A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization

A new method for obtaining strong S-boxes based on chaotic map and Teaching–Learning-Based Optimization (TLBO) is presented in this paper. Our method presents eight rounds; each round contains two transformations: row left shifting and columnwise rotation. The vectors for the transformations are different from one round to another, and they are controlled by two keys to the logistic map. These two keys are optimized by using TLBO which aims to construct a strong S-box that satisfies to the criteria set in advance. Test for the following criteria such as bijectivity, nonlinearity, strict avalanche criteria, equiprobable inputs/outputs XOR distribution is analyzed. Additionally, we will provide many comparisons with other S-boxes and test of the sensitivity to keys. The results of performance test show that the proposed design S-boxes presents good cryptography proprieties and can resist to several attacks.     

A predictor–corrector time integration algorithm for dynamic analysis of nonlinear systems

Nonlinear Dynamics - This paper presents a step-by-step time integration algorithm for efficiently solving second-order nonlinear dynamic problems. The method employs the rewriting of motion as two...     

CABC–CSA: a new chaotic hybrid algorithm for solving optimization problems

Recently a lot of methods have been presented for solving optimization problems. In this paper, we are trying to propose a new hybrid algorithm for solving these kinds of problem. The proposed algorithm is based on chaotic artificial bee colony and chaotic simulated annealing, CABC–CSA. The chaotic artificial bee colony finds new locations chaotically. Actually, the proposed algorithm provides a combination of local search accuracy of simulated annealing and the ability of global search of artificial bee colony. Furthermore, we used a different method for generating the initial population. The proposed algorithm is validated using 12 benchmark functions. The results are compared with those of the artificial bees’ algorithm, the hybrid algorithm of artificial bee colony and simulated annealing and particle swarm optimization. Simulation results show the efficiency of the proposed algorithm.     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

Efficient method for designing chaotic S-boxes based on generalized Baker’s map and TDERC chaotic sequence

The theory of chaos is applied to the construction of substitution boxes used in encryption applications. The synthesis process of the proposed substitution boxes is presented, which is based on chaotic Baker’s map and TDERC chaotic sequences. The objectives of the new substitution box are to provide enhanced resistance against differential and linear cryptanalysis. The constructed substitution boxes uses Galois field elements and relies on discrete chaotic maps while keeping differential and linear approximation probabilities to desired levels.     

A new perturbation procedure for limit cycle analysis in three-dimensional nonlinear autonomous dynamical systems

By introducing a new parametric transformation and a suitable nonlinear frequency expansion, the modified Lindstedt–Poincaré method is extended to derive analytical approximations for limit cycles in three-dimensional nonlinear autonomous dynamical systems. By considering two typical examples, it can be seen that the results of the present method are in good agreement with those obtained numerically even if the control parameter is moderately large. Moreover, the present prediction is considerably more accurate than some published results obtained by the multiple time scales method and the normal form method.     

A New Stable Bubble Element for Incompressible Fluid Flow Based on a Mixed Petrov–Galerkin Finite Element Formulation

A new mixed Petrov–Galerkin formulation employing the MINI element with a non-confirming bubble function for an incompressible media governed by the Stokes equations, which is equivalent to the stabilized finite element by P ¹-P ¹ approximation, is proposed. The new formulation possesses better stability properties than the conventional Bubnov–Galerkin formulation employing the MINI element. In this aspect, the stabilizing effect of this formulation is evaluated by a stabilizing parameter determined by both shapes of the trial and the weighting bubble functions.     

A novel nonlinear contact stiffness model of concrete–steel joint based on the fractal contact theory

The heavy-duty machine tool is usually assumed in the concrete foundation, in which the machine tool-foundation joints have a critical effect on the working accuracy and life of heavy-duty machine tool. This paper proposed a novel contact stiffness model of concrete–steel joint based on the fractal theory. The topography of contact surface exist in concrete–steel joint has a fractal feature and can be described by fractal parameters. Asperities are considered as elastic, plastic deformation in micro-scale. However, the asperities of concrete surface will be crushed when the stress is larger than their yield limit. Then, the force balance of contact surfaces will be broken. Here, an iteration model is proposed to describe the contact state of concrete–steel joint. Because the contact asperities cover a very small proportion (less than 1%), the load on crushed asperities is assumed carried by other no contact asperities. This process will be repeated again and again until the crushed asperities are not being produced under external load. After that, the real contact area, contact stiffness of the concrete–steel joint can be calculated by integrating the asperities of contact surfaces. Nonlinear relationships between contact stiffness and load, fractal roughness parameter G, fractal dimension D can be revealed based on the presented model. An experimental setup with concrete–steel test-specimens is designed to validate the proposed model. Results indicate that the theoretical vibration mode shapes agree well with the experimental variation mode shapes. The errors between theoretical and experimental natural frequencies are less than 4.18%. The presented model can be used to predict the contact stiffness of concrete–steel joint, which will provide a theoretical basis for optimizing the connection characteristic of machine tool-concrete foundation.     

An efficient Galerkin averaging-incremental harmonic balance method for nonlinear dynamic analysis of rigid multibody systems governed by differential–algebraic equations

Nonlinear Dynamics - An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed for steady-state nonlinear dynamic analysis of index-3 differential algebraic...