Fairness in opinion dynamics

The opinion dynamics studies how a final consensus emerges from a diversified initial configuration. The final result can be an artifact arising in the voting processes and overlook the features of the initial configuration, which leads to the unfair result. We explore the concept of fairness in opinion dynamics and propose a quantitative measurement in a model system, which allows us to reach a final consensus reflecting impartially the major opinion. For a two-choice system, the unfairness alternates with the increase of meeting agents M. With an odd M, the fair results can be expected; with an even M, the unfairness decays monotonically with an increasing M. When the number of choices is larger than two, such an alternating is smeared out. The fairness at an odd M can no longer be reached. The unfairness increases a bit with the increasing number of choices. Similar M-dependence can be observed for different number of choices. We conclude that the number of choices plays a minor role in reaching a fair final consensus. The fairness is mainly controlled by the meeting size.     

New Bose Operator Realization of SU(2) Algebra and Its Application in Optical Propagation

We introduce a new Bose operator realization of SU(2) Lie algebra and applied it to optical propagation in GRIN media or some lens-setup.     

Propagation of the kurtosis parameter of Hermite-cosh-Gaussian beams

Starting from the propagation equation of Hermite-cosh-Gaussian (HChG) beams and the intensity moments definition, an analytical expression for the propagation of the kurtosis parameter of unapertured HChG beams passing through paraxial optical ABCD systems is derived and illustrated numerically. Special interesting cases are discussed, in particular, the kurtosis parameter of HChG beams at the waist plane is obtained readily from our general propagation expression.     

Comparative study on the propagation performance of coherently combined and incoherently combined beams

Taking phase error, turbulent atmosphere, jitter, vacancy factor and tilt error into consideration, we propose a general propagation formula for both coherent and incoherent combined beams with different kinds of aberrations. Comparative study on the propagation performance of coherent and incoherent combined beams is presented. Beam propagation factor (BPF) defined as laser output power in a specified far-field bucket divided by the total output power radiating from the effective near-field exit aperture of the laser beam is introduced as the beam quality factor to give a quantitative study. It is revealed that the coherent combined beam has great advantage when propagating in free-space compared with the incoherent combined beams. However, the coherent combined beam is more sensitive to the environmental aberrations, and the beam quality degrades faster with an increase in the aberrations’ intensity. Scintillation index as the high moments of the combined intensity field is also studied. It is revealed that both coherent and incoherent combined beams exhibit less scintillations compared with a single-aperture beam, and the incoherent combined beam demonstrates better scintillations reducing the performance. Our methodology offers an all-round performance evaluation on the two kinds of laser systems.     

An alternative method for plotting dispersion curves

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.     

Microwave propagation parameters in magnetic fluids

Complex dielectric permittivity and complex magnetic permeability measurements of two magnetic fluids (as microwave propagation media), in the approximate range 0.2-5GHz were performed. The two samples consisted of magnetite nanoparticles, dispersed in kerosene and in water, respectively. Based on the dielectric and magnetic measurements, the frequency (f ) dependence of the attenuation parameter, , the phase constant, , the propagation constant, , the intrinsic impedance, Z_m, the refractive index, n , the reflection coefficient, R , the wavelength, and the skin depth, , of the investigated samples were determined.     

A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic–acoustic media. A velocity–strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic–acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic–acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.     

Comparison of 1D, 2D and 3D quench onset simulations

Measured and simulated minimum quench energies (MQE) for short samples are doubtful when estimating disturbance tolerance of an impregnated superconducting magnet. If measurements are performed at liquid cryogen, the cooling provided by the cryogen causes MQE to be high. At a conduction-cooled system, the transverse heat conduction is neglected causing low MQE. Even though these conditions can be artificially brought closer to the ones in an impregnated magnet, it is difficult to estimate by short-sample measurement the MQE of a superconducting coil. These similar difficulties are present at simulations. On the other hand, 1D and 2D measurements and simulations can be used, e.g., to compare wires or consider effect of insulation layer thickness, but according to the results only in a rough quantitative way. In this paper, we compare MQE and normal zone propagation velocity simulations of an MgB₂ wire with 1D, 2D and 3D finite element method models to focus on the different results given by the models employing different dimensions.     

Design of Hamming Code Checker Using Titanium-Diffused Lithium Niobate-Based Waveguide

ABSTRACT

This work presents an electro-optic effect-based design for the widely used Hamming code for checking single bit errors in the received data. The structure is based on Mach-Zehnder Interferometer, designed using Titanium-diffused Lithium Niobate-based waveguides. The proposed device has been successfully tested using the beam propagation method. For a received 7-bit code, the three simultaneously generated check bits are combined to check the error position. Critical performance parameters like extinction ratio (24.39dB), contrast ratio (25.711dB), insertion loss (0.041dB), and amplitude modulation (0.079dB) calculated for the overall device are within acceptable limits for the feasibility of the device.