation of stable mesoporous silica films with structures that closely resembled those of the initial template films.

Overall electromechanical properties of a binary composite with 622 symmetry constituents.: Antiplane shear piezoelectric state

A binary composite is studied here, where the electroelastic properties of the constituent materials belong to the crystal class 622. A square arrangement of long continuous circular cylinders, the fiber phase, embedded in a homogeneous medium is consider here. The composite is in a state of antiplane shear piezoelectricity, that is, a coupled state of out-of-plane mechanical displacement and in-plane electric field, which is characterized by three electroelastic parameters: longitudinal shear modulus, shear stress piezoelectric coefficient and transverse dielectric constant. Our interest here lies in the determination of its effective properties. They are derived by means of the method of two spatial scales. Closed-form expressions are obtained for them. Only one of the four local (or canonical) problems that arise is needed. Two properties are thus found. The Milgrom–Shtrikman compatibility relation is used to fix the remaining one. The local problem is solved using potential methods of a complex variable. The solution involves doubly periodic Weierstrass elliptic and related functions. The final formulae for the overall properties show explicitly the dependence on (i) the properties of the phases, (ii) the radius of the cylindrical fiber and (iii) the lattice sums associated with the square array. The shear modulus is shown to depend explicitly not only on the rigidity of the phases but also on their piezoelectric and dielectric coefficients. Some natural organic substances have the symmetry 622 like collagen. Recently Silva et al. measured its electroelastic properties. Their data is used to show some numerical results of the derived formulae as a function of the fiber volumetric fraction.

Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders

The two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders is studied. The incident Gaussian beam is expressed as a superposition of plane waves of different amplitudes and different incident angles, using the plane-wave spectrum technique based on Fourier optics. For each plane wave, the scattered field is calculated with the T-matrix of an isolated circular cylinder and its lattice sums characterizing a periodic arrangement of the circular cylinders. The circular cylinders may be perfect conductors, dielectric or gyrotropic cylinders, as long as their T-matrices are known.