Search results for: parametric equation

Authors: Ih-Ching Hsu

Abstract:

Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Olukunle C. Olawole, Dilip Kumar De

Abstract:

We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

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Authors: Pushpendra S. Bharti

Abstract:

Process yield of electric discharge machining (EDM) is directly related to optimal combination(s) of process parameters. Optimization of process parameters of EDM is a multi-objective optimization problem owing to the contradictory behavior of performance measures. This paper employs Grey Relation Analysis (GRA) method as a multi-objective optimization technique for the optimal selection of process parameters combination. In GRA, multi-response optimization is converted into optimization of a single response grey relation grade which ultimately gives the optimal combination of process parameters. Experiments were carried out on die-sinking EDM by taking D2 steel as work piece and copper as electrode material. Taguchi's orthogonal array L36 was used for the design of experiments. On the experimental values, GRA was employed for the parametric optimization. A significant improvement has been observed and reported in the process yield by taking the parametric combination(s) obtained through GRA.

Keywords: electric discharge machining, grey relation analysis, material removal rate, optimization

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Authors: Philip Speranza

Abstract:

As everyday transit options are shifting from autocentric to pedestrian and bicycle oriented modes for healthy living, downtown streets are becoming more attractive places to live. However, tools and methods to measure the natural environment at the small scale of streets do not exist. Fortunately, a combination of mobile data collection technology and parametric urban design software now allows an interface to relate urban ecological conditions. This paper describes creation of an interactive tool to measure urban phenomena of air, water, and heat/light at the scale of new three-by-three block pedestrianized areas in Barcelona called Superilles. Each Superilla limits transit to the exterior of the blocks and to create more walkable and bikeable interior streets for healthy living. The research will describe the integration of data collection, analysis, and design output via a live interface using parametric software Rhino Grasshopper and the Human User Interface (UI) plugin.

Keywords: transit, urban design, GIS, parametric design, Superilles, Barcelona, urban ecology

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Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

Abstract:

In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

Abstract:

Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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Authors: A. A. Soliman

Abstract:

The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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Authors: Mostafa Refat Ismail, Hazem Eldaly

Abstract:

The adaptation of architecture design to building function is getting highly needed in contemporary designs, especially with the great progression in design methods and tools. This, in turn, requires great flexibility in design strategies, as well as a wider spectrum of space settings to achieve the required environment that special activities imply. Acoustics is an essential factor influencing cognitive acts and behavior as well as, on the extreme end, the physical well-being inside a space. The complexity of this constrain is fueled up by the extended geometric dimensions of multipurpose halls, making acoustic adequateness a great concern that could not easily be achieved for each purpose. To achieve a performance oriented acoustic environment, various parametric shaped false ceilings based on origami folded notion are simulated. These parametric origami shapes are able to fold and unfold forming an interactive structure that changes the mutual acoustic environment according to the geometric shapes' position and its changing exposed surface areas. The mobility of the facets in the origami surface can stretch up the range from a complete plain surface to an unfolded element where a considerable amount of absorption is added to the space. The behavior of the parametric origami shapes are being modeled employing a ray tracing computer simulation package for various shapes topology. The conclusion shows a great variation in the acoustical performance due to the variation in folding faces of the origami surfaces, which cause different reflections and consequently large variations in decay curves.

Keywords: parametric, origami, acoustics, architecture

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Authors: Junaid Kameran Ahmed

Abstract:

A laminated plate composite of graphite/epoxy has been analyzed dynamically in the present work by using a quadratic element (8-node diso-parametric), and by depending on 1^st order shear deformation theory, every node in this element has 6-degrees of freedom (displacement in x, y, and z axis and twist about x, y, and z axis). The dynamic analysis in the present work covered parametric studies on a composite laminated plate (square plate) to determine its effect on the natural frequency of the plate. The parametric study is represented by set of changes (plate thickness, number of layers, support conditions, layer orientation), and the plates have been simulated by using ANSYS package 12. The boundary conditions considered in this study, at all four edges of the plate, are simply supported and fixed boundary condition. The results obtained from ANSYS program show that the natural frequency for both fixed and simply supported increases with increasing the number of layers, but this increase in the natural frequency for the first five modes will be neglected after 10 layers. And it is observed that the natural frequency of a composite laminated plate will change with the change of ply orientation, the natural frequency increases and it will be at maximum with angle 45 of ply for simply supported laminated plate, and maximum natural frequency will be with cross-ply (0/90) for fixed laminated composite plate. It is also observed that the natural frequency increase is approximately doubled when the thickness is doubled.

Keywords: laminated plate, orthotropic plate, square plate, natural frequency (free vibration), composite (graphite / epoxy)

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Authors: Hamid Hamli Benzahar

Abstract:

The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.

Keywords: composite beam, shear deformation, moments, finites elements

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Authors: Khaled Moaddy

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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

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Authors: Robert Pečenko, Karin Tomažič, Igor Planinc, Sabina Huč, Tomaž Hozjan

Abstract:

Timber is favourable structural material due to high strength to weight ratio, recycling possibilities, and green credentials. Despite being flammable material, it has relatively high fire resistance. Everyday engineering practice around the word is based on an outdated design of timber structures considering standard fire exposure, while modern principles of performance-based design enable use of advanced non-standard fire curves. In Europe, standard for fire design of timber structures EN 1995-1-2 (Eurocode 5) gives two methods, reduced material properties method and reduced cross-section method. In the latter, fire resistance of structural elements depends on the effective cross-section that is a residual cross-section of uncharred timber reduced additionally by so called zero strength layer. In case of standard fire exposure, Eurocode 5 gives a fixed value of zero strength layer, i.e. 7 mm, while for non-standard parametric fires no additional comments or recommendations for zero strength layer are given. Thus designers often implement adopted 7 mm rule also for parametric fire exposure. Since the latest scientific evidence suggests that proposed value of zero strength layer can be on unsafe side for standard fire exposure, its use in the case of a parametric fire is also highly questionable and more numerical and experimental research in this field is needed. Therefore, the purpose of the presented study is to use advanced calculation methods to investigate the thickness of zero strength layer and parametric charring rates used in effective cross-section method in case of parametric fire. Parametric studies are carried out on a simple solid timber beam that is exposed to a larger number of parametric fire curves Zero strength layer and charring rates are determined based on the numerical simulations which are performed by the recently developed advanced two step computational model. The first step comprises of hygro-thermal model which predicts the temperature, moisture and char depth development and takes into account different initial moisture states of timber. In the second step, the response of timber beam simultaneously exposed to mechanical and fire load is determined. The mechanical model is based on the Reissner’s kinematically exact beam model and accounts for the membrane, shear and flexural deformations of the beam. Further on, material non-linear and temperature dependent behaviour is considered. In the two step model, the char front temperature is, according to Eurocode 5, assumed to have a fixed temperature of around 300°C. Based on performed study and observations, improved levels of charring rates and new thickness of zero strength layer in case of parametric fires are determined. Thus, the reduced cross section method is substantially improved to offer practical recommendations for designing fire resistance of timber structures. Furthermore, correlations between zero strength layer thickness and key input parameters of the parametric fire curve (for instance, opening factor, fire load, etc.) are given, representing a guideline for a more detailed numerical and also experimental research in the future.

Keywords: advanced numerical modelling, parametric fire exposure, timber structures, zero strength layer

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Authors: Jiya Mohammed, Ibrahim Ismail Giwa

Abstract:

Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

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Authors: Abdelrahman Elsehsah, Hany Madkour, Khalid Farah

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This article presents a 3-D modified non-linear elastic model in the strain space. The Helmholtz free energy function is introduced with the existence of a dissipation potential surface in the space of thermodynamic conjugate forces. The constitutive equation and the damage evolution were derived as well. The modified damage has been examined to model the nonlinear behavior of reinforced concrete (RC) slabs with an opening. A parametric study with RC was carried out to investigate the impact of different factors on the behavior of RC slabs. These factors are the opening area, the opening shape, the place of opening, and the thickness of the slabs. And the numerical results have been compared with the experimental data from literature. Finally, the model showed its ability to be applied to the structural analysis of RC slabs.

Keywords: damage mechanics, 3-D numerical analysis, RC, slab with opening

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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: Lawrence A. Farinola

Abstract:

Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

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Authors: Alexander Marx

Abstract:

Measuring and mitigating market risk is essential for the stability of enterprises, especially for major banking corporations and investment bank firms. To employ these risk measurement and mitigation processes, the Value at Risk (VaR) is the most commonly used risk metric by practitioners. In the past years, we have seen significant weaknesses in the predictive performance of the VaR in times of financial market crisis. To address this issue, the purpose of this study is to investigate the value-at-risk (VaR) estimation models and their predictive performance by applying a series of backtesting methods on the stock market indices of the G7 countries (Canada, France, Germany, Italy, Japan, UK, US, Europe). The study employs parametric, non-parametric, and semi-parametric VaR estimation models and is conducted during three different periods which cover the most recent financial market crisis: the overall period (2006–2022), the global financial crisis period (2008–2009), and COVID-19 period (2020–2022). Since the regulatory authorities have introduced and mandated the Conditional Value at Risk (Expected Shortfall) as an additional regulatory risk management metric, the study will analyze and compare both risk metrics on their predictive performance.

Keywords: value at risk, financial market risk, banking, quantitative risk management

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Authors: E. V. Krishnan

Abstract:

In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

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

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Apurv Kulkarni, Shreyas Badave, B. Rajiv

Abstract:

Non-parametric reliability technique is useful for assessment of reliability of systems for which failure rates are not available. This is useful when detection of malfunctioning of any component is the key purpose during ongoing operation of the system. The main purpose of the Heat Exchanger Cycle discussed in this paper is to provide hot water at a constant temperature for longer periods of time. In such a cycle, certain components play a crucial role and this paper presents an effective way to predict the malfunctioning of the components by determination of system reliability. The method discussed in the paper is feasible and this is clarified with the help of various test cases.

Keywords: heat exchanger cycle, k-statistics, PID controller, system reliability

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Authors: Tai-Ping Chang

Abstract:

In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: P. Srinivas, P. V. N. Prasad

Abstract:

Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands. The DTC of SRM is analysed by two methods. In one of the methods, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.

Keywords: direct toque control, simplified torque equation, finite element analysis, torque ripple

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Authors: Hossein Shokouhmand, Majid Hasanpour

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A new modification to the Strelow method of chevron-type plate heat exchangers (PHX) modeling is proposed. The effects of maldistribution are accounted in the resulting equation. The results of calculations are validated by reported experiences. The good accuracy of heat transfer performance prediction is shown. The results indicate that considering flow maldistribution improve the accuracy of predicting the flow and thermal behavior of the plate exchanger. Additionally, a wide range of the parametric study has been presented which brings out the effects of chevron angle of PHE on its thermal efficiency with considering maldistribution effect. In addition, the thermally optimal corrugation discussed for the chevron-type PHEs.

Keywords: chevron angle, plate heat exchangers, maldistribution, strelow method

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Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Rebecca Owusu Coffie, Atakelty Hailu

Abstract:

Variants of production frontier models have emerged, however, only a limited number of them are applied in empirical research. Hence the effects of these alternative frontier models are not well understood, particularly within sub-Saharan Africa. In this paper, we apply recent advances in the production frontier to examine levels of technical efficiency and efficiency drivers. Specifically, we compare the heteroscedastic parametric and the semiparametric stochastic smooth coefficient (SPSC) models. Using rice production data from Ghana, our empirical estimates reveal that alternative specification of efficiency estimators results in either downward or upward bias in the technical efficiency estimates. Methodologically, we find that the SPSC model is more suitable and generates high-efficiency estimates. Within the parametric framework, we find that parameterization of both the mean and variance of the pre-truncated function is the best model. For the drivers of technical efficiency, we observed that longer farm distances increase inefficiency through a reduction in labor productivity. High soil quality, however, increases productivity through increased land productivity.

Keywords: pre-truncated, rice production, smooth coefficient, technical efficiency

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Authors: Elisha Kyirem

Abstract:

Undoubtedly, climate change is a major global challenge that could threaten the very foundation upon which life on earth is anchored, with its impacts on human mobility attracting the attention of policy makers and researchers. There is an increasing body of literature and case studies suggesting that migration could be a way through which the vulnerable move away from areas exposed to climate extreme events to improve their lives and that of their families. This presents migration as a way through which people voluntarily move to seek opportunities that could help reduce their exposure and avoid danger from climate events. Thus, migration is seen as a proactive adaptation strategy aimed at building resilience and improving livelihoods to enable people to adapt to future changing events. However, there has not been any mathematical equation linking migration and climate change adaptation. Drawing from literature in development studies, this paper develops an equation that seeks to link the relationship between migration and climate change adaptation. The mathematical equation establishes the linkages between migration, resilience, poverty reduction and vulnerability, and these the paper maintains, are the key variables for conceptualizing the migration-climate change adaptation nexus. The paper then tests the validity of the equation using the sustainable livelihood framework and publicly available data on migration and tourism in Ghana.

Keywords: migration, adaptation, climate change, adaptation, poverty reduction

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Authors: Satyanarayana Engu, Ahmed Mohd, V. Murugan

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We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time.

Keywords: Burgers equation, Cole-Hopf transformation, Hermite polynomials, large time asymptotics

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Authors: Saeed Ghali, Hoda El-Faramawy, Mamdouh Eissa, Michael Mishreky

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Scale-resistant austenitic stainless steel, X45CrNiW 18-9, has been developed, and modified steels produced through partial and total nickel replacement by nitrogen. These modified steels were produced in a 10 kg induction furnace under different nitrogen pressures and were cast into ingots. The produced modified stainless steels were forged, followed by air cooling. The phases of modified stainless steels have been investigated using the Schaeffler diagram, dilatometer, and microstructure observations. Both partial and total replacement of nickel using 0.33-0.50% nitrogen are effective in producing fully austenitic stainless steels. The nitrogen contents were determined and compared with those calculated using the Institute of Metal Science (IMS) equation. The results showed great deviations between the actual nitrogen contents and predicted values through IMS equation. So, an equation has been derived based on chemical composition, pressure, and temperature at 1600oC. [N%] = 0.0078 + 0.0406*X, where X is a function of chemical composition and nitrogen pressure. The derived equation has been used to calculate the nitrogen content of different steels using published data. The results reveal the difficulty of deriving a general equation for the prediction of nitrogen content covering different steel compositions. So, it is necessary to use a narrow composition range.

Keywords: solubility, nitrogen, stainless steel, Schaeffler

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Authors: Azad A. Mohammed, Dunyazad K. Assi, Alan S. Abdulrahman

Abstract:

Current ACI 318 Code provides two limits for minimum steel ratio for concrete beams. When concrete compressive strength be larger than 31 MPa the limit of √(fc')/4fy usually governs. In this paper shortcomings related to using this limit was fairly discussed and showed that the limit is based on 90% safety factor and was derived based on modulus of rupture equation suitable for concretes of compressive strength lower than 31 MPa. Accordingly, the limit is nor suitable and critical for concretes of higher compressive strength. An alternative equation was proposed for minimum steel ratio of rectangular beams and was found that the proposed limit is accurate for beams of wide range of concrete compressive strength. Shortcomings of the current ACI 318 Code equation and accuracy of the proposed equation were supported by test data obtained from testing six reinforced concrete beams.

Keywords: concrete beam, compressive strength, minimum steel ratio, modulus of rupture

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