Monte Carlo simulation of Ising model on decagonal covering structure

We study the Ising model on a two-dimensional quasilattice developed from the decagonal covering structure. The periodic boundary conditions are applied to a patch of rhombus-like covering pattern. By means of the Monte Carlo simulation and the finite-size scaling analysis the critical temperature is estimated as 2.317±0.002. Two critical exponents are obtained being 1/v=0.992±0.003 and η=0.247±0.002, which are close to the values of the two-dimensional regular lattices as well as the Penrose tilings.     

Transient Non-Thermal Mobility of CO for CO--NO Catalytic Reaction on Square Lattice: Monte Carlo Simulation

We study a model based on precursor mechanism for CO-NO catalytic reaction on square lattice with Monte Carlo simulation. The precursor mechanism clearly demonstrates its impact on the phase diagram. The steady reactive state （SRS） gets established. The width of reactive region increases by increasing the range of precursor mobility. When the precursor mobility is increased to third-nearest neighbourhood, the second-order transition disappears.     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Risk analysis in investment appraisal based on the Monte Carlo simulation technique by A. Hacura, M. Jadamus-Hacura and A. Kocot

Comment on Eur. Phys. J. B 20, 551 (2001) Since Hertz major work on investment appraisal using the Monte Carlo Simulation technique, the so called “Risk Analysis” has become a standard tool for supporting investment decisions [1,2]. A main problem in investment appraisal is to consider and specify the risk of investment projects in an appropriate way, for enabling consistent project evaluation. In calculating a risky project's net present value (NPV) the major difficulty is to quantify the project's risk for quantifying an appropriate risk adjusted discount rate (RADR). Theoretically not founded risk adjusted discount rates face a lot of critique. Furthermore it is discussed that the incorporation of a constant risk factor into the discount rate makes a certain assumption about the resolution of uncertainty over time [3] and finally that a single net present value could not in general reflect risk properly. Especially in consequence of the last point the proponents of simulation argue that a whole distribution of net present values shows a project's risk better than a single number. In the special issue “Econophysics” of this journal Hacura et al. tried to describe the methodology and use of Monte Carlo Simulation in investment appraisal [4]. The purpose of this comment is to point out three fundamental flaws in that article. Received 29 April 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: robert.obermaier@wiwi.uni-regensburg.de     

Optical substrate thickness measurement system using hybrid fiber-freespace optics and selective wavelength interferometry

Proposed and demonstrated is a simple few components non-contact thickness measurement system for optical quality semi-transparent samples such as Silicon (Si) and 6H Silicon Carbide (SiC) optical chips used for designing sensors. The instrument exploits a hybrid fiber-freespace optical design that enables self-calibrating measurements via the use of confocal imaging via single mode fiber-optics and a self-imaging type optical fiber collimating lens. Data acquisition for fault-tolerant measurements is accomplished via a sufficiently broadband optical source and a tunable laser and relevant wavelength discriminating optics. Accurate sample thickness processing is achieved using the known material dispersion data for the sample and the few (e.g., 5) accurately measured optical power null wavelengths produced via the sample etalon effect. Thicknesses of 281.1 μm and 296 μm are measured for given SiC and Si optical chips, respectively.     

Topological Properties of Spatial Coherence Function

The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.     

Generation of Optical Vortex Using a Spiral Phase Plate Fabricated in Quartz by Direct Laser Writing and Inductively Coupled Plasma Etching

A simple, economical and reliable technique is proposed for fabricating a spiral phase plate （SPP） in a quartz substrate to generate optical vortex with a unit topological charge at the wavelengths of 632.8nm. The spiral phase plate is first formed in the photoresist by direct laser writing lithography and then transferred into the quartz substrate by inductively coupled plasma etching. The performance of the fabricated SPP is verified by using beam intensity distribution, which is in agreement with the theoretical calculation result. The interference measurement suggests that we have succeeded to generate optical vortex with a unit topological charge with the fabricated SPP.     

Hybrid Lifting Wavelet-Like Transform for Solution of Electromagnetic Integral Equation

A hybrid lifting wavelet-like transform scheme is successfully applied to the solution of electric field integral equation using Rao-Wilton-Glisson basis functions. To speed up the matrix transform process, the lifting scheme is adopted. Numerical examples of different three-dimensional perfectly electric conducting objects are considered. Compared with the method of moments, the proposed matrix transform scheme can save considerable CPU time and memory.     

Rubinowicz transform of the MTPO surface integrals

The surface integral of the modified theory of physical optics is reduced to a line integral by using the Rubinowicz transform for the incident scattered fields by an arbitrary aperture in a black surface. The integral theorem of Kirchhoff is applied to the scattering geometry and the diffracted fields are expressed in terms of a line integral along the contour of the diffracting edge.     

The effect of impedance boundary conditions on the potential function of the boundary diffraction wave theory

A novel potential function of the boundary diffraction wave theory is obtained for the impedance surfaces by the asymptotic reduction of the modified theory of physical integrals. The function is expressed in terms of the direction vectors of the incident and scattered rays. The application of the method is performed on the problem of diffraction of plane waves by an impedance half plane for oblique incidence.     

Prevailing effects of interference or diffraction by multiple apertures

The effects of interference and diffraction produced by a bidimensional structure composed of multiple and identical apertures are studied. Such effects are competitive during the propagation, that is, in some planes the interference effects are more visible, while in others prevail the diffraction ones. Using the number of Fresnel zones, the spatial domains where the interference or diffraction effects prevail are defined and parameterized. Simulation and experimental results are further introduced to verify the proposed method.     

Turbulence Modulations in the Boundary Layer of a Horizontal Particle-Laden Channel Flow

Turbulence modulations are experimentally investigated using particle image velocimetry （PIV） in the lower boundary layer of a fully developed horizontal channel flow. A simultaneous two-phase PIV measurement technique is adopted to acquire the turbulent statistics quantities and to examine the coherent structures in the near-wall region. Polythene beads with diameters of 60 μm are used as dispersed phases, and the PIV measurements have been performed at three mass loadings varying from 2.5 ×10^-4 to 5 × 10^-3. All the experiments are performed at a wall shear Reynolds number of Reτ = 430. The results show that the presence of the particles suppresses the coherent structures, with shorter streamwise extent of the quasistrearnwise structures, and then, the wall-normal velocity fluctuations and shear Reynolds stresses are both decreased in the near-core region. In addition, as a result of the particle wake, the turbulence intensity and shear Reynolds stress both increase in the vicinity of the wall. Due to the drag effects of the particles on the gas, the streamwise velocity gradients decrease in the outer region and increase in the viscous sublayer, meanwhile the thickness of the viscous sublayer also decreases. These results cause the peak values of the streamwise velocity fluctuations adjacent to the wall to increase, and the peak positions shift to the wall. This is the reason for decreasing the near-wall region and increasing the near-core region of the streamwise velocity fluctuations in appearance.     

Formation of Small Bottle Light Beams

A method for obtaining small bottle light beams, e.g. 0.92λ×0.4λ, in a high numerical-aperture lens system is proposed and numerically demonstrated. This can be achieved by changing the radius of each zone of the binary element and polarization rotation angle of the cylindrically polarized vectorial vortex beam. It is found that the transversal and axial sizes of this bottle beam are equal to about 0.92λ and 0.4λ, respectively. In addition, the connection between angular momentum and topological Pancharatnam charge is also shown.     

Experimental observations of the spectrum of light diffracted at a slit as a secondary source

In this paper, we investigated both theoretically and experimentally the normalized spectrum of partially coherent light radiated from a secondary source which is produced by an imaging system. The experimental results show that, if the imaging lens is achromatic, the normalized spectrum of the light radiated from a secondary source shifts either towards the red side or towards the blue side, compared to the spectrum of the source, and the spectral shifts change for different position of the observation points. It is found that the experimental results are consistent with the theoretical ones. A chromatic lens, acting as the imaging lens, is used to investigate the effect of the chromatic aberration on the normalized spectrum of the light field. The results show that the influence of the chromatic aberration on the normalized spectrum is considerable and cannot be neglected in high-precision spectral measurement experiments.     

Debye Series of Scattering by a Multi-Layered Cylinder in an Off-Axis 2D Gaussian Beam

The Debye series of light scattering by an infinite multi-layered cylinder in an off-axis 21） Gaussian beam is studied. A simplified but rigorous iterative formula for scattering coefficients is presented. The numerical calculations of scattering intensity by a cylinder in on-axis and off-axis beams are developed. It is indicated that the results of Debye series reach an agreement with those of generalized Lorenz-Mie theory and the off-axis distances vary the results to a great extent. The Debye series components of a two-layered cylinder are further discussed. The relations between them with rainbow phenomena are analysed.     

Lattice Boltzmann Simulation for the Optimized Surface Pattern in a Micro-Channel

Based on the Bhatangar-Gross-Krook （BGK） models, numerical simulation using the lattice Boltzmann model is performed to investigate the optimized surface pattern in a micro-channel. In order to simulate the practical situation correctly, a slip/no-slip boundary condition is applied with making several assumptions. To assess the validity and efficiency of the model, one benchmark problem with considering the surface patterns is studied. Numerical results show the value of rms velocity Vrms increases with the increasing ratio β and larger Reynolds number Re, higher fluctuation of the rms oscillating velocity. Furthermore, the results show that a good mixing effect can be obtained when Re is large enough and the ratio β is about 1.618,which is the appropriate choice, i.e. the well known golden section phenomenon.     

Experimental observation of focal shifts in focused partially coherent beams

We report the experimental observation of focal shifts in partially coherent beams of Gaussian Schell-model (GSM) type focused by a circularly apertured thin lens. The relative focal shift increases as the aperture radius or the state of coherence of the GSM source decrease. The experimental results agree well with theoretical predictions.     

Tightly Focusing of Circularly Polarized Vortex Beams through a Uniaxial Birefringent Crystal

Under the approximation of small birefringence, the properties of circularly polarized vortex beams tightly focused through a uniaxial birefringent crystal are studied. With the proper combination of the topological charge and the birefringence, the small focus, the small bottle beam and the inverse c-shaped intensity profile can be obtained. The effects of the focal shift and the Strehl ratio on the birefringence are analysed. A relation between angular momentum （included spin and orbital） and topological Pancharatnam charge is also presented.     

Design of Super-resolution Filters with a Gaussian Beam in Optical Data Storage Systems

Super-resolution filters based on a Gaussian beam are proposed to reduce the focusing spot in optical data storage systems. Both of amplitude filters and pure-phase filters are designed respectively to gain the desired intensity distributions. Their performances are analysed and compared with those based on plane wave in detail. The energy utilizations are presented. The simulation results show that our designed super-resolution filters are favourable for use in optical data storage systems in terms of performance and energy utilization.     

Coherent effects of multiple scattering for scalar and electromagnetic fields: Monte-Carlo simulation and Milne-like solutions

Based on an expansion of the Bethe-Salpeter equation in scattering orders a semi-analytic approach for simulation of coherent phenomena of multiple scattering in random media has been developed. We found that for scalar field the manifestation of these phenomena, observed as temporal field correlation function and coherent backscattering, are universal and well agreed with the results predicted by diffusion approximation. For the electromagnetic field the temporal correlation function and coherent backscattering are noticeably differ from those found for the scalar field, depending strongly on the scattering anisotropy. The obtained numerical results, for the first time to our knowledge, are compared directly with the known generalizations of the Milne solution.