Volume 20, Issue 2 -

We study the noise induced directed transport of an inertial Brownian particle moving in a symmetric spatially periodic potential and is subjected to correlated colored noises. Under the assumption of small correlation times of colored fluctuations we obtain an analytical expression for resulting current in overdamped systems. Our analytical and numerical calculations indicate the directed current is controlled by the correlation parameters. It has been pointed out that the nonzero correlation time makes an important contribution to current only at large enough values of noise intensities. The role of other system parameters is investigated from the viewpoint of optimization the current amplitude.

The effect of nonlinear damping including fractional damping on the onset of horseshoe chaos is studied both analytically and numerically in the double-well Duffing–Vander Pol (DVP) oscillator driven by various sinusoidal forces. The sinusoidal type periodic forces of our interest are sine wave, rectified sine wave, and modulus of sine wave. Using the Melnikov analytical method, the threshold condition for the onset of horseshoe chaos is obtained for each sinusoidal force. Melnikov threshold curves are drawn in ( f ,\; ω ) parameters space for each force. When the damping component ( p ) increases from a small value, the Melnikov threshold value (fM)$(f_{M})$ is decreased for each force. Suppression of horseshoe chaos is predicted due to the effect of weak periodic perturbation and nonlinear fractional damping. Analytical predictions are demonstrated through direct numerical simulations.

In this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

We propose a fourth-order spatial and second-order temporal accurate and unconditionally stable compact finite-difference scheme for the Cahn–Hilliard equation. The proposed scheme has a higher-order accuracy in space than conventional central difference schemes even though both methods use a three-point stencil. Its compactness may be useful when applying the scheme to numerical implementation. In a temporal discretization, the secant-type algorithm, which is known as the second-order accurate scheme, is applied. Furthermore, the unique solvability regardless of the temporal and spatial step size, unconditionally gradient stability, and discrete mass conservation are proven. It guarantees that large temporal and spatial step sizes could be used with the high-order accuracy and the original properties of the CH equation. Then, numerical results are presented to confirm the efficiency and accuracy of the proposed scheme. The efficiency of the proposed scheme is better than other low order accurate stable schemes.

Mean reversion of financial data, especially interest rates is often tested by linear unit root tests. However, there are times where linear unit root test results can be misleading especially when mean reverting jump formations are at stage. Considering this framework, we provide a new unit root testing methodology and compute its asymptotic critical values via Monte Carlo simulation. Moreover, we numerically compare the power of this generalized mean reversion test with the pioneering linear unit root test in the literature namely the Augmented Dickey Fuller (ADF) test. We deduce that our test is a refinement of ADF test with a higher power. We apply our findings to US 10-year Treasury bond yields. We aim to shed light to the discussion among researchers whether interest rates can sometimes revert to a long-term constant mean or not from an unorthodox point of view.

In this work, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation is studied and more accurate results obtained in respect of the previous investigations. The advanced heat transfer models have been used to study the effects of thermo-geometric parameters, coefficient of heat transfer and thermal conductivity parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. It is applied a novel intelligent computational approach for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem.

In this paper, a new chaotic image encryption scheme is proposed, which uses the combination of stream cipher and block cipher to spread and then uses the Logistic mapping matrix to perform the block sort transformation to complete the confusion. The specific method is as follows: First, perform the triple XOR operation, non-linear S-box transformation and linear cyclic shift transformation on the key. Second, the triple XOR operation of the transformed key and the plaintext and Logistic mapping sequence are used to obtain the semi-ciphertext. And set the obtained semi-ciphertext and plaintext as key components of the next round of encryption. Finally, the transformation of sorting and partition of the Logistic mapping matrix are used to confuse the semi-ciphertext. The experimental results show that the proposed algorithm improves the encryption efficiency, has good security and can resist common attacks.

The application of the composite materials in the aeronautical and aerospace industries has been increasing over the last several decades. Compared to conventional metallic materials, they present better strength to weight and stiffness to weight ratio. However, they can also present a high level of uncertainty, mainly associated with the manufacturing processes. Besides the uncertainty in the composite material parameters, which can play a role in the structural dynamic response, randomness can also be associated with boundary condition and external excitation sources. This paper treats the dynamic analysis of a composite beam under random excitation and uncertainties in the boundary condition. The beam is modelled by the spectral element method, a wave propagation technique. Some numerical examples are used to study the influence of random source on the dynamic behaviour of the composite structure.

The basic aim of this paper is to develop new numerical algorithms for solving some linear and nonlinear fractional-order differential equations. We have developed a new type of Chebyshev polynomials, namely, Chebyshev polynomials of sixth kind. This type of polynomials is a special class of symmetric orthogonal polynomials, involving four parameters that were constructed with the aid of the extended Sturm–Liouville theorem for symmetric functions. The proposed algorithms are basically built on reducing the fractional-order differential equations with their initial/boundary conditions to systems of algebraic equations which can be efficiently solved. The new proposed algorithms are supported by a detailed study of the convergence and error analysis of the sixth-kind Chebyshev expansion. New connection formulae between Chebyshev polynomials of the second and sixth kinds were established for this study. Some examples were displayed to illustrate the efficiency of the proposed algorithms compared to other methods in literature. The proposed algorithms have provided accurate results, even using few terms of the proposed expansion.

In this paper, we study finite time stability for linear and nonlinear delay systems with linear impulsive conditions and linear parts defined by permutable matrices. We introduce a new concept of impulsive delayed matrix function and apply the variation of constants method to seek a representation of solution of linear impulsive delay systems, which can be well used to deal with finite time stability. We establish sufficient conditions for the finite time stability results by using the properties of impulsive delayed matrix exponential and Gronwall’s integral inequalities. Finally, we give numerical examples to demonstrate the validity of theoretical results and present some possible advantage by comparing the current work with the previous literature.

In this paper, the propagation of particles with different sizes from a coal-based thermal power plant was investigated. It was found that the deterioration of the environment is due to the release of a large amount of SOx, NOx and the volatile particles of Suspended Particulate Matter and Respirable Suspended Particles matter, which cause human and animal diseases. This paper presents the numerical simulation results of air pollution by particles which having different sizes from thermal power plants in real sizes using a 3D model. For the adequacy of the mathematical model, a test problem was solved using different turbulent models. To assess the applicability of the mathematical model, the numerical algorithm and the choice of the optimal turbulent model, experimental data and numerical results of other authors were used. The obtained numerical simulation results are in good agreement with the experimental results and the numerical results of other authors. And to obtain more accurate numerical results for the experimental data for turbulent models (k−ε$k - \varepsilon $, k−ω$k - \omega $), there were certain corresponding boundary conditions for kinetic energy. Also, profiles of all flow characteristics were compared with and without particles and some effects of the particle on the flow were identified.