Parallel Cylinders Research Articles

Generalisation of the method of images for the calculation of inviscid potential flow past several arbitrarily moving parallel circular cylinders

An application of the conventional method of images is sufficient for the calculation of the velocity profile of potential flow of inviscid fluid past two moving cylinders. In this case, the flow is described by the potential of an infinite sequence of dipoles. However, for a description of flow past more than two cylinders, the conventional method of images fails and there is a need for its generalisation. To achieve this aim, the flow is represented as a sequence of levels of dipoles. Each consecutive level added to the solution makes the velocity attained on the cylinders’ walls closer to the boundary conditions. The whole procedure is documented through a calculation of the potential flow about a cylinder moving arbitrarily between two parallel walls. The generalised method of images is verified by means of the already known solutions of the special cases.

Solvent Dependence of the Morphology of Spin-Coated Thin Films of Polydimethylsiloxane-Rich Polystyrene-block-Polydimethylsiloxane Copolymers

The as-spun, thin film morphologies of a series polydimethylsiloxane-rich cylinder and lamellar-forming polystyrene-block-polydimethylsiloxane (PS-b-PDMS) copolymers with constant PDMS molecular weight and varying PS volume fraction were studied with a range of solvents of varying solubility parameter. It was found that PDMS occupies the surface of the thin films regardless of the choice of solvent used in spin-coating due to its extremely low surface tension. The morphology shifted from parallel cylinders to hexagonally perforated lamellar to parallel lamellar as the solvent was varied from PDMS to PS selective solvents (increasing solvent solubility parameter). The transition points between each morphology were also dependent on the volume fraction of the block copolymer where the transitions were observed at lower solubility parameter with increasing PS volume fraction of the polymer. The morphology variations are attributed to selective swelling effects of the individual blocks even under good solvent conditions. These results are discussed in the context of current theories of solvent evaporation induced ordering of block copolymer thin films.

Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence

The near field solution for the scattering of a plane monochromatic electromagnetic wave by an ensemble of parallel infinite dielectric cylinders at perpendicular incidence is presented in this paper. The solution is given for the calculation of the electric and magnetic near fields and the Poynting vector. A MATLAB program has been developed to solve the near field formulas which is introduced and validated. The near to far field transition as well as formation and transport of photonic nanojets have been calculated for multiple cylinder scattering.

Quantitative characterization of the microstructure and transport properties of biopolymer networks

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation and the Torquato approximation. The Hashin–Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Torquato and Yeong (1997 J. Chem. Phys. 106 8814). We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed.

Localized surface plasmon modes in a system of two interacting metallic cylinders

We study an optical response of a system of two parallel close metallic cylinders having nanoscale dimensions. Surface plasmon excitation in the gap between the cylinders are specifically analyzed. In particular, resonance frequencies and field enhancement were investigated as functions of geometrical characteristics of the system and Ohmic losses in the metal. The results of numerical simulations were systematically compared with the analytical theory, obtained in the quasi-static limit. The analytical method was generalized in order to take into account the retardation effects. We also present the physical qualitative picture of the plasmon modes, which is validated by numerical simulations and analytical theory.

Numerical investigation of effects of buoyancy around a heated circular cylinder in parallel and contra flow

Two-dimensional, steady, incompressible Navier-Stokes and energy equations are expressed in the stream function/vorticity formula- tion and solved numerically by finite difference method to study effects of buoyancy on fluid flow and heat transfer from a horizontal circular cylinder. The cylinder is exposed to approaching flow stream, for parallel (parallel flow) and opposing (contra flow) directions to the buoyant force. Two different thermal boundary conditions were considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results elucidating the dependence of the flow and heat transfer characteristics on the Richardson number 02 Ri ≤≤ , Prandtl number 0 100 Pr ≤≤ and Reynolds number 0 40 Re ≤ ≤ are presented. Overall, for parallel flow regime, an increase in the Ri led to a raise in both Nusselt number and drag coefficient. However, for contra flow regime, these trends were reversed. For both regimes, the aforementioned behaviors were more pronounced for CT boundary condition than that for the CHF boundary con- dition.

Water wave problems using null-field boundary integral equations: ill-posedness and remedies

In this article, we focus on the hydrodynamic scattering of water wave problems containing circular and/or elliptical cylinders. Regarding water wave problems, the phenomena of numerical instability due to fictitious frequencies may appear when the boundary element method (BEM) is used. We examine the occurring mechanism of fictitious frequency in the BEM through a water wave problem containing an elliptical cylinder. In order to study the fictitious frequency analytically, the null-field boundary integral equation method in conjunction with degenerate kernels is employed to derive the analytical solution. The modal participation factor for the numerical instability of zero divided by zero can be exactly determined in a continuous system even though the circulant matrix cannot be obtained in a discrete system for the elliptical case. It is interesting to find that irregular values depend on the geometry of boundaries as well as integral representations and happen to be zeros of the mth-order (even or odd) modified Mathieu functions of the first kind or their derivatives. To avoid using the addition theorem to translate the Bessel functions to the Mathieu functions, the present approach can solve for the water wave problem containing circular and/or elliptical cylinders at the same time in a semi-analytical manner by using the adaptive observer system. The closed-form fundamental solution is expressed in terms of the degenerate kernel in the polar and elliptic coordinates for circular and elliptical cylinders, respectively. Three examples are considered to demonstrate the validity of the present approach, including an elliptical cylinder, two parallel identical elliptical cylinders and one circular cylinder and one elliptical cylinder. Finally, two regularization techniques, the combined Helmholtz interior integral equation formulation method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

Lamb waves in phononic crystal slabs: Truncated plane parallels to the axis of periodicity

A theoretical study is presented on the propagation properties of Lamb wave modes in phononic crystal slabs consisting of a row or more of parallel square cylinders placed periodically in the host material. The surfaces of the slabs are parallel to the axis of periodicity. The dispersion curves of Lamb wave modes are calculated based on the supercell method. The finite element method is employed to calculate the band structures and the transmission power spectra, which are in good agreement with the results by the supercell method. We also have found that the dispersion curves of Lamb waves are strongly dependent on the crystal termination, which is the position of the cut plane through the square cylinders. There exist complete or incomplete (truncated) layers of square cylinders with the change of the crystal termination. The influence of the crystal termination on the band gaps of Lamb wave modes is analyzed by numerical simulations. The variation of the crystal termination leads to obvious changes in the dispersion curves of the Lamb waves and the widths of the band gaps.

Casimir interaction between inclined metallic cylinders

The Casimir interaction between one-dimensional metallic objects (cylinders, wires) displays unconventional features. Here we study the orientation dependence of this interaction by computing the Casimir energy between two inclined cylinders over a wide range of separations. We consider Dirichlet, Neumann and perfect metal boundary conditions, both at zero temperature and in the classical high temperature limit. For all types of boundary conditions, we find that at large distances the interaction decays slowly with distance, similarly to the case of parallel cylinders, and at small distances scales as the interaction of two spheres (but with different numerical coefficients). Our numerical results at intermediate distances agree with our analytic predictions at small and large separations. Experimental implications are discussed.

Large Eddy Simulation of Hydraulic Characteristics of Flow around Two Parallel Circular Cylinders

large eddy simulation cooperated with a physical fractional-step method was applied to simulate steady flow around two parallel circular cylinders. The total velocity vectors, pressure contours and vorticity magnitude are obtained. The modeling results conform to physical law, and show that the large eddy simulation theory has powerful capacity in simulation of microstructures of turbulent flows, and can be widely applied to the solution of real engineering problems.

Space group of heterogeneous cylinder packing with six 〈110〉 directions

The space group of a periodic cylinder packing structure is reported. Congruent cylinders of infinite length are packed parallel to the six cubic 〈110〉 directions. The structure belongs not to the cubic system but to the tetragonal system. Although the parallel cylinders form the same rhombic lattice along each of the six directions, the packing structure as a whole is heterogeneous: cylinders along two of the directions occupy one Wyckoff position, and cylinders along the remaining four directions occupy the other Wyckoff position. Their combined structure belongs to the space group I4122, which provides two enantiomorphic structures.

Capillary attraction of floating rods

The capillary attraction of two parallel cylinders with circular cross-section representing slender particles floating at the interface between two immiscible fluids is considered. Given the particle separation, the elevation of the particle centers in hydrostatics is computed to satisfy the vertical force balance involving the buoyancy force, the capillary force, and the particle weight. A numerical procedure is developed for calculating the horizontal force exerted on a pair of cylinders in solitary or periodic arrangement. The results confirm that the particles attract each other under the conditions considered. The particle motion and transient flow due to the particle attraction are computed using a boundary-integral method for Stokes flow. In the algorithm, the particle center velocity of translation and angular velocity of rotation are calculated to satisfy force and torque balances. Numerical simulations using a boundary-element method subject to an initial state provided by hydrostatics illustrate the nature of the motion and furnish estimates for the particle velocity induced by capillarity.

Free Convection Heat Transfer from a Row of Horizontal Cylinders

Steady laminar free convection in air from parallel circular cylinders set side-by-side is studied numerically. The SIMPLE-C algorithm is used for the solution of the mass, momentum, and energy transfer governing equations. Simulations are performed for tube-arrays consisting of 10 equally-spaced cylinders, for different center-to-center separation distances in the range between 1.4 and 6 cylinder-diameters, and for Rayleigh numbers spanning between 101 and 105.

Exact Matrix Representation of the Transverse Magnetic Multiple Scattering of Obliquely Incident Plane Waves by the Diffraction Grating of Penetrable Cylinders

“An exact matrix conformation model” associated with the equations describing the exact behavior of the Fourier‐Bessel multiple scattering coefficients of the diffraction grating consisting of an infinite number of infinitely long parallel penetrable circular cylinders, corresponding to the obliquely incident transverse‐magnetic plane waves in “Twersky-Wait-Kavaklıoğlu representation,” originally excogitated in (Kavaklıoğlu, 2000), is acquired, and the exact solution for “the Fourier-Bessel multiple scattering coefficients of the diffraction grating at oblique incidence” is obtained by a matrix inversion procedure.

Effects of Cross Cylinders on Aerodynamic Sound from Two Parallel Circular Cylinders

Effects of Cross Cylinders on Aerodynamic Sound from Two Parallel Circular Cylinders

Identification of a laminar-turbulent interface in partially turbulent flow

Viscous incompressible fluid flow along the clearance between two parallel eccentric circular cylinders is studied numerically. The geometric parameters and the Reynolds number are taken so that the turbulent flow regime takes place in a part of flow, namely, in the zone where the clearance is wide, while the low is laminar in the narrow clearance zone. Criteria using which these zones can be distinguished are discussed.

Boundary element method for bandgap computation of photonic crystals

A boundary element method for computing bandgap structures of two-dimensional photonic crystals is developed. For photonic crystals composed of a square or triangular lattice of parallel cylinders with arbitrarily shaped cross-sections, the boundary integral equations are formulated for a unit cell. Constant boundary elements are adopted to discretize the boundaries. Applying the periodic boundary conditions and the interface conditions, we obtain a linear eigenvalue equation with relatively small matrices. The solution of the eigenvalue equation yields the Bloch wave vectors for given frequencies. The convergence of the method for the desired accuracy and efficiency is examined by some typical numerical examples. It is shown that the present method is efficient and accurate and thus provides a flexible treatment of electromagnetic waves in periodic structures with inclusions of arbitrary shape.

Influences of gradient profile on the band gap of two-dimensional phononic crystal

Propagation characteristics of elastic waves in two-dimensional (2D) phononic crystal consisting of parallel cylinders or cylindrical shells embedded periodically in a homogeneous host are investigated. The cylinders or cylindrical shells with varying material parameters along the radial direction are considered. The influences of the gradient profile on the band gap are the main concern. First, the multiple scattering method and the Bloch theorem are used to derive the dispersive equation. Second, the transfer matrix of graded medium is derived based on the laminated cylindrical shell model. Three cases of combination are considered: (1) Solid cylinders embedded in solid host (solid-solid type). (2) Solid cylinders embedded in liquid host (solid-liquid type). (3) Hollow cylinder filled with liquid embedded in liquid host (liquid-solid-liquid type). Next, the dispersive curves and the band gaps between them are evaluated numerically in the reduced Brillouin zone. Five kinds of typical gradient profiles and two limited cases are considered. At last, the influence of the graded medium with different gradient profiles upon dispersive curves and the band gaps are discussed based on the numerical results.

Force among magnetic nanocylinders trapped in triangular arrays

We study the effect of the forces among magnetic nanocylinders trapped in a membrane such as those used to produce them. The interaction force between two parallel and identical magnetic nanocylinders is revisited to obtain expressions that can later be used to add them both in a discrete and a continuum approximation. At this point a particular geometry has to be assumed and we use a particular configuration reported in the literature, namely, a bundle of parallel magnetic cylinders trapped in a circular membrane. When a strong enough external magnetic field is imposed along the axis of the membrane (also along the axes of the cylinders) all magnetizations point along this direction and cylinders repel among themselves. In a first approximation we will consider a soft enough membrane so energy is mostly relaxed through a deformation of the membrane leaving the magnetization of the cylinders basically as it was in the absence of external field. Then we obtain the forces among these cylinders by two methods: one summing the contributions of a discrete number of objects and another one in which we consider a continuum distribution of them to reach larger systems. Numerical evaluation of these forces can reach 50mdyn approximately. Such forces will act on the membrane at the positions of the magnetic cylinders; in the case of a circular silicon membrane of radius 1.0mm the radial expansion of the membrane can be of the order of 1nm. This effect could be larger for softer membranes. A discussion of experimental techniques to detect this phenomenon is also done followed by the proposal of a possible application.

Band Gaps of 2D Phononic Crystal with Graded Interphase

Propagation characteristics of elastic waves in 2D phononic crystal consisting of parallel cylinders embedded periodically in a homogeneous host medium are investigated. The multiple scattering method and the Bloch theorem are used to derive the dispersive equation. The dispersive curves and the band gaps between them are evaluated numerically in the reduced Brillouin zone. The graded interphase between the cylinders and the host are considered. The influences of the graded interphase with different gradient profiles are discussed based on the numerical results.