Circular Cylinder Of Infinite Length Research Articles

Plasmon resonances of isolated metal wire and shell

The surface and bulk plasmons of isolated metal wire and shell are investigated. The metal wire model was a circular cylinder of infinite length, the medium inside which was described by the Drude formula.The eigenstates of the field, existing in the absence of sources, and the vibrations excited by external fields are studied. Bulk plasmons in the metal transparency domain are considered. The main attention is paid to the study of surface plasmons existing in the metal opacity domain and only for H-polarized fields. Their complex eigenfrequencies, Q-factors and field distributions are investigated. Despite the fact that the dispersion equation for the isolated wire has a solution for an arbitrary number of angular field variations, it has been found that in the Scattering Cross Section (SCS) for an optically thin nanowire there is only one resonance peak corresponding to a dipole plasmon. With an increase in the radius of the wire the maximum of the SCS shifts toward multipole plasmons. With a decrease in absorption additional resonance peaks appear in the SCS of isolated wire.It is found that in contrast to isolated wire the dispersion equation has two different solutions for a nanoshell for each fixed number of angular variations in the field. There are plasmons whose magnetic field on the inner and outer sides of the shell has the same sign (even plasmons) or different signs (odd plasmons). The splitting of plasmon resonances is shown. The odd plasmons are shifted to the region of lower frequencies and the even plasmons are shifted to the region of higher frequencies compared to the plasmon resonances of wire. It was found that the splitting of the resonant frequencies increases with decreasing thickness of shell. In this case the width of the resonance peaks also decreases which indicates an increase in the Q-factor.

Scattering from a topological insulator circular cylinder coated with DNG/MNG/ENG metamaterials

Abstract Scattering of electromagnetic plane wave from a metamaterial coated topological insulator circular cylinder of infinite length is studied. Metamaterials used for coating include epsilon-negative, mu-negative and double-negative. The scattering behavior is observed in terms of co- and cross-polarized components of the scattered field. Effects of different types of metamaterial coating on scattered field are investigated. To validate the formulation and numerical results, the reduction of scattering behavior of TI circular cylinder to insulator circular cylinder is also accomplished.

Upper Bounds on Packing Density for Circular Cylinders with High Aspect Ratio

In the early 1990s, A. Bezdek and W. Kuperberg used a relatively simple argument to show a surprising result: The maximum packing density of circular cylinders of infinite length in $\mathbb{R}^3$ is exactly $\pi/\sqrt{12}$, the planar packing density of the circle. This paper modifies their method to prove a bound on the packing density of finite length circular cylinders. In fact, the maximum packing density for unit radius cylinders of length $t$ in $\mathbb{R}^3$ is bounded above by $\pi/\sqrt{12} + 10/t$.

Modelling Of Heat Conduction Along Vein Walls In Endovenous Laser Treatment

Modelling Of Heat Conduction Along Vein Walls In Endovenous Laser Treatment

Effects of rarefaction in microflows between coaxial cylinders

Microscale gas flows between two rotating coaxial circular cylinders of infinite length with different temperatures are investigated. Navier-Stokes-Fourier (NSF) and regularized 13-moment (R13) equations in their linear form are used to independently analyze velocity and temperature fields in shear-driven rotary flows, i.e., cylindrical Couette flows. Knudsen boundary layers, which present non-Newtonian stress and non-Fourier heat flow, are predicted as the dominant rarefaction effects in the linear theory. We show that the R13 system yields more accurate results for this boundary value problem by predicting the Knudsen boundary layers, which are not accessible for NSF equations. Furthermore, a set of second-order boundary conditions for velocity slip and temperature jump are derived for the NSF system. It is shown that the proposed boundary conditions effectively improve the classical hydrodynamics. The accuracy of NSF and R13 equations is discussed based on their comparison with available direct simulation Monte Carlo data.

Direct numerical simulation of three-dimensional flow past a yawed circular cylinder of infinite length

Direct numerical simulation of flow past a stationary circular cylinder at yaw angles (α) in the range of 0–60° was conducted at Reynolds number of 1000. The three-dimensional (3-D) Navier–Stokes equations were solved using the Petrov–Galerkin finite element method. The transition of the flow from 2-D to 3-D was studied. The phenomena that were observed in flow visualization, such as the streamwise vortices, the vortex dislocation and the instability of the shear layer, were reproduced numerically. The effects of the yaw angle on wake structures, vortex shedding frequency and hydrodynamic forces of the cylinder were investigated. It was found that the Strouhal number at different yaw angles (α) follows the independence principle. The mean drag coefficient agrees well with the independence principle. It slightly increases with the increase of α and reaches a maximum value at α=60°, which is about 10% larger than that when α=0°. The root-mean-square (r.m.s.) values of the lift coefficient are noticeably dependent on α.

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived. Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.

Nonsingular boundary integral equation for two‐dimensional electromagnetic scattering problems

AbstractThis paper is concerned with the application of the nonsingular boundary integral equation (NSBIE) for 2D electromagnetic scattering problems in the frequency domain. In the proposed NSBIE, the conventional treatment of the singular integral for the boundary integral equation is circumvented by employing the Gauss flux theorem and the concept of equipotential. Then the NSBIE for the Helmholtz equation is used to predict the scattering of plane wave by a perfectly electric conducting circular cylinder of infinite length at normal incidence. Based on the good results, as compared with solutions of the analytical and boundary‐element methods, it is verified that the NSBIE is a highly simple and efficient numerical scheme for 2D electromagnetic scattering simulations. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 760–765, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21467

Linear stability of the cylindrical Couette flow of a rarefied gas

A rarefied gas between two coaxial circular cylinders of infinite length, rotating with different angular velocities and kept at a common temperature, is considered. The stability of the circumferentially as well as axially uniform flow (cylindrical Couette flow) for circumferentially uniform small disturbances is investigated on the basis of kinetic theory. The linear-stability analysis is performed using the Bhatnagar-Gross-Krook model of the Boltzmann equation and the diffuse reflection condition on the cylinders. The maximum growth rate of the disturbances is determined numerically by solving the initial and boundary value problem for the disturbances for relatively small Knudsen numbers and wide ranges of angular velocities of the cylinders. As a result, the parameter range where the cylindrical Couette flow is unstable is clarified. The result is compared with the corresponding result based on the continuum model of the compressible Navier-Stokes type. A comparison is also made with the result of a direct numerical analysis of the original Boltzmann system, obtained by the direct simulation Monte Carlo method in previous papers as well as in the present study.

Dispersion of torsional waves in a thick-walled transversely isotropic circular cylinder of infinite length

The dispersion properties of torsional waves of a thick-walled transversely isotropic circular cylinder of infinite length are investigated. The assumed waves are axisymmetric and propagate along the x-axis of the cylinder. The wall of the cylinder consists of a transversely isotropic material with the axis of isotropy parallel to the x-axis of the cylinder. The dispersion curves for both the phase and group velocities are determined and graphically illustrated. The amplitudes of the tangential displacements for some dispersion branches are shown. The purpose of the paper is to show the present technique is useful in solving some energy flow problems when torsional waves travel along arbitrarily laminated cylinders with various kinds of anisotropy. It seems that by controlling the anisotropy of a shell-like structure, the optimisation of amplitude and energy flow distributions in different parts of the structure can be achieved.

Effects of disorder in two-dimensional photonic crystal waveguides.

The effects of randomness on the guiding properties of waveguides embedded in disordered two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length are investigated for TM-polarized radiation. Different degrees of disorder in the radius, filling fraction, refractive index, and position are considered for both straight and 90 degrees bent guides. The crystals exhibit similar sensitivity to refractive index and radius disorder, with a degree of disorder from 15%-20% yielding little substantial change in the guiding properties. A smaller range of position disorder is also considered. For strong disorder in radius and refractive index, the guide effectively closes. These results were obtained by a Monte Carlo simulation method, and the performance of this method is analyzed. The method requires at least ten realizations in some cases for convergence to commence; substantially more realizations are required for moderate and strong disorder to achieve accurate results.

Two-dimensional Green tensor and local density of states in finite-sized two-dimensional photonic crystals

The two-dimensional Green tensor for two-dimensional photonic crystals, consisting of clusters of circular cylinders of infinite length, is constructed using the exact theory of multipole expansions. On the basis of this Green tensor, the local density of states for both polarizations is calculated, showing how the density of states depends on the position inside the crystal. We include results for clusters with a waveguide, obtained by removing a line of cylinders, and a cavity, obtained by forming a localized defect.

Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length

Using the exact theory of multipole expansions, we construct the two-dimensional Green's function for photonic crystals, consisting of a finite number of circular cylinders of infinite length. From this Green's function, we compute the local density of states (LDOS), showing how the photonic crystal affects the radiation properties of an infinite fluorescent line source embedded in it. For frequencies within the photonic band gap of the infinite crystal, the LDOS decreases exponentially inside the crystal; within the bands, we find "hot" and "cold" spots. Our method can be extended to three dimensions as well as to treating disorder and represents an important and efficient tool for the design of photonic crystal devices.

Two-dimensional local density of states in two-dimensional photonic crystals

We calculate the two-dimensional local density of states (LDOS) for two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length. The LDOS determines the dynamics of radiation sources embedded in a photonic crystal. We show that the LDOS decreases exponentially inside the crystal for frequencies within a photonic band gap of the associated infinite array and demonstrate that there exist ;;hot' and ;;cold' spots inside the cluster even for wavelengths inside a gap, and also for wavelengths corresponding to pass bands. For long wavelengths the LDOS exhibits oscillatory behavior in which the local density of states can be more than 30 times higher than the vacuum level.

Model and experiments of multiple acoustical scattering from small obstacles

A self-consistent model is presented to calculate acoustical scattering of waves from many discrete obstacles, including multiple scattering. The model provides a formulation for incorporating single scattering Green’s functions into a multiple scattering solution using auxiliary sources. Geometry and material parameters of the scatterers in the ensemble may be different, and are arbitrary as long as each single scattering solution is known. In restricting the number of auxiliary sources the model is approximate, yet it is empirically shown to work in a quantitative manner for scatterers of ka up to about one, where k is the wave number of the background medium and a is half of the cross section of a scatterer. To ease experimental verification, a two-dimensional setup is considered where obstacles are circular cylinders of infinite length. The model is tested against experimental data gathered from ultrasonic experiments in a water tank. Ensembles of two to ten strong scattering cylinders were used, their radius being chosen such that ka =3D 0.5 at the mean frequency of the transducers. Numerical and experimental results are compared in time and frequency domain and show quantitative agreement in all investigated arrangements. Results of a numerical experiment including 50 different cylinders are also shown.

Time-dependent decay of the motion of a sphere translating and rotating in a viscous liquid

An exact solution of the Navier-Stokes equations is found for the (axisymmetric) motion (with swirl) representing exponentially time-dependent decay of a solid sphere translating and rotating in a viscous fluid relative to a uniform stream whose speed also decays exponentially with time. A similar solution is also described for the two-dimensional analogue where the sphere is replaced by a circular cylinder of infinite length.

Backscatter RCS for TE and TM excitations of dielectric-filled cavity-backed apertures in two-dimensional bodies

Transverse electric (TE) and transverse magnetic (TM) scattering from dielectric-filled, cavity-backed apertures in two-dimensional bodies are treated using the method of moments technique to solve a set of combined-field integral equations for the equivalent induced electric and magnetic currents on the exterior of the scattering body and on the associated aperture. Results are presented for the backscatter radar cross section (RCS) versus the electrical size of the scatterer for two different dielectric-filled cavity-backed geometries. The first geometry is a circular cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the cylinder is dielectric filled and is also of circular cross section. The two cylinders (external and internal) are of different radii and their respective longitudinal axes are parallel but not collocated. The second is a square cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the square cylinder is dielectric-filled and is also of square cross section. >

Maximum density space packing with congruent circular cylinders of infinite length

We determine what is the maximum possible (by volume) portion of the three-dimensional Euclidean space that can be occupied by a family of non-overlapping congruent circular cylinders of infinite length in both directions. We show that the ratio of that portion to the whole of the space cannot exceed π/√12 and it attains π/√12 when all cylinders are parallel to each other and each of them touches six others. In the terminology of the theory of packings and coverings, we prove that the space packing density of the cylinder equals π/√12, the same as the plane packing density of the circular disk.

Sound scattering of a spherical wave incident on a cylinder

The problem of the scattering of a spherical acoustic wave by an elastic circular cylinder of infinite length is investigated theoretically in this paper. In a cylindrical coordinate system, the mathematical form of a spherical wave is similar to that of a plane wave. Thus it is not necessary to solve the relevant differential equations and boundary conditions. An exact solution to the present problem can be directly formulated by using the already known solution for plane-wave incidence. This solution is expressed by an integral, which always involves a numerical treatment. The scattered pressure is calculated for an aluminum cylinder in water. A detailed discussion of the results reveals the features of the scattering of a spherical wave.

Quasi-static normal indentation of an elasto-plastic half-space by a rigid circular cylinder of infinite length

The title problem is treated under the conditions of frictionless and completely adhesive contact within the context of incremental elasto-plasticity. The analysis employs a constant-strain-triangle, finite element code, together with a grid expansion technique which aids computational efficiency. Attendant results are checked where possible then processed to furnish: the indentation extent with increasing pressure, the contact and interior stresses on loading and unloading, yield region growth, and relative displacement profiles at the surface. Comparisons with related experiments in the literature are made and generally show reasonable agreement.