Search results for: Cell-centered Lagrangian method

Authors: Rado Flajs

Abstract:

In the present paper the extreme shear stresses with the corresponding planes are established using the freely available computer tools like the Gnuplot, Sage, R, Python and Octave. In order to support these freely available computer tools, their strong symbolical and graphical abilities are illustrated. The nature of the stationary points obtained by the Method of Lagrangian Multipliers can be determined using freely available computer symbolical tools like Sage. The characters of the stationary points can be explained in the easiest way using freely available computer graphical tools like Gnuplot, Sage, R, Python and Octave. The presented figures improve the understanding of the problem and the obtained solutions for the majority of students of civil or mechanical engineering.

Keywords: engineering, continuum mechanics, extreme shear stresses, Gnuplot, Sage, R, Python, Octave

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Authors: Xie Kefeng, Zhang He

Abstract:

For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, Dynamics, Lagrange, Parallel platform.

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Authors: Tsung-Chia Chen

Abstract:

The orthogonal processes to shape the triangle steel plate into a equilateral vertical steel are examined by an incremental elasto-plastic finite-element method based on an updated Lagrangian formulation. The highly non-linear problems due to the geometric changes, the inelastic constitutive behavior and the boundary conditions varied with deformation are taken into account in an incremental manner. On the contact boundary, a modified Coulomb friction mode is specially considered. A weighting factor r-minimum is employed to limit the step size of loading increment to linear relation. In particular, selective reduced integration was adopted to formulate the stiffness matrix. The simulated geometries of verticality could clearly demonstrate the vertical processes until unloading. A series of experiments and simulations were performed to validate the formulation in the theory, leading to the development of the computer codes. The whole deformation history and the distribution of stress, strain and thickness during the forming process were obtained by carefully considering the moving boundary condition in the finite-element method. Therefore, this modeling can be used for judging whether a equilateral vertical steel can be shaped successfully. The present work may be expected to improve the understanding of the formation of the equilateral vertical steel.

Keywords: Elasto-plastic, finite element, orthogonal pressing process, vertical steel.

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Authors: Tapas Kumar Sinha, Joseph Mathew

Abstract:

Based on the Lagrangian for the Gross –Pitaevskii equation as derived by H. Sakaguchi and B.A Malomed [5] we have derived a double well model for the nonlinear optical lattice. This model explains the various features of nonlinear optical lattices. Further, from this model we obtain and simulate the probability for tunneling from one well to another which agrees with experimental results [4].

Keywords: Double well model, nonlinear optical lattice, Solitons, tunneling.

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Authors: Mutuku Muvengei, John Kihiu

Abstract:

This paper focuses on the development of bond graph dynamic model of the mechanical dynamics of an excavating mechanism previously designed to be used with small tractors, which are fabricated in the Engineering Workshops of Jomo Kenyatta University of Agriculture and Technology. To develop a mechanical dynamics model of the manipulator, forward recursive equations similar to those applied in iterative Newton-Euler method were used to obtain kinematic relationships between the time rates of joint variables and the generalized cartesian velocities for the centroids of the links. Representing the obtained kinematic relationships in bondgraphic form, while considering the link weights and momenta as the elements led to a detailed bond graph model of the manipulator. The bond graph method was found to reduce significantly the number of recursive computations performed on a 3 DOF manipulator for a mechanical dynamic model to result, hence indicating that bond graph method is more computationally efficient than the Newton-Euler method in developing dynamic models of 3 DOF planar manipulators. The model was verified by comparing the joint torque expressions of a two link planar manipulator to those obtained using Newton- Euler and Lagrangian methods as analyzed in robotic textbooks. The expressions were found to agree indicating that the model captures the aspects of rigid body dynamics of the manipulator. Based on the model developed, actuator sizing and valve sizing methodologies were developed and used to obtain the optimal sizes of the pistons and spool valve ports respectively. It was found that using the pump with the sized flow rate capacity, the engine of the tractor is able to power the excavating mechanism in digging a sandy-loom soil.

Keywords: Actuators, bond graphs, inverse dynamics, recursive equations, quintic polynomial trajectory.

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Authors: Fanqiang Kong, Chending Bian

Abstract:

In this work, we exploit two assumed properties of the abundances of the observed signatures (endmembers) in order to reconstruct the abundances from hyperspectral data. Joint-sparsity is the first property of the abundances, which assumes the adjacent pixels can be expressed as different linear combinations of same materials. The second property is rank-deficiency where the number of endmembers participating in hyperspectral data is very small compared with the dimensionality of spectral library, which means that the abundances matrix of the endmembers is a low-rank matrix. These assumptions lead to an optimization problem for the sparse unmixing model that requires minimizing a combined l_2,p-norm and nuclear norm. We propose a variable splitting and augmented Lagrangian algorithm to solve the optimization problem. Experimental evaluation carried out on synthetic and real hyperspectral data shows that the proposed method outperforms the state-of-the-art algorithms with a better spectral unmixing accuracy.

Keywords: Hyperspectral unmixing, joint-sparse, low-rank representation, abundance estimation.

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Authors: Djamel Boutagouga, Kamel Djeghaba

Abstract:

The choice of finite element to use in order to predict nonlinear static or dynamic response of complex structures becomes an important factor. Then, the main goal of this research work is to focus a study on the effect of the in-plane rotational degrees of freedom in linear and geometrically non linear static and dynamic analysis of thin shell structures by flat shell finite elements. In this purpose: First, simple triangular and quadrilateral flat shell finite elements are implemented in an incremental formulation based on the updated lagrangian corotational description for geometrically nonlinear analysis. The triangular element is a combination of DKT and CST elements, while the quadrilateral is a combination of DKQ and the bilinear quadrilateral membrane element. In both elements, the sixth degree of freedom is handled via introducing fictitious stiffness. Secondly, in the same code, the sixth degrees of freedom in these elements is handled differently where the in-plane rotational d.o.f is considered as an effective d.o.f in the in-plane filed interpolation. Our goal is to compare resulting shell elements. Third, the analysis is enlarged to dynamic linear analysis by direct integration using Newmark-s implicit method. Finally, the linear dynamic analysis is extended to geometrically nonlinear dynamic analysis where Newmark-s method is used to integrate equations of motion and the Newton-Raphson method is employed for iterating within each time step increment until equilibrium is achieved. The obtained results demonstrate the effectiveness and robustness of the interpolation of the in-plane rotational d.o.f. and present deficiencies of using fictitious stiffness in dynamic linear and nonlinear analysis.

Keywords: Flat shell, dynamic analysis, nonlinear, Newmark, drilling rotation.

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Authors: A. Hamidi, S. Khelladi, L. Illoul, A. Tcharkhtchi

Abstract:

Reactive rotational molding (RRM) is a process to manufacture hollow plastic parts with reactive material has several advantages compared to conventional roto molding of thermoplastic powders: process cycle time is shorter; raw material is less expensive because polymerization occurs during processing and high-performance polymers may be used such as thermosets, thermoplastics or blends. However, several phenomena occur during this process which makes the optimization of the process quite complex. In this study, we have used a mixture of isocyanate and polyol as a reactive system. The chemical transformation of this system to polyurethane has been studied by thermal analysis and rheology tests. Thanks to these results of the curing process and rheological measurements, the kinetic and rheokinetik of polyurethane was identified. Smoothed Particle Hydrodynamics, a Lagrangian meshless method, was chosen to simulate reactive fluid flow in 2 and 3D configurations of the polyurethane during the process taking into account the chemical, and chemiorehological results obtained experimentally in this study.

Keywords: Reactive rotational molding, free surface flows, simulation, smoothed particle hydrodynamics, surface tension.

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Authors: E. Al Daoud

Abstract:

In many cases, theoretical treatments are available for models for which there is no perfect physical realization. In this situation, the only possible test for an approximate theoretical solution is to compare with data generated from a computer simulation. In this paper, Monte Carlo tools are used to study and compare the elementary particles models. All the experiments are implemented using 10000 events, and the simulated energy is 13 TeV. The mean and the curves of several variables are calculated for each model using MadAnalysis 5. Anomalies in the results can be seen in the muons masses of the minimal supersymmetric standard model and the two Higgs doublet model.

Keywords: Feynman rules, hadrons, Lagrangian, Monte Carlo, simulation.

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Authors: Mohammad Talha, B. N. Singh

Abstract:

This paper deals with the thermo-mechanical deformation behavior of shear deformable functionally graded ceramicmetal (FGM) plates. Theoretical formulations are based on higher order shear deformation theory with a considerable amendment in the transverse displacement using finite element method (FEM). The mechanical properties of the plate are assumed to be temperaturedependent and graded in the thickness direction according to a powerlaw distribution in terms of the volume fractions of the constituents. The temperature field is supposed to be a uniform distribution over the plate surface (XY plane) and varied in the thickness direction only. The fundamental equations for the FGM plates are obtained using variational approach by considering traction free boundary conditions on the top and bottom faces of the plate. A C0 continuous isoparametric Lagrangian finite element with thirteen degrees of freedom per node have been employed to accomplish the results. Convergence and comparison studies have been performed to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index and temperature rise with different loading and boundary conditions. Numerical results for the FGM plates are provided in dimensionless tabular and graphical forms. The results proclaim that the temperature field and the gradient in the material properties have significant role on the thermo-mechanical deformation behavior of the FGM plates.

Keywords: Functionally graded material, higher order shear deformation theory, finite element method, independent field variables.

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Authors: Jixiao Tao, Xiaoqiao He

Abstract:

The present study deals with the finite element (FE) analysis of thermally-induced bistable plate using various plate elements. The quadrilateral plate elements include the 4-node conforming plate element based on the classical laminate plate theory (CLPT), the 4-node and 9-node Mindlin plate element based on the first-order shear deformation laminated plate theory (FSDT), and a displacement-based 4-node quadrilateral element (RDKQ-NL20). Using the von-Karman’s large deflection theory and the total Lagrangian (TL) approach, the nonlinear FE governing equations for plate under thermal load are derived. Convergence analysis for four elements is first conducted. These elements are then used to predict the stable shapes of thermally-induced bistable plate. Numerical test shows that the plate element based on FSDT, namely the 4-node and 9-node Mindlin, and the RDKQ-NL20 plate element can predict two stable cylindrical shapes while the 4-node conforming plate predicts a saddles shape. Comparing the simulation results with ABAQUS, the RDKQ-NL20 element shows the best accuracy among all the elements.

Keywords: Finite element method, geometrical nonlinearity, bistable, quadrilateral plate elements.

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Authors: Troy L. Story

Abstract:

A mathematical model for the Dynamics of Economic Profit is constructed by proposing a characteristic differential oneform for this dynamics (analogous to the action in Hamiltonian dynamics). After processing this form with exterior calculus, a pair of characteristic differential equations is generated and solved for the rate of change of profit P as a function of revenue R (t) and cost C (t). By contracting the characteristic differential one-form with a vortex vector, the Lagrangian is obtained for the Dynamics of Economic Profit.

Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics, economic functions, and dynamics

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Authors: R. Amrollahi, M. Habibi

Abstract:

When the shock front (SF) hits the central electrode axis of plasma focus device, a reflected shock wave moves radially outwards. The current sheath (CS) results from ionization of filled gas between two electrodes continues to compress inwards until it hits the out-going reflected shock front. In this paper the Lagrangian equations are solved for a parabolic shock trajectory yielding a first and second approximation for the CS path. To determine the accuracy of the approximation, the same problem is solved for a straight shock.

Keywords: Radial compression, Shock wave trajectory, Current sheath, Slog model.

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Authors: Zhengsheng Wang, Jing Qi, Chuntao Liu, Yuanjun Li

Abstract:

The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

Keywords: Harmonic Arnoldi method, weighted harmonic Arnoldi method, eigenpair, interior eigenproblem, non symmetric matrix.

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: Nishant Shrivastava, D. K. Sehgal

Abstract:

In Finite Element Technique nodal stresses are calculated through displacement as nodes. In this process, the displacement calculated at nodes is sufficiently good enough but stresses calculated at nodes are not sufficiently accurate. Therefore, the accuracy in the stress computation in FEM models based on the displacement technique is obviously matter of concern for computational time in shape optimization of engineering problems. In the present work same is focused to find out unique points within the element as well as the boundary of the element so, that good accuracy in stress computation can be achieved. Generally, major optimal stress points are located in domain of the element some points have been also located at boundary of the element where stresses are fairly accurate as compared to nodal values. Then, it is subsequently concluded that there is an existence of unique points within the element, where stresses have higher accuracy than other points in the elements. Therefore, it is main aim is to evolve a generalized procedure for the determination of the optimal stress location inside the element as well as at the boundaries of the element and verify the same with results from numerical experimentation. The results of quadratic 9 noded serendipity elements are presented and the location of distinct optimal stress points is determined inside the element, as well as at the boundaries. The theoretical results indicate various optimal stress locations are in local coordinates at origin and at a distance of 0.577 in both directions from origin. Also, at the boundaries optimal stress locations are at the midpoints of the element boundary and the locations are at a distance of 0.577 from the origin in both directions. The above findings were verified through experimentation and findings were authenticated. For numerical experimentation five engineering problems were identified and the numerical results of 9-noded element were compared to those obtained by using the same order of 25-noded quadratic Lagrangian elements, which are considered as standard. Then root mean square errors are plotted with respect to various locations within the elements as well as the boundaries and conclusions were drawn. After numerical verification it is noted that in a 9-noded element, origin and locations at a distance of 0.577 from origin in both directions are the best sampling points for the stresses. It was also noted that stresses calculated within line at boundary enclosed by 0.577 midpoints are also very good and the error found is very less. When sampling points move away from these points, then it causes line zone error to increase rapidly. Thus, it is established that there are unique points at boundary of element where stresses are accurate, which can be utilized in solving various engineering problems and are also useful in shape optimizations.

Keywords: Finite element, Lagrangian, optimal stress location, serendipity.

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Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

Abstract:

The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial or non-inertial reference frame.

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Authors: Xi Gu, Guan Heng Yeoh, Victoria Timchenko

Abstract:

In the current work, a three-dimensional geometry of a 75% stenosed blood vessel is analyzed. Large eddy simulation (LES) with the help of a dynamic subgrid scale Smagorinsky model is applied to model the turbulent pulsatile flow. The geometry, the transmural pressure and the properties of the blood and the elastic boundary were based on clinical measurement data. For the flexible wall model, a thin solid region is constructed around the 75% stenosed blood vessel. The deformation of this solid region was modelled as a deforming boundary to reduce the computational cost of the solid model. Fluid-structure interaction is realized via a twoway coupling between the blood flow modelled via LES and the deforming vessel. The information of the flow pressure and the wall motion was exchanged continually during the cycle by an arbitrary Lagrangian-Eulerian method. The boundary condition of current time step depended on previous solutions. The fluctuation of the velocity in the post-stenotic region was analyzed in the study. The axial velocity at normalized position Z=0.5 shows a negative value near the vessel wall. The displacement of the elastic boundary was concerned in this study. In particular, the wall displacement at the systole and the diastole were compared. The negative displacement at the stenosis indicates a collapse at the maximum velocity and the deceleration phase.

Keywords: Large Eddy Simulation, Fluid Structural Interaction, Constricted Artery, Computational Fluid Dynamics.

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Authors: Gulshan Taj M. N. A., Anupam Chakrabarti, Vipul Prakash

Abstract:

In the present investigation, free vibration of functionally graded material (FGM) skew plates under thermal environment is studied. Kinematics equations are based on the Reddy’s higher order shear deformation theory and a nine noded isoparametric Lagrangian element is adopted to mesh the plate geometry. The issue of C₁ continuity requirement related to the assumed displacement field has been circumvented effectively to develop C₀ finite element formulation. Effective mechanical properties of the constituents of the plate are considered to be as position and temperature dependent and assumed to vary in the thickness direction according to a simple power law distribution. The displacement components of a rectangular plate are mapped into skew plate geometry by means of suitable transformation rule. One dimensional Fourier heat conduction equation is used to ascertain the temperature profile of the plate along thickness direction. Influence of different parameters such as volume fraction index, boundary condition, aspect ratio, thickness ratio and temperature field on frequency parameter of the FGM skew plate is demonstrated by performing various examples and the related findings are discussed briefly. New results are generated for vibration of the FGM skew plate under thermal environment, for the first time, which may be implemented in the future research involving similar kind of problems.

Keywords: Functionally graded material, finite element method, higher order shear deformation theory, skew plate, thermal vibration.

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Authors: Ampon Dhamacharoen, Kanittha Chompuvised

Abstract:

In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.

Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.

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Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: Z. Veselý, M. Honner

Abstract:

High power laser – total emissivity method (HPL-TE method) for determination of coatings relative total emissivity dependent on the temperature is introduced. Method principle, experimental and evaluation parts of the method are described. Computer model of HPL-TE method is employed to perform the sensitivity analysis of the effect of method parameters on the sample surface temperature in the positions where the surface temperature and radiation heat flux are measured.

Keywords: High temperature laser testing, measurement ofthermal properties, emissivity, coatings.

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Authors: Ibrahim Abu-Alshaikh

Abstract:

In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.

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Authors: James Kuria, John Kihiu

Abstract:

This work presents a numerical model developed to simulate the dynamics and vibrations of a multistage tractor gearbox. The effect of time varying mesh stiffness, time varying frictional torque on the gear teeth, lateral and torsional flexibility of the shafts and flexibility of the bearings were included in the model. The model was developed by using the Lagrangian method, and it was applied to study the effect of three design variables on the vibration and stress levels on the gears. The first design variable, module, had little effect on the vibration levels but a higher module resulted to higher bending stress levels. The second design variable, pressure angle, had little effect on the vibration levels, but had a strong effect on the stress levels on the pinion of a high reduction ratio gear pair. A pressure angle of 25o resulted to lower stress levels for a pinion with 14 teeth than a pressure angle of 20o. The third design variable, contact ratio, had a very strong effect on both the vibration levels and bending stress levels. Increasing the contact ratio to 2.0 reduced both the vibration levels and bending stress levels significantly. For the gear train design used in this study, a module of 2.5 and contact ratio of 2.0 for the various meshes was found to yield the best combination of low vibration levels and low bending stresses. The model can therefore be used as a tool for obtaining the optimum gear design parameters for a given multistage spur gear train.

Keywords: bending stress levels, frictional torque, gear designparameters, mesh stiffness, multistage gear train, vibration levels.

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Authors: Richard L. Summers

Abstract:

The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems is fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.

Keywords: Semiotic meaning, Shannon information, Lyapunov, living systems.

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Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: Abouzar Moshfegh, Mehrzad Shams, Goodarz Ahmadi, Reza Ebrahimi

Abstract:

A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier-Stokes equations were solved and the velocity jump at the gas-particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The Simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed.

Keywords: CFD, Cunningham correction, Slip correction factor, Spherical aerosol.

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