Search results for: nonlinear Takagi’s equations

Authors: Aneri Mehta, Krunal Mehta

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The unpredictable and vacillating relationship between India and Pakistan since days of Independence struggle is known world over. And this instability has never lost its magnitude to decrease the tensions between the two countries. Since India aspires to run for the race of future superpower and Pakistan struggles to remove the tag of a highly fickle and under developed economy; ruined largely not by the outsiders, but its own people and systems; it becomes really important to gauge what steps would these neighbors take in years to come. The progress and stability of both countries heavily relies on the favorable equations between the two nations. Therefore the paper tries to trace some roots of their faltering relationship and attempts to predict their future in a multidimensional perspective.

Keywords: economy, faltering relationship, multidimensional perspective, international relations

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: Manoj Parmar

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The article uses reflexivity as a research method to investigate and propose an architectural theory plan for climate change. It hypothecates that to discuss or formulate discourse on "Architectural Thinking in a Time of Climate Emergency," firstly, we need to understand the modes of integration that enable architectural thinking with climate change. The study intends to study the various integration modes that have evolved historically and situate them in time. Subsequently, it analyses the integration pattern, challenges the existing model, and finds a way towards climate change as central to architectural thinking. The study is fundamental on-premises that ecology and climate change scholarship has consistently out lashed the asymmetrical and nonlinear knowledge and needs approaches for architecture that are less burden to climate change to people and minimize its impact on ecology.

Keywords: climate change, architectural theory, reflexivity, modernity

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Authors: A. Chellil, A. Nour, S. Lecheb , H. Mechakra, L. Addar, H. Kebir

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This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems. Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: aluminum alloys, plate, crack, failure

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Authors: Flora Babongo, Valerie Chavez

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Inferring causality from observational data is one of the fundamental subjects, especially in quantitative finance. So far most of the papers analyze additive noise models with either linearity, nonlinearity or Gaussian noise. We fill in the gap by providing a nonlinear and non-gaussian causal multiplicative noise model that aims to distinguish the cause from the effect using a two steps method based on Bayesian additive models for location, scale and shape (BAMLSS) and on causal additive models (CAM). We have tested our method on simulated and real data and we reached an accuracy of 0.86 on average. As real data, we considered the causality between financial indices such as S&P 500, Nasdaq, CAC 40 and Nikkei, and companies' log-returns. Our results can be useful in inferring causality when the data is heteroskedastic or non-injective.

Keywords: causal inference, DAGs, BAMLSS, financial index

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: M. Ndaw, G. Mendy, S. Ouya

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Risk management in banking sector is a key issue linked to financial system stability and its importance has been elevated by technological developments and emergence of new financial instruments. In this paper, we improve the model previously defined for quantifying internal control impact on banking risks by automatizing the residual criticality estimation step of FMECA. For this, we defined three equations and a maturity coefficient to obtain a mathematical model which is tested on all banking processes and type of risks. The new model allows an optimal assessment of residual criticality and improves the correlation rate that has become 98%.

Keywords: risk, control, banking, FMECA, criticality

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: M. Ndaw, G. Mendy, S. Ouya

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Information system risk management helps to reduce or eliminate risk by implementing appropriate controls. In this paper, we propose a quantification model of controls impact on information system risks by automatizing the residual criticality estimation step of FMECA which is based on a inductive reasoning. For this, we defined three equations based on type and maturity of controls. For testing, the values obtained with the model were compared to estimated values given by interlocutors during different working sessions and the result is satisfactory. This model allows an optimal assessment of controls maturity and facilitates risk analysis of information system.

Keywords: information system, risk, control, FMECA method

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Authors: Ruichong Zhang

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This study proposes a recording-based approach to characterize and quantify earthquake-induced site nonlinearity, exemplified as soil nonlinearity and/or liquefaction. Alternative to Fourier spectral analysis (FSA), the paper introduces time-frequency analysis of earthquake ground motion recordings with the aid of so-called Hilbert-Huang transform (HHT), and offers justification for the HHT in addressing the nonlinear features shown in the recordings. With the use of the 2001 Nisqually earthquake recordings, this study shows that the proposed approach is effective in characterizing site nonlinearity and quantifying the influences in seismic ground responses.

Keywords: site nonlinearity, site amplification, site damping, Hilbert-Huang Transform (HHT), liquefaction, 2001 Nisqually Earthquake

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Authors: Derrouazin Mohammed Redhouane, Souakri Mohammed Lotfi, Henini Ghania

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This work consists, first of all, of mastering one of the powerful process simulation tools currently used in the industrial processes, which is the HYSYS sizing software, and second, of simulating a petroleum distillation column. This study is divided into two parts; where the first one consists of a dimensioning of the column with a fast approximating method using state equations, iterative calculations, and then a precise simulation method with the HYSYS software. The second part of this study is a hydrodynamic study in order to verify by obtained results the proper functioning of the plates.

Keywords: industry process engineering, water distillation, environment, HYSYS simulation tool

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Dong Wook Lee, Adrian Mistreanu

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The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: computer aided engineering, containment analysis, finite element analysis, impact analysis, penetration analysis

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Authors: R. S. Hassani, S. Chikh, L. Tadrist, S. Radev

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A bubbly flow in a vertical miniature tube is analyzed theoretically. The liquid and gas phase are co-current flowing upward. The gas phase is injected via a nozzle whose inner diameter is 0.11mm and it is placed on the axis of the tube. A force balance is applied on the bubble at its detachment. The set of governing equations are solved by use of Mathematica software. The bubble diameter and the bubble generation frequency are determined for various inlet phase velocities represented by the inlet mass quality. The results show different behavior of bubble growth and detachment depending on the tube size.

Keywords: two phase flow, bubble growth, mini-channel, generation frequency

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Authors: Sammani Danwawu Abdullahi

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Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: counting with uncertainties, mathematical programming, optimization, vertex enumeration

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Authors: Turky Al-Qahtani, Roustem Miftahof

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Introduction: Under common assumptions of excitabi-lity, morphological (cellular) homogeneity, and spatial structural anomalies added as required, it has been shown that biological systems are able to display travelling wave dynamics. Being not self-sustainable, existence depends on the electrophysiological state of transmembrane ion channels and it requires an extrinsic/intrinsic periodic source. However, organs in the body are highly multicellular, heterogeneous, and their functionality is the outcome of electro-mechanical conjugation, rather than excitability only. Thus, peristalsis in the gut relies on spatiotemporal myoelectrical pattern formations between the mechanical, represented by smooth muscle cells (SM), and the control, comprised of a chain of primary sensory and motor neurones, components. Synaptically linked through the afferent and efferent pathways, they form a functional unit (FU) of the gut. Aims: These are: i) to study numerically the complex dynamics, and ii) to investigate the possibility of self-sustained myoelectrical activity in the FU. Methods: The FU recreates the following sequence of physiological events: deformation of mechanoreceptors of located in SM; generation and propagation of electrical waves of depolarisation - spikes - along the axon to the soma of the primary neurone; discharge of the primary neurone and spike propagation towards the motor neurone; burst of the motor neurone and transduction of spikes to SM, subsequently producing forces of contraction. These are governed by a system of nonlinear partial and ordinary differential equations being a modified version of the Hodgkin-Huxley model and SM fibre mechanics. In numerical experiments; the source of excitation is mechanical stretches of SM at a fixed amplitude and variable frequencies. Results: Low frequency (0.5 < v < 2 Hz) stimuli cause the propagation of spikes in the neuronal chain and, finally, the generation of active forces by SM. However, induced contractions are not sufficient to initiate travelling wave dynamics in the control system. At frequencies, 2 < v < 4 Hz, multiple low amplitude and short-lasting contractions are observed in SM after the termination of stretching. For frequencies (0.5 < v < 4 Hz), primary and sensory neurones demonstrate strong connectivity and coherent electrical activity. Significant qualitative and quantitative changes in dynamics of myoelectical patterns with a transition to a self-organised mode are recorded with the high degree of stretches at v = 4.5 Hz. Increased rates of deformation lead to the production of high amplitude signals at the mechanoreceptors with subsequent self-sustained excitation within the neuronal chain. Remarkably, the connection between neurones weakens resulting in incoherent firing. Further increase in a frequency of stimulation (v > 4.5 Hz) has a detrimental effect on the system. The mechanical and control systems become disconnected and exhibit uncoordinated electromechanical activity. Conclusion: To our knowledge, the existence of periodic activity in a multicellular, functionally heterogeneous biological system with mechano-electrical dynamics, such as the FU, has been demonstrated for the first time. These findings support the notion of possible peristalsis in the gut even in the absence of intrinsic sources - pacemaker cells. Results could be implicated in the pathogenesis of intestinal dysrythmia, a medical condition associated with motor dysfunction.

Keywords: complex dynamics, functional unit, the gut, dysrythmia

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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: M. Y. Malik, Farzana Khan

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In this article, we discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered. Thermal conductivity is considered as a linear function of temperature. By using homotopy analysis method and Fehlberg method we compare the graphical results for both momentum and energy equations. The effect of different parameters on velocity and temperature fields are shown graphically.

Keywords: slip conditions, stretching cylinder, heat generation/absorption, stagnation point flow, variable thermal conductivity

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Authors: Jade Martínez-Llinàs, Pere Colet

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By exploring the possible dynamical regimes in a prototypical model for mutually delay-coupled OEOs, here it is shown that two mutually coupled non-identical OEOs, besides in- and out-of-phase square-waves, can generate stable square-wave pulses synchronized at a quarter of the period (T/4) in a broad parameter region. The key point to obtain T/4 solutions is that the two OEO operate with mixed feedback, namely with negative feedback in one and positive in the other. Furthermore, the coexistence of multiple solutions provides a large degree of flexibility for tuning the frequency in the GHz range without changing any parameter. As a result the two coupled OEOs system is good candidate to be implemented for information encoding as a high-capacity memory device.

Keywords: nonlinear optics, optoelectronic oscillators, square waves, synchronization

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Authors: Natasha Sharma, Kulbhushan Agnihotri

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Cellular Automata are discrete dynamical systems which are based on local character and spatial disparateness of the spreading process. These factors are generally neglected by traditional models based on differential equations for epidemic spread. The aim of this work is to introduce an SEIR model based on cellular automata on graphs to imitate epidemic spreading. Distinctively, it is an SEIR-type model where the population is divided into susceptible, exposed, infected and recovered individuals. The results obtained from simulations are in accordance with the spreading behavior of a real time epidemics.

Keywords: cellular automata, epidemic spread, graph, susceptible

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Authors: Wieslaw Marszalek, Zdzislaw Trzaska

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Interesting properties of various one-period loops of singularly perturbed memristive circuits with mixed-mode oscillations (MMOs) are analyzed in this paper. The analysis is mixed, both analytical and numerical and focused on the properties of pinched hysteresis of the memristive element and other one-period loops formed by pairs of time-series solutions for various circuits' variables. The memristive element is the only nonlinear element in the two circuits. A theorem on periods of mixed-mode oscillations of the circuits is formulated and proved. Replacements of memristors by parallel G-C or series R-L circuits for a MMO response with equivalent RMS values is also discussed.

Keywords: mixed-mode oscillations, memristive circuits, pinched hysteresis, one-period loops, singularly perturbed circuits

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Authors: Lele Zhang, Hui Leng Choo, Alexander Konyukhov, Shuguang Li

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Finite Element (FE) model of simplified e-bike structure was generated by main frame with two tiers, which consisted of pipe, mass, beam, and shell elements (pipe 289, beam188, shell 181, shell 281, combin14, link11, mass21). These elements would be introduced and demonstrated using mathematical formulas. Based on coupling theory, constrain equations was proposed. Exporting all the parameters obtained from theory part, the connection stiffness matrix of the whole e-bike structure between each of these elements was detected.

Keywords: coupling theory, stiffness matrix, e-bike, finite element model

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Authors: A. Zanj, F. He

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In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: multi-physical domain, conduction model, port based modeling, dynamic interaction, physical modeling

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Authors: T. G. Kassem, A. K. Adunchezor, J. P. Chollom

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This paper describes a mathematical model developed to predict the dynamics of Hepatitis B virus (HBV) infection and to evaluate the potential impact of vaccination and treatment on its dynamics. We used a compartmental model expressed by a set of differential equations based on the characteristic of HBV transmission. With these, we find the threshold quantity R0, then find the local asymptotic stability of disease free equilibrium and endemic equilibrium. Furthermore, we find the global stability of the disease free and endemic equilibrium.

Keywords: hepatitis B virus, epidemiology, vaccination, mathematical model

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Authors: Jun Liu

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This paper introduces a new bipartite key agreement (2PKA) protocol which provides unconditionally security and lightweight. The unconditional security is stemmed from the known impossibility of distinguishing a particular solution from all possible solutions of an underdetermined system of equations. The indistinguishability prevents an adversary from inferring to the common secret-key even with the access to an unlimited amount of computing capability. This new 2PKA protocol is also lightweight because that the calculation of a common secret-key only makes use of simple modular arithmetic. This information-theoretic 2PKA scheme provides the desired features of Key Confirmation (KC), Session Key (SK) security, Know-Key (KK) security, protection of individual privacy, and uniformly distributed value of a common key under prime modulus.

Keywords: bipartite key agreement, information-theoretic cryptography, perfect security, lightweight

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Authors: Shabnam Najafi, Metin Turkay

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Network design problem (NDP) is used to determine the set of optimal values for certain pre-specified decision variables such as capacity expansion of nodes and links by optimizing various system performance measures including safety, congestion, and accessibility. The designed transportation network should improve objective functions defined for the system by considering the route choice behaviors of network users at the same time. The NDP studies mostly investigated the random demand and route selection constraints separately due to computational challenges. In this work, we consider both random demand and route selection constraints simultaneously. This work presents a nonlinear stochastic model for land use and road network design problem to address the development of different functional zones in urban areas by considering both cost function and air pollution. This model minimizes cost function and air pollution simultaneously with random demand and stochastic route selection constraint that aims to optimize network performance via road capacity expansion. The Bureau of Public Roads (BPR) link impedance function is used to determine the travel time function in each link. We consider a city with origin and destination nodes which can be residential or employment or both. There are set of existing paths between origin-destination (O-D) pairs. Case of increasing employed population is analyzed to determine amount of roads and origin zones simultaneously. Minimizing travel and expansion cost of routes and origin zones in one side and minimizing CO emission in the other side is considered in this analysis at the same time. In this work demand between O-D pairs is random and also the network flow pattern is subject to stochastic user equilibrium, specifically logit route choice model. Considering both demand and route choice, random is more applicable to design urban network programs. Epsilon-constraint is one of the methods to solve both linear and nonlinear multi-objective problems. In this work epsilon-constraint method is used to solve the problem. The problem was solved by keeping first objective (cost function) as the objective function of the problem and second objective as a constraint that should be less than an epsilon, where epsilon is an upper bound of the emission function. The value of epsilon should change from the worst to the best value of the emission function to generate the family of solutions representing Pareto set. A numerical example with 2 origin zones and 2 destination zones and 7 links is solved by GAMS and the set of Pareto points is obtained. There are 15 efficient solutions. According to these solutions as cost function value increases, emission function value decreases and vice versa.

Keywords: epsilon-constraint, multi-objective, network design, stochastic

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Authors: A. Morsli, A. Tlemçani, N. Ould Cherchali, M. S. Boucherit

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This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to an Active Power Filter shunt (APFs) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: fuzzy logic controller, P-Q method, pulse width modulation (PWM), shunt active power filter (sAPF), total harmonic distortion (THD)

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Authors: William Kelly, Sorelle Veigne, Xianhua Li, Zuyi Huang, Shyamsundar Subramanian, Eugene Schaefer

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The ambr15™ bioreactor is a single-use microbioreactor for cell line development and process optimization. The ambr system offers fully automatic liquid handling with the possibility of fed-batch operation and automatic control of pH and oxygen delivery. With operating conditions for large scale biopharmaceutical production properly scaled down, micro bioreactors such as the ambr15™ can potentially be used to predict the effect of process changes such as modified media or different cell lines. In this study, gassing rates and dilution rates were varied for a semi-continuous cell culture system in the ambr15™ bioreactor. The corresponding changes to metabolite production and consumption, as well as cell growth rate and therapeutic protein production were measured. Conditions were identified in the ambr15™ bioreactor that produced metabolic shifts and specific metabolic and protein production rates also seen in the corresponding larger (5 liter) scale perfusion process. A Dynamic Flux Balance model was employed to understand and predict the metabolic changes observed. The DFB model-predicted trends observed experimentally, including lower specific glucose consumption when CO₂ was maintained at higher levels (i.e. 100 mm Hg) in the broth. A Computational Fluid Dynamic (CFD) model of the ambr15™ was also developed, to understand transfer of O₂ and CO₂ to the liquid. This CFD model predicted gas-liquid flow in the bioreactor using the ANSYS software. The two-phase flow equations were solved via an Eulerian method, with population balance equations tracking the size of the gas bubbles resulting from breakage and coalescence. Reasonable results were obtained in that the Carbon Dioxide mass transfer coefficient (kLa) and the air hold up increased with higher gas flow rate. Volume-averaged kLa values at 500 RPM increased as the gas flow rate was doubled and matched experimentally determined values. These results form a solid basis for optimizing the ambr15™, using both CFD and FBA modelling approaches together, for use in microscale simulations of larger scale cell culture processes.

Keywords: cell culture, computational fluid dynamics, dynamic flux balance analysis, microbioreactor

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Authors: Daniel Y. Abebe, Jeonghyun Jang, Jaehyouk Choi

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This study aims to evaluate the effective size, section and structural characteristics of circular hollow steel (CHS) damper. CHS damper is among steel dampers which are used widely for seismic energy dissipation because they are easy to install, maintain and are inexpensive. CHS damper dissipates seismic energy through metallic deformation due to the geometrical elasticity of circular shape and fatigue resistance around connection part. After calculating the effective size, which is found to be height to diameter ratio of √("3"), nonlinear FE analyses were carried out to evaluate the structural characteristics and effective section (diameter-to-ratio).

Keywords: circular hollow steel damper, structural characteristics, effective size, effective section, large deformation, FE analysis

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