Search results for: non-linear exponential (NLINEX) loss function

Authors: Haider M. Alsaeq

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The present research is an attempt to figure out the best configuration of composite cylindrical shells of the sandwich type, i.e. the lightest design of such shells required to sustain a certain load over a certain area. The optimization is based on elastic-plastic geometrically nonlinear incremental-iterative finite element analysis. The nine-node degenerated curved shell element is used in which five degrees of freedom are specified at each nodal point, with a layered model. The formulation of the geometrical nonlinearity problem is carried out using the well-known total Lagrangian principle. For the structural optimization problem, which is dealt with as a constrained nonlinear optimization, the so-called Modified Hooke and Jeeves method is employed by considering the weight of the shell as the objective function with stress and geometrical constraints. It was concluded that the optimum design of composite sandwich cylindrical shell that have a rigid polyurethane foam core and steel facing occurs when the area covered by the shell becomes almost square with a ratio of core thickness to facing thickness lies between 45 and 49, while the optimum height to length ration varies from 0.03 to 0.08 depending on the aspect ratio of the shell and its boundary conditions.

Keywords: composite structure, cylindrical shell, optimization, non-linear analysis, finite element

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Authors: S. U. Durgadsimi, S. Chouguleb, S. Belladc

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(y) Li0.5Ni0.7Zn0.05Fe2O4 + (1-y) Ba0.5Sr0.5TiO3 magnetoelectric composites with y = 0.1, 0.3 and 0.5 were prepared by a conventional standard double sintering ceramic technique. X-ray diffraction analysis confirmed the phase formation of ferrite, ferroelectric and their composites. logρdc Vs 1/T graphs reveal that the dc resistivity decreases with increasing temperature exhibiting semiconductor behavior. The plots of logσac Vs logω2 are almost linear indicating that the conductivity increases with increase in frequency i.e, conductivity in the composites is due to small polaron hopping. Dielectric constant (έ) and dielectric loss (tan δ) were studied as a function of frequency in the range 100Hz–1MHz which reveals the normal dielectric behavior except the composite with y=0.1 and as a function of temperature at four fixed frequencies (i.e. 100Hz, 1KHz, 10KHz, 100KHz). ME voltage coefficient decreases with increase in ferrite content and was observed to be maximum of about 7.495 mV/cmOe for (0.1) Li0.5Ni0.7Zn0.05Fe2O4 + (0.9) Ba0.5Sr0.5TiO3 composite.

Keywords: XRD, dielectric constant, dielectric loss, DC and AC conductivity, ME voltage coefficient

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Authors: Ahmed Gaber Abdel Raheem, Nashwa Ahmed Mohamed

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Introduction: Sensorineural hearing loss (SNHL) is largely caused by the degeneration of the cochlea. Therapeutic options for SNHL are limited to hearing aids and cochlear implants. The cell transplantation approach to the regeneration of hair cells has gained considerable attention because stem cells are believed to accumulate in the damaged sites and have the potential for the repair of damaged tissues. The aim of the work: was to assess the use of bone marrow transplantation in repair of damaged inner ear hair cells in rats after the damage had been inflicted by Amikacin injection. Material and Methods: Thirty albino rats were used in this study. They were divided into three groups. Each group ten rats. Group I: used as control. Group II: Were given Amikacin- intratympanic injection till complete loss of hearing function. This could be assessed by Distortion product Otoacoustic Emission (DPOAEs) and / or auditory brain stem evoked potential (ABR). GroupIII: were given intra-peritoneal injection of bone marrow stem cell after complete loss of hearing caused by Amikacin. Clinical assessment was done using DPOAEs and / or auditory brain stem evoked potential (ABR), before and after bone marrow injection. Histological assessment of the inner ear was done by light and electron microscope. Also, Detection of stem cells in the inner ear by immunohistochemistry. Results: Histological examination of the specimens showed promising improvement in the structure of cochlea that may be responsible for the improvement of hearing function in rats detected by DPOAEs and / or ABR. Conclusion: Bone marrow stem cells transplantation might be useful for the treatment of SNHL.

Keywords: amikacin, hair cells, sensorineural hearing loss, stem cells

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Authors: D. Ravinder, K. S. Nagaraju

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Ni–Al ferrite with composition of NiAlxFe2-xO4 (x=0.2, 0.4 0.6, and 0.8, ) were prepared by citrate gel method. The dielectric properties for all the samples were investigated at room temperature as a function of frequency. The dielectric constant shows dispersion in the lower frequency region and remains almost constant at higher frequencies. The frequency dependence of dielectric loss tangent (tanδ) is found to be abnormal, giving a peak at certain frequency for mixed Ni-Al ferrites. A qualitative explanation is given for the composition and frequency dependence of the dielectric loss tangent.

Keywords: ferrites, citrate method, lattice parameter, dielectric constant

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Authors: Toshinori Nawata

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In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designing the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics

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Authors: Yugander Arra, Florence Auguy, Melissa Stiebner, Sophie Chéron, Michael M. Wudick, Van Schepler-Luu, Sébastien Cunnac, Wolf B. Frommer, Laurence Albar

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Rice yellow mottle virus (RYMV) is one of the most important diseases affecting rice in Africa. The most promising strategy to reduce yield losses is the use of highly resistant varieties. The resistance gene RYMV2 is homolog of the Arabidopsis constitutive expression of pathogenesis related protein-5 (AtCPR5) nucleoporin gene. Resistance alleles are originating from African cultivated rice Oryza glaberrima, rarely cultivated, and are characterized by frameshifts or early stop codons, leading to a non-functional or truncated protein. Rice possesses two paralogs of CPR5 and function of these genes are unclear. Here, we evaluated the role of the two rice candidate nucleoporin paralogs OsCPR5.1 (pathogenesis-related gene 5; RYMV2) and OsCPR5.2 by CRISPR/Cas9 genome editing. Despite striking sequence and structural similarity, only loss-of-function of OsCPR5.1 led to full resistance, while loss-of-function oscpr5.2 mutants remained susceptible. Short N-terminal deletions in OsCPR5.1 also did not lead to resistance. In contrast to Atcpr5 mutants, neither OsCPR5.1 nor OsCPR5.2 knock out mutants showed substantial growth defects. Taken together, the candidate nucleoporin OsCPR5.1, but not its close homolog OsCPR5.2, plays a specific role for the susceptibility to RYMV, possibly by impairing the import of viral RNA or protein into the nucleus. Whereas gene introgression from O. glaberrima to high yielding O. sativa varieties is impaired by strong sterility barriers and the negative impact of linkage drag, genome editing of OsCPR5.1, while maintaining OsCPR5.2 activity, thus provides a promising strategy to generate O. sativa elite lines that are resistant to RYMV.

Keywords: CRISPR Cas9, genome editing, knock out mutant, recessive resistance, rice yellow mottle virus

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Authors: Fernando P. Silva, Valter J. S. Leite, Erivelton G. Nepomuceno

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In this paper, a nonlinear controller design for an omnidirectional mobile is presented. The robot controller consists of an inner-loop controller and an outer-loop controller, the first is designed using state feedback (robust allocation) and the second controller is designed based on Robust Multi Inversion (RMI) approach. The objective of RMI controller is rendering the robust inversion of the dynamic, when the model is affected by uncertainties. A model nonlinear MIMO of an omni-directional robot (small-league of Robocup) is used to simulate the RMI approach. The parameters of linear and nonlinear model are varied to cause modelling uncertainties among the model and the real model (real system) generating an error in inner-loop controller signal that must be compensated by RMI controller. The simulation test results show that the RMI is capable of compensating the uncertainties and keep the system stable and controlled under uncertainties.

Keywords: robust multi inversion, omni-directional robot, robocup, nonlinear control

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Authors: Magdi. M. Nabi, Ding-Li Yu

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Control of a semi-batch polymerization reactor using an adaptive radial basis function (RBF) neural network method is investigated in this paper. A neural network inverse model is used to estimate the valve position of the reactor; this method can identify the controlled system with the RBF neural network identifier. The weights of the adaptive PID controller are timely adjusted based on the identification of the plant and self-learning capability of RBFNN. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance and the nonlinear system is achieved.

Keywords: Chylla-Haase polymerization reactor, RBF neural networks, feed-forward, feedback control

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Rickard Grassman

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In this paper, Lacanian theory will be used to illustrate the way discourses interact with the material by way of reifying antagonisms to shape our sense of identities in and around organizations. The ability to ‘sustain the loss’ is, in this view, the common structure here discerned in the very texture of a discourse, which reifies ‘lack’ as an ontological condition into something contingently absent (loss) that the subject hopes to overcome (desire). These fundamental human tendencies of identification are illustrated in the paper by examples drawn from history, cinema, and literature. Turning to a select sample of empirical accounts from a management consultancy firm, it is argued that this ‘sustaining the loss’ operates in discourse to enact identification in an organizational context.

Keywords: Lacan, identification, discourse, desire, loss

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Authors: Diala Bitar, Emmanuel Gourdon, Claude H. Lamarque, Manuel Collet

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Acoustic absorber devices play an important role reducing the noise at the propagation and reception paths. An electroacoustic absorber consists of a loudspeaker coupled to an electric shunt circuit, where the membrane is playing the role of an absorber/reflector of sound. Although the use of linear shunt resistors at the transducer terminals, has shown to improve the performances of the dynamical absorbers, it is nearly efficient in a narrow frequency band. Therefore, and since nonlinear phenomena are promising for their ability to absorb the vibrations and sound on a larger frequency range, we propose to couple a nonlinear electric shunt circuit at the loudspeaker terminals. Then, the equivalent model can be described by a 2 degrees of freedom system, consisting of a primary linear oscillator describing the dynamics of the loudspeaker membrane, linearly coupled to a cubic nonlinear energy sink (NES). The system is analytically treated for the case of 1:1 resonance, using an invariant manifold approach at different time scales. The proposed methodology enables us to detect the equilibrium points and fold singularities at the first slow time scales, providing a predictive tool to design the nonlinear circuit shunt during the energy exchange process. The preliminary results are promising; a significant improvement of acoustic absorption performances are obtained.

Keywords: electroacoustic absorber, multiple-time-scale with small finite parameter, nonlinear energy sink, nonlinear passive shunt

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Authors: Jiangbo Pu, Hanhui Xu, Yazhou Wang, Hongyan Cui, Yong Hu

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Spinal cord injury (SCI) brings great negative influence to the patients and society. Neurological loss in human after SCI is a major challenge in clinical. Instead, neural regeneration could have been seen in animals after SCI, and such regeneration could be retarded by blocking neural plasticity pathways, showing the importance of neural plasticity in functional recovery. Here we used sample entropy as an indicator of nonlinear dynamical in the brain to quantify plasticity changes in spontaneous EEG recordings of rats before and after SCI. The results showed that the entropy values were increased after the injury during the recovery in one week. The increasing tendency of sample entropy values is consistent with that of behavioral evaluation scores. It is indicated the potential application of sample entropy analysis for the evaluation of neural plasticity in spinal cord injury rat model.

Keywords: spinal cord injury (SCI), sample entropy, nonlinear, complex system, firing pattern, EEG, spontaneous activity, Basso Beattie Bresnahan (BBB) score

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Vera Karla S. Caingles, Glen A. Lorenzo

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Soil, as the main material of landslides, plays a vital role in landslide assessment. An efficient and accurate method of doing an assessment is significantly important to prevent damage of properties and loss of lives. The study has two phases: to establish an empirical correlation of the residual soil thickness with the slope angle and to investigate the geotechnical characteristics of residual soil. Digital Elevation Model (DEM) in Geographic Information System (GIS) was used to establish the slope map and to program sampling points for field investigation. Physical and index property tests were undertaken on the 20 soil samples obtained from the area with Pliocene-Pleistocene geology and different slope angle in Kibawe, Bukidnon. The regression analysis result shows that the best fitting model that can describe the soil thickness-slope angle relationship is an exponential function. The physical property results revealed that soils contain a high percentage of clay and silts ranges from 41% - 99.52%. Based on the index properties test results, the soil exhibits a high degree of plasticity and expansion but not collapsible. It is deemed that this compendium will serve as primary data for slope stability analysis and deterministic landslide assessment.

Keywords: collapsibility, correlation, expansiveness, landslide, plasticity

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Vinesh Janarthanan, Mohammad H. Rahman

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There are numerous neurological conditions that may result in a loss of motor function. Such conditions may include cerebral palsy, Parkinson’s disease, stroke or multiple sclerosis. Due to impaired motor function, specifically in the hand and arm, living independently becomes tremendously more difficult. Rehabilitation programs are the main method to treat these kinds of disabled individuals. However, these programs require longtime commitment from the clinicians/therapists, demand person to person caring, and typically the treatment duration is usually very long. Aside from the treatment received from the therapist, the continuation of neuroplasticity at home is essential to maximizing development and restoring the biological function. To contribute in this area, we have researched and developed a portable and comfortable hand glove for fine motor skills rehabilitation. The glove provides interactive home-based therapy to engage the patient with simple games. The key to this treatment is the repetition of moving the hand and being capable of positioning the hand in various ways.

Keywords: home based, wearable sensors, glove, rehabilitation, motor function, video games

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Authors: Jai Heui Kim, Sotheara Veng

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This paper studies the portfolio optimization problem for a pension fund under a hybrid model of stochastic volatility and constant elasticity of variance (CEV) using asymptotic analysis method. When the volatility component is fast mean-reverting, it is able to derive asymptotic approximations for the value function and the optimal strategy for general utility functions. Explicit solutions are given for the exponential and hyperbolic absolute risk aversion (HARA) utility functions. The study also shows that using the leading order optimal strategy results in the value function, not only up to the leading order, but also up to first order correction term. A practical strategy that does not depend on the unobservable volatility level is suggested. The result is an extension of the Merton's solution when stochastic volatility and elasticity of variance are considered simultaneously.

Keywords: asymptotic analysis, constant elasticity of variance, portfolio optimization, stochastic optimal control, stochastic volatility

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Authors: Wu Xiaoguang, Liu Jiaxin, Fang Miaomiao, Wei Saidong

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There are many prestressed concrete prefabricated girder Bridges with small and medium span and the damage is serious. This paper mainly study the effect of prestress loss of prefabricated bridge bearing performance, through the establishment of ANSYS finite element model, from the condition of different prestress loss research, get the stress and strain data, draw curve, finally get the following conclusion: loss of prestress can reduce the ultimate bearing capacity of Bridges, the side span across the deflection value than the influence of times side span, the influence of the deflection in the midspan cross value. Therefore, the prestress loss and the effective prestress should be strictly considered in the design and construction process.

Keywords: across the deflection, loss of prestress, prefabricated girder bridge, the main tensile stress

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Dan James

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The Medial Axis of the Main Canyon of Valles Marineris is determined geometrically with maximally inscribed discs aligned with the boundaries or rims of the Main Canyon. Inscribed discs are placed at evenly spaced longitude intervals and, using the radius function, the locus of the centre of all discs is determined, together with disc centre co-ordinates. These centre co-ordinates result in arrays of x, y co-ordinates which are curve fitted to a Sinusoidal function and residuals appropriate for nonlinear regression are evaluated using the R-squared value (R2) and the Root Mean Squared Error (RMSE). This evaluation demonstrates that a Sinusoidal Curve closely fits to the co-ordinate data

Keywords: medial axis, MAT, valles marineris, sinusoidal

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Authors: I. Khabbazi, R. Ghasemi

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This paper presents a combination of both robust nonlinear controller and nonlinear controller for a class of nonlinear 4Y Octorotor UAV using Back-stepping and sliding mode controller. The robustness against internal and external disturbance and decoupling control are the merits of the proposed paper. The proposed controller decouples the Octorotor dynamical system. The controller is then applied to a 4Y Octorotor UAV and its feature will be shown.

Keywords: sliding mode, backstepping, decoupling, octorotor UAV

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Authors: Kanica Goel, Nilam

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Infectious diseases are a leading cause of death worldwide and hence a great challenge for every nation. Thus, it becomes utmost essential to prevent and reduce the spread of infectious disease among humans. Mathematical models help to better understand the transmission dynamics and spread of infections. For this purpose, in the present article, we have proposed a nonlinear time-delayed SVIRS (Susceptible-Vaccinated-Infected-Recovered-Susceptible) mathematical model with nonlinear type incidence rate and nonlinear type treatment rate. Analytical study of the model shows that model exhibits two types of equilibrium points, namely, disease-free equilibrium and endemic equilibrium. Further, for the long-term behavior of the model, stability of the model is discussed with the help of basic reproduction number R₀ and we showed that disease-free equilibrium is locally asymptotically stable if the basic reproduction number R₀ is less than one and unstable if the basic reproduction number R₀ is greater than one for the time lag τ≥0. Furthermore, when basic reproduction number R₀ is one, using center manifold theory and Casillo-Chavez and Song theorem, we showed that the model undergoes transcritical bifurcation. Moreover, numerical simulations are being carried out using MATLAB 2012b to illustrate the theoretical results.

Keywords: nonlinear incidence rate, nonlinear treatment rate, stability, time delayed SVIRS epidemic model

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Authors: Hesham Kozou

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Sensorineural hearing loss (SNHL) poses a significant challenge due to limited access to the inner ear for therapies. Emerging treatments such as regenerative, genetic, and pharmacotherapies offer hope for addressing this condition. This study aims to highlight the potential of cochlear implants and emerging therapies in managing sensorineural hearing loss by improving access to the inner ear. The study is conducted through a review of relevant literature and research articles in the field of cochlear implants and emerging therapies for hearing loss. It outlines how advancements in cochlear implant technologies, electrodes, and surgical techniques can facilitate the delivery of therapies to the inner ear, potentially revolutionizing the treatment of sensorineural hearing loss. The study underscores the potential of cochlear implants and emerging therapies in revolutionizing the treatment landscape for sensorineural hearing loss, emphasizing the feasibility of curing this condition by leveraging technological advancements.

Keywords: therapies for hearing loss management, future of CI as a cochlear delivery channel, regenerative, genetic and pharmacotherapeutic management of hearing loss

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

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Authors: Dchieche Amina, Aboulaich Rajae

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Profit and loss sharing suggests an equitable sharing of risks and profits between the parts involved in a financial transaction. Salam is a contract in which advance payment is made for goods to be delivered at a future date. The purpose of this work is to price a new contract for profit and loss sharing based on Salam contract, using Khiyar Al Ghabn which is an agreement of choice in case of misrepresent facts.

Keywords: Islamic finance, shariah compliance, profit and loss sharing, derivatives, risks, hedging, salam contract

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Authors: Fares Jnaid, Riyad Aboutaha

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In this paper, a nonlinear Finite Element Analysis (FEA) was carried out using ANSYS software to build a model able of predicting the behavior of Reinforced Concrete (RC) beams with unbonded reinforcement. The FEA model was compared to existing experimental data by other researchers. The existing experimental data consisted of 16 beams that varied from structurally sound beams to beams with unbonded reinforcement with different unbonded lengths and reinforcement ratios. The model was able to predict the ultimate flexural strength, load-deflection curve, and crack pattern of concrete beams with unbonded reinforcement. It was concluded that when the when the unbonded length is less than 45% of the span, there will be no decrease in the ultimate flexural strength due to the loss of bond between the steel reinforcement and the surrounding concrete regardless of the reinforcement ratio. Moreover, when the reinforcement ratio is relatively low, there will be no decrease in ultimate flexural strength regardless of the length of unbond.

Keywords: FEA, ANSYS, unbond, strain

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

Abstract:

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: nonlinear optics, plasmonic waveguide, chalcogenide, propagation equation

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Authors: Ebrahim Hassan Kapeel, Ahmed Mohsen Kamel, Hossan Hendy, Yehia Z. Elhalwagy

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Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control lawisdesigned for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: UAV dynamic model, attitude control, nonlinear PID, dynamic inversion

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Authors: Shubham Jaiswal

Abstract:

During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: Fatemeh Shahi, Mehdi Sharifian, Laia Shahrassai, Elham Eskandari A.

Abstract:

A new mechanism is reported here for magnetic field generation in laser-plasma interaction by means of nonlinear ponderomotive force. The plasma considered here is unmagnetized inhomogeneous plasma with an exponentially decreasing profile. A damped periodic magnetic field with a relatively lower frequency is obtained using the ponderomotive force exerted on plasma electrons. Finally, with an electric field and by using Faraday’s law, the magnetic field profile in the plasma has been obtained. Because of the negative exponential density profile, the generated magnetic field is relatively slowly oscillating and damped through the plasma.

Keywords: magnetic field generation, laser-plasma interaction, ponderomotive force, inhomogeneous plasma

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