Roughness of Limestone and Quartzite Pebbles by the Modified Fourier Method

Author(s):  
Eliza Czarnecka, J. E. Gillott
Keyword(s):  
2018 ◽  
Vol 1 (3) ◽  
pp. 2
Author(s):  
José Stênio De Negreiros Júnior ◽  
Daniel Do Nascimento e Sá Cavalcante ◽  
Jermana Lopes de Moraes ◽  
Lucas Rodrigues Marcelino ◽  
Francisco Tadeu De Carvalho Belchior Magalhães ◽  
...  

Simulating the propagation of optical pulses in a single mode optical fiber is of fundamental importance for studying the several effects that may occur within such medium when it is under some linear and nonlinear effects. In this work, we simulate it by implementing the nonlinear Schrödinger equation using the Split-Step Fourier method in some of its approaches. Then, we compare their running time, algorithm complexity and accuracy regarding energy conservation of the optical pulse. We note that the method is simple to implement and presents good results of energy conservation, besides low temporal cost. We observe a greater precision for the symmetrized approach, although its running time can be up to 126% higher than the other approaches, depending on the parameters set. We conclude that the time window must be adjusted for each length of propagation in the fiber, so that the error regarding energy conservation during propagation can be reduced.


2012 ◽  
Vol 28 (9) ◽  
pp. 095002 ◽  
Author(s):  
Chu-Li Fu ◽  
Yuan-Xiang Zhang ◽  
Hao Cheng ◽  
Yun-Jie Ma

2002 ◽  
Vol 464 ◽  
pp. 81-111 ◽  
Author(s):  
OLEG ZIKANOV ◽  
DONALD N. SLINN ◽  
MANHAR R. DHANAK

We present the results of large-eddy simulations (LES) of turbulent thermal convection generated by surface cooling in a finite-depth stably stratified horizontal layer with an isothermal bottom surface. The flow is a simplified model of turbulent convection occurring in the warm shallow ocean during adverse weather events. Simulations are performed in a 6 × 6 × 1 aspect ratio computational domain using the pseudo-spectral Fourier method in the horizontal plane and finite-difference discretization on a high-resolution clustered grid in the vertical direction. A moderate value of the Reynolds number and two different values of the Richardson number corresponding to a weak initial stratification are considered. A version of the dynamic model is applied as a subgrid-scale (SGS) closure. Its performance is evaluated based on comparison with the results of direct numerical simulations (DNS) and simulations using the Smagorinsky model. Comprehensive study of the spatial structure and statistical properties of the developed turbulent state shows some similarity to Rayleigh–Bénard convection and other types of turbulent thermal convection in horizontal layers, but also reveals distinctive features such as the dominance of a large-scale pattern of descending plumes and strong turbulent fluctuations near the surface.


1944 ◽  
Vol 11 (3) ◽  
pp. A176-A182
Author(s):  
Gerald Pickett

Abstract The paper shows how the Fourier method may be used to obtain exact solutions for stresses in rectangular prisms or circular cylinders for any boundary condition.


2021 ◽  
pp. 111-119
Author(s):  
D. Levkin ◽  

The article investigates some issues of complex systems analysis and synthesis that contain local, discrete sources of temperature fields. The emphasis of the author's research lies in the calculation and optimization of the parameters of the laser action on the embryo. The biotechnological process is described by the boundary value problem of a non-stationary, multidimensional differential equation of thermal conductivity which satisfies the boundary conditions of heat flux, beginning and end of the laser action process. The author proposes an algorithm for calculation and optimization of the control parameters of laser action on multilayer microbiological material. The object of the study is the embryo under the action of a laser beam for fission. As a first approximation, at the stage of calculation and optimization of the parameters of the biotechnological process, the embryo is considered as a homogeneous body. The values of thermophysical characteristics are calculated by the method of expert evaluation of the parameters of the emitters. The correctness of the boundary value problem of the process of laser action on the embryo is proved by the author using the method of pseudodifferential operators. Seeking the solution of the boundary value problem in the form of the series, the analytical function of the temperature field distribution is obtained using the Fourier method of the separated variables in the article. Using the method of indeterminate coefficients, the author found the temperature of the laser action on the embryo. Using the approximate gradient method of finding local extrema and the method of directed search of local extrema, it is possible to obtain rational values of optimized parameters of the biotechnological process. The author outlines possible approaches for optimization of technical parameters of laser emitters. In his opinion, the results of research can be considered fundamental for the calculation and optimization of the parameters of the laser action on the embryo, taking into account the multilayer structure of the latter.


Sign in / Sign up

Export Citation Format

Share Document