Search results for: nonlinear systems of equations

Authors: S. Obregon-Cano, R. Moreno-Rojas, E. Cartea-Gonzalez, A. De Haro-Bailon

Abstract:

The potential of near-infrared spectroscopy (NIRS) for screening the total glucosinolate (t-GSL) content, and also, the aliphatic glucosinolates gluconapin (GNA), progoitrin (PRO) and glucobrassicanapin (GBN) in turnip greens and turnip tops was assessed. This crop is grown for edible leaves and stems for human consumption. The reference values for glucosinolates, as they were obtained by high performance liquid chromatography on the vegetable samples, were regressed against different spectral transformations by modified partial least-squares (MPLS) regression (calibration set of samples n= 350). The resulting models were satisfactory, with calibration coefficient values from 0.72 (GBN) to 0.98 (tGSL). The predictive ability of the equations obtained was tested using a set of samples (n=70) independent of the calibration set. The determination coefficients and prediction errors (SEP) obtained in the external validation were: GNA=0.94 (SEP=3.49); PRO=0.41 (SEP=1.08); GBN=0.55 (SEP=0.60); tGSL=0.96 (SEP=3.28). These results show that the equations developed for total glucosinolates, as well as for gluconapin can be used for screening these compounds in the leaves and stems of this species. In addition, the progoitrin and glucobrassicanapin equations obtained can be used to identify those samples with high, medium and low contents. The calibration equations obtained were accurate enough for a fast, non-destructive and reliable analysis of the content in GNA and tGSL directly from NIR spectra. The equations for PRO and GBN can be employed to identify samples with high, medium and low contents.

Keywords: brassica rapa, glucosinolates, gluconapin, NIRS, turnip greens

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Authors: Diyar Yousif Ali

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Braced frames, besides other structural systems, such as shear walls or moment resisting frames, have been a valuable and effective technique to increase structures against seismic loads. In wind or seismic excitations, diagonal members react as truss web elements which would afford tension or compression stresses. This study proposes to consider the effect of bracing diagonal configuration on values of base shear and displacement of building. Two models were created, and nonlinear pushover analysis was implemented. Results show that bracing members enhance the lateral load performance of the Concentric Braced Frame (CBF) considerably. The purpose of this article is to study the nonlinear response of reinforced concrete structures which contain hollow pipe steel braces as the major structural elements against earthquake loads. A five-storey reinforced concrete structure was selected in this study; two different reinforced concrete frames were considered. The first system was an un-braced frame, while the last one was a braced frame with diagonal bracing. Analytical modelings of the bare frame and braced frame were realized by means of SAP 2000. The performances of all structures were evaluated using nonlinear static analyses. From these analyses, the base shear and displacements were compared. Results are plotted in diagrams and discussed extensively, and the results of the analyses showed that the braced frame was seemed to capable of more lateral load carrying and had a high value for stiffness and lower roof displacement in comparison with the bare frame.

Keywords: reinforced concrete structures, pushover analysis, base shear, steel bracing

Procedia PDF Downloads 90

Authors: Mrinal Jana, Geetanjali Panda

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In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

Procedia PDF Downloads 520

Authors: Alexander Norbach

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The script in this paper describes the use of advanced simulation environment using electronic systems (Microcontroller, Operational Amplifiers, and FPGA). The simulation may be used for all dynamic systems with the diffusion and the ionisation behaviour also. By additionally required observer structure, the system works with parallel real-time simulation based on diffusion model and the state-space representation for other dynamics. The proposed deposited model may be used for electrodynamic effects, including ionising effects and eddy current distribution also. With the script and proposed method, it is possible to calculate the spatial distribution of the electromagnetic fields in real-time. For further purpose, the spatial temperature distribution may be used also. With upon system, the uncertainties, unknown initial states and disturbances may be determined. This provides the estimation of the more precise system states for the required system, and additionally, the estimation of the ionising disturbances that occur due to radiation effects. The results have shown that a system can be also developed and adopted specifically for space systems with the real-time calculation of the radiation effects only. Electronic systems can take damage caused by impacts with charged particle flux in space or radiation environment. In order to be able to react to these processes, it must be calculated within a shorter time that ionising radiation and dose is present. All available sensors shall be used to observe the spatial distributions. By measured value of size and known location of the sensors, the entire distribution can be calculated retroactively or more accurately. With the formation, the type of ionisation and the direct effect to the systems and thus possible prevent processes can be activated up to the shutdown. The results show possibilities to perform more qualitative and faster simulations independent of kind of systems space-systems and radiation environment also. The paper gives additionally an overview of the diffusion effects and their mechanisms. For the modelling and derivation of equations, the extended current equation is used. The size K represents the proposed charge density drifting vector. The extended diffusion equation was derived and shows the quantising character and has similar law like the Klein-Gordon equation. These kinds of PDE's (Partial Differential Equations) are analytically solvable by giving initial distribution conditions (Cauchy problem) and boundary conditions (Dirichlet boundary condition). For a simpler structure, a transfer function for B- and E- fields was analytically calculated. With known discretised responses g₁(k·Ts) and g₂(k·Ts), the electric current or voltage may be calculated using a convolution; g₁ is the direct function and g₂ is a recursive function. The analytical results are good enough for calculation of fields with diffusion effects. Within the scope of this work, a proposed model of the consideration of the electromagnetic diffusion effects of arbitrary current 'waveforms' has been developed. The advantage of the proposed calculation of diffusion is the real-time capability, which is not really possible with the FEM programs available today. It makes sense in the further course of research to use these methods and to investigate them thoroughly.

Keywords: advanced observer, electrodynamics, systems, diffusion, partial differential equations, solver

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

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The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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Authors: S. Arun Prakash, V. Malathi, M. S. Mani Rajan

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The analytical bright two soliton solution of the 3-coupled nonlinear Schrödinger equations with variable coefficients in birefringent optical fiber is obtained by Darboux transformation method. To the design of ultra-speed optical devices, Soliton interaction and control in birefringence fiber is investigated. Lax pair is constructed for N coupled NLS system through AKNS method. Using two soliton solution, we demonstrate different interaction behaviors of solitons in birefringent fiber depending on the choice of control parameters. Our results shows that interactions of optical solitons have some specific applications such as construction of logic gates, optical computing, soliton switching, and soliton amplification in wavelength division multiplexing (WDM) system.

Keywords: optical soliton, soliton interaction, soliton switching, WDM

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

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Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers' equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile

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Authors: Ju-Young Hwang, Hyo-Gyoung Kwak

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This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical nonlinearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC, high temperature, after-cooling analysis, nonlinear analysis

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Authors: Somayyeh Karimiyan

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To evaluate the seismic vulnerability of vital offshore structures with the highest possible precision, Nonlinear Time History Analyses (NLTHA), is the most reliable method. However, since it is very time-consuming, a quick procedure is greatly desired. This paper presents a quick method by combining the Push Over Analysis (POA) and the NLTHA. The POA is preformed first to recognize the more critical members, and then the NLTHA is performed to evaluate more precisely the critical members’ vulnerability. The proposed method has been applied to jacket type structure. Results show that combining POA and NLTHA is a reliable seismic evaluation method, and also that none of the earthquake characteristics alone, can be a dominant factor in vulnerability evaluation.

Keywords: jacket structure, seismic evaluation, push-over and nonlinear time history analyses, critical members

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Authors: Gebreegziabher Hailu

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This paper presents the development of residual power series methods aimed at efficiently solving stiff differential equations, which pose significant challenges in numerical analysis due to their rapid changes in solution behavior. The RPSM is a numerical approach that generates polynomial-based approximate solutions without the need for linearization, discretization, or perturbation techniques, making it straightforward to implement and less prone to computational errors. We introduce an approach that utilizes power series expansions combined with residual minimization techniques to enhance convergence and stability. By analyzing the theoretical foundations of stiffness, we delve into the formulation of the residual power series method, detailing how it effectively captures the dynamics of stiff systems while maintaining computational efficiency. Numerical experiments demonstrate the method's superiority in terms of accuracy and computational cost when compared to traditional methods like implicit Runge-Kutta or multistep techniques. We also explore adaptive strategies within our framework to automatically adjust parameters based on the stiffness characteristics of the problem at hand. Ultimately, our findings contribute to the broader toolkit for tackling stiff differential equations, offering a robust alternative that promises to streamline computational workflows in various applied mathematics and engineering contexts.

Keywords: residual power series methods, stiff differential equoations, numerical approach, Runge Kutta methods

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Authors: Leonard Kabeya Mukeba Yakasham

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The theoretical machinery from singularity theory introduced by Glolubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problem is completed and expanded wile generalized to the multiparameter context. In this setting the finite deterinancy theorem or normal forms, the stability of equivariant bifurcation problem, and the structural stability of universal unfolding are discussed. With Yakam Matrix the solutions are limited for some partial differential equations stochastic nonlinear of the open questions in singularity artificial intelligence for future.

Keywords: equivariant bifurcation, symmetry singularity, equivariant jets and transversality, normal forms, universal unfolding instability, structural stability

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Authors: M. H. Korayem, Sh. Ameri, N. Yousefi Lademakhi

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To ensure the stability of closed-loop nonlinear model predictive control (NMPC) within a finite horizon, there is a need for appropriate design terminal ingredients, which can be a time-consuming and challenging effort. Otherwise, in order to ensure the stability of the control system, it is necessary to consider an infinite predictive horizon. Increasing the prediction horizon increases computational demand and slows down the implementation of the method. In this study, a new technique has been proposed to ensure system stability without terminal ingredients. This technique has been employed in the design of the NMPC algorithm, leading to a reduction in the computational complexity of designing terminal ingredients and computational burden. The studied system is a wheeled mobile robot (WMR) subjected to non-holonomic constraints. Simulation has been investigated for two problems: trajectory tracking and adjustment mode.

Keywords: wheeled mobile robot, nonlinear model predictive control, stability, without terminal ingredients

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Authors: Jaan Lellep, Shahid Mubasshar

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A numerical solution is developed for simply supported nanoarches based on the non-local theory of elasticity. The nanoarch under consideration has a step-wise variable cross-section and is weakened by crack-like defects. It is assumed that the cracks are stationary and the mechanical behaviour of the nanoarch can be modeled by Eringen’s non-local theory of elasticity. The physical and thermal properties are sensitive with respect to changes of dimensions in the nano level. The classical theory of elasticity is unable to describe such changes in material properties. This is because, during the development of the classical theory of elasticity, the speculation of molecular objects was avoided. Therefore, the non-local theory of elasticity is applied to study the vibration of nanostructures and it has been accepted by many researchers. In the non-local theory of elasticity, it is assumed that the stress state of the body at a given point depends on the stress state of each point of the structure. However, within the classical theory of elasticity, the stress state of the body depends only on the given point. The system of main equations consists of equilibrium equations, geometrical relations and constitutive equations with boundary and intermediate conditions. The system of equations is solved by using the method of separation of variables. Consequently, the governing differential equations are converted into a system of algebraic equations whose solution exists if the determinant of the coefficients of the matrix vanishes. The influence of cracks and steps on the natural vibration of the nanoarches is prescribed with the aid of additional local compliance at the weakened cross-section. An algorithm to determine the eigenfrequencies of the nanoarches is developed with the help of computer software. The effects of various physical and geometrical parameters are recorded and drawn graphically.

Keywords: crack, nanoarches, natural frequency, step

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Anthony R. Hassan, Jacob A. Gbadeyan

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In this paper, the analysis of a reactive hydromagnetic Poiseuille fluid flow under each of sensitized, Arrhenius and bimolecular chemical kinetics through a channel in the presence of heat source is carried out. An exothermic reaction is assumed while the concentration of the material is neglected. Adomian Decomposition Method (ADM) together with Pade Approximation is used to obtain the solutions of the governing nonlinear non – dimensional differential equations. Effects of various physical parameters on the velocity and temperature fields of the fluid flow are investigated. The entropy generation analysis and the conditions for thermal criticality are also presented.

Keywords: chemical kinetics, entropy generation, thermal criticality, adomian decomposition method (ADM) and pade approximation

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Authors: Lahlou Dahmani, Warda Mekiri, Ahmed Boudjemia

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This scientific paper explores the comparison between the ultimate buckling load obtained through the Eurocode 3 methodology and the ultimate buckling load obtained through finite element simulations for steel columns under compression. The study aims to provide insights into the adequacy of the design rules proposed in Eurocode 3 for different slenderness ratios. The finite element simulations with the Ansys commercial program involve a geometrical and material non-linear analysis of the columns with imperfections. The loss of equilibrium is generally caused by the geometrically nonlinear effects where the column begins to buckle and lose its stability when the load reaches a certain critical value. The linear buckling analysis predicts the theoretical buckling strength of an elastic structure but the nonlinear one is more accurate with taking into account the initial imperfection.

Keywords: Ansys, linear buckling, eigen value, nonlinear buckling, slenderness ratio, Eurocode 3

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Authors: Shangerganesh Lingeshwaran

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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

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The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial reference frame, non-inertial reference frame

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Authors: Rasaq Kareem, Jacob Gbadeyan

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In this study, analysis of the entropy generation of an unsteady reactive hydromagnetic generalized couette fluid flow of a two-step exothermic chemical reaction through a channel with isothermal wall temperature under the influence of different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics was investigated. The modelled nonlinear dimensionless equations governing the fluid flow were simplified and solved using the combined Laplace Differential Transform Method (LDTM). The effects of fluid parameters associated with the problem on the fluid temperature, entropy generation rate and Bejan number were discussed and presented through graphs.

Keywords: couette, entropy, exothermic, unsteady

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Authors: Nabil Mezhoud

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The economic operation of electric energy generating systems is one of the predominant problems in energy systems. Due to the need for better reliability, high energy quality, lower losses, lower cost and a clean environment, the application of renewable and sustainable energy sources, such as wind energy, solar energy, etc., in recent years has become more widespread. In this work, one of a bio-inspired meta-heuristic algorithm inspired by the flashing behavior of fireflies at night called the Firefly Algorithm (FFA) is applied to solve the Optimal Energy Management (OEM) and the environmental index (EI) problems of a micro-grid (MG) operating by Renewable and Sustainable Generation Systems (RSGS). Our main goal is to minimize the nonlinear objective function of an electrical microgrid, taking into account equality and inequality constraints. The FFA approach was examined and tested on a standard MG system composed of different types of RSGS, such as wind turbines (WT), photovoltaic systems (PV), and non-renewable energy, such as fuel cells (FC), micro turbine (MT), diesel generator (DEG) and loads with energy storage systems (ESS). The results are promising and show the effectiveness and robustness of the proposed approach to solve the OEM and the EI problems. The results of the proposed method have been compared and validated with those known references published recently.

Keywords: renewable energy sources, energy management, distributed generator, micro-grids, firefly algorithm

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Authors: Syed M. Jawwad Riaz

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There has been a lot of interest in exploring the thermodynamic properties at the horizon of a black hole geometry. Earlier, it has been shown, for different spacetimes, that the Einstein field equations at the horizon can be expressed as a first law of black hole thermodynamics. In this paper, considering r = constant slices, for the Kerr-Newman black hole, shown that the Einstein field equations for the induced 3-metric of the hypersurface is expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can only be written as a first law of black hole thermodynamics. It is to be mentioned here that the procedure adopted is much easier, to obtain such results, as here one has to essentially deal with (n - 1)-dimensional induced metric for an n-dimensional spacetime.

Keywords: black hole space-times, Einstein's field equation, foliation, hyper-surfaces

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Authors: R. Ramesh, M. Y. M. Yunus, K. Ramesh

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The study conducted in this research are Viscosities, η, and Densities ,ρ, of 1, 4-dioxane with Bromobenzene at different mole fractions and various temperatures in the atmospheric pressure condition. From experimentations excess volumes, VE, and deviations in viscosities, Δη, of mixtures at infinite dilutions have been obtained. The measured systems exhibited positive values of VmE and negative values of Δη. The binary mixture 1, 4 dioxane + Bromobenzene show positive VE and negative Δη with increasing temperatures. The outcomes clearly indicate that weak interactions present in mixture. It is mainly because of number and position of methyl groups exist in these aromatic hydrocarbons. These measured data tailored to the nonlinear models to derive the binary coefficients. Standard deviations have been considered between the fitted outcomes and the calculated data is helpful deliberate mixing behavior of the binary mixtures. It can conclude that in our cases, the data found with the values correlated by the corresponding models very well. The molecular interactions existing between the components and comparison of liquid mixtures were also discussed.

Keywords: 1, 4 dioxane, bromobenzene, density, excess molar volume

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

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We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: dam-break problems, finite volume method, run-up waves, shallow water flows, wet/dry interfaces

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Authors: Hocine Hammoum, Karima Bouzelha, Lounis Ziani, Lounis Hamitouche

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In this paper, we study a complex structure which is an apartment building surmounted by a reinforced concrete water tank. The tank located on the top floor of the building is a container with capacity of 1000 m³. The building is complex in its design, its calculation and by its behavior under earthquake effect. This structure located in Algiers and aged of 53 years has been subjected to several earthquakes, but the earthquake of May 21^st, 2003 with a magnitude of 6.7 on the Richter scale that struck Boumerdes region at 40 Kms East of Algiers was fatal for it. It was downgraded after an investigation study because the central core sustained serious damage. In this paper, to estimate the degree of its damages, the seismic performance of the structure will be evaluated taking into account the hydrodynamic effect, using a static equivalent nonlinear analysis called pushover.

Keywords: performance analysis, building, reinforced concrete tank, seismic analysis, nonlinear analysis, hydrodynamic, pushover

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

Procedia PDF Downloads 305