Search results for: fractional Black-Scholes equations

Authors: Vandana N. Purav

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Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials.

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Procedia PDF Downloads 363

Authors: Shahin A. Abdel-Naby, James P. Colgan, Michael S. Pindzola

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A time-dependent close-coupling method is developed to calculate a total, double and triple autoionization rates for hollow atomic ions of four-electron systems. This work was motivated by recent observations of the four-electron Auger process in near K-edge photoionization of C+ ions. The time-dependent close-coupled equations are solved using lattice techniques to obtain a discrete representation of radial wave functions and all operators on a four-dimensional grid with uniform spacing. Initial excited states are obtained by relaxation of the Schrodinger equation in imaginary time using a Schmidt orthogonalization method involving interior subshells. The radial wave function grids are partitioned over the cores on a massively parallel computer, which is essential due to the large memory requirements needed to store the coupled-wave functions and the long run times needed to reach the convergence of the ionization process. Total, double, and triple autoionization rates are obtained by the propagation of the time-dependent close-coupled equations in real-time using integration over bound and continuum single-particle states. These states are generated by matrix diagonalization of one-electron Hamiltonians. The total autoionization rates for each L excited state is found to be slightly above the single autoionization rate for the excited configuration using configuration-average distorted-wave theory. As expected, we find the double and triple autoionization rates to be much smaller than the total autoionization rates. Future work can be extended to study electron-impact triple ionization of atoms or ions. The work was supported in part by grants from the American University of Sharjah and the US Department of Energy. Computational work was carried out at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, California, USA.

Keywords: hollow atoms, autoionization, auger rates, time-dependent close-coupling method

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Authors: S. Kohestani, R. Amrollahi, P. Daryabor

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Microwave diagnostics such as reflectometry are receiving growing attention in magnetic confinement fusionresearch. In order to obtain the better understanding of plasma confinement physics, more detailed measurements on density profile and its fluctuations might be required. A 2D full-wave simulation of ordinary mode propagation has been written in an effort to model effects seen in reflectometry experiment. The code uses the finite-difference-time-domain method with a perfectly-matched-layer absorption boundary to solve Maxwell’s equations.The code has been used to simulate the reflectometer measurement in Alborz Tokamak.

Keywords: reflectometry, simulation, ordinary mode, tokamak

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Authors: H. T. Le Luong, C. Hénaux, F. Messine, G. Bueno-Mariani, S. Mollov, N. Voyer

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This paper presents a comparative study of different modular brushless wound rotor synchronous machine (MB-WRSM). The goal of the study is to highlight the structure which offers the best fault tolerant capability and the highest output performances. The fundamental winding factor is calculated by using the method based on EMF phasors as a significant criterion to select the preferred number of phases, stator slots, and poles. With the limited number of poles for a small machine (3.67kW/7000rpm), 15 different machines for preferred phase/slot/pole combinations are analyzed using two-dimensional (2-D) finite element method and compared according to three criteria: torque density, torque ripple and efficiency. The 7phase/7slot/6pole machine is chosen with the best compromise of high torque density, small torque ripple (3.89%) and high nominal efficiency (95%). This machine is then compared with a reference design surface permanent magnet synchronous machine (SPMSM). In conclusion, this paper provides an electromagnetic analysis of a new brushless wound-rotor synchronous machine using multiphase non-overlapping fractional slot double layer winding. The simulation results are discussed and demonstrate that the MB-WRSM presents interesting performance features, with overall performance closely matching that of an equivalent SPMSM.

Keywords: finite element method (FEM), machine performance, modular wound rotor synchronous machine, non-overlapping concentrated winding

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Authors: N. Smaoui, B. Chentouf

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The boundary stabilization problem of the rotating disk-beam system is a topic of interest in research studies. This system involves a flexible beam attached to the center of a disk, and the control and stabilization of this system have been extensively studied. This research focuses on the case where the center of mass is fixed in an inertial frame, and the rotation of the center is non-uniform. The system is represented by a set of nonlinear coupled partial differential equations and ordinary differential equations. The boundary stabilization problem of this system via a delayed boundary control is considered. We assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. The aim of this research is threefold: First, we demonstrate that the rotating disk-beam system is well-posed in an appropriate functional space. Then, we establish the exponential stability property of the system. Finally, we provide numerical simulations that illustrate the theoretical findings. The research utilizes the semigroup theory to establish the well-posedness of the system. The resolvent method is then employed to prove the exponential stability property. Finally, the finite element method is used to demonstrate the theoretical results through numerical simulations. The research findings indicate that the rotating disk-beam system can be stabilized using a boundary control with a time delay. The proof of stability is based on the resolvent method and a variation of constants formula. The numerical simulations further illustrate the theoretical results. The findings have potential implications for the design and implementation of control strategies in similar systems. In conclusion, this research demonstrates that the rotating disk-beam system can be stabilized using a boundary control with time delay. The well-posedness and exponential stability properties are established through theoretical analysis, and these findings are further supported by numerical simulations. The research contributes to the understanding and practical application of control strategies for flexible structures, providing insights into the stability of rotating disk-beam systems.

Keywords: rotating disk-beam, delayed force control, delayed moment control, torque control, exponential stability

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Authors: S. Kopylov, C. Z. Bo

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This study is aimed at exploring the possibility of energy recovery through the suppression of vibrations. The article describes design of electromagnetic dynamic damper. The magnetic part of the device performs the function of a tuned mass damper, thereby providing both energy regeneration and damping properties to the protected mass. According to the theory of tuned mass damper, equations of mathematical models were obtained. Then, under given properties of current system, amplitude frequency response was investigated. Therefore, main ideas and methods for further research were defined.

Keywords: electromagnetic damper, oscillations with two degrees of freedom, regeneration systems, tuned mass damper

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Authors: Lukas Vierus, Thomas Schuster

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A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.

Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions

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Authors: Angelo I. Aquino, Luis Ma. T. Bo-ot

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We use the Homotopy Analysis Method (HAM) to solve the system of equations modeling the two-level system and extract results which will pinpoint to turbulent behavior. We look at multi-valued solutions as indicative of turbulence or turbulent-like behavior. We take dierent specic cases which result in multi-valued velocities. The solutions are in series form and application of HAM ensures convergence in some region.

Keywords: multivalued solutions, homotopy analysis method, two-level system, equation

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Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale

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This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.

Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories

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Authors: Roger Yu

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A numerical scheme has been developed to solve wave equations for chaotic systems such as stadium-shaped cavity. The same numerical method can also be used for finding wave properties of rectangle cavities with randomly placed obstacles. About 30k eigenvalues have been obtained accurately on a normal circumstance. For comparison, we also initiated an experimental study which determines both eigenfrequencies and eigenfunctions of a stadium-shaped cavity using pulse and normal mode analyzing techniques. The acoustic cavity was made adjustable so that the transition from nonchaotic (circle) to chaotic (stadium) waves can be investigated.

Keywords: quantum dot, chaos, numerical method, eigenvalues

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Authors: Maja Andrić, Josip Pečarić

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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: Aziza Altaibayeva, Ertan Güdekli, Ratbay Myrzakulov

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In this letter, we explore exact solutions for the Horava-Lifshitz gravity. We use of an extension of this theory with first order dynamical lapse function. The equations of motion have been derived in a fully consistent scenario. We assume that there are some spherically symmetric families of exact solutions of this extended theory of gravity. We obtain exact solutions and investigate the singularity structures of these solutions. Specially, an exact solution with the regular horizon is found.

Keywords: quantum gravity, Horava-Lifshitz gravity, black hole, spherically symmetric space times

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Authors: Abdulatif Abdulsalam Mohamed Shaban

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A.C motors, in general, have superior performance characteristics to their d.c. counterparts. However, despite these advantage a.c. motors lack the controllability and simplicity and so d.c. motors retain a competitive edge where precise control is required. As part of an overall project to develop an improved cycloconverter control strategy for induction motors. Simulation and modelling techniques have been developed. This contribution describes a method used to simulate an induction motor drive using the SIMULINK toolbox within MATLAB software. The cycloconverter fed induction motor is principally modelled using the d-q axis equations. Results of the simulation for a given set of induction motor parameters are also presented.

Keywords: simulation, converter, motor, cycloconverter

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Authors: Marcelo Hayashi, João Lima, Bruno Chieregatti, Ernani Volpe

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The adjoint method has been used as a successful tool to obtain sensitivity gradients in aerodynamic design and optimisation for many years. This work presents an alternative approach to the continuous adjoint formulation that enables one to compute gradients of a given measure of merit with respect to control parameters other than those pertaining to geometry. The procedure is then applied to the steady 2–D compressible Euler and incompressible Navier–Stokes flow equations. Finally, the results are compared with sensitivities obtained by finite differences and theoretical values for validation.

Keywords: adjoint method, aerodynamics, sensitivity theory, non-geometric sensitivities

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Authors: Nidhi Adhlakha, K. L. Yadav

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Three phase magnetoelectric (ME) composites (1-x)(0.7BiFeO3-0.3CoFe2O4)-xPbTiO3 (or equivalently written as (1-x)(0.7BFO-0.3CFO)-xPT) with x variations 0, 0.30, 0.35, 0.40, 0.45 and 1.0 were synthesized using hybrid processing route. The effects of PT addition on structural, multiferroic and optical properties have been subsequently investigated. A detailed Rietveld refinement analysis of X-ray diffraction patterns has been performed, which confirms the presence of structural phases of individual constituents in the composites. Field emission scanning electron microscopy (FESEM) images are taken for microstructural analysis and grain size determination. Transmission electron microscopy (TEM) analysis of 0.3CFO-0.7BFO reveals the average particle size to be lying in the window of 8-10 nm. The temperature dependent dielectric constant at various frequencies (1 kHz, 10 kHz, 50 kHz, 100 kHz and 500 kHz) has been studied and the dielectric study reveals that the increase of dielectric constant and decrease of average dielectric loss of composites with incorporation of PT content. The room temperature ferromagnetic behavior of composites is confirmed through the observation of Magnetization vs. Magnetic field (M-H) hysteresis loops. The variation of magnetization with temperature indicates the presence of spin glass behavior in composites. Magnetoelectric coupling is evidenced in the composites through the observation of the dependence of the dielectric constant on the magnetic field, and magnetodielectric response of 2.05 % is observed for 45 mol% addition of PT content. The fractional change of magnetic field induced dielectric constant can also be expressed as ∆ε_r~γM^2 and the value of γ is found to be ~1.08×10-2 (emu/g)-2 for composite with x=0.40. Fourier transformed infrared (FTIR) spectroscopy of samples is carried out to analyze various bonds formation in the composites.

Keywords: composite, X-ray diffraction, dielectric properties, optical properties

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Authors: A. M. Tahsini, S. A. Hosseini

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In the present study, the surface temperature history of the adaptor part in a two-stage supersonic launch vehicle is accurately predicted. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux. The one-dimensional heat conduction in solid phase is used to compute the temperature history. The instantaneous surface temperature is used to improve the applied heat flux, to improve the accuracy of the results.

Keywords: aerodynamic heating, heat conduction, numerical simulation, supersonic flight, launch vehicle

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Authors: Manoj Sarda, Abhishek Agarwal, Juhi Kaushik, Vatsal Sanjay, Arup Kumar Das

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Railways in India remain primary mode of transport having one of the largest networks in the world and catering to billions of transits yearly. Catastrophic economic damage and loss to life is encountered over the past few decades due to fire to locomotives. Study of fire dynamics and fire propagation plays an important role in evacuation planning and reducing losses. Simulation based study of propagation of fire and soot inside an air conditioned coach of Indian locomotive is done in this paper. Finite difference based solver, Fire Dynamic Simulator (FDS) version 6 has been used for analysis. A single air conditioned 3 tier coupe closed to ambient surroundings by glass windows having occupancy for 8 people is the basic unit of the domain. A system of three such coupes combined is taken to be fundamental unit for the entire study to resemble effect to an entire coach. Analysis of flame and soot contours and concentrations is done corresponding to variations in heat release rate per unit volume (HRRPUA) of fire source, variations in conditioned air velocity being circulated inside coupes by vents and an alternate fire initiation and propagation mechanism via ducts. Quantitative results of fractional area in top and front view of the three coupes under fire and smoke are obtained using MATLAB (IMT). Present simulations and its findings will be useful for organizations like Commission of Railway Safety and others in designing and implementing safety and evacuation measures.

Keywords: air conditioned coaches, fire propagation, flame contour, soot flow, train fire

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: stochastic integrals, single–server queue model, catastrophes, busy period

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Authors: M. Salih Taci, N. Tayebi, I. Bozkır

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This paper investigates the operation of a sinusoidal supplied autotransformer on the different states of magnetic polarity of primary and secondary terminals for four different step-up and step-down analytical conditions. In this paper, a new analytical modeling and equations for dot-marked and polarity-based step-up and step-down autotransformer are presented. These models are validated by the simulation of current and voltage waveforms for each state. PSpice environment was used for simulation.

Keywords: autotransformer modeling, autotransformer simulation, step-up autotransformer, step-down autotransformer, polarity

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Zaki Abiza, Miguel Chavez, David M. Holman, Ruddy Brionnaud

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In this paper, the prediction of the aerodynamic behavior of the flow around a Finned Projectile will be validated using a Computational Fluid Dynamics (CFD) solution, XFlow, based on the Lattice-Boltzmann Method (LBM). XFlow is an innovative CFD software developed by Next Limit Dynamics. It is based on a state-of-the-art Lattice-Boltzmann Method which uses a proprietary particle-based kinetic solver and a LES turbulent model coupled with the generalized law of the wall (WMLES). The Lattice-Boltzmann method discretizes the continuous Boltzmann equation, a transport equation for the particle probability distribution function. From the Boltzmann transport equation, and by means of the Chapman-Enskog expansion, the compressible Navier-Stokes equations can be recovered. However to simulate compressible flows, this method has a Mach number limitation because of the lattice discretization. Thanks to this flexible particle-based approach the traditional meshing process is avoided, the discretization stage is strongly accelerated reducing engineering costs, and computations on complex geometries are affordable in a straightforward way. The projectile that will be used in this work is the Army-Navy Basic Finned Missile (ANF) with a caliber of 0.03 m. The analysis will consist in varying the Mach number from M=0.5 comparing the axial force coefficient, normal force slope coefficient and the pitch moment slope coefficient of the Finned Projectile obtained by XFlow with the experimental data. The slope coefficients will be obtained using finite difference techniques in the linear range of the polar curve. The aim of such an analysis is to find out the limiting Mach number value starting from which the effects of high fluid compressibility (related to transonic flow regime) lead the XFlow simulations to differ from the experimental results. This will allow identifying the critical Mach number which limits the validity of the isothermal formulation of XFlow and beyond which a fully compressible solver implementing a coupled momentum-energy equations would be required.

Keywords: CFD, computational fluid dynamics, drag, finned projectile, lattice-boltzmann method, LBM, lift, mach, pitch

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Authors: Hamidreza Bayat, Arash Mirabdolah Lavasani, Meysam Bolhasani, Sajad Moosavi

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Flow around a flat tube is studied numerically. Reynolds number is defined base on equivalent circular tube and it is varied in range of 100 to 300. Equations are solved by using finite volume method and results are presented in form of drag and lift coefficient. Results show that drag coefficient of flat tube is up to 66% lower than circular tube with equivalent diameter. In addition, by increasing l/D from 1 to 2, the drag coefficient of flat tube is decreased about 14-27%.

Keywords: laminar flow, flat-tube, drag coefficient, cross-flow, heat exchanger

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Authors: Ahmed I. Raheem

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In this thesis, stratified and stratified wavy flow regimes have been investigated numerically for the oil (1.57 mPa s viscosity and 780 kg/m3 density) and water twophase flow in small and large horizontal steel pipes with a diameter between 0.0254 to 0.508 m by ANSYS Fluent software. Volume of fluid (VOF) with two phases flows using two equations family models (Realizable k-

Keywords: CFD, two-phase flow, pressure gradient, volume of fluid, large diameter, horizontal pipe, oil-water stratified and stratified wavy flow

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Authors: Esther Cabezas-Rivas

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Ordinary differential equations (ODE) are a fundamental part of the curriculum for most engineering degrees, and students typically have difficulties in the subsequent abstract mathematical calculations. To enhance their motivation and profit that they are digital natives, we propose a teamwork project that includes the creation of a video. It should explain how to model mathematically a real-world problem transforming it into an ODE, which should then be solved using the tools learned in the lectures. This idea was indeed implemented with first-year students of a BSc in Engineering and Management during the period of online learning caused by the outbreak of COVID-19 in Spain. Each group of 4 students was assigned a different topic: model a hot water heater, search for the shortest path, design the quickest route for delivery, cooling a computer chip, the shape of the hanging cables of the Golden Gate, detecting land mines, rocket trajectories, etc. These topics should be worked out through two complementary channels: a written report describing the problem and a 10-15 min video on the subject. The report includes the following items: description of the problem to be modeled, detailed obtention of the ODE that models the problem, its complete solution, and interpretation in the context of the original problem. We report the outcomes of this teaching in context and active learning experience, including the feedback received by the students. They highlighted the encouragement of creativity and originality, which are skills that they do not typically relate to mathematics. Additionally, the video format (unlike a common presentation) has the advantage of allowing them to critically review and self-assess the recording, repeating some parts until the result is satisfactory. As a side effect, they felt more confident about their oral abilities. In short, students agreed that they had fun preparing the video. They recognized that it was tricky to combine deep mathematical contents with entertainment since, without the latter, it is impossible to engage people to view the video till the end. Despite this difficulty, after the activity, they claimed to understand better the material, and they enjoyed showing the videos to family and friends during and after the project.

Keywords: active learning, contextual teaching, models in differential equations, student-produced videos

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Authors: Asmaa Tahiri, Mouktafi Amine

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A substantial number of traditional medical research has been put forward to managing and treating mental disorders. At the present time, to our best knowledge, it is believed that fundamental understanding of the underlying causes of the majority psychological disorders needs to be explored further to inform early diagnosis, managing symptoms and treatment. The emerging field of evolutionary psychology is a promising prospect to address the origin of mental disorders, potentially leading to more effective treatments. Schizophrenia as a topical mental disorder has been linked to the evolutionary adaptation of the human brain represented in the brain connectivity and asymmetry directly linked to humans higher brain cognition in contrast to other primates being our direct living representation of the structure and connectivity of our earliest common African ancestors. As proposed in the evolutionary psychology scientific literature the pathophysiology of schizophrenia is expressed and directly linked to altered connectivity between the Hippocampal Formation (HF) and Dorsolateral Prefrontal Cortex (DLPFC). This research paper presents the results of the use of tractography analysis using multiple open access Diffusion Weighted Imaging (DWI) datasets of healthy subjects, schizophrenia-affected subjects and primates to illustrate the relevance of the aforementioned brain regions connectivity and the underlying evolutionary changes in the human brain. Deterministic fiber tracking and streamline analysis were used to generate connectivity matrices from the DWI datasets overlaid to compute distances and highlight disconnectivity patterns in conjunction with other fiber tracking metrics; Fractional Anisotropy (FA), Mean Diffusivity (MD) and Radial Diffusivity (RD).

Keywords: tractography, evolutionary psychology, schizophrenia, brain connectivity

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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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: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar

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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem

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Authors: Arcady Ponosov

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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

Procedia PDF Downloads 350