Finite Cross Section Research Articles

Comparison of Surface and Volume Currents Models for Electromagnetic Scattering From Finite Dielectric Cylinders

The accuracy of modeling plane wave scattering by dielectric cylinders of finite length and circular cross section for microwave remote sensing applications is investigated. Exact expressions for their scattering cross section do not exist, leading to the use of approximate analytical methods. Two widely used models, based on the approximation of the induced currents, are considered here, and the validity of their results is evaluated by comparison with a corresponding numerical solution.

Tunnel magnetoresistance of a single-molecule junction

Based on the nonequilibrium Green’s function technique and the Landauer–Büttiker theory, the possibility of a molecular spintronic device, which consists of a single C60 molecule attached to two ferromagnetic electrodes with finite cross sections, is investigated. By studying the coherent spin-dependent transport through the energy levels of the molecule, it is shown that the tunnel magnetoresistance (TMR) of the molecular junction depends on the applied voltages and the number of contact points between the device electrodes and the molecule. The TMR values more than 60% are obtained by adjusting the related parameters.

Spatial Kerr solitons in optical fibres of finite size cross section: beyond the Townes soliton

We propose a new and efficient numerical method to find spatial solitons in optical fibres with a nonlinear Kerr effect including microstructured ones. A nonlinear non-paraxial scalar model of the electric field in the fibre is used (nonlinear Helmholtz equation) and an iterative algorithm is proposed to obtain the nonlinear solutions using the finite element method. The field is supposed to be harmonic in time and along the direction of invariance of the fibre but inhomogeneous in the cross section. In our approach, we solve a nonlinear eigenvalue problem in which the propagation constant is the eigenvalue. Several examples dealing with step-index fibres and microstructured optical fibres with a finite size cross section are described. In each geometry, a single self-coherent nonlinear solution is obtained. This solution, which also depends on the size of the structure, is different from the Townes soliton—but converges towards it at small wavelengths.

A new approach to the quantized electrical conductance

The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a nanowire of finite cross section area and to electrons in magnetic field, and the quantization of the electrical conductance is shown. An additional application is made to the two-dimensional electron gas.

Flexible-to-semiflexible chain crossover on the pressure-area isotherm of a lipid bilayer

We find theoretically that competition between ∼Kfq4 and ∼Qq2 terms in the Fourier-transformed conformational energy of a single-lipid chain, in combination with interchain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)∼(A−A0)−α. The crossover manifests itself in the transition from α = 5/3 to α = 3. Our microscopic model represents a single-lipid molecule as a worm-like chain with a finite irreducible cross-section area A0, a flexural rigidity Kf, and a stretching modulus Q in a parabolic potential with the self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area A* obeys the relation Q/√KfB(A*) ≈ 2. We predict a peculiar possibility of deducing the effective elastic moduli Kf and Q of an individual hydrocarbon chain from the analysis of the isotherm with such a crossover. Also calculated is the crossover-related behavior of the area compressibility modulus KA, the equilibrium area per lipid At, and the chain order parameter S(θ).

NLO QCD corrections to inclusive jet and hadron production in DIS

We analyze the order a 2 corrections to the single inclusive jet and hadron cross sections in lepton-nucleon deep inelastic scattering. The full calculations are done analytically, obtaining finite NLO partonic level cross sections for these processes. We show that in both cases the dominant partonic mechanism starts at order a 2 , being effectively a lowest order estimate, with the consequent large factorization scale uncertainty, and the likelihood of non-negligible corrections at the subsequent order in perturbation theory.

Effective material properties for shear-horizontal acoustic waves in fiber composites

The effective dynamic properties of composites made of elastic cylindrical fibers randomly distributed in another elastic solid can be evaluated with plane shear-horizontal acoustic waves. In this paper, it is shown that the effective mass density and the effective shear stiffness are complex valued and frequency dependent. Simple formulas are derived for these effective quantities. The low-frequency limit of these formulas is found to be in agreement with physical expectations. The derivation is based on the multiple-scattering approach of Waterman and Truell, where each cylinder of finite cross section is replaced with an equivalent line scatterer. Numerical results are presented for the effective mass density and effective shear stiffness for various values of frequency, cylinder concentration, and elastic properties of the cylinders and matrix.

Ab initioinvestigations of the transport properties of aGe7cluster

Based on first-principles calculations, we have systematically investigated the electrical transport properties of a ${\mathrm{Ge}}_{7}$ cluster, which is respectively coupled with two kinds of atomic scale Ag(110) and Ag(100) electrodes with finite cross sections. Our results clearly suggest that, under strong cluster-electrode coupling, the equilibrium conductance of the ${\mathrm{Ge}}_{7}$ cluster coupled with thin Ag nanowires takes the value of about 3 and 4 (units of ${G}_{0}=2{e}^{2}∕h$) in the case of Ag(110) and Ag(100), respectively. The eigenchannel and electronic structure analyses show that, in the strong cluster-electrode coupling regime, the transport properties of ${\mathrm{Ge}}_{7}$ cluster connected to thin Ag wires are very closely related to the band structure of the nanowire electrode in both equilibrium and nonequilibrium situations. Under zero bias, the number of the electrode bands crossing the Fermi level determines the number of conductance channels of the ${\mathrm{Ge}}_{7}$ cluster. Therefore, for the Ag(100) electrode case, more bands crossing the Fermi energy results in a larger conductance than that in the Ag(110) case. By varying the cluster-electrode contact distances, we observe that the equilibrium conductance of the ${\mathrm{Ge}}_{7}$ cluster in contact with the Ag(100) electrode is larger than that in the case of the Ag(110) electrode for most of investigated contact distances. With the bias voltage applied, our results also elucidate that there also exists a close correlation between the nonequilibrium properties of this cluster and the band matching between left and right electrodes in these two cases.

The role of nano-contacts in electrical transport through a molecular wire

Theoretical studies on electrical transport in a nano-device which consisting of two semi-infinite cubic leads with finite cross-sections separated by a typical molecular wire (MW) are carried out by including the effect of single and multiple contacts. The calculations are based on the tight-binding model and Green’s function method in the coherent regime. In order to calculate the effect of contact coupling on molecular wire transport, we derive a theoretical formula based on the nearest and next nearest neighbor coupling strengths between the MW and the surface atoms in the simple cubic leads. This approach can be generalized to other leads with different lattice structure. The results show small changes in the transport properties with changing next nearest neighbor coupling strength. Some asymmetry is noted in the strong multiple contact limit. Also, we observe that with enlarging the cross-section size of leads, the current density increases and then leads to the quantum unit of conductance. Hence, our derived formalism can be used for devices attached to macroscopic surfaces. The theoretical results obtained, can be a base for developments in designing nano-electronic devices.

Rotating wave solutions of the FitzHugh–Nagumo equations

This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion coefficients in which RW solutions are observed will be described using bifurcation theory and continuation methods. The bifurcation of time-periodic solutions of these FHN equations without diffusion is described first. Similar methods are then used to find RW solutions on a circular ring and numerical simulations are described. These results are then extended to investigate RW solutions on annular rings of finite cross-section. Scaling arguments are used to show how the existence of solutions depends on either the diffusion coefficient or on the size of the region.

EFFECT OF AN IMPURITY IN THE WIDE-NARROW-WIDE QUANTUM WAVEGUIDE STRUCTURE

We present a numerical study of the influence of junction-geometries and disorder on quantum-mechanical transmission by considering the presence of an impurity in a wide-narrow-wide (W-N-W) quantum-wire junction. The device is modeled as an electron waveguide of finite cross section. Transmission and reflection probabilities as well as conductance are computed by using model expansions of the wave function together with a waveguide-matching technique. The calculations show that the transmission of the two-dimensional electron gas through the W-N-W geometry is highly sensitive to geometries of junction and can be suppressed by the presence of a repulsive or attractive impurity potential. Furthermore, the depression effect becomes more visible if the absolute value of potential strength becomes bigger.

Michell cantilevers constructed within trapezoidal domains

The paper concerns the Michell-like cantilevers transmitting a point load to a straight segment of a support. The feasible domain is of trapezoidal infinite shape, as in the previous parts of the paper. The ratio of allowable stresses in tension and compression is arbitrary, not necessarily equal to 1. The present, last part of the paper includes detailed geometric and static analyses of the optimal cantilevers for various admissible data, thus providing new benchmarks of topology optimization. All results are found by using analytical methods developed in the previous parts of the paper. Particular attention is put on the force field distribution within the fibrous domains. These force fields turn out to be defined in certain subdomains forming a static division. The volumes of the optimal cantilevers are computed in two manners: by direct integration of the density of fibres and summing it up with the volume of the reinforcing bars of finite cross sections, and by using the kinematic formula of Michell according to which the volume is proportional to the virtual work. The examples analysed prove that both approaches lead to identical results of the volumes, thus showing that the possible duality gaps vanish. The analytical solutions are verified by considering appropriately chosen sequences of trusses of finite number of joints converging to the exact Michell cantilevers.

Reduction of acoustic radiation by perforated board and honeycomb layer systems

A perforated system, proposed previously for reducing the radiated sound from a plate at arbitrary frequencies, is applied to three-dimensional problem. Plates are assumed to be supported in a duct of a finite cross-section and excited by a harmonic point force. The sound radiation is investigated from the viewpoint of acoustic power and it is discussed whether the attenuation effect shown previously in the one-dimensional system can be obtained with the three-dimensional system. The effect of support conditions on attenuation characteristics is discussed by using clamped and simply supported circular models. Allowing for the effect, a simply supported rectangular model is studied in detail and its problems are revealed. In order to overcome the problems, a new system including subdivided air cavities in the form of a honeycomb layer instead of a undivided backing cavity is proposed. Each of the honeycomb cells can create local one-dimensional sound fields. Calculated theoretical results are compared to data obtained in a 1/5th scale reverberation chamber. The results for the reduction effect, which are in good agreement, show that the honeycomb layer system can achieve the same reduction of the radiated sound power at arbitrary frequencies as the one-dimensional perforated system.

Magnetic forces for axisymmetric eddy current problems using a hybrid FE/BE method

In this paper, the magnetic force acting on the currents induced in a nonmagnetic ring of finite cross section, taking into account the presence of eddy currents, is determined by the use of Laplace's force formula. The required magnetic flux and current densities are obtained from vector potential values evaluated by a hybrid finite-element/boundary-element method. The magnetic flux density is found from the potentials using a linear operator capable of yielding accurate results notwithstanding the discrete nature of the problem. Equivalent results obtained by the virtual-work principle are presented for comparison.

Magnonics: Experiment to prove the concept

An experimental scheme for studying spin wave propagation across thin magnetic film samples is proposed. The scheme is based upon the creation of picosecond pulses of strongly localized effective magnetic field via ultrafast optical irradiation of a specially deposited exchange bias or exchange spring layer. The spin waves are excited near the irradiated surface before propagating across the thickness of the sample. They are then detected near the other surface either within the finite optical skin depth using the linear magneto-optical Kerr effect in metallic samples or by the magnetic second harmonic generation. The experiment can facilitate investigations of propagating spin waves with wavelengths down to several nanometers and frequencies in excess of hundreds of Gigahertz. An experiment upon a periodically layered nanowire (a finite cross-section magnonic crystal) is numerically simulated, although the sample might equally well be a continuous film or an array of elements (e.g. nanowires) that either have uniform composition or are periodically layered as in a magnonic crystal. The experiments could be extended to study domain wall-induced spin wave phase shifts and can be used for the creation of spin wave magnetic logic devices.

Order(αs2)QCD corrections to inclusive jet production in deep inelastic scattering

We analyze the order ${\ensuremath{\alpha}}_{s}^{2}$ corrections to the single inclusive jet cross section in lepton-nucleon deep inelastic scattering. The full calculation is done analytically, in the small cone approximation, obtaining finite NLO partonic level cross sections for these processes. A detailed study of the different underlying partonic reactions is presented focusing in the size of the corrections they get at NLO accuracy, their relative weight, and the residual scale uncertainty they leave in the full cross section depending on the kinematical region explored. In agreement with what has already been found in forward production of ${\ensuremath{\pi}}^{0}$, we show that the dominant partonic process in very forward jet production is found to start at order ${\ensuremath{\alpha}}_{s}^{2}$, being effectively a lowest order estimate, with the consequent large factorization scale uncertainty, and the likelihood of non-negligible corrections at the subsequent order in perturbation theory.

Calculation and simulation of impedance diagrams of planar rectangular spiral coils for eddy current testing

The knowledge of analytical expressions for the electromagnetic (EM) fields produced by the coils used in eddy current testing is an important point in the development and application of these devices. In the present work, the second order vector potential formulation is used for the calculation of the fields produced by planar rectangular spiral coils of arbitrary number of turns and finite rectangular cross-section placed on a conducting half-space. Impedance plane diagrams are calculated for different frequencies, lift-off and half-space conductivity. Tests for conductivity assessment are also simulated. The theoretical results are compared with experimental measurements.

Predicting AC loss in practical superconductors

Recent progress in the development of methods used to predict AC loss in superconductingconductors is summarized. It is underlined that the loss is just one of the electromagneticcharacteristics controlled by the time evolution of magnetic field and current distributioninside the conductor. Powerful methods for the simulation of magnetic flux penetration,like Brandt’s method and the method of minimal magnetic energy variation, allow usto model the interaction of the conductor with an external magnetic field or atransport current, or with both of them. The case of a coincident action of ACfield and AC transport current is of prime importance for practical applications.Numerical simulation methods allow us to expand the prediction range fromsimplified shapes like a (infinitely high) slab or (infinitely thin) strip to morerealistic forms like strips with finite rectangular or elliptic cross-section. Anothersubstantial feature of these methods is that the real composite structure containing anarray of superconducting filaments can be taken into account. Also, the case of aferromagnetic matrix can be considered, with the simulations showing a dramaticimpact on the local field. In all these circumstances, it is possible to indicate howthe AC loss can be reduced by a proper architecture of the composite. On theother hand, the multifilamentary arrangement brings about a presence of couplingcurrents and coupling loss. Simulation of this phenomenon requires 3D formulationwith corresponding growth of the problem complexity and computation time.

The role of the electrodes in a molecular conductor: an eigenchannel analysis

In order to investigate the role of the electrodes in a molecular conductor, we have studied the effects of diatomic molecules H2 and O2 on the eigenchannels of a nanocontact formed by two Au(100) electrodes with finite cross sections by first principles calculations combined with non-equilibrium Green's function technique. Two cases where the axes of the molecules are placed along the electrode axis and vertically to the electrode axis are studied. We find that the maximum number of the eigenchannels and their energy ranges are always determined by the band structure of the electrodes. The molecules only modify the electron transmission probability of each channel.

Statistics of Lyapunov exponents of quasi-one-dimensional disordered systems

Statistical properties of Lyapunov exponents (LE) are numerically calculated in a quasi-one-dimensional (1D) Anderson model, which is in a 2D or 3D lattice with a finite cross section. The single-parameter scaling (SPS) variable $\ensuremath{\tau}$ relating the Lyapunov exponents $\ensuremath{\gamma}$ and their variances $\ensuremath{\sigma}$ by $\ensuremath{\tau}\ensuremath{\equiv}{\ensuremath{\sigma}}^{2}L∕⟨\ensuremath{\gamma}⟩$ is calculated for different lateral coupling $t$ and disorder strength $W$. In a wide range of $t$, $\ensuremath{\tau}$ is approximately independent of $W$, but it has different values for LEs in different channels. For small $t$, the distribution of the smallest LE is non-Gaussian and $\ensuremath{\tau}$ strongly depends on $W$, remarkably different from the 1D SPS hypothesis.