Search results for: Peng Robinson equation

Authors: M. A. Sedghamiz, S. Raeissi

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This study presents three different approaches to estimate bubble point pressures for the binary system of CO2 and ethyl palmitate fatty acid ethyl ester. The first method involves the Peng-Robinson (PR) Equation of State (EoS) with the conventional mixing rule of Van der Waals. The second approach involves the PR EOS together with the Wong Sandler (WS) mixing rule, coupled with the Uniquac Ge model. In order to model the bubble point pressures with this approach, the volume and area parameter for ethyl palmitate were estimated by the Hansen group contribution method. The last method involved the Peng-Robinson, combined with the Wong-Sandler Method, but using NRTL as the GE model. Results using the Van der Waals mixing rule clearly indicated that this method has the largest errors among all three methods, with errors in the range of 3.96–6.22 %. The Pr-Ws-Uniquac method exhibited small errors, with average absolute deviations between 0.95 to 1.97 percent. The Pr-Ws-Nrtl method led to the least errors where average absolute deviations ranged between 0.65-1.7%.

Keywords: bubble pressure, Gibbs excess energy model, mixing rule, CO2 solubility, ethyl palmitate

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Authors: Arash Esmaeili, Zhibang Liu, Yang Xiang, Jimmy Yun, Lei Shao

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A high pressure carbon dioxide (CO₂) absorption from a specific gas in a conventional column has been evaluated by the Aspen HYSYS simulator using a wide range of single absorbents and blended solutions to estimate the outlet CO₂ concentration, absorption efficiency and CO₂ loading to choose the most proper solution in terms of CO₂ capture for environmental concerns. The property package (Acid Gas-Chemical Solvent) which is compatible with all applied solutions for the simulation in this study, estimates the properties based on an electrolyte non-random two-liquid (E-NRTL) model for electrolyte thermodynamics and Peng-Robinson equation of state for the vapor and liquid hydrocarbon phases. Among all the investigated single amines as well as blended solutions, piperazine (PZ) and the mixture of piperazine and monoethanolamine (MEA) have been found as the most effective absorbents respectively for CO₂ absorption with high reactivity based on the simulated operational conditions.

Keywords: absorption, amine solutions, Aspen HYSYS, carbon dioxide, simulation

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Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

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This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility

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Authors: Arash Esmaeili, Zhibang Liu, Yang Xiang, Jimmy Yun, Lei Shao

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A high-pressure carbon dioxide (CO₂) absorption from a specific off-gas in a conventional column has been evaluated for the environmental concerns by the Aspen HYSYS simulator using a wide range of single absorbents and piperazine (PZ) blended solutions to estimate the outlet CO₂ concentration, CO₂ loading, reboiler power supply, and regeneration heat duty to choose the most efficient solution in terms of CO₂ removal and required heat duty. The property package, which is compatible with all applied solutions for the simulation in this study, estimates the properties based on the electrolyte non-random two-liquid (E-NRTL) model for electrolyte thermodynamics and Peng-Robinson equation of state for vapor phase and liquid hydrocarbon phase properties. The results of the simulation indicate that piperazine, in addition to the mixture of piperazine and monoethanolamine (MEA), demands the highest regeneration heat duty compared with other studied single and blended amine solutions, respectively. The blended amine solutions with the lowest PZ concentrations (5wt% and 10wt%) were considered and compared to reduce the cost of the process, among which the blended solution of 10wt%PZ+35wt%MDEA (methyldiethanolamine) was found as the most appropriate solution in terms of CO₂ content in the outlet gas, rich-CO₂ loading, and regeneration heat duty.

Keywords: absorption, amine solutions, aspen HYSYS, CO₂ loading, piperazine, regeneration heat duty

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Authors: Shyh Ming Chern

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Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and, reasonable accuracy are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, They often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: equation of state, EoS, supercritical water, SCW

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Authors: Samsher Gautam, Apoorva Roy, Bhuvan Aggarwal

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Vapor absorption refrigeration systems can replace vapor compression systems in many applications as they can operate on a low-grade heat source and are environment-friendly. Widely used refrigerants such as CFCs and HFCs cause significant global warming. Natural refrigerants can be an alternative to them, among which carbon dioxide is promising for use in automotive air conditioning systems. Its inherent safety, ability to withstand high pressure and high heat transfer coefficient coupled with easy availability make it a likely choice for refrigerant. Various properties of the ionic liquid [bmim][PF₆], such as non-toxicity, stability over a wide temperature range and ability to dissolve gases like carbon dioxide, make it a suitable absorbent for a vapor absorption refrigeration system. In this paper, an absorption chiller consisting of a generator, condenser, evaporator and absorber was studied at an operating temperature of 70⁰C. A thermodynamic model was set up using the Peng-Robinson equations of state to predict the behavior of the refrigerant and absorbent pair at different points in the system. A MATLAB code was used to obtain the values of enthalpy and entropy at selected points in the system. The exergy destruction in each component and exergetic coefficient of performance (ECOP) of the system were calculated by performing an exergy analysis based on the second law of thermodynamics. Graphs were plotted between varying operating conditions and the ECOP obtained in each case. The effect of every component on the ECOP was examined. The exergetic coefficient of performance was found to be lesser than the coefficient of performance based on the first law of thermodynamics.

Keywords: [bmim][PF₆] as absorbent, carbon dioxide as refrigerant, exergy analysis, Peng-Robinson equations of state, vapor absorption refrigeration

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Authors: F. S. Alavi, D. Mowla, F. Esmaeilzadeh

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In this paper, the Eclipse 300 simulator was used to perform compositional modeling of gas injection process for enhanced condensate recovery of a real gas condensate well in south of Iran here referred to as SA4. Some experimental data were used to tune the Peng-Robinson equation of state for this case. Different scenarios of gas injection at current reservoir pressure and at abandonment reservoir pressure had been considered with different gas compositions. Methane, carbon dioxide, nitrogen and two other gases with specified compositions were considered as potential gases for injection. According to the obtained results, nitrogen leads to highest pressure maintenance in the reservoir but methane results in highest condensate recovery among the selected injection gases. At low injection rates, condensate recovery percent is strongly affected by gas injection rate but this dependency shifts to zero at high injection rates. Condensate recovery is higher in all cases of injection at current reservoir pressure than injection at abandonment pressure. Using a constant injection rate, increasing the production well bottom hole pressure results in increasing the condensate recovery percent and time of gas breakthrough.

Keywords: gas-condensate reservoir, case-study, compositional modelling, enhanced condensate recovery, gas injection

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Authors: Vorya Shabrandi

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The study factors of poverty and inequality causes in countries is the subject of many scholars and economists in the last century, theorists in various areas of economic science know different factors as the roots of poverty and inequality in Iran after the 1979 revolution. Economists have emphasized political elements and political scientists on political elements. This research reviews the political economy of poverty and corruption in Iran after the revolution. The findings of this research, based on AcemOgluand Robinson theory, show how the institutional structural dependence of Iran's economy to raw has led to the growth of its non-economic economic institutions and its consequence of the continuity of the release and looting economy and poverty and inequality in Iran's political economy Is. This research was carried out using descriptive-analytical and comparative methods. Many economists try to justify the conditions of the country based on war, sanctions; And the external factors, and ... knows. In this study, we tried to examine the roots of poverty and the looting economy of Iran by implementing Research AcemOgluand Robinson on the institutions and roots of poverty. Looking for a framework for understanding why countries, such as Iran, the reason for the difference in revenue in different countries, as well as the poor or wealth of countries, regardless of the non-effective and non-professional institutions, and why inefficient institutions in some countries, such as Iran, such as Iran It remains and does not have a voluntary political powers to change these institutions. Findings The research shows that institutions are broadly the main reason for the roots of the robust and looting economy (poverty and inequality) in Iran.

Keywords: Iran, plunderable (Loot) economy, raw shopping, poverty and inequality, acem oglu and robinson, non-inclusive institutions

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

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

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

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Authors: Jian-Jun Shu

Abstract:

It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Halil Baris Cit, Mert Durmaz

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Subsequent to the design of the compact centrifugal compressor, which is specifically intended to be used in aviation platforms, the process has been evaluated within the context of this study. A trade-off study matrix for future studies has been formed after making comparison between the design and the previous studies taking part in literature. While the power consumption of the designed compressor will be approximately 25 kW, the working fluid will be refrigerant. Properties such as thermodynamic properties and Global Warmin Potential(GWP)-Ozone Depletion Potential(ODP) Values of the fluid have been taken into consideration during the selection process of the refrigerant. Concepts NREC and ANSYS Vista CCD software have been used in the part of conceptual design, and R1233ZD has been selected as the refrigerant. Real-gas Computational Fluid Dynamic(CFD) analysis has been carried out with different cubic equations of state in the ANSYS CFX solver so as to figure out the most suitable solution method. These equations are named as “The Redlich Kwong”, “Soave Redlich Kwong”, “Augnier Redlick Kwong,” and “Peng Robinson.” By being used the mentioned solution equations in the same compressor configuration, analysis also have been carried out with two gases having different characteristics. As a result of the 12 analysis carried out with three different refrigerants—R11, R134A, and R1233zd—and four different solution equations mentioned above, the most accurate solution method has been selected by comparing the densities of the gases at different pressure and temperature points. The results have been analyzed within two titles following to the completion of the design with the selected equation. The first one is a trade-off study matrix presenting a comparison regarding the compact centrifugal compressor operating with the refrigerant to be designed. This comparison is between some dimensionless and dimensional parameters determined before the design and their values in the literature. Second one will show the differences between the actual density and the density in the design software in each real gas analysis method, along with the effects of it on the design.

Keywords: turbocompressor, refrigerant, aviation, aerospace compressor

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Authors: U. P. L. Wijayarathne, K. C. Wasalathilake

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This work presents the modelling and simulation of saponification of ethyl acetate in the presence of sodium hydroxide in a plug flow reactor using Aspen Plus simulation software. Plug flow reactors are widely used in the industry due to the non-mixing property. The use of plug flow reactors becomes significant when there is a need for continuous large scale reaction or fast reaction. Plug flow reactors have a high volumetric unit conversion as the occurrence for side reactions is minimum. In this research Aspen Plus V8.0 has been successfully used to simulate the plug flow reactor. In order to simulate the process as accurately as possible HYSYS Peng-Robinson EOS package was used as the property method. The results obtained from the simulation were verified by the experiment carried out in the EDIBON plug flow reactor module. The correlation coefficient (r2) was 0.98 and it proved that simulation results satisfactorily fit for the experimental model. The developed model can be used as a guide for understanding the reaction kinetics of a plug flow reactor.

Keywords: aspen plus, modelling, plug flow reactor, simulation

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Hamidreza Bagheri, Alireza Shariati

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There are many difficulties in the purification of raw components and products. However, researchers are seeking better ways for purification. One of the recent methods is extraction using supercritical fluids. In this study, the phase equilibria of benzoic acid-supercritical carbon dioxide system were investigated. Regarding the phase equilibria of this system, the modeling of solid-supercritical fluid behavior was performed using the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) and Peng-Robinson equations of state (PR EoS). For this purpose, five PC-SAFT EoS parameters for pure benzoic acid were obtained using its experimental vapor pressure. Benzoic acid has association sites and the behavior of the benzoic acid-supercritical fluid system was well-predicted using both equations of state, while the binary interaction parameter values for PR EoS were negative. Genetic algorithm, which is one of the most accurate global optimization algorithms, was also used to optimize the pure benzoic acid parameters and the binary interaction parameters. The AAD% value for the PC-SAFT EoS, were 0.22 for the carbon dioxide-benzoic acid system.

Keywords: supercritical fluids, solubility, solid, PC-SAFT EoS, genetic algorithm

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Yen-Ku Kuo, Chie-Bein Chen, Jyh-Yi Shih, Kuang-Yi Lin, Chien-Han Peng

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This study is primarily concerned with exploring what factors affect the consumer’s intention of using mobile phone e-book. In developing research structure, we adopted technology acceptance model (TAM) and Innovation Diffusion Theory (IDT) as a foundation. The analysis method of structural equation model (SEM) was used to carry out this study. Subjects were 261 users who are using or used the mobile phone e-book. The findings can be summed up as follows: (1) The subjective norm and job relevance has non-significant and positive influence to the perceived usefulness. This represents now the user are still in a small number and most of them used it in non-work related purpose. (2) The output quality, result demonstrability and perceived ease of use were confirmed to have positive and significant influence to the perceived usefulness. (3) The moderator “innovative diffusion” affects the relationship between the attitude and behavior intention. These findings could be a reference for the practice and future study to make further exploration.

Keywords: mobile phone e-book, technology acceptance model (TAM), innovation diffusion theory (IDT), structural equation model (SEM)

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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Authors: Adriana Estokova, Lenka Palascakova, Martina Kovalcikova

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Cement is a basic material used for building construction. Chromium as an indelible non-volatile trace element of raw materials occurs in cement clinker in the trivalent or hexavalent form. Hexavalent form of chromium is harmful and allergenic having very high water solubility and thus can easily come into contact with the human skin. The paper is aimed at analyzing the content of total chromium in Portland cements and leaching rate of hexavalent chromium in various leachants: Deionized water, Britton-Robinson buffer, used to simulate the natural environment, and hydrochloric acid (HCl). The concentration of total chromium in Portland cement samples was in a range from 173.2 to 218.5 mg/kg. The content of dissolved hexavalent chromium ranged 0.23-3.19, 2.0-5.78 and 8.88-16.25 mg/kg in deionized water, Britton-Robinson solution and hydrochloric acid, respectively. The calculated leachable fraction of Cr(VI) from cement samples was observed in the range 0.1--7.58 %.

Keywords: environment, cement, chromium, leaching

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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

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

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

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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