Numerical modelling of multimode fibre-optic communication lines

The results of numerical modelling of nonlinear propagation of an optical signal in multimode fibres with a small differential group delay are presented. It is found that the dependence of the error vector magnitude (EVM) on the differential group delay can be reduced by increasing the number of ADC samples per symbol in the numerical implementation of the differential group delay compensation algorithm in the receiver. The possibility of using multimode fibres with a small differential group delay for data transmission in modern digital communication systems is demonstrated. It is shown that with increasing number of modes the strong coupling regime provides a lower EVM level than the weak coupling one.

Multi-threaded parallel numerical modelling of femtosecond pulse propagation in laser machining

Femtosecond laser microfabrication has emerged over the last decade as a 3D flexible technology in photonics. Numerical simulations provide an important insight into spatial and temporal beam and pulse shaping during the course of extremely intricate nonlinear propagation (see e.g. [1,2]). Electromagnetics of such propagation is typically described in the form of the generalized Non-Linear Schrdinger Equation (NLSE) coupled with Drude model for plasma [3]. In this paper we consider a multi-threaded parallel numerical solution for a specific model which describes femtosecond laser pulse propagation in transparent media [4, 5]. However our approach can be extended to similar models. The numerical code is implemented in NVIDIA Graphics Processing Unit (GPU) which provides an effitient hardware platform for multi-threded computing. We compare the performance of the described below parallel code implementated for GPU using CUDA programming interface [3] with a serial CPU version used in our previous papers [4,5]. © 2011 IEEE.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Numerical calculation of diffraction coefficients from building edges using FDTD method

Finite Difference Time Domain (FDTD) Method and software are applied to obtain diffraction waves from modulated Gaussian plane wave illumination for right angle wedges and Fast Fourier Transform (FFT) is used to get diffraction coefficients in a wideband in the illuminated lit region. Theta and Phi polarization in 3-dimensional, TM and TE polarization in 2-dimensional cases are considered respectively for soft and hard diffraction coefficients. Results using FDTD method of perfect electric conductor (PEC) wedge are compared with asymptotic expressions from Uniform Theory of Diffraction (UTD). Extend the PEC wedges to some homogenous conducting and dielectric building materials for diffraction coefficients that are not available analytically in practical conditions. ^

Quantifying the effects of temperature and concentration on variable-density flow in numerical modeling of groundwater systems: Implications for predictive uncertainty and data collection

Groundwater systems of different densities are often mathematically modeled to understand and predict environmental behavior such as seawater intrusion or submarine groundwater discharge. Additional data collection may be justified if it will cost-effectively aid in reducing the uncertainty of a model's prediction. The collection of salinity, as well as, temperature data could aid in reducing predictive uncertainty in a variable-density model. However, before numerical models can be created, rigorous testing of the modeling code needs to be completed. This research documents the benchmark testing of a new modeling code, SEAWAT Version 4. The benchmark problems include various combinations of density-dependent flow resulting from variations in concentration and temperature. The verified code, SEAWAT, was then applied to two different hydrological analyses to explore the capacity of a variable-density model to guide data collection. ^ The first analysis tested a linear method to guide data collection by quantifying the contribution of different data types and locations toward reducing predictive uncertainty in a nonlinear variable-density flow and transport model. The relative contributions of temperature and concentration measurements, at different locations within a simulated carbonate platform, for predicting movement of the saltwater interface were assessed. Results from the method showed that concentration data had greater worth than temperature data in reducing predictive uncertainty in this case. Results also indicated that a linear method could be used to quantify data worth in a nonlinear model. ^ The second hydrological analysis utilized a model to identify the transient response of the salinity, temperature, age, and amount of submarine groundwater discharge to changes in tidal ocean stage, seasonal temperature variations, and different types of geology. The model was compared to multiple kinds of data to (1) calibrate and verify the model, and (2) explore the potential for the model to be used to guide the collection of data using techniques such as electromagnetic resistivity, thermal imagery, and seepage meters. Results indicated that the model can be used to give insight to submarine groundwater discharge and be used to guide data collection. ^

Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape Enclosure

This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM). The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number.

Mechanisms governing the eyewall replacement cycle in numerical simulations of tropical cyclones

Eyewall replacement cycle (ERC) is frequently observed during the evolution of intensifying Tropical Cyclones (TCs). Although intensely studied in recent years, the underlying mechanisms of ERC are still poorly understood, and the forecast of ERC remains a great challenge. To advance our understanding of ERC and provide insights in improvement of numerical forecast of ERC, a series of numerical simulations is performed to investigate ERCs in TC-like vortices on a f-plane. The simulated ERCs possess key features similar to those observed in real TCs including the formation of a secondary tangential wind maximum associated with the outer eyewall. The Sawyer-Eliassen equation and tangential momentum budget analyses are performed to diagnose the mechanisms underlying the secondary eyewall formation (SEF) and ERC. Our diagnoses reveal crucial roles of outer rainband heating in governing the formation and development of the secondary tangential wind maximum and demonstrate that the outer rainband convection must reach a critical strength relative to the eyewall before SEF and the subsequent ERC can occur. A positive feedback among low-level convection, acceleration of tangential winds in the boundary layer, and surface evaporation that leads to the development of ERC and a mechanism for the demise of inner eyewall that involves interaction between the transverse circulations induced by eyewall and outer rainband convection are proposed. The tangential momentum budget indicates that the net tendency of tangential wind is a small residual resultant from a large cancellation between tendencies induced by the resolved and sub-grid scale (SGS) processes. The large SGS contribution to the tangential wind budget explains different characteristics of ERC shown in previous numerical studies and poses a great challenge for a timely correct forecast of ERC. The sensitivity experiments show that ERCs are strongly subjected to model physics, vortex radial structure and background wind. The impact of model physics on ERC can be well understood with the interaction among eyewall/outer rainband heating, radilal inflow in the boundary layer, surface layer turbulent processes, and shallow convection in the moat. However, further investigations are needed to fully understand the exhibited sensitivities of ERC to vortex radial structure and background wind.

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

Numerical modeling of gyroscopic effect in bidirectional ultrafast Erbium-doped fibre laser

We demonstrate the numerical model which allows investigation of gyroscopic effect in hybrid mode-locked bidirectional Erbium-doped fibre ring laser. The model is based on transport theory with accounting of dispersion, gain in EDFA and saturable absorption. The predictions of gyroscopic effect are also presented for the particular laser cavity.

Numerical detection of the Gardner transition in a mean-field glass former.

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.

Mechanisms Governing the Eyewall Replacement Cycle in Numerical Simulations of Tropical Cyclones

Eyewall replacement cycle (ERC) is frequently observed during the evolution of intensifying Tropical Cyclones (TCs). Although intensely studied in recent years, the underlying mechanisms of ERC are still poorly understood, and the forecast of ERC remains a great challenge. To advance our understanding of ERC and provide insights in improvement of numerical forecast of ERC, a series of numerical simulations is performed to investigate ERCs in TC-like vortices on a f-plane. The simulated ERCs possess key features similar to those observed in real TCs including the formation of a secondary tangential wind maximum associated with the outer eyewall. The Sawyer-Eliassen equation and tangential momentum budget analyses are performed to diagnose the mechanisms underlying the secondary eyewall formation (SEF) and ERC. Our diagnoses reveal crucial roles of outer rainband heating in governing the formation and development of the secondary tangential wind maximum and demonstrate that the outer rainband convection must reach a critical strength relative to the eyewall before SEF and the subsequent ERC can occur. A positive feedback among low-level convection, acceleration of tangential winds in the boundary layer, and surface evaporation that leads to the development of ERC and a mechanism for the demise of inner eyewall that involves interaction between the transverse circulations induced by eyewall and outer rainband convection are proposed. The tangential momentum budget indicates that the net tendency of tangential wind is a small residual resultant from a large cancellation between tendencies induced by the resolved and sub-grid scale (SGS) processes. The large SGS contribution to the tangential wind budget explains different characteristics of ERC shown in previous numerical studies and poses a great challenge for a timely correct forecast of ERC. The sensitivity experiments show that ERCs are strongly subjected to model physics, vortex radial structure and background wind. The impact of model physics on ERC can be well understood with the interaction among eyewall/outer rainband heating, radilal inflow in the boundary layer, surface layer turbulent processes, and shallow convection in the moat. However, further investigations are needed to fully understand the exhibited sensitivities of ERC to vortex radial structure and background wind.

Numerical study of neutron beam divergence in a beam-fusion scenario employing laser driven ions

The most established route to create a laser-based neutron source is by employing laser accelerated, low atomic-number ions in fusion reactions. In addition to the high reaction cross-sections at moderate energies of the projectile ions, the anisotropy in neutron emission is another important feature of beam-fusion reactions. Using a simple numerical model based on neutron generation in a pitcher–catcher scenario, anisotropy in neutron emission was studied for the deuterium–deuterium fusion reaction. Simulation results are consistent with the narrow-divergence ( ∼ 70 ° full width at half maximum) neutron beam recently served in an experiment employing multi-MeV deuteron beams of narrow divergence (up to 30° FWHM, depending on the ion energy) accelerated by a sub-petawatt laser pulse from thin deuterated plastic foils via the Target Normal Sheath Acceleration mechanism. By varying the input ion beam parameters, simulations show that a further improvement in the neutron beam directionality (i.e. reduction in the beam divergence) can be obtained by increasing the projectile ion beam temperature and cut-off energy, as expected from interactions employing higher power lasers at upcoming facilities.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.