In this article, we investigate the temperature distribution in a one-dimensional metallic nanograting heated by a nanosecond Gaussian pulse laser using the finite element method. It is assumed that the nanograting slits are filled with a Kerr-type nonlinear material. The results indicate a strong dependency of the system's temperature distribution on the incident laser fluence. Also, the temperature distributions are completely different for linear and nonlinear regimes at high laser fluences around the pulse peak and after that. Indeed, exciting the nonlinear optical Kerr effect, especially at high laser fluences, leads to a change in the temperature response of the nonlinear regime compared to the linear one. Moreover, depending on the applied laser wavelength, there is a possibility of increasing or decreasing the temperature compared to the linear case. On the other hand, one can not enhance the laser fluence to any amount, as this may raise the temperature even higher than the melting point of the materials. Therefore, as the strong laser pulses are applied, temperature investigations should be conducted to prevent excessive heating and damage to the system.

One of the nonlinear optical phenomena which arise out of a (3) ,nonlinearity, is the intensity dependence of the refractive index. In this paper, we describe this phenomenon based on the nonlinear coherent states approach. We show that the deformed two-dimensional oscillator algebra can be used to describe this nonlinear optical system. Then, we construct the nonlinear coherent states for this nonlinear optical system and study their quantum statistical properties. Finally, we find that by changing nonlinearity of the media, it is possible to control the nonclassical properties of the system.

In this paper, we report the simulation results for impact of nonlinear Kerr effect on band structures of a two dimensional photonic crystal (2D-PhC) with no defect, a PhC based W1-waveguide (W1W), and also Coupled-Cavity Waveguides (CCWs). All PhC structures are assumed to a square lattice of constant a made of GaAs rods of radius r=0.2a, in an air background. The numerical simulation was performed using the nonlinear finite difference time domain (NFDTD) technique. In doing so, we have normalized the electric field and the electric flux density vectors, and used a multi probe procedure. These have resulted in very accurate dispersion relations that, in turn, have enabled us to make some novel observations. For instance, simulations show that with an increase in the input light intensity (in the nonlinear regime) the band edges for all three PhC structures experience some red shifts. The red shifts observed for CCWs are, of course, larger than the red shifts experienced by other two structures. Furthermore, the numerical results for CCWs also show that the larger the light input intensity, the smaller the corresponding maximum light group velocity becomes. To the best of our knowledge, this is the first instance that such observations on the impact of the nonlinear Kerr effect on the band diagram of 2D-PhC waveguides are reported.

In this paper, a Hamiltonian model, which includes the interaction of two two-level atoms with a codirectional Kerr nonlinear coupler via the Raman non-degenerate two-photon transition, is introduced. The atomic interaction is assumed to be in the dipole-dipole form, and the total system is also in thermal equilibrium with the environment. The total excitation number operator, as the constant of the motion of the system, provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a result, the representation of the Hamiltonian becomes a block-diagonal matrix. By diagonalizing each of the blocks, we obtain eigenvalues and the corresponding eigenstates of the Hamiltonian. Then we obtain the thermal state of the system in the whole Hilbert space and within its excitation subspaces. We quantify the thermal entanglement between the atoms in the Hilbert space of the system and within its excitation subspaces using the measure of the concurrence. Finally, the effect of temperature and system parameters on the degree of thermal entanglement is investigated. The results show that in the subspaces with an odd excitation number, the atomic thermal entanglement is thermally robust and remains constant.

Ever-increasing demands of the modern world and the growth of industry requirements toward more accurate analyses have made the engineering community develop the first fundamental step and meet the needs by extending the previous prevalent linear methods into nonlinear areas. In this regard, the improvement of linear modes as one of the most pervasive and widespread analytical methods opens a new window to analyses with more closeness to reality. In this paper, after the deep identification of Nonlinear Normal Modes, an approach is proposed to analyze the multidegree-of-freedom structures with nonlinear material under undamped free vibration. Afterward, through an in-depth investigation of the calculation methods, a novel algorithm for identifying Nonlinear Normal Modes was proposed, and by expanding this algorithm to the existing invariable motion equation used in free vibration analysis, the possibility of the extraction of all Nonlinear Normal Modes has emerged. After that, to investigate the functionality of the proposed approach, the Finite Elements Method-based Model of a 2-story steel structure was developed and, after verification, it was used to form the invariable differential equations. Finally, after verifying the Independent Periodic Method, pseudo-continuous masses of Nonlinear Normal Modes and FrequencyEnergy curves of the mentioned structure were calculated. It is worth noting that the independency of resulted response to previous points, the possibility of capturing Nonlinear Normal Modes with different frequencies in each degree-of-freedom, the potential of capturing all internal resonances, the expendability of Finite Elements Model to a set of invariable motion equations, and considering material nonlinearity are among achievements of the current paper.

In this study, the photonic band structure of two-dimensional photonic crystals with square and honeycomb lattices consisting of air holes in the Kerr nonlinear material background has been investigated. We assumed that the holes with different geometrical shapes are filled with plasma. The numerical results based on the finite difference time method show that most of the designed structures represent a complete photonic bandgap with noticeable width at optimum values of structural parameters for low-intensity incident waves, in which the width can be changed through varying the incident light intensity. The calculations show that when the shape of the plasmafilled holes is the same as the shape of the unit cell of the structures, the most change in the total photonic bandgap is visible in the frequency range as , ,,0 / 03(, c / a) the light intensity of the incident light changes. Furthermore, the maximum width of the photonic gap in these structures was reached , ,= 0. 0711(, c / a), which has increased approximately 0. 015(, c / a) in comparison with similar previously studied structures. The obtained result can be used for designing tunable optical devices.

This investigation presents material nonlinear analysis of a cantilever bar element made of functionally graded material with porosity properties. The material properties of bar element are considered as changing though axial direction based on the Power-Law distribution and uniform porosity distribution. The stress-strain relation of the material is considered as a nonlinear property according to a Power-Law function. The cantilever bar element is subjected to a point load at the free end. In order to obtain more realistic solution for the nonlinear problem and axially material distribution, nonlinear finite element method is used. In the obtaining of finite element equations, the virtual work principle is used and, after linearization step, the tangent stiffness matrix and residual vector are obtained. In the nonlinear solution process, the incremental force method is implemented and, each load step, the nonlinear equations are solved by using the Newton-Raphson iteration method. In the numerical results, effects of material nonlinearity parameters, porosity coefficients, material distribution parameter and aspect ratios on nonlinear static deflections of the bar are presented and discussed. The obtained results show that the material nonlinear behaviour of the bar element is considerably affected with porosity and material graduation.

In recent years, growing attention has been directed toward developing more realistic physical models for simulating complex and technically significant problems. This approach often leads to the formulation of nonlinear, multidimensional, and highly intricate models, whose analysis and solution require advanced numerical and analytical techniques. One of the most notable examples in this context is the transient and nonlinear heat conduction problem with temperature-dependent material properties. This paper presents, analyzes, and evaluates a comprehensive set of possible mathematical models for simulating this phenomenon, some of which are introduced here for the first time. Special emphasis is placed on the application of the Kirchhoff integral transform, typically used in steady-state nonlinear problems, and its precise implementation under transient conditions is thoroughly investigated. Based on this transform, both linear and nonlinear models are derived and compared. The linear models are particularly valuable due to their ability to yield accurate analytical solutions, facilitate inverse heat conduction analyses, enable temperature field control strategies, and offer clearer physical interpretations. Additionally, three new nonlinear models are proposed, two of which demonstrate very high accuracy, while the third, despite its lower precision, provides superior computational simplicity and faster performance. The findings of this study can serve as a foundation for developing more advanced thermal models and optimizing the design of engineering heat transfer systems

In this study, we propose a Feynman gate based on two-dimensional photonic crystals taking into account the non-linear Kerr effects. These devices can operate at high speed, with low power consumption. The performance of the Feynman logic gate presented in this paper is based on the nonlinear effects of Kerr and the formation of identical waveguides to alternate the structure. The wavelength of this design is set in the range of 1550 nm. One of the advantages of this design is its small size of 7. 54×8. 55 µ m2 which has been achieved due to the use of three waveguides. The minimum optical power for the case of logic 1 is 0. 95 and for case of logic 0 is 0. 2. So, the contrast ratio of 8. 4 dB can be obtained. Hence, the Feynman optical gate provided in this article is a good option for photonic computing circuits.