The article presents theoretical values of reverberation times calculated on the basis of the diffusion equation for three room models: flat, cubic, and long. The article shows that not only the average absorption coefficient, but also location of the absorbent material, as well as the place where the time is counted have an impact on the reverberation time, calculated on the basis of the diffusion equation. Despite that, the diffusion model is based on statistical assumptions. The primary goal of the article was to show that the model has geometrical features.
Refined Schwarz-Christoffel (SC) conformal transformations allow us to perform reliable quantitative evaluation of the accuracy of local computation of electric and magnetic fields with limited effort, which can be useful to complement well known comparisons of global results. In this paper some examples are presented for mesh point potentials obtained by means of finite difference (FD) methods, but it is possible that similar considerations will be useful in the case of finite element methods (FEM) or meshless computations too.
This paper presents the concept of using algorithms for reducing the dimensions of finite-difference equations of two-dimensional (2D) problems, for second-order partial differential equations. Solutions are predicted as two-variable functions over the rectangular domain, which are periodic with respect to each variable and which repeat outside the domain. Novel finite-difference operators, of both the first and second orders, are developed for such functions. These operators relate the value of derivatives at each point to the values of the function at all points distributed uniformly over the function domain. A specific feature of the novel operators follows from the arrangement of the function values as well as the values of derivatives, which are rectangular matrices instead of vectors. This significantly reduces the dimensions of the finite-difference operators to the numbers of points in each direction of the 2D area. The finite-difference equations are created exemplary elliptic equations. An original iterative algorithm is proposed for reducing the process of solving finite-difference equations to the multiplication of matrices.
The deformation modulus of the rock mass as a very important parameter in rock mechanic projects generally is determined by the plate load in-situ tests. While this test is very expensive and time-consuming, so in this study a new method is developed to combin artificial neural networks and numerical modeling for predicting deformation modulus of rock masses. For this aim, firstly, the plate load test was simulated using a Finite Difference numerical model that was verified with actual results of the plate load test in Pirtaghi dam galleries in Iran. Secondly, an artificial neural network is trained with a set of data resulted from numerical simulations to estimate the deformation modulus of the rock mass. The results showed that an ANN with five neurons in the input layer, three hidden layers with 4, 3 and 2 neurons, and one neuron in the output layer had the best accuracy for predicting the deformation modulus of the rock mass.
The main purpose of the study is to investigate the mechanical properties around an underground gas storage cavern in bedded salt rock. Firstly, considering the characteristics of the salt rock formation in China, the mechanical model was simplified into a hollow cylinder, which containing non-salt interlayer. In terms of elastic theory, Love displacement function was developed, and the elastic general solution of stress and deformation components were obtained after determining the undetermined coefficients. Under the same condition, numerical simulation was carried out. The validity of the elastic general solution is verified by comparing to numerical simulation results. Furthermore, Based on the feasible general elastic solution, viscoelastic solution was obtained through Laplace transformation and inverse Laplace transform, which could provide reference for the study on the stability and tightness of underground gas storage carven during operation to some extent.
In this attempt, Two Dimensional Photonic Crystal (2DPC) Quasi Square Ring Resonator (QSRR) based four channel demultiplexer is proposed and designed for Wavelength Division Multiplexing systems. The performance parameters of the demultiplexer such as transmission efficiency, passband width, line spacing, Q factor and crosstalk are investigated. The proposed demultiplexer is composed of bus waveguide, drop waveguide and QSRR. In the proposed demultiplexer, the output ports are arranged separately in odd and even number, where an odd number of ports are located on the right side and even number of ports are located on the left side of the bus waveguide that are used to reduce the channel interference or crosstalk. Further, the refractive index of rods around the center rod is increased linearly one to another in order to improve the signal quality. The resonant wavelengths of the proposed demultiplexer are of 1521.1 nm, 1522.0 nm, 1523.2 nm and 1524.3 nm, respectively. The footprint of the device is of 180.96 μm2. Then, a four channel point to point network is designed and the proposed four channel demultiplexer is implemented by replacing a conventional demultiplexer. Finally, functional parameters of the network, namely, BER, receiver sensitivity and Q factor are estimated by varying the link distance. This attempt could create new dimensions of research in the domain of photonic networks.
Recent years, the design of photonic crystal (PC) based optical devices is receiving keen interest in research and scientific community. In this paper, two dimensional (2D) PC based eight channel demultiplexer is proposed and designed and the functional characteristics of demultiplexer namely resonant wavelength, transmission efficiency, quality factor, spectral width, channel spacing and crosstalk are investigated. The demultiplexer is designed to drop the wavelength centred at 1537.6 nm, 1538.5 nm, 1539.4 nm, 1540.4 nm, 1541.2 nm, 1541.9 nm, 1542.6 nm and 1543.1 nm. The proposed demultiplexer is primarily composed of bus waveguide, drop waveguide and quasi square ring resonator. The quasi square ring resonator and square ring micro cavity (inner rods) are playing a vital role for a desired channel selection. The operating range of the devices is identified through a photonic band gap (PBG) which is obtained using a plane wave expansion (PWE) method. The functional characteristics of the proposed demultiplexer are attained using a 2D finite difference time domain (FDTD) method. The proposed device offers low crosstalk and high transmission efficiency with ultra-compact size, hence, it is highly desirable for DWDM applications.