Search results for: non-linear feed-back

Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Ghania Zidani, Said Drid, Larbi Chrifi-Alaoui, Abdeslam Benmakhlouf, Souad Chaouch

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In this paper, we focus on the study for path tracking control of unicycle-type Wheeled Mobile Robots (WMR), by applying the Backstepping technic. The latter is a relatively new technic for nonlinear systems. To solve the problem of constraints nonholonomics met in the path tracking of such robots, an adaptive Backstepping based nonlinear controller is developed. The stability of the controller is guaranteed, using the Lyapunov theory. Simulation results show that the proposed controller achieves the objective and ensures good path tracking.

Keywords: Backstepping control, kinematic and dynamic controllers, Lyapunov methods, nonlinear control systems, Wheeled Mobile Robot (WMR).

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Authors: Ramonika Sengupta, Stuti Kachhwaha, Asha Adhiya, K. Satya Raja Sekhar, Rajwinder Kaur

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Numerous efforts have been done in the past decade to develop the methods of secure communication that are free from interception and eavesdropping. In fiber optic communication, chaotic optical carrier signals are used for data encryption in secure data transmission. Mach-Zehnder Modulators (MZM) are the key components for generating the chaotic signals to be used as optical carriers. This paper presents the dynamics of a lithium niobate MZM modulator under various biasing conditions. The chaotic fluctuations of the intensity of a laser diode have been generated using the electro-optic MZM modulator operating in a highly nonlinear regime. The modulator is driven in closed loop by its own output at an earlier time. When used as an electro-optic oscillator employing delayed feedback, the MZM displays a wide range of output waveforms of varying complexity. The dynamical behavior of the system ranges from periodic to nonlinear oscillations. The nonlinearity displayed by the system is reproducible and is easily controllable. In this paper, we demonstrate a wide variety of optical signals generated by MZM using easily controllable device parameters in both open and close loop bias conditions.

Keywords: chaotic carrier, fiber optic communication, Mach-Zehnder modulator, secure data transmission

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: H. Cha, J. Kim, D. Kim, J. Shin, K. Lee

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Since 1980's, the rapid economic growth resulted in so many aged apartment buildings in South Korea. Nevertheless, there is insufficient maintenance practice of buildings. In this study, to facilitate the building maintenance the authors classified the building defects into three levels according to their level of performance and developed a mobile application tool based on each level's appropriate feedback. The feedback structure consisted of 'Maintenance manual phase', 'Online feedback phase', 'Repair work phase of the specialty contractors'. In order to implement each phase the authors devised the necessary database for each phase and created a prototype system that can develop on its own. The authors expect that the building users can easily maintain their buildings by using this application.

Keywords: building defect, maintenance practice, mobile application, system algorithm

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Authors: Pawel Martynowicz

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Vibrations are a crucial problem for slender structures such as towers, masts, chimneys, wind turbines, bridges, high buildings, etc., that is why most of them are equipped with vibration attenuation or fatigue reduction solutions. In this work, a slender structure (i.e., wind turbine tower-nacelle model) equipped with nonlinear, semiactive tuned vibration absorber(s) is analyzed. For this study purposes, magnetorheological (MR) dampers are used as semiactive actuators. Several optimal-based approaches to structural vibration attenuation are investigated against the standard ‘ground-hook’ law and passive tuned vibration absorber(s) implementations. The common approach to optimal control of nonlinear systems is offline computation of the optimal solution, however, so determined open loop control suffers from lack of robustness to uncertainties (e.g., unmodelled dynamics, perturbations of external forces or initial conditions), and thus perturbation control techniques are often used. However, proper linearization may be an issue for highly nonlinear systems with implicit relations between state, co-state, and control. The main contribution of the author is the development as well as numerical and experimental verification of the Pontriagin maximum-principle-based vibration control concepts that produce directly actuator control input (not the demanded force), thus force tracking algorithm that results in control inaccuracy is entirely omitted. These concepts, including one-step optimal control, quasi-optimal control, and optimal-based modified ‘ground-hook’ law, can be directly implemented in online and real-time feedback control for periodic (or semi-periodic) disturbances with invariant or time-varying parameters, as well as for non-periodic, transient or random disturbances, what is a limitation for some other known solutions. No offline calculation, excitations/disturbances assumption or vibration frequency determination is necessary, moreover, all of the nonlinear actuator (MR damper) force constraints, i.e., no active forces, lower and upper saturation limits, hysteresis-type dynamics, etc., are embedded in the control technique, thus the solution is optimal or suboptimal for the assumed actuator, respecting its limitations. Depending on the selected method variant, a moderate or decisive reduction in the computational load is possible compared to other methods of nonlinear optimal control, while assuring the quality and robustness of the vibration reduction system, as well as considering multi-pronged operational aspects, such as possible minimization of the amplitude of the deflection and acceleration of the vibrating structure, its potential and/or kinetic energy, required actuator force, control input (e.g. electric current in the MR damper coil) and/or stroke amplitude. The developed solutions are characterized by high vibration reduction efficiency – the obtained maximum values of the dynamic amplification factor are close to 2.0, while for the best of the passive systems, these values exceed 3.5.

Keywords: magnetorheological damper, nonlinear tuned vibration absorber, optimal control, real-time structural vibration attenuation, wind turbines

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: M. Zamurad Shah, M. Kemal Ozgoren, Raza Samar

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This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: unmanned aerial vehicles, sliding mode control, 3D guidance, nonlinear sliding manifolds

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Authors: Salihu Abdullahi Galle

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Students' performance in Economics in schools and on standardized exams in Nigeria has been worrying throughout the years, owing to some teachers' use of conventional and lecture teaching methods. Other obstacles include a lack of training, standardized testing pressure, and aversion to change, all of which can have an impact on students' cognitive ability in Economics and future careers. The researchers employed formative evaluation with feedback (FEFB) to support the teaching and learning process by providing constant feedback to both teachers and students. The researchers employed a quasi-experimental research design to examine two teaching methods (FEFB and traditional). The pre-test and post-test interaction effects were evaluated between students in the experimental group (FEFB) and those in the conventional group. The interaction effects of pre-test and post-test on male and female in the two groups were also examined, with 90 participants. The findings show that students exposed to a FEFB-based teaching approach outperform pupils taught in a traditional classroom setting, and there is no gender interaction effect between the two groups. In light of these findings, the researchers urge that Economics teachers employ FEFB during teaching and learning to ensure timely feedback, and that policymakers ensure that Economics teachers receive training and re-training on FEFB approaches.

Keywords: formative evaluation with feedback (FEFB), students, economics achievement, secondary education

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Authors: Adina Dudau, Georgios Kominis, Melinda Szocs

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This paper links distinct bodies of literature around innovation and public services by examining a case of perceived innovation failure. Through a mixed methodology investigating student attitudes to, and behaviour around, technological innovation in higher education, the paper makes a contribution to the public service innovation literature by focusing on the duality of innovation outcomes, suggestive of an innovation typology in public services. The study was conducted in a UK Russell Group university and it focused on a technological process innovation. The innovation consisted of the provision of feedback to students in the form of a digital video (mp4), tailored to each individual submission, with extended voice-over commentary from the course coordinator and visual cues intended to help students see the relevance of comments to their submissions. The sample of the study consisted of a class of 79 undergraduate students. To investigate student attainment, we designed a field (also known as quasi or natural) experiment, essentially a manipulation of a social setting (in this case, the form of feedback given to students), but as part of a naturally occurring social arrangement (a real course which students attend and in which they are assessed). A two group control group design (see figure 3) was utilised to examine the effectiveness of the feedback innovation (video feedback). Two outcome variables of the service innovation were measured: student satisfaction and student attainment. In other words, the study examined not only students’ perceptions of whether VF was deemed to be beneficial towards their subsequent assignments; but also evidence of actual incremental benefits in students’ performance from one assignment to the next after VF was provided. The results were baffling and indicating competing agendas in higher education.

Keywords: higher education, audio-video, feedback, innovation

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Authors: Jitendra Kumar Chawla, Mukesh Kumar Mishra

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The nonlinear amplitude modulation of ion-acoustic wave is studied in the presence of two-electron temperature distribution in unmagnetized electron-positron-ion plasmas. The Krylov-Bogoliubov-Mitropolosky (KBM) perturbation method is used to derive the nonlinear Schrödinger equation. The dispersive and nonlinear coefficients are obtained which depend on the temperature and concentration of the hot and cold electron species as well as the positron density and temperature. The modulationally unstable regions are studied numerically for a wide range of wave number. The effects of the temperature and concentration of the hot and cold electron on the modulational stability are investigated in detail.

Keywords: modulational instability, ion acoustic wave, KBM method

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Authors: Yin Yuanling

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A Deep Feedback Recurrent Neural Network (DFRNN) and Bidirectional Long Short-Term Memory (BiLSTM) are designed to address the problem of low accuracy of traditional relationship extraction models. This method combines a deep feedback-based recurrent neural network (DFRNN) with a bi-directional long short-term memory (BiLSTM) approach. The method combines DFRNN, which extracts local features of text based on deep feedback recurrent mechanism, BiLSTM, which better extracts global features of text, and Self-Attention, which extracts semantic information. Experiments show that the method achieves an F1 value of 76.69% on the CEC dataset, which is 0.0652 better than the BiLSTM+Self-ATT model, thus optimizing the performance of the deep learning method in the event relationship extraction task.

Keywords: event relations, deep learning, DFRNN models, bi-directional long and short-term memory networks

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Authors: Abderrahmane El Kachani, El Mahjoub Chakir, Anass Ait Laachir, Abdelhamid Niaaniaa, Jamal Zerouaoui, Tarik Jarou

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This paper presents a wind turbine based on the doubly fed induction generator (DFIG) connected to the utility grid through a shunt active power filter (SAPF). The whole system is controlled by a double nonlinear predictive controller (DNPC). A Taylor series expansion is used to predict the outputs of the system. The control law is calculated by optimization of the cost function. The first nonlinear predictive controller (NPC) is designed to ensure the high performance tracking of the rotor speed and regulate the rotor current of the DFIG, while the second one is designed to control the SAPF in order to compensate the harmonic produces by the three-phase diode bridge supplied by a passive circuit (rd, Ld). As a result, we obtain sinusoidal waveforms of the stator voltage and stator current. The proposed nonlinear predictive controllers (NPCs) are validated via simulation on a 1.5 MW DFIG-based wind turbine connected to an SAPF. The results obtained appear to be satisfactory and promising.

Keywords: wind power, doubly fed induction generator, shunt active power filter, double nonlinear predictive controller

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Pelin Su Firat, Sohyung Cho

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Biopsy or aspiration procedures are known to be complicated as they involve the penetration of a needle through human tissues, including vital organs. This research presents the design of a force sensor-guided device to be used with syringes and needles for aspiration and biopsy. The development of the device was aimed to help accomplish accurate needle placement and increase the performance of the surgeon in navigating the tool and tracking the target. Specifically, a prototype for a force-sensor embedded syringe has been created using 3D (3-Dimensional) modeling and printing techniques in which two different force sensors were used to provide significant force feedback to users during the operations when needles pernitrate different tissues. From the extensive tests using synthetic tissues, it is shown that the proposed syringe design has accomplished the desired accuracy, efficiency, repeatability, and effectiveness. Further development is desirable through usability tests.

Keywords: biopsy, syringe, force sensors, haptic feedback

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Authors: Mami Miyasaka, Kaichi Yanaoka

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Attention Deficit/Hyperactivity Disorder (ADHD) is a neurodevelopmental disorder characterized by inattention, hyperactivity, and impulsivity; symptoms often manifest during childhood. In children with ADHD, the development of inhibitory processes is impaired. Inhibitory control allows people to avoid processing unnecessary stimuli and to behave appropriately in various situations; thus, people with ADHD require interventions to improve inhibitory control. Positive or negative reinforcements (i.e., reward or punishment) help improve the performance of children with such difficulties. However, in order to optimize impact, reward and punishment must be presented immediately following the relevant behavior. In regular elementary school classrooms, such supports are uncommon; hence, an alternative practical intervention method is required. One potential intervention involves setting goals to keep children motivated to perform tasks. This study examined whether goal setting improved inhibitory performances, especially for children with severe ADHD-related symptoms. We also focused on giving feedback on children's task performances. We expected that giving children feedback would help them set reasonable goals and monitor their performance. Feedback can be especially effective for children with severe ADHD-related symptoms because they have difficulty monitoring their own performance, perceiving their errors, and correcting their behavior. Our prediction was that goal setting by itself would be effective for children with mild ADHD-related symptoms, and goal setting based on feedback would be effective for children with severe ADHD-related symptoms. Japanese elementary school children and their parents were the sample for this study. Children performed two kinds of go/no-go tasks, and parents completed a checklist about their children's ADHD symptoms, the ADHD Rating Scale-IV, and the Conners 3rd edition. The go/no-go task is a cognitive task to measure inhibitory performance. Children were asked to press a key on the keyboard when a particular symbol appeared on the screen (go stimulus) and to refrain from doing so when another symbol was displayed (no-go stimulus). Errors obtained in response to a no-go stimulus indicated inhibitory impairment. To examine the effect of goal-setting on inhibitory control, 37 children (Mage = 9.49 ± 0.51) were required to set a performance goal, and 34 children (Mage = 9.44 ± 0.50) were not. Further, to manipulate the presence of feedback, in one go/no-go task, no information about children’s scores was provided; however, scores were revealed for the other type of go/no-go tasks. The results revealed a significant interaction between goal setting and feedback. However, three-way interaction between ADHD-related inattention, feedback, and goal setting was not significant. These results indicated that goal setting was effective for improving the performance of the go/no-go task only with feedback, regardless of ADHD severity. Furthermore, we found an interaction between ADHD-related inattention and feedback, indicating that informing inattentive children of their scores made them unexpectedly more impulsive. Taken together, giving feedback was, unexpectedly, too demanding for children with severe ADHD-related symptoms, but the combination of goal setting with feedback was effective for improving their inhibitory control. We discuss effective interventions for children with ADHD from the perspective of goal setting and feedback. This work was supported by the 14th Hakuho Research Grant for Child Education of the Hakuho Foundation.

Keywords: attention deficit disorder with hyperactivity, feedback, goal-setting, go/no-go task, inhibitory control

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Authors: Jaroslav Krutil, Simona Fialová, , František Pochylý

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A nonlinear mathematical model of mutual fluid-structure interaction is presented in the work. The model is applicable to the general shape of sealing gaps. An in compressible fluid and turbulent flow is assumed. The shaft carries a rotational and procession motion, the gap is axially flowed through. The achieved results of the additional mass, damping and stiffness matrices may be used in the solution of the rotor dynamics. The usage of this mathematical model is expected particularly in hydraulic machines. The method of control volumes in the ANSYS Fluent was used for the simulation. The obtained results of the pressure and velocity fields are used in the mathematical model of additional effects.

Keywords: nonlinear mathematical model, CFD modeling, hydrodynamic sealing gap, matrices of mass, stiffness, damping

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Authors: D. Gvozdikov

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The purpose of this study is an attempt to describe an online action as a system that combines disjointed events and behavioral chains into a whole. The research focuses on patterns of naturally-formed chains of actions united by an orientation towards the online environment. A key characteristic of the system of online action is that it acts as an attractor for separate actions and chains of behavioral repertoire accumulating time and efforts made by users. The article demonstrates how the chains of online-offline actions are combined into a single pattern due to a simple identifiable mechanism, a positive feedback system. Using methods of digital ethnography and analyzing the content of the Instagram application and media blogs, the research reveals how through the positive feedback mechanism the entire system of online action acquires stability and can expand involving new spheres of human activity.

Keywords: digital anthropology, internet studies, systems theory, social media

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Authors: Rupu Yang, Cong Toan Tran, Assaad Zoughaib

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The work provides an iterative nonlinear programming method to synthesize a heat exchanger network by manipulating the trade-offs between the heat load of process heat exchangers (HEs) and utilities. We consider for the synthesis problem two cases, the first one without fixed cost for HEs, and the second one with fixed cost. For the no fixed cost problem, the nonlinear programming (NLP) model with all the potential HEs is optimized to obtain the global optimum. For the case with fixed cost, the NLP model is iterated through adding/removing HEs. The method was applied in five case studies and illustrated quite well effectiveness. Among which, the approach reaches the lowest TAC (2,904,026$/year) compared with the best record for the famous Aromatic plants problem. It also locates a slightly better design than records in literature for a 10 streams case without fixed cost with only 1/9 computational time. Moreover, compared to the traditional mixed-integer nonlinear programming approach, the iterative NLP method opens a possibility to consider constraints (such as controllability or dynamic performances) that require knowing the structure of the network to be calculated.

Keywords: heat exchanger network, synthesis, NLP, optimization

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Authors: A. Chouaih, N. Benhalima, N. Boukabcha, R. Rahmani, F. Hamzaoui

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Zwitterionic compounds have received the interest of chemists and physicists due to their applications as nonlinear optical materials. Recently, zwitterionic compounds exhibiting high nonlinear optical activity have been investigated. In this context, the molecular electron charge density distribution of the title compound is described accurately using the multipolar model of Hansen and Coppens. The net atomic charge and the molecular dipole moment have been determined in order to understand the nature of inter- and intramolecular charge transfer. The study reveals the nature of intermolecular interactions including charge transfer and hydrogen bonds in the title compound. In this crystal, the molecules form dimers via intermolecular hydrogen bonds. The dimers are further linked by C–H...O hydrogen bonds into chains along the c crystallographic axis. This study has also allowed us to determine various nonlinear optical properties such as molecular electrostatic potential, polarizability, and hyperpolarizability of the title compound.

Keywords: organic compounds, polarizability, hyperpolarizability, dipole moment

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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Authors: Sandeep Kumar, Naveen Gupta

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Terahertz (THz) generation has been investigated by beating two cosh-Gaussian laser beams of the same amplitude but different wavenumbers and frequencies through rippled collisionless plasma. The ponderomotive force is operative which is induced due to the intensity gradient of the laser beam over the cross-section area of the wavefront. The electrons evacuate towards a low-intensity regime, which modifies the dielectric function of the medium and results in cross focusing of cosh-Gaussian laser beams. The evolution of spot size of laser beams has been studied by solving nonlinear Schrodinger wave equation (NLSE) with variational technique. The laser beams impart oscillations to electrons which are enhanced with ripple density. The nonlinear oscillatory motion of electrons gives rise to a nonlinear current density driving THz radiation. It has been observed that the periodicity of the ripple density helps to enhance the THz radiation.

Keywords: rippled collisionless plasma, cosh-gaussian laser beam, ponderomotive force, variational technique, nonlinear current density

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Authors: Farhad Ghasemi

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Along with transforming the international system into a complex and chaotic system, the fundamental question arises: how can deterrence be reconstructed conceptually and theoretically in this system model? The deterrence system is much more complex today than it was seven decades ago. This article suggests that the perception of deterrence as a linear system is a fundamental mistake because it does not consider the new dynamics of the international system, including network power dynamics. The author aims to improve this point by focusing on complexity and chaos theories, especially their nonlinearity and cascading failure principles. This article proposes that the perception of deterrence as a linear system is a fundamental mistake, as the new dynamics of the surrounding international system do not take into account. The author recognizes deterrence as a nonlinear system and introduces it as a concept in strategic studies.

Keywords: complexity, international system, deterrence, linear deterrence, nonlinear deterrence

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Authors: Young Hee Geum

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We compare optimal quartic order method for the multiple zeros of nonlinear equations illustrating the basins of attraction. To construct basins of attraction effectively, we take a 600×600 uniform grid points at the origin of the complex plane and paint the initial values on the basins of attraction with different colors according to the iteration number required for convergence.

Keywords: basins of attraction, convergence, multiple-root, nonlinear equation

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Authors: Ashkan Golgoon, Souhayl Sadik, Arash Yavari

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Eigenstrains in nonlinear solids are created due to anelastic effects such as non-uniform temperature distributions, growth, remodeling, and defects. Eigenstrains understanding is indispensable, as they can generate residual stresses and strongly affect the overall response of solids. Here, we study the residual stress and deformation fields of an incompressible isotropic infinite wedge with a circumferentially-symmetric distribution of finite eigenstrains. We construct a material manifold, whose Riemannian metric explicitly depends on the eigenstrain distribution, thereby we turn the problem into a classical nonlinear elasticity problem, where we find an embedding of the Riemannian material manifold into the ambient Euclidean space. In particular, we find exact solutions for the residual stress and deformation fields of a neo-Hookean wedge having a symmetric inclusion with finite radial and circumferential eigenstrains. Moreover, we numerically solve a similar problem when a symmetric Mooney-Rivlin inhomogeneity with finite eigenstrains is placed in a neo-Hookean wedge. Generalization of the eigenstrain problem to other geometries are also discussed.

Keywords: finite eigenstrains, geometric mechanics, inclusion, inhomogeneity, nonlinear elasticity

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Authors: Gigih Priyandoko, Mohd Fairusham Ghazali, Tan Siew Fun

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This paper discusses about the defect detection of plastic pipe by using nonlinear acoustic wave modulation method. It is a sensitive method for damage detection and it is based on the propagation of high frequency acoustic waves in plastic pipe with low frequency excitation. The plastic pipe is excited simultaneously with a slow amplitude modulated vibration pumping wave and a constant amplitude probing wave. The frequency of both the excitation signals coincides with the resonances of the plastic pipe. A PVP pipe is used as the specimen as it is commonly used for the conveyance of liquid in many fields. The results obtained are being observed and the difference between uncracked specimen and cracked specimen can be distinguished clearly.

Keywords: plastic pipe, defect detection, nonlinear acoustic modulation, excitation

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Authors: A. Abdikian

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Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.

Keywords: bifurcation theory, phase portrait, magnetized electron-positron plasma, the Zakharov-Kuznetsov equation

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