Search results for: nonlinear optics

Authors: Rajkumar N. Ingle

Abstract:

In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Remzi Yildirim, Fatih. V. Çelebi, H. Haldun Göktaş, A. Behzat Şahin

Abstract:

This study is about a single component cylindrical structured lens with gradient curve which we used for bending laser beams. It operates under atmospheric conditions and bends the laser beam independent of temperature, pressure, polarity, polarization, magnetic field, electric field, radioactivity, and gravity. A single piece cylindrical lens that can bend laser beams is invented. Lenses are made of transparent, tinted or colored glasses and used for undermining or absorbing the energy of the laser beams.

Keywords: laser, bending, lens, light, nonlinear optics

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Authors: Remzi Yildirim, Fatih V. Çelebi, H. Haldun Göktaş, A. Behzat Şahin

Abstract:

This study is about a single component cylindrical structured lens with gradient curve which we used for bending laser beams. It operates under atmospheric conditions and bends the laser beam independent of temperature, pressure, polarity, polarization, magnetic field, electric field, radioactivity, and gravity. A single piece cylindrical lens that can bend laser beams is invented. Lenses are made of transparent, tinted or colored glasses and used for undermining or absorbing the energy of the laser beams.

Keywords: laser, bending, lens, light, nonlinear optics

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Authors: A. Belmeguenai, K. Mansouri, R. Djemili

Abstract:

This work present a new algorithm based on the nonlinear filter generator for speech encryption and decryption. The proposed algorithm consists on the use a linear feedback shift register (LFSR) whose polynomial is primitive and nonlinear Boolean function. The purpose of this system is to construct Keystream with good statistical properties, but also easily computable on a machine with limited capacity calculated. This proposed speech encryption scheme is very simple, highly efficient, and fast to implement the speech encryption and decryption. We conclude the paper by showing that this system can resist certain known attacks.

Keywords: nonlinear filter generator, stream ciphers, speech encryption, security analysis

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Authors: Nicolò Vaiana, Giorgio Serino

Abstract:

The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Keywords: base isolation, computational efficiency, nonlinear exponential model, nonlinear time history analysis

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Authors: Oibar Martinez, Clara Oliver, Jose Miguel Miranda

Abstract:

The study of dispersion phenomena in electromagnetic waves reflected by conductors at infrared and lower frequencies is a topic which finds a number of applications. We aim to explain in this work what are the most relevant ones and how this phenomenon is modeled from both optics and electromagnetics points of view. We also explain here how the amplitude of an electromagnetic wave reflected by a lossy conductor could depend on both the frequency of the incident wave, as well as on the electrical properties of the conductor, and we illustrate this phenomenon with a practical example. The mathematical analysis made by a specialist in electromagnetics or a microwave engineer is apparently very different from the one made by a specialist in optics. We show here how both approaches lead to the same physical result and what are the key concepts which enable one to understand that despite the differences in the equations the solution to the problem happens to be the same. Our study starts with an analysis made by using the complex refractive index and the reflectance parameter. We show how this reflectance has a dependence with the square root of the frequency when the reflecting material is a good conductor, and the frequency of the wave is low enough. Then we analyze the same problem with a less known approach, which is based on the reflection coefficient of the electric field, a parameter that is most commonly used in electromagnetics and microwave engineering. In summary, this paper presents a mathematical study illustrated with a worked example which unifies the modeling of dispersion effects made by specialists in optics and the one made by specialists in electromagnetics. The main finding of this work is that it is possible to reproduce the dependence of the Fresnel reflectance with frequency from the intrinsic impedance of the reflecting media.

Keywords: dispersion, electromagnetic waves, microwaves, optics

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Authors: Melusi Khumalo, Anastacia Dlamini

Abstract:

In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Doğan Yıldız, Aydan Müşerref Erkmen

Abstract:

The controller of the octocopter is mostly based on the PID controller. For complex maneuvers, PID controllers have limited performance capability like in collision avoidance. When an octocopter needs avoidance from an obstacle, it must instantly show an agile maneuver. Also, this kind of maneuver is affected severely by the nonlinear characteristic of octocopter. When these kinds of limitations are considered, the situation is highly challenging for the PID controller. In the proposed study, these challenges are tried to minimize by using the model predictive controller (MPC) for collision avoidance with a nonlinear octocopter model. The aim is to show that MPC-based collision avoidance has the capability to deal with fast varying conditions in case of obstacle detection and diminish the nonlinear effects of octocopter with varying disturbances.

Keywords: model predictive control, nonlinear octocopter model, collision avoidance, obstacle detection

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Authors: Win Ko Ko, A. N. Temnov

Abstract:

The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: nonlinear oscillations, two-layered liquid, instability region, hydrodynamic coefficients, resonance frequency

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Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Z. Zerdoumi, D. Benatia, , D. Chicouche

Abstract:

This paper investigates the application of artificial neural network to the problem of nonlinear channel equalization. The difficulties caused by channel distortions such as inter symbol interference (ISI) and nonlinearity can overcome by nonlinear equalizers employing neural networks. It has been shown that multilayer perceptron based equalizer outperform significantly linear equalizers. We present a multilayer perceptron based equalizer with decision feedback (MLP-DFE) trained with the back propagation algorithm. The capacity of the MLP-DFE to deal with nonlinear channels is evaluated. From simulation results it can be noted that the MLP based DFE improves significantly the restored signal quality, the steady state mean square error (MSE), and minimum Bit Error Rate (BER), when comparing with its conventional counterpart.

Keywords: Artificial Neural Network, signal restoration, Nonlinear Channel equalization, equalization

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

Abstract:

Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: Shan-Jen Cheng, Te-Jen Chang, Kuang-Hsiung Tan, Shou-Ling Kuo

Abstract:

Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently.

Keywords: PEMFC, neural network, nonlinear modeling, NNARX

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Authors: Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy

Abstract:

Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.

Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari

Abstract:

In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.

Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load

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Authors: Mohammad Reza Rahimi Khoygani, Reza Ghasemi

Abstract:

In this paper, designing direct adaptive neural controller is applied for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) is used for the Neural network (NN). The adaptive neural controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are the merits of this paper. The promising performance of the proposed controllers investigates in simulation results.

Keywords: adaptive control, pendulum dynamical system, nonlinear control, adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: Hamza Nejib, Okba Taouali

Abstract:

This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS

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Authors: Kunwar Mrityunjai Sharma, Trilok Nath Singh

Abstract:

The Navier-Stokes equation is used to study nonlinear fluid flow in rough 2D fractures. The major goal is to investigate the influence of inertial flow owing to fracture wall roughness on nonlinear flow behavior. Roughness profiles are developed using Barton's Joint Roughness Coefficient (JRC) and used as fracture walls to assess wall roughness. Four JRC profiles (5, 11, 15, and 19) are employed in the study, where a higher number indicates higher roughness. A parametric study has been performed using varying pressure gradients, and the corresponding Forchheimer number is calculated to observe the nonlinear behavior. The results indicate that the fracture roughness has a significant effect on the onset of nonlinearity. Additionally, the validity of the cubic law is evaluated and observed that it overestimates the flow in rough fractures and should be used with utmost care.

Keywords: fracture flow, nonlinear flow, cubic law, Navier-stokes equation

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Authors: Shivani Singla, Om Prakash Pandey, Gopi Sharma

Abstract:

Metallic nanoparticle doped glasses has lead to rapid development in the field of optics. Large third order non-linearity, ultrafast time response, and a wide range of resonant absorption frequencies make these metallic nanoparticles more important in comparison to their bulk material. All these properties are highly dependent upon the size, shape, and surrounding environment of the nanoparticles. In a quest to find a suitable material for optical applications, several efforts have been devoted to improve the properties of such glasses in the past. In the present study, bismuth borate glass doped with different size gold nanoparticles (AuNPs) has been prepared using the conventional melt-quench technique. Synthesized glasses are characterized by X-ray diffraction (XRD) and Fourier Transformation Infrared spectroscopy (FTIR) to observe the structural modification in the glassy matrix with the variation in the size of the AuNPs. Glasses remain purely amorphous in nature even after the addition of AuNPs, whereas FTIR proposes that the main structure contains BO₃ and BO₄ units. Field emission scanning electron microscopy (FESEM) confirms the existence and variation in the size of AuNPs. Differential thermal analysis (DTA) depicts that prepared glasses are thermally stable and are highly suitable for the fabrication of optical fibers. The nonlinear optical parameters (nonlinear absorption coefficient and nonlinear refractive index) are calculated out by using the Z-scan technique with a Ti: sapphire laser at 800 nm. It has been concluded that the size of the nanoparticles highly influences the structural thermal and optical properties system.

Keywords: bismuth borate glass, different size, gold nanoparticles, nonlinearity

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Authors: Abdullah Eqal Al Mazrooei

Abstract:

In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system.

Keywords: Lorenz models, nonlinear systems, nonlinear estimator, state-space model

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Authors: Hamid Havasi, Mohamad Reza Gholami Dehbalaei, Hamed Khorami, Shahram Karimi, Hamdi Abdi

Abstract:

Doubly-fed induction generator (DFIG) equipped with a power converter is an efficient tool for converting mechanical energy of a variable speed system to a fixed-frequency electrical grid. Since electrical energy sources faces with production problems such as harmonics caused by nonlinear loads, so in this paper, compensation performance of DPC and FOC method on harmonics reduction of a DFIG wind turbine connected to a nonlinear load in MATLAB Simulink model has been simulated and effect of each method on nonlinear load harmonic elimination has been compared. Results of the two mentioned control methods shows the advantage of the FOC method on DPC method for harmonic compensation. Also, the fifth and seventh harmonic components of the network and THD greatly reduced.

Keywords: DFIG machine, energy conversion, nonlinear load, THD, DPC, FOC

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

Abstract:

The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

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Authors: Ersin Bozkurt

Abstract:

The aim of the study is to develop materials for understanding image formations through virtual objects in geometric optics. The images in physics course books are formed by using real objects. This results in mistakes in the features of images because of generalizations which leads to conceptual misunderstandings in learning. In this study it was intended to identify pre-service physics teachers misunderstandings arising from false generalizations. Focused group interview was used as a qualitative method. The findings of the study show that students have several misconceptions such as "the image in a plain mirror is always virtual". However a real image can be formed in a plain mirror. To explain a virtual object's image formation in a more understandable way an overhead projector and episcope and their design was illustrated. The illustrations are original and several computer simulations will be suggested.

Keywords: computer simulations, geometric optics, physics education, students' misconceptions in physics

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

Abstract:

In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: M. Seguini, D. Nedjar

Abstract:

An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.

Keywords: finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability

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Authors: Hao Chen, Bo Guo, Ping Jiang

Abstract:

Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: M. Seguini, D. Nedjar

Abstract:

In this paper, the nonlinear analysis of Timoshenko beam undergoing moderate large deflections and resting on nonlinear two-parameter random foundation is presented, taking into account the effects of shear deformation, beam’s properties variation and the spatial variability of soil characteristics. The finite element probabilistic analysis has been performed by using Timoshenko beam theory with the Von Kàrmàn nonlinear strain-displacement relationships combined to Vanmarcke theory and Monte Carlo simulations, which is implemented in a Matlab program. Numerical examples of the newly developed model is conducted to confirm the efficiency and accuracy of this later and the importance of accounting for the foundation second parameter (Winkler-Pasternak). Thus, the results obtained from the developed model are presented and compared with those available in the literature to examine how the consideration of the shear and spatial variability of soil’s characteristics affects the response of the system.

Keywords: nonlinear analysis, soil-structure interaction, large deflection, Timoshenko beam, Euler-Bernoulli beam, Winkler foundation, Pasternak foundation, spatial variability

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Authors: Praveen Kumar, R. Uma, R. P. Sharma

Abstract:

This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range.

Keywords: water waves, modulation instability, hydrodynamics, nonlinear Schrödinger's equation

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Authors: Hoda Aleali, Nastran Mansour, Maryam Mirzaie

Abstract:

In this paper, we study the optical nonlinearities of Silver sulfide (Ag2S) nanostructures dispersed in the Dimethyl sulfoxide (DMSO) under exposure to 532 nm, 15 nanosecond (ns) pulsed laser irradiation. Ultraviolet–visible absorption spectrometry (UV-Vis), X-ray diffraction (XRD), and transmission electron microscopy (TEM) are used to characterize the obtained nanocrystal samples. The band gap energy of colloid is determined by analyzing the UV–Vis absorption spectra of the Ag2S NPs using the band theory of semiconductors. Z-scan technique is used to characterize the optical nonlinear properties of the Ag2S nanoparticles (NPs). Large enhancement of two photon absorption effect is observed with increase in concentration of the Ag2S nanoparticles using open Z-scan measurements in the ns laser regime. The values of the nonlinear absorption coefficients are determined based on the local nonlinear responses including two photon absorption. The observed aperture dependence of the Ag2S NP limiting performance indicates that the nonlinear scattering plays an important role in the limiting action of the sample.The concentration dependence of the optical liming is also investigated. Our results demonstrate that the optical limiting threshold decreases with increasing the silver sulfide NPs in DMSO.

Keywords: nanoscale materials, silver sulfide nanoparticles, nonlinear absorption, nonlinear scattering, optical limiting

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

Abstract:

The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

Procedia PDF Downloads 49