Search results for: nonlinear mathematical model

Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

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In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: bifurcation, heteroclinic orbits, steady state, traveling wave

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An in-compressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping

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Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

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Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

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Over the last several years, concern has developed over how to minimize the spread of HIV/AIDS epidemic in many countries. AIDS epidemic has tremendously stimulated the development of mathematical models of infectious diseases. The transmission dynamics of HIV infection that eventually developed AIDS has taken a pivotal role of much on building mathematical models. From the initial HIV and AIDS models introduced in the 80s, various improvements have been taken into account as how to model HIV/AIDS frameworks. In this paper, we present the impact of migration on the spread of HIV/AIDS. Epidemic model is considered by a system of nonlinear differential equations to supplement the statistical method approach. The model is calibrated using HIV incidence data from Malaysia between 1986 and 2011. Bayesian inference based on Markov Chain Monte Carlo is used to validate the model by fitting it to the data and to estimate the unknown parameters for the model. The results suggest that the migrants stay for a long time contributes to the spread of HIV. The model also indicates that susceptible individual becomes infected and moved to HIV compartment at a rate that is more significant than the removal rate from HIV compartment to AIDS compartment. The disease-free steady state is unstable since the basic reproduction number is 1.627309. This is a big concern and not a good indicator from the public heath point of view since the aim is to stabilize the epidemic at the disease equilibrium.

Keywords: epidemic model, HIV, MCMC, parameter estimation

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Authors: Ebru Dural, M. Zulfu Asık

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Laminated glass is a kind of safety glass, which is made by 'sandwiching' two glass sheets and a polyvinyl butyral (PVB) interlayer in between them. When the glass is broken, the interlayer in between the glass sheets can stick them together. Because of this property, the hazards of sharp projectiles during natural and man-made disasters reduces. They can be widely applied in building, architecture, automotive, transport industries. Laminated glass can easily undergo large displacements even under their own weight. In order to explain their true behavior, they should be analyzed by using large deflection theory to represent nonlinear behavior. In this study, a nonlinear mathematical model is developed for the analysis of laminated glass cylindrical shell which is free in radial directions and restrained in axial directions. The results will be verified by using the results of the experiment, carried out on laminated glass cylindrical shells. The behavior of laminated composite cylindrical shell can be represented by five partial differential equations. Four of the five equations are used to represent axial displacements and radial displacements and the fifth one for the transverse deflection of the unit. Governing partial differential equations are derived by employing variational principles and minimum potential energy concept. Finite difference method is employed to solve the coupled differential equations. First, they are converted into a system of matrix equations and then iterative procedure is employed. Iterative procedure is necessary since equations are coupled. Problems occurred in getting convergent sequence generated by the employed procedure are overcome by employing variable underrelaxation factor. The procedure developed to solve the differential equations provides not only less storage but also less calculation time, which is a substantial advantage in computational mechanics problems.

Keywords: laminated glass, mathematical model, nonlinear behavior, PVB

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Authors: Aarthi Sridhar, Henri Gavin, Karah Kelly

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Rolling Isolation Systems (RISs) are simple and effective means to mitigate earthquake hazards to equipment in critical and precious facilities, such as hospitals, network collocation facilities, supercomputer centers, and museums. The RIS works by isolating components acceleration the inertial forces felt by the subsystem. The RIS consists of two platforms with counter-facing concave surfaces (dishes) in each corner. Steel balls lie inside the dishes and allow the relative motion between the top and bottom platform. Formerly, a mathematical model for the dynamics of RISs was developed using Lagrange’s equations (LE) and experimentally validated. A new mathematical model was developed using Gauss’s Principle of Least Constraint (GPLC) and verified by comparing impulse response trajectories of the GPLC model and the LE model in terms of the peak displacements and accelerations of the top platform. Mathematical models for the RIS are tedious to derive because of the non-holonomic rolling constraints imposed on the system. However, using Gauss’s Principle of Least constraint to find the equations of motion removes some of the obscurity and yields a system that can be easily extended. Though the GPLC model requires more state variables, the equations of motion are far simpler. The non-holonomic constraint is enforced in terms of accelerations and therefore requires additional constraint stabilization methods in order to avoid the possibility that numerical integration methods can cause the system to go unstable. The GPLC model allows the incorporation of more physical aspects related to the RIS, such as contribution of the vertical velocity of the platform to the kinetic energy and the mass of the balls. This mathematical model for the RIS is a tool to predict the motion of the isolation platform. The ability to statistically quantify the expected responses of the RIS is critical in the implementation of earthquake hazard mitigation.

Keywords: earthquake hazard mitigation, earthquake isolation, Gauss’s Principle of Least Constraint, nonlinear dynamics, rolling isolation system

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Authors: Madhu Aneja, Sapna Sharma

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Thermal conductivity of ordinary heat transfer fluids is not adequate to meet today’s cooling rate requirements. Nanoparticles have been shown to increase the thermal conductivity and convective heat transfer to the base fluids. One of the possible mechanisms for anomalous increase in the thermal conductivity of nanofluids is the Brownian motions of the nanoparticles in the basefluid. In this paper, the natural convection of incompressible nanofluid over a nonlinear stretching sheet in the presence of magnetic field is studied. The flow and heat transfer induced by stretching sheets is important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. For computational purpose, Finite Element Method is used. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo – Klienstreuer – Li) correlation. In this model effect of Brownian motion on thermal conductivity is considered. The effect of important parameter i.e. nonlinear parameter, volume fraction, Hartmann number, heat source parameter is studied on velocity and temperature. Skin friction and heat transfer coefficients are also calculated for concerned parameters.

Keywords: Brownian motion, convection, finite element method, magnetic field, nanofluid, stretching sheet

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Authors: S. A. Al-Qallaf, S. A. Al-Mawsawi, A. Haider

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In order to evaluate the performance of a unified power flow controller (UPFC), mathematical models for steady state and dynamic analysis are to be developed. The steady state model is mainly concerned with the incorporation of the UPFC in load flow studies. Several load flow models for UPFC have been introduced in literature, and one of the most reliable models is the decoupled UPFC model. In spite of UPFC decoupled load flow model simplicity, it is more robust compared to other UPFC load flow models and it contains unique capabilities. Some shortcoming such as additional set of nonlinear equations are to be solved separately after the load flow solution is obtained. The aim of this study is to investigate the different control strategies that can be realized in the decoupled load flow model (individual control and combined control), and the impact of the location of the UPFC in the network on its control parameters.

Keywords: UPFC, decoupled model, load flow, control parameters

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Authors: E. Shahsavari, R. Ghasemi, A. Akramizadeh

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This paper presents a new method to design nonlinear feedback linearization controller for polymer electrolyte membrane fuel cells (PEMFCs). A nonlinear controller is designed based on nonlinear model to prolong the stack life of PEM fuel cells. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEM fuel cell system so that the deviation can be kept as small as possible during disturbances or load variations. To obtain an accurate feedback linearization controller, tuning the linear parameters are always important. So in proposed study NSGA_II method was used to tune the designed controller in aim to decrease the controller tracking error. The simulation result showed that the proposed method tuned the controller efficiently.

Keywords: nonlinear dynamic model, polymer electrolyte membrane fuel cells, feedback linearization, optimal control, NSGA_II

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Authors: Mohamed Belhorma, Aboubakar S. Bouchikhi, Belkacem Bounab

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This paper addresses modeling a Double A-Arm suspension, a three-dimensional nonlinear model has been developed using the multibody systems formalism. Dynamical study of the different components responses was done, particularly for the wheel assembly. To validate those results, the system was constructed and simulated by RecurDyn, a professional multibody dynamics simulation software. The model has been used as the Objectif function in an optimization algorithm for ride quality improvement.

Keywords: double A-Arm suspension, multibody systems, ride quality optimization, dynamic simulation

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Authors: Pham Van Nha, Le Cam Binh

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Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: analysis of optimization, artificial intelligence based optimization, optimization for learning and data analysis, global optimization

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Authors: Hamza Nejib, Okba Taouali

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This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS

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Authors: Hacina Abchiche, Mounir Mellal, Imene Bouchelkia

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The knowledge of the rheological behavior of the used products in different fields is essential, both in digital simulation and the understanding of phenomenon involved during the flow of these products. The fluids presenting a nonlinear behavior represent an important category of materials used in the process of food-processing, chemical, pharmaceutical and oil industries. The issue is that the rheological characterization by classical rheometer cannot simulate, or take into consideration, the different parameters affecting the characterization of a complex fluid flow during real-time. The main objective of this study is to investigate the influence of the diameter of the flow conducts or pipe on the rheological behavior of a non-Newtonian fluid and Propose a mathematical model linking the rheologic parameters and the diameter of the conduits of flow. For this purpose, we have developed an experimental system based on the principal of a capillary rheometer.

Keywords: rhéologie, non-Newtonian fluids, experimental stady, mathematical model, cylindrical conducts

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Authors: Hamid Havasi, Mohamad Reza Gholami Dehbalaei, Hamed Khorami, Shahram Karimi, Hamdi Abdi

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Doubly-fed induction generator (DFIG) equipped with a power converter is an efficient tool for converting mechanical energy of a variable speed system to a fixed-frequency electrical grid. Since electrical energy sources faces with production problems such as harmonics caused by nonlinear loads, so in this paper, compensation performance of DPC and FOC method on harmonics reduction of a DFIG wind turbine connected to a nonlinear load in MATLAB Simulink model has been simulated and effect of each method on nonlinear load harmonic elimination has been compared. Results of the two mentioned control methods shows the advantage of the FOC method on DPC method for harmonic compensation. Also, the fifth and seventh harmonic components of the network and THD greatly reduced.

Keywords: DFIG machine, energy conversion, nonlinear load, THD, DPC, FOC

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Authors: Chandra Mukherjee

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The prevalent knowledge of the biological systems is based on the standard scientific perception of natural equilibrium, determination and predictability. Recently, a rethinking of concepts was presented and a new scientific perspective emerged that involves complexity theory with deterministic chaos theory, nonlinear dynamics and theory of fractals. The unpredictability of the chaotic processes probably would change our understanding of diseases and their management. The mathematical definition of chaos is defined by deterministic behavior with irregular patterns that obey mathematical equations which are critically dependent on initial conditions. The chaos theory is the branch of sciences with an interest in nonlinear dynamics, fractals, bifurcations, periodic oscillations and complexity. Recently, the biomedical interest for this scientific field made these mathematical concepts available to medical researchers and practitioners. Any biological network system is considered to have a nominal state, which is recognized as a homeostatic state. In reality, the different physiological systems are not under normal conditions in a stable state of homeostatic balance, but they are in a dynamically stable state with a chaotic behavior and complexity. Biological systems like heart rhythm and brain electrical activity are dynamical systems that can be classified as chaotic systems with sensitive dependence on initial conditions. In biological systems, the state of a disease is characterized by a loss of the complexity and chaotic behavior, and by the presence of pathological periodicity and regulatory behavior. The failure or the collapse of nonlinear dynamics is an indication of disease rather than a characteristic of health.

Keywords: HRV, HRVI, LF, HF, DII

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Authors: V. Nagaraju, G. Murali, Nagarjunavarma Ganna, Atluri Pavan Kalyan, N. Sree Sai Ganesh, V. S. V. S. Badrinath

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The present work focuses on the development of a mathematical model for the yield obtained by single slope solar still incorporated with cylindrical pipes filled with sand. The mathematical results obtained were validated with the experimental results for the 3 cm of water level at the basin. The mathematical model and results obtained with the experimental investigation are within 11% of deviation. The theoretical model to predict the yield obtained due to the capillary effect was proposed first. And then, to predict the total yield obtained, the thermal effect model was integrated with the capillary effect model. With the obtained results, it is understood that the yield obtained is more in the case of solar stills with sand-filled cylindrical pipes when compared to solar stills without sand-filled cylindrical pipes. And later model was used for predicting yield for 1 cm and 2 cm of water levels at the basin. And it is observed that the maximum yield was obtained for a 1 cm water level at the basin. It means solar still produces better yield with the lower depth of water level at the basin; this may be because of the availability of more space in the sand for evaporation.

Keywords: solar still, cylindrical pipes, still efficiency, mathematical modeling, capillary effect model, yield, solar desalination

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

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

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

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Authors: N. Ibrahim-Rassoul, A. Kessi, E. K. Si-Ahmed, N. Djilali, J. Legrand

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The static and dynamic formation of liquid water bridges is analyzed using a combination of visualization experiments in a microchannel with a mathematical model. This paper presents experimental and theoretical findings of water plug/capillary bridge formation in a 250 μm squared microchannel. The approach combines mathematical and numerical modeling with experimental visualization and measurements. The generality of the model is also illustrated for flow conditions encountered in manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The predictions of the model agree favorably the observations as well as with the experimental recordings.

Keywords: green energy, mathematical modeling, fuel cell, water plug, gas diffusion layer, surface of revolution

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Authors: Muleya Nqobile, Winston Garira

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We presented a compartmental deterministic multi-scale model which encompass internal plant defensive mechanism and pathogen interaction, then we consider nesting the model into the epidemiological model. The objective was to improve our understanding of the transmission dynamics of within host and between host of Guignardia citricapa Kiely. The inflow of infected class was scaled down to individual level while the outflow was scaled up to average population level. Conceptual model and mathematical model were constructed to display a theoretical framework which can be used for predicting or identify disease pattern.

Keywords: epidemiological model, mathematical modelling, multi-scale modelling, immunological model

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Authors: Adam Ahmed Hosney

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The existence of a culture of corruption within an institution, such as the police, could be a sign of failure from various angles. There is a general perception among Ghanaians that the most corrupt institution is the police service. The purpose of this study is to formulate and analyze a nonlinear mathematical model to investigate corruption as an epidemic within the Ghana police service, this study revealed the basic reproduction number for corruption extinction and corruption survival. The threshold conditions for all kinds of equilibrium points are obtained using linearization methods and Lyapunov functional methods, and they demonstrate local asymptotic stability for both corrupt endemic and corrupt free equilibrium states. The model was analyzed qualitatively, and the solution was derived. The model appears to be positively invariant and attractive. Therefore, the region exhibits positive invariance. Thus, it is adequate to think about the dynamics of the model. For the purpose of illustrating the solution, the graphic result was presented and discussed. Results show that corruption will die out within the police service if the government shows no tolerance for those involved in corrupt practices. Study findings indicate that leaders should be trustworthy, demonstrate a complete and viable commitment to addressing corruption, and make it a priority to provide mass education to all citizens as well as using religious leaders to fight corruption since most Ghanaians are religious and trust their leaders.

Keywords: mathematical model, differential equation, dynamical system, simulation

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of cancer growth under the influence of radiation therapy. The effect of this type of therapy is considered as an additional equation of discussed model. Numerical simulations show that delay, which is added to ordinary differential equations and represent time needed for transformation from one type of cells to the other one, affects the behavior of the system. The validation and verification of proposed model is based on medical data. Analytical results are illustrated by numerical examples of the model dynamics. The model is able to reconstruct dynamics of treatment of cancer and may be used to determine the most effective treatment regimen based on the study of the behavior of individual treatment protocols.

Keywords: mathematical modeling, numerical simulation, ordinary differential equations, radiation therapy

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Authors: Song Hyok Choe

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This study presented a method to determine the optimum design parameters based on a mathematical model of the operating process in a manual electromagnetic hammer using solenoid electromagnets. The operating process of the electromagnetic hammer depends on the circuit scheme of the power controller. Mathematical modeling of the operating process was carried out by considering the energy transfer process in the forward and reverse windings and the electromagnetic force acting on the impact and brake pistons. Using the developed mathematical model, the initial design data of a manual electromagnetic hammer proposed in this paper are encoded and analyzed in Matlab. On the other hand, a measuring experiment was carried out by using a measurement device to check the accuracy of the developed mathematical model. The relative errors of the analytical results for measured stroke distance of the impact piston, peak value of forward stroke current and peak value of reverse stroke current were −4.65%, 9.08% and 9.35%, respectively. Finally, it was shown that the mathematical model of the operating process of an electromagnetic hammer is relatively accurate, and it can be used to determine the design parameters of the electromagnetic hammer. Therefore, the design parameters that can provide the required impact energy in the manual electromagnetic hammer were determined using a mathematical model developed. The proposed method will be used for the further design and development of the various types of percussion rock drills.

Keywords: solenoid electromagnet, electromagnetic hammer, stone processing, mathematical modeling

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Authors: Yasser Rammah, Wolf-Christian Mueller

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Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: Minas Balyan

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In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: Shank Kulkarni, Alireza Tabarraei

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The fantastic properties of polyurea such as flexibility, durability, and chemical resistance have brought it a wide range of application in various industries. Effective prediction of the response of polyurea under different loading and environmental conditions necessitates the development of an accurate constitutive model. Similar to most polymers, the behavior of polyurea depends on both strain and strain rate. Therefore, the constitutive model should be able to capture both these effects on the response of polyurea. To achieve this objective, in this paper, a nonlinear hyper-viscoelastic constitutive model is developed by the superposition of a hyperelastic and a viscoelastic model. The proposed constitutive model can capture the behavior of polyurea under compressive loading conditions at various strain rates. Four parameter Ogden model and Mooney Rivlin model are used to modeling the hyperelastic behavior of polyurea. The viscoelastic behavior is modeled using both a three-parameter standard linear solid (SLS) model and a K-BKZ model. Comparison of the modeling results with experiments shows that Odgen and SLS model can more accurately predict the behavior of polyurea. The material parameters of the model are found by curve fitting of the proposed model to the uniaxial compression test data. The proposed model can closely reproduce the stress-strain behavior of polyurea for strain rates up to 6500 /s.

Keywords: constitutive modelling, ogden model, polyurea, SLS model, uniaxial compression test

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Authors: Amin Jamili

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Nowadays, the majority of international trade in goods is carried by sea, and especially by ships deployed in the industrial and tramp segments. This paper addresses routing the tramp ships and determining the schedules including the arrival times to the ports, berthing times at the ports, and the departure times in an operational planning level. In the operational planning level, the weather can be almost exactly forecasted, however in some routes some uncertainties may remain. In this paper, the voyaging times between some of the ports are considered to be uncertain. To that end, a two-stage stochastic mathematical model is proposed. Moreover, a case study is tested with the presented model. The computational results show that this mathematical model is promising and can represent acceptable solutions.

Keywords: routing, scheduling, tram ships, two stage stochastic model, uncertainty

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Authors: David C. Ni

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In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s decomposition method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load

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Authors: Juliana A. Knocikova, Yann Bouret, Médéric Argentina, Laurent Counillon

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Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.

Keywords: eukaryotic cell, mathematical modeling, osmosis, volume alterations

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