Search results for: Maxwell’s equations

Authors: A. Abdikian

Abstract:

Using the linearized quantum hydrodynamic model (QHD) and by considering the role of quantum parameter (Bohm’s potential) and electron exchange-correlation potential in conjunction with Maxwell’s equations, electromagnetic wave propagation in a single-walled carbon nanotubes was studied. The electronic excitations are described. By solving the mentioned equations with appropriate boundary conditions and by assuming the low-frequency electromagnetic waves, two general expressions of dispersion relations are derived for the transverse magnetic (TM) and transverse electric (TE) modes, respectively. The dispersion relations are analyzed numerically and it was found that the dependency of dispersion curves with the exchange-correlation effects (which have been ignored in previous works) in the low frequency would be limited. Moreover, it has been realized that asymptotic behaviors of the TE and TM modes are similar in single wall carbon nanotubes (SWCNTs). The results show that by adding the function of electron exchange-correlation potential lead to the phenomena and make to extend the validity range of QHD model. The results can be important in the study of collective phenomena in nanostructures.

Keywords: transverse magnetic, transverse electric, quantum hydrodynamic model, electron exchange-correlation potential, single-wall carbon nanotubes

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Authors: M. Yusefzad

Abstract:

Law of energy conservation is one of the fundamental laws of physics. Energy is conserved, and the total amount of energy is constant. It can be transferred from one object to another and changed from one state to another. However, in the case of wave interference, this law faces important contradictions. Based on the presented mathematical relationship in this paper, it seems that validity of this law depends on the path of energy wave, like light, in which it is located. In this paper, by using some fundamental concepts in physics like the constancy of the electromagnetic wave speed in a specific media and wave theory of light, it will be shown that law of energy conservation is not valid in every condition and in some circumstances, it is possible to increase energy of a system with a determined amount of energy without any input.

Keywords: power, law of energy conservation, electromagnetic wave, interference, Maxwell’s equations

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Authors: Muhammad Hassan Khalil, Xu Jiadong

Abstract:

Early detection through screening is the best tool short of a perfect treatment against the malignant tumor inside the breast of a woman. By detecting cancer in its early stages, it can be recognized and treated before it has the opportunity to spread and change into potentially dangerous. Microwave tomography is a new imaging method based on contrast in dielectric properties of materials. The mathematical theory of microwave tomography involves solving an inverse problem for Maxwell’s equations. In this paper, we present designed antenna for breast cancer detection, which will use in microwave tomography configuration.

Keywords: microwave imaging, inverse scattering, breast cancer, malignant tumor detection

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Divij Gupta

Abstract:

Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Farhad Aalizadeh, Ali Moosavi

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When a blood vessel is injured, the cells of your blood bond together to form a blood clot. The blood clot helps you stop bleeding. Blood clots are made of a combination of blood cells, platelets(small sticky cells that speed up the clot-making process), and fibrin (protein that forms a thread-like mesh to trap cells). Doctors call this kind of blood clot a “thrombus.”We study the effects of different parameters on the deposition of Nanoparticles on the surface of a bump in the blood vessels by the magnetic field. The Maxwell and the flow equations are solved for this purpose. It is assumed that the blood is non-Newtonian and the number of particles has been considered enough to rely on the results statistically. Using MHD and its property it is possible to control the flow velocity, remove the fouling on the walls and return the system to its original form.

Keywords: MHD, fouling, in-vivo, blood clots, simulation

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: S. Bennoud, M. Zergoug

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The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models. The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces. The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations. In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: eddy current, finite element method, non destructive testing, numerical simulations

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Authors: Zahra Emami, H. Reza Mesgarzade, A. Morad Ghorbami, S. Reza Motahari

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This paper presents a method for calculation of parasitic elements consisting of leakage inductance and parasitic capacitance in a high voltage pulse transformer. The parasitic elements of pulse transformers significantly influence the resulting pulse shape of a power modulator system. In order to prevent the effects on the pulse shape before constructing the transformer an electrical model is needed. The technique procedures for computing these elements are based on finite element analysis. The finite element model of pulse transformer is created using software "Ansys Maxwell 3D". Finally, the transformer parasitic elements is calculated and compared with the value obtained from the actual test and pulse modulator is simulated and results is compared with actual test of pulse modulator. The results obtained are very similar with the test values.

Keywords: pulse transformer, simulation, modeling, Maxwell 3D, modulator

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Sang Kompiang Wirawan, Chandra Purnomo

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Carbon dioxide (CO2) adsorption on the activated Klaten-Indonesian natural zeolite (AKINZ) in a packed bed adsorber has been studied. Experiment works consisted of acid activation and adsorption experiments. The natural zeolite sample was activated using 0.3 M HCl at the temperature of 353 K. In the adsorption experiments the feed gas concentrations were 40 and 80 % CO2 in helium within various temperatures of 303; 323 and 373 K. The experiments were conducted by using transient step change adsorption and 20 % Ar/He tracer experiment was conducted to measure dispersion and time lag effect of the packed bed system. A mathematical model of CO2 adsorption had been set up by assuming plug flow;isothermal;isobaric and no gas film mass transport resistance. Single site Langmuir physisorption and Maxwell Stefan mass transport in micropore were applied. All the data were then optimized to get the best value of modified fitted parameter. The model was in a good agreement with the experiment data. Diffusivity tended to increase by increasing temperatures.

Keywords: adsorption, Langmuir, Maxwell-Stefan, natural zeolite, surface diffusion

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Authors: Matevž Breška, Iztok Peruš, Vlado Stankovski

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Systematic overview of existing Ground Motion Prediction Equations (GMPEs) has been published by Douglas. The number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration (PGA) the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.

Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database, peak ground acceleration

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Authors: Zahid Ullah, Atlas Khan

Abstract:

The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: Mark Watson, J.-F. Bousquet, Adam Forget

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A magnetic induction based underwater communication link is evaluated using an analytical model and a custom Finite-Difference Time-Domain (FDTD) simulation tool. The analytical model is based on the Sommerfeld integral, and a full-wave simulation tool evaluates Maxwell’s equations using the FDTD method in cylindrical coordinates. The analytical model and FDTD simulation tool are then compared and used to predict the system performance for various transmitter depths and optimum frequencies of operation. To this end, the system bandwidth, signal to noise ratio, and the magnitude of the induced voltage are used to estimate the expected channel capacity. The models show that in seawater, a relatively low-power and small coils may be capable of obtaining a throughput of 40 to 300 kbps, for the case where a transmitter is at depths of 1 to 3 m and a receiver is at a height of 1 m.

Keywords: magnetic induction, FDTD, underwater communication, Sommerfeld

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Authors: Firano Zakaria, Filali Adib Fatine

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The issue f convergence in theoretical models (classical or Keynesian) has been widely discussed. The results of the work affirm that most countries are seeking to get as close as possible to a steady state in order to catch up with developed countries. In this paper, we have retested this question whether it is absolute or conditional. The results affirm that the degree of convergence of countries like Morocco is very low and income is still far from its equilibrium state. Moreover, the analysis of financial convergence, of the countries in our panel, states that the pace in this sector is more intense: countries are converging more rapidly in financial terms. The question arises as to why, with a fairly convergent financial system, growth does not respond, yet the financial system should facilitate this economic convergence. Our results confirm that the degree of information exchange between the financial system and the economic system did not change significantly between 1985 and 2017. This leads to the hypothesis that the financial system is failing to serve its role as a creator of information in developing countries despite all the reforms undertaken, thus making the existence of an economic demon in the Maxwell prevail.

Keywords: economic convergence, financial convergence, financial system, entropy

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Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Melusi Khumalo, Anastacia Dlamini

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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: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: M. Pienaar, J. W. Odendaal, J. C. Smit, J. Joubert

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Simulations are commonly used to predict the bistatic radar cross section (RCS) of military targets since characterization measurements can be expensive and time consuming. It is thus important to accurately predict the bistatic RCS of targets. Computational electromagnetic (CEM) methods can be used for bistatic RCS prediction. CEM methods are divided into full-wave and asymptotic methods. Full-wave methods are numerical approximations to the exact solution of Maxwell’s equations. These methods are very accurate but are computationally very intensive and time consuming. Asymptotic techniques make simplifying assumptions in solving Maxwell's equations and are thus less accurate but require less computational resources and time. Asymptotic techniques can thus be very valuable for the prediction of bistatic RCS of electrically large targets, due to the decreased computational requirements. This study extends previous work by validating the accuracy of asymptotic techniques to predict bistatic RCS through comparison with full-wave simulations as well as measurements. Validation is done with canonical structures as well as complex realistic aircraft models instead of only looking at a complex slicy structure. The slicy structure is a combination of canonical structures, including cylinders, corner reflectors and cubes. Validation is done over large bistatic angles and at different polarizations. Bistatic RCS measurements were conducted in a compact range, at the University of Pretoria, South Africa. The measurements were performed at different polarizations from 2 GHz to 6 GHz. Fixed bistatic angles of β = 30.8°, 45° and 90° were used. The measurements were calibrated with an active calibration target. The EM simulation tool FEKO was used to generate simulated results. The full-wave multi-level fast multipole method (MLFMM) simulated results together with the measured data were used as reference for validation. The accuracy of physical optics (PO) and geometrical optics (GO) was investigated. Differences relating to amplitude, lobing structure and null positions were observed between the asymptotic, full-wave and measured data. PO and GO were more accurate at angles close to the specular scattering directions and the accuracy seemed to decrease as the bistatic angle increased. At large bistatic angles PO did not perform well due to the shadow regions not being treated appropriately. PO also did not perform well for canonical structures where multi-bounce was the main scattering mechanism. PO and GO do not account for diffraction but these inaccuracies tended to decrease as the electrical size of objects increased. It was evident that both asymptotic techniques do not properly account for bistatic structural shadowing. Specular scattering was calculated accurately even if targets did not meet the electrically large criteria. It was evident that the bistatic RCS prediction performance of PO and GO depends on incident angle, frequency, target shape and observation angle. The improved computational efficiency of the asymptotic solvers yields a major advantage over full-wave solvers and measurements; however, there is still much room for improvement of the accuracy of these asymptotic techniques.

Keywords: asymptotic techniques, bistatic RCS, geometrical optics, physical optics

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Authors: Guram Adamashvili

Abstract:

Surface plasmon polariton is a surface optical wave which undergoes a strong enhancement and spatial confinement of its wave amplitude near an interface of two-dimensional layered structures. Phosphorene (single-layer black phosphorus) and other two-dimensional anisotropic phosphorene-like materials are recognized as promising materials for potential future applications of surface plasmon polariton. A theory of an optical breather of self-induced transparency for surface plasmon polariton propagating in monolayer or few-layer phosphorene is developed. A theory of an optical soliton of self-induced transparency for surface plasmon polariton propagating in monolayer or few-layer phosphorene have been investigated earlier Starting from the optical nonlinear wave equation for surface TM-modes interacting with a two-dimensional layer of atomic systems or semiconductor quantum dots and a phosphorene monolayer (or other two-dimensional anisotropic material), we have obtained the evolution equations for the electric field of the breather. In this case, one finds that the evolution of these pulses become described by the damped Bloch-Maxwell equations. For surface plasmon polariton fields, breathers are found to occur. Explicit relations of the dependence of breathers on the local media, phosphorene anisotropic conductivity, transition layer properties and transverse structures of the SPP, are obtained and will be given. It is shown that the phosphorene conductivity reduces exponentially the amplitude of the surface breather of SIT in the process of propagation. The direction of propagation corresponding to the maximum and minimum damping of the amplitude are assigned along the armchair and zigzag directions of black phosphorus nano-film, respectively. The most rapid damping of the intensity occurs when the polarization of breather is along the armchair direction.

Keywords: breathers, nonlinear waves, solitons, surface plasmon polaritons

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Authors: C. Yin, B. Zhang, Y. Liu, J. Cai

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Airborne EM (AEM) is an effective geophysical exploration tool, especially suitable for ridged mountain areas. In these areas, topography will have serious effects on AEM system responses. However, until now little study has been reported on topographic effect on airborne EM systems. In this paper, an edge-based unstructured finite-element (FE) method is developed for 3D topographic modeling for both frequency and time-domain airborne EM systems. Starting from the frequency-domain Maxwell equations, a vector Helmholtz equation is derived to obtain a stable and accurate solution. Considering that the AEM transmitter and receiver are both located in the air, the scattered field method is used in our modeling. The Galerkin method is applied to discretize the Helmholtz equation for the final FE equations. Solving the FE equations, the frequency-domain AEM responses are obtained. To accelerate the calculation speed, the response of source in free-space is used as the primary field and the PARDISO direct solver is used to deal with the problem with multiple transmitting sources. After calculating the frequency-domain AEM responses, a Hankel’s transform is applied to obtain the time-domain AEM responses. To check the accuracy of present algorithm and to analyze the characteristic of topographic effect on airborne EM systems, both the frequency- and time-domain AEM responses for 3 model groups are simulated: 1) a flat half-space model that has a semi-analytical solution of EM response; 2) a valley or hill earth model; 3) a valley or hill earth with an abnormal body embedded. Numerical experiments show that close to the node points of the topography, AEM responses demonstrate sharp changes. Special attentions need to be paid to the topographic effects when interpreting AEM survey data over rugged topographic areas. Besides, the profile of the AEM responses presents a mirror relation with the topographic earth surface. In comparison to the topographic effect that mainly occurs at the high-frequency end and early time channels, the EM responses of underground conductors mainly occur at low frequencies and later time channels. For the signal of the same time channel, the dB/dt field reflects the change of conductivity better than the B-field. The research of this paper will serve airborne EM in the identification and correction of the topographic effects.

Keywords: 3D, Airborne EM, forward modeling, topographic effect

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Authors: Majid Karimabadi, Ahmad Farzaneh Kore, Behnam Azadegan

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The evolution of magnetized quark gluon plasma (QGP) in the framework of magneto- hydrodynamics is the focus of our study. We are investigating the temporal and spatial evolution of QGP using a second order viscous hydrodynamic framework. The fluid is considered to be magnetized and subjected to the influence of a magnetic field that is generated during the early stages of relativistic heavy ion collisions. We assume boost invariance along the beam line, which is represented by the z coordinate, and fluid expansion in the x direction. Additionally, we assume that the magnetic field is perpendicular to the reaction plane, which corresponds to the y direction. The fluid is considered to have infinite electrical conductivity. To analyze this system, we solve the coupled Maxwell and conservation equations. By doing so, we are able to determine the time and space dependence of the energy density, velocity, and magnetic field in the transverse plane of the viscous magnetized hot plasma. Furthermore, we obtain the spectrum of hadrons and compare it with experimental data.

Keywords: QGP, magnetohydrodynamics, hadrons, conversation

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Authors: Minas Balyan

Abstract:

Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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