Search results for: implicit equation

Authors: Itissam Abuiziah

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In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

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Authors: Swarn Singh, Suruchi Singh

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In this paper, we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme. In this paper we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme.

Keywords: convergence, finite difference scheme, Pennes bio-heat equation, stability

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Authors: M. H. Kazemi, D. Salac

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A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method

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Authors: Takahiro Togawa, Nguyen Huu Phuc, Shigeyuki Haruyama, Oke Oktavianty

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Our research focuses on a framework which analyses the relationship between product/process architecture, manufacturing organizational capability and manufacturing "implicit competitiveness" in order to improve manufacturing implicit competitiveness. We found that 1) there is a relationship between architecture-based manufacturing organizational capability and manufacturing implicit competitiveness, and 2) analysis and measures conducted in manufacturing organizational capability proved effective to improve manufacturing implicit competitiveness.

Keywords: implicit competitiveness, QCD, organizational capacity, architectural strategy

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Authors: Lawrence A. Farinola

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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: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

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In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

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Authors: Murzabekova Gulden

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Directional implicit functions for underdetermined nonsmooth systems in terms of the new tool of the Nonsmooth analysis - exhausters are considered. A method for finding an implicit function for underdetermined nonsmooth systems is proposed.

Keywords: implicit function, exhauster, nonsmooth systems

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Authors: Kellina Craig-Henderson

Abstract:

Today, there is increased attention to the role of social perceptions in the selection, hiring, and management of employees and the evaluation and promotion of students. In some contexts, where women or members of certain social groups have been historically underrepresented there is evidence that these perceptions reflect the implicit biases people harbor. Research in the social and psychological sciences reveals that implicit biases against women unfairly disadvantage them in academic and work settings. This presentation will provide an overview of the current state of knowledge on an implicit bias as well as the problems associated with it. How employers, educators and other evaluators can inoculate themselves from the pernicious effects of these biases will be considered.

Keywords: gender equity, implicit bias, social psychology, unconscious bias

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Authors: Nia Mair Fry, Matthew Profit, Chenfeng Li

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This work focuses on the development and implementation of a fully implicit-implicit, coupled mechanical deformation and porous flow, finite element software tool. The fully implicit software accurately predicts classical fundamental analytical solutions such as the Terzaghi consolidation problem. Furthermore, it can capture other analytical solutions less well known in the literature, such as Gibson’s sedimentation rate problem and Coussy’s problems investigating wellbore stability for poroelastic rocks. The mechanical volume strains are transferred to the porous flow governing equation in an implicit framework. This will overcome some of the many current industrial issues, which use explicit solvers for the mechanical governing equations and only implicit solvers on the porous flow side. This can potentially lead to instability and non-convergence issues in the coupled system, plus giving results with an accountable degree of error. The specification of a fully monolithic implicit-implicit coupled porous media code sees the solution of both seepage-mechanical equations in one matrix system, under a unified time-stepping scheme, which makes the problem definition much easier. When using an explicit solver, additional input such as the damping coefficient and mass scaling factor is required, which are circumvented with a fully implicit solution. Further, improved accuracy is achieved as the solution is not dependent on predictor-corrector methods for the pore fluid pressure solution, but at the potential cost of reduced stability. In testing of this fully monolithic porous media code, there is the comparison of the fully implicit coupled scheme against an existing staggered explicit-implicit coupled scheme solution across a range of geotechnical problems. These cases include 1) Biot coefficient calculation, 2) consolidation theory with Terzaghi analytical solution, 3) sedimentation theory with Gibson analytical solution, and 4) Coussy well-bore poroelastic analytical solutions.

Keywords: coupled, implicit, monolithic, porous media

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Authors: M. Salmanzadeh

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In paper, we will deal with incompressible Couette flow, which represents an exact analytical solution of the Navier-Stokes equations. Couette flow is perhaps the simplest of all viscous flows, while at the same time retaining much of the same physical characteristics of a more complicated boundary-layer flow. The numerical technique that we will employ for the solution of the Couette flow is the Crank-Nicolson implicit method. Parabolic partial differential equations lend themselves to a marching solution; in addition, the use of an implicit technique allows a much larger marching step size than would be the case for an explicit solution. Hence, in the present paper we will have the opportunity to explore some aspects of CFD different from those discussed in the other papers.

Keywords: incompressible couette flow, numerical method, partial differential equation, Crank-Nicolson implicit

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Authors: Magali Mari, Fabrice Clement

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The present study investigated the influence of implicit stereotypes on adults’ visual information processing, using an eye-tracking device. Implicit stereotyping is an automatic and implicit process; it happens relatively quickly, outside of awareness. In the presence of a member of a social group, a set of expectations about the characteristics of this social group appears automatically in people’s minds. The study aimed to shed light on the cognitive processes involved in stereotyping and to further investigate the use of eye movements to measure implicit stereotypes. With an eye-tracking device, the eye movements of participants were analyzed, while they viewed everyday scenes depicting women and men in congruent or incongruent gender role activities (e.g., a woman ironing or a man ironing). The settings of these scenes had to be analyzed to infer the character’s role. Also, participants completed an implicit association test that combined the concept of gender with attributes of occupation (home/work), while measuring reaction times to assess participants’ implicit stereotypes about gender. The results showed that implicit stereotypes do influence people’s visual attention; within a fraction of a second, the number of returns, between stereotypical and counter-stereotypical scenes, differed significantly, meaning that participants interpreted the scene itself as a whole before identifying the character. They predicted that, in such a situation, the character was supposed to be a woman or a man. Also, the study showed that eye movements could be used as a fast and reliable supplement for traditional implicit association tests to measure implicit stereotypes. Altogether, this research provides further understanding of implicit stereotypes processing as well as a natural method to study implicit stereotypes.

Keywords: eye-tracking, implicit stereotypes, social cognition, visual attention

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Authors: Asabe Ahmad Tijani, Y. A. Yahaya

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The paper considers the derivation of implicit Adams-Moulton type method, with k=4 and 5. We adopted the method of interpolation and collocation of power series approximation to generate the continuous formula which was evaluated at off-grid and some grid points within the step length to generate the proposed block schemes, the schemes were investigated and found to be consistent and zero stable. Finally, the methods were tested with numerical experiments to ascertain their level of accuracy.

Keywords: Adam-Moulton Type (AMT), off-grid, block method, consistent and zero stable

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: Vivienne Langhorne, Helen Sharpe

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Body dissatisfaction begins developing in middle childhood, with wide-ranging implications for mental health and well-being. Previous research on parent behavior has focused on the role of explicit parent behaviors in adolescent and young adult body dissatisfaction, leaving a gap in understanding how implicit parent behaviors relate to body dissatisfaction in childhood. The current study investigated how implicit parent behavior (such as modeling own body dissatisfaction and dieting) relates to parent and child body dissatisfaction. It was hypothesized that implicit behavior would be directly related to parent and child body dissatisfaction and mediate the relationship between the two. Furthermore, this study aimed to examine child gender as a potential moderator in this mediation, as research shows that boys and girls experience body dissatisfaction differently. This study analyzed survey responses on parent body dissatisfaction, implicit behavior, and child body dissatisfaction measures from a sample of 166 parent-child dyads with children between the ages of 6 to 9 years old. Regression analyses revealed that parent body dissatisfaction is related to both parent-implicit behavior and child body dissatisfaction. However, implicit behavior did not mediate the relationship between the two body dissatisfaction variables. Additionally, the results of moderated mediation indicated there were no child gender differences in the strength of the association between parental implicit behaviors and child body dissatisfaction. These findings highlight the need for further research into the mechanisms behind parent and child body dissatisfaction to better understand the process through which intergenerational transmission occurs.

Keywords: body dissatisfaction, implicit behaviour, middle childhood, parenting

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Authors: Ih-Ching Hsu

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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: Raoul Ouambo Tobou, Alexis Kuitche, Marcel Edoun

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The FWM (Finite Window Method) is a new numerical meshfree technique for solving problems defined either in terms of PDEs (Partial Differential Equation) or by a set of conservation/equilibrium laws. The principle behind the FWM is that in such problem each element of the concerned domain is interacting with its neighbors and will always try to adapt to keep in equilibrium with respect to those neighbors. This leads to a very simple and robust problem solving scheme, well suited for transfer problems. In this work, we have applied the FWM to an unsteady scalar convection-diffusion equation. Despite its simplicity, it is well known that convection-diffusion problems can be challenging to be solved numerically, especially when convection is highly dominant. This has led researchers to set the scalar convection-diffusion equation as a benchmark one used to analyze and derive the required conditions or artifacts needed to numerically solve problems where convection and diffusion occur simultaneously. We have shown here that the standard FWM can be used to solve convection-diffusion equations in a robust manner as no adjustments (Upwinding or Artificial Diffusion addition) were required to obtain good results even for high Peclet numbers and coarse space and time steps. A comparison was performed between the FWM scheme and both a first order implicit Finite Volume Scheme (Upwind scheme) and a third order implicit Finite Volume Scheme (QUICK Scheme). The results of the comparison was that for equal space and time grid spacing, the FWM yields a much better precision than the used Finite Volume schemes, all having similar computational cost and conditioning number.

Keywords: Finite Window Method, Convection-Diffusion, Numerical Technique, Convergence

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Slah Alsaleh

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In the recent years and with popularity of internet and technology, e-learning became a major part of majority of education systems. One of the advantages the e-learning systems provide is the large amount of information available about the students' behavior while communicating with the e-learning system. Such information is very rich and it can be used to improve the capability and efficiency of e-learning systems. This paper discusses how e-learning can benefit from implicit data in different ways including; creating homogeneous groups of student, evaluating students' learning, creating behavior profiles for students and identifying the students through their behaviors.

Keywords: e-learning, implicit data, user behavior, data mining

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Authors: Basant K. Jha, M. L. Kaurangini

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An approximate analytical solution is presented for convective flow in a horizontal channel filled with porous material. The Brinkman-Forchheimer extension of Darcy equation is utilized to model the fluid flow while the energy equation is utilized to model temperature distribution in the channel. The solutions were obtained utilizing the newly suggested technique and compared with those obtained from an implicit finite-difference solution.

Keywords: approximate analytical, convective flow, porous material, Brinkman-Forchiemer

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Authors: Huangmei Liu, Si Liu, Jia’nan Liu

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The present experiment investigated and compared the effectiveness of two kinds of methods of attention control: Task distraction and visual enhancement. In the study, the effectiveness of task distractions to explicit features and of visual enhancement to implicit features of the same group of Chinese characters were compared based on their effect on the participants’ reaction time, subjective confidence rating, and verbal report. We found support that the visual enhancement on implicit features did overcome the contrary effect of training distraction and led to awareness of those implicit features, at least to some extent.

Keywords: task distraction, visual enhancement, attention, awareness, learning

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Authors: F. Fekak, A. Gravouil, M. Brun, B. Depale

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During an earthquake, a bridge crane may be subjected to multiple impacts between crane wheels and rail. In order to model such phenomena, a time-history dynamic analysis with a multi-scale approach is performed. The high frequency aspect of the impacts between wheels and rails is taken into account by a Lagrange explicit event-capturing algorithm based on a velocity-impulse formulation to resolve contacts and impacts. An implicit temporal scheme is used for the rest of the structure. The numerical coupling between the implicit and the explicit schemes is achieved with a heterogeneous asynchronous time-integrator.

Keywords: bridge crane, earthquake, dynamic analysis, explicit, implicit, impact

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

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The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

Keywords: base-isolated structures, earthquake engineering, mixed time integration, nonlinear exponential model

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

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Authors: Yi-Tung Lin

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Researchers commonly assess implicit self-esteem with the Implicit Association Test (IAT). The IAT’s measure, often referred to as the IAT effect, indicates the strengths of automatic preferences for the self relative to others, which is often considered an index of implicit self-esteem. However, based on the Dual-process theory, the IAT does not rely entirely on the automatic process; it is also influenced by a controlled process. The present study, therefore, analyzed the IAT data with the Quad model, separating four processes on the IAT performance: the likelihood that automatic association is activated by the stimulus in the trial (AC); that a correct response is discriminated in the trial (D); that the automatic bias is overcome in favor of a deliberate response (OB); and that when the association is not activated, and the individual fails to discriminate a correct answer, there is a guessing or response bias drives the response (G). The AC and G processes are automatic, while the D and OB processes are controlled. The AC parameter is considered as the strength of the association activated by the stimulus, which reflects what implicit measures of social cognition aim to assess. The stronger the automatic association between self and positive valence, the more likely it will be activated by a relevant stimulus. Therefore, the AC parameter was used as the index of implicit self-esteem in the present study. Meanwhile, the relationship between implicit self-esteem and depression is not fully investigated. In the cognitive theory of depression, it is assumed that the negative self-schema is crucial in depression. Based on this point of view, implicit self-esteem would be negatively associated with depression. However, the results among empirical studies are inconsistent. The aims of the present study were to examine the psychometric properties of the AC (i.e., test-retest reliability and its correlations with explicit self-esteem and depression) and compare it with that of the IAT effect. The present study had 105 patients with depressive disorders completing the Rosenberg Self-Esteem Scale, Beck Depression Inventory-II and the IAT on the pretest. After at least 3 weeks, the participants completed the second IAT. The data were analyzed by the latent-trait multinomial processing tree model (latent-trait MPT) with the TreeBUGS package in R. The result showed that the latent-trait MPT had a satisfactory model fit. The effect size of test-retest reliability of the AC and the IAT effect were medium (r = .43, p < .0001) and small (r = .29, p < .01) respectively. Only the AC showed a significant correlation with explicit self-esteem (r = .19, p < .05). Neither of the two indexes was correlated with depression. Collectively, the AC parameter was a satisfactory index of implicit self-esteem compared with the IAT effect. Also, the present study supported the results that implicit self-esteem was not correlated with depression.

Keywords: cognitive modeling, implicit association test, implicit self-esteem, quad model

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Authors: Linnan Zhang

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Linguists, as well as psychologists, have shown great interests in implicit causality in reference processing. However, most frequently-used approaches to this issue are psychological experiments (such as eye tracking or self-paced reading, etc.). This research is a corpus-based one and is assisted with statistical tool – software R. The main focus of the present study is about the competition between verb-based implicit causality and theme structure’s influence on anaphora bias in Mandarin Chinese sentences. In Accessibility Theory, it is believed that salience, which is also known as accessibility, and relevance are two important factors in reference processing. Theme structure, which is a special syntactic structure in Chinese, determines the salience of an antecedent on the syntactic level while verb-based implicit causality is a key factor to the relevance between antecedent and anaphora. Therefore, it is a study about anaphora, combining psychology with linguistics. With analysis of the sentences from corpus as well as the statistical analysis of Multinomial Logistic Regression, major findings of the present study are as follows: 1. When the sentence is stated in a ‘cause-effect’ structure, the theme structure will always be the antecedent no matter forward biased verbs or backward biased verbs co-occur; in non-theme structure, the anaphora bias will tend to be the opposite of the verb bias; 2. When the sentence is stated in a ‘effect-cause’ structure, theme structure will not always be the antecedent and the influence of verb-based implicit causality will outweigh that of theme structure; moreover, the anaphora bias will be the same with the bias of verbs. All the results indicate that implicit causality functions conditionally and the noun in theme structure will not be the high-salience antecedent under any circumstances.

Keywords: accessibility theory, anaphora, theme strcture, verb-based implicit causality

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Authors: Prasenjit Singha, Sunil Yadav, Soumya Ranjan Mohantry, Ajay Kumar Shukla

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Temperature distribution in the hematite ore mixed with 7.5% coal was predicted by solving a 1-D heat conduction equation using an implicit finite difference approach. In this work, it was considered a square slab of 20 cm x 20 cm, which assumed the coal to be uniformly mixed with hematite ore. It was solved the equations with the use of MATLAB 2018a software. Heat transfer effects in this 1D dimensional slab convective and the radiative boundary conditions are also considered. Temperature distribution obtained inside hematite slab by considering microwave heating time, thermal conductivity, heat capacity, carbon percentage, sample dimensions, and many other factors such as penetration depth, permittivity, and permeability of coal and hematite ore mixtures. The resulting temperature profile can be used as a guiding tool for optimizing the microwave-assisted carbothermal reduction process of hematite slab was extended to other dimensions as well, viz., 1 cm x 1 cm, 5 cm x 5 cm, 10 cm x 10 cm, 20 cm x 20 cm. The model predictions are in good agreement with experimental results.

Keywords: hematite ore, coal, microwave processing, heat transfer, implicit method, temperature distribution

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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: Takashi Shimizu, Tomoaki Hashimoto

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A class of implicit systems is known as a more generalized class of systems than a class of explicit systems. To establish a control method for such a generalized class of systems, we adopt model predictive control method which is a kind of optimal feedback control with a performance index that has a moving initial time and terminal time. However, model predictive control method is inapplicable to systems whose all state variables are not exactly known. In other words, model predictive control method is inapplicable to systems with limited measurable states. In fact, it is usual that the state variables of systems are measured through outputs, hence, only limited parts of them can be used directly. It is also usual that output signals are disturbed by process and sensor noises. Hence, it is important to establish a state estimation method for nonlinear implicit systems with taking the process noise and sensor noise into consideration. To this purpose, we apply the model predictive control method and unscented Kalman filter for solving the optimization and estimation problems of nonlinear implicit systems, respectively. The objective of this study is to establish a model predictive control with unscented Kalman filter for nonlinear implicit systems.

Keywords: optimal control, nonlinear systems, state estimation, Kalman filter

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Authors: Jian-Jun Shu

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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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