Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 57

Search results for: Lagrangian

57 The Practical MFCAV Riemann Solver is Applied to a New Cell-centered Lagrangian Method

Authors: Yan Liu, Weidong Shen, Dekang Mao, Baolin Tian

Abstract:

The MFCAV Riemann solver is practically used in many Lagrangian or ALE methods due to its merit of sharp shock profiles and rarefaction corners, though very often with numerical oscillations. By viewing it as a modification of the WWAM Riemann solver, we apply the MFCAV Riemann solver to the Lagrangian method recently developed by Maire. P. H et. al.. The numerical experiments show that the application is successful in that the shock profiles and rarefaction corners are sharpened compared with results obtained using other Riemann solvers. Though there are still numerical oscillations, they are within the range of the MFCAV applied in onther Lagrangian methods.

Keywords: Cell-centered Lagrangian method, approximated Riemann solver, HLLC Riemann solver

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56 Lagrangian Method for Solving Unsteady Gas Equation

Authors: Amir Taghavi, kourosh Parand, Hosein Fani

Abstract:

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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55 Applying Lagrangian Relaxation-Based Algorithm for the Airline Coordinated Flight Scheduling Problems

Authors: Chia-Hung Chen, Shangyao Yan

Abstract:

The solution algorithm, based on Lagrangian relaxation, a sub-gradient method and a heuristic to find the upper bound of the solution, is proposed to solve the coordinated fleet routing and flight scheduling problems. Numerical tests are performed to evaluate the proposed algorithm using real operating data from two Taiwan airlines. The test results indicate that the solution algorithm is a significant improvement over those obtained with CPLEX, consequently they could be useful for allied airlines to solve coordinated fleet routing and flight scheduling problems.

Keywords: Coordinated flight scheduling, multiple commodity network flow problem, Lagrangian relaxation.

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54 Lagrangian Flow Skeletons Captured in the Wake of a Swimming Nematode C. elegans Using an Immersed Boundary Fluid-Structure Interaction Approach

Authors: Arash Taheri

Abstract:

In this paper, Lagrangian coherent structure (LCS) concept is applied to wake flows generated in the up/down-stream of a swimming nematode C. elegans in an intermediate Re number range, i.e., 250-1200. It materializes Lagrangian hidden structures depicting flow transport barriers. To pursue the goals, nematode swimming in a quiescent fluid flow environment is numerically simulated by a two-way fluid-structure interaction (FSI) approach with the aid of immersed boundary method (IBM). In this regard, incompressible Navier-Stokes equations, fully-coupled with Lagrangian deformation equations for the immersed body, are solved using IB2d code. For all simulations, nematode’s body is modeled with a parametrized spring-fiber built-in case available in the computational code. Reverse von-Kármán vortex street formation and vortex shedding characteristics are studied and discussed in details via LCS approach, including grid resolution, integration time and Reynolds number effects. Results unveil presence of different flow regions with distinct fluid particle fates in the swimming animal’s wake and formation of so-called ‘mushroom-shaped’ structures in attracting LCS identities.

Keywords: Lagrangian coherent structure, nematode swimming, fluid-structure interaction, immersed boundary method, bionics.

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53 Evaluation of Eulerian and Lagrangian Method in Analysis of Concrete Gravity Dam Including Dam Water Foundation Interaction

Authors: L. Khan mohammadi, J. Vaseghi Amiri, B. Navayi neya , M. Davoodi

Abstract:

Because of the reservoir effect, dynamic analysis of concrete dams is more involved than other common structures. This problem is mostly sourced by the differences between reservoir water, dam body and foundation material behaviors. To account for the reservoir effect in dynamic analysis of concrete gravity dams, two methods are generally employed. Eulerian method in reservoir modeling gives rise to a set of coupled equations, whereas in Lagrangian method, the same equations for dam and foundation structure are used. The Purpose of this paper is to evaluate and study possible advantages and disadvantages of both methods. Specifically, application of the above methods in the analysis of dam-foundationreservoir systems is leveraged to calculate the hydrodynamic pressure on dam faces. Within the frame work of dam- foundationreservoir systems, dam displacement under earthquake for various dimensions and characteristics are also studied. The results of both Lagrangian and Eulerian methods in effects of loading frequency, boundary condition and foundation elasticity modulus are quantitatively evaluated and compared. Our analyses show that each method has individual advantages and disadvantages. As such, in any particular case, one of the two methods may prove more suitable as presented in the results section of this study.

Keywords: Lagrangian method, Eulerian method, Earthquake, Concrete gravity dam

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52 An Efficient Backward Semi-Lagrangian Scheme for Nonlinear Advection-Diffusion Equation

Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.

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51 A Cohesive Lagrangian Swarm and Its Application to Multiple Unicycle-like Vehicles

Authors: Jito Vanualailai, Bibhya Sharma

Abstract:

Swarm principles are increasingly being used to design controllers for the coordination of multi-robot systems or, in general, multi-agent systems. This paper proposes a two-dimensional Lagrangian swarm model that enables the planar agents, modeled as point masses, to swarm whilst effectively avoiding each other and obstacles in the environment. A novel method, based on an extended Lyapunov approach, is used to construct the model. Importantly, the Lyapunov method ensures a form of practical stability that guarantees an emergent behavior, namely, a cohesive and wellspaced swarm with a constant arrangement of individuals about the swarm centroid. Computer simulations illustrate this basic feature of collective behavior. As an application, we show how multiple planar mobile unicycle-like robots swarm to eventually form patterns in which their velocities and orientations stabilize.

Keywords: Attractive-repulsive swarm model, individual-based swarm model, Lagrangian swarm model, Lyapunov stability, Lyapunov-like function, practical stability, unicycle.

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50 Numerical Simulation of Fluid Structure Interaction Using Two-Way Method

Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

Abstract:

The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure interaction, one-way method, two-way method.

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49 Gimbal Structure for the Design of 3D Flywheel System

Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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48 Gimbal Structure for the Design of 3D Flywheel System

Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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47 Semi-Lagrangian Method for Advection Equation on GPU in Unstructured R3 Mesh for Fluid Dynamics Application

Authors: Irakli V. Gugushvili, Nickolay M. Evstigneev

Abstract:

Numerical integration of initial boundary problem for advection equation in 3 ℜ is considered. The method used is  conditionally stable semi-Lagrangian advection scheme with high order interpolation on unstructured mesh. In order to increase time step integration the BFECC method with limiter TVD correction is used. The method is adopted on parallel graphic processor unit environment using NVIDIA CUDA and applied in Navier-Stokes solver. It is shown that the calculation on NVIDIA GeForce 8800  GPU is 184 times faster than on one processor AMDX2 4800+ CPU. The method is extended to the incompressible fluid dynamics solver. Flow over a Cylinder for 3D case is compared to the experimental data.

Keywords: Advection equations, CUDA technology, Flow overthe 3D Cylinder, Incompressible Pressure Projection Solver, Parallel computation.

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46 Residence Time Distribution in a Two Impinging Streams Cyclone Reactor: CFD Prediction and Experimental Validation

Authors: Nahid Ghasemi, Morteza Sohrabi, Yasan Soleymani

Abstract:

The quantified residence time distribution (RTD) provides a numerical characterization of mixing in a reactor, thus allowing the process engineer to better understand mixing performance of the reactor.This paper discusses computational studies to investigate flow patterns in a two impinging streams cyclone reactor(TISCR) . Flow in the reactor was modeled with computational fluid dynamics (CFD). Utilizing the Eulerian- Lagrangian approach, implemented in FLUENT (V6.3.22), particle trajectories were obtained by solving the particle force balance equations. From simulation results obtained at different Δts, the mean residence time (tm) and the mean square deviation (σ2) were calculated. a good agreement can be observed between predicted and experimental data. Simulation results indicate that the behavior of complex reactor systems can be predicted using the CFD technique with minimum data requirement for validation.

Keywords: Impinging streams reactor, Residence timedistribution, CFD, Eulerian-Lagrangian approach

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45 Comparison of Two Types of Preconditioners for Stokes and Linearized Navier-Stokes Equations

Authors: Ze-Jun Hu, Ting-Zhu Huang, Ning-Bo Tan

Abstract:

To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package. 

Keywords: Navier-Stokes equations, Krylov subspace method, preconditioner, dimensional splitting, augmented Lagrangian preconditioner.

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44 Multisymplectic Geometry and Noether Symmetries for the Field Theories and the Relativistic Mechanics

Authors: H. Loumi-Fergane, A. Belaidi

Abstract:

The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used.  In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qi, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

Keywords: Field theories, relativistic mechanics, Lagrangian formalism, multisymplectic geometry, symmetries, Noether theorem, conservation laws.

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43 The Search of Anomalous Higgs Boson Couplings at the Large Hadron Electron Collider and Future Circular Electron Hadron Collider

Authors: Ilkay Turk Cakir, Murat Altinli, Zekeriya Uysal, Abdulkadir Senol, Olcay Bolukbasi Yalcinkaya, Ali Yilmaz

Abstract:

The Higgs boson was discovered by the ATLAS and CMS experimental groups in 2012 at the Large Hadron Collider (LHC). Production and decay properties of the Higgs boson, Standard Model (SM) couplings, and limits on effective scale of the Higgs boson’s couplings with other bosons are investigated at particle colliders. Deviations from SM estimates are parametrized by effective Lagrangian terms to investigate Higgs couplings. This is a model-independent method for describing the new physics. In this study, sensitivity to neutral gauge boson anomalous couplings with the Higgs boson is investigated using the parameters of the Large Hadron electron Collider (LHeC) and the Future Circular electron-hadron Collider (FCC-eh) with a model-independent approach. By using [email protected] multi-purpose event generator with the parameters of LHeC and FCC-eh, the bounds on the anomalous Hγγ, HγZ and HZZ couplings in e− p → e− q H process are obtained. Detector simulations are also taken into account in the calculations.

Keywords: Anomalous Couplings, Effective Lagrangian, Electron-Proton Colliders, Higgs Boson.

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42 Flow Modeling and Runner Design Optimization in Turgo Water Turbines

Authors: John S. Anagnostopoulos, Dimitrios E. Papantonis

Abstract:

The incorporation of computational fluid dynamics in the design of modern hydraulic turbines appears to be necessary in order to improve their efficiency and cost-effectiveness beyond the traditional design practices. A numerical optimization methodology is developed and applied in the present work to a Turgo water turbine. The fluid is simulated by a Lagrangian mesh-free approach that can provide detailed information on the energy transfer and enhance the understanding of the complex, unsteady flow field, at very small computing cost. The runner blades are initially shaped according to hydrodynamics theory, and parameterized using Bezier polynomials and interpolation techniques. The use of a limited number of free design variables allows for various modifications of the standard blade shape, while stochastic optimization using evolutionary algorithms is implemented to find the best blade that maximizes the attainable hydraulic efficiency of the runner. The obtained optimal runner design achieves considerably higher efficiency than the standard one, and its numerically predicted performance is comparable to a real Turgo turbine, verifying the reliability and the prospects of the new methodology.

Keywords: Turgo turbine, Lagrangian flow modeling, Surface parameterization, Design optimization, Evolutionary algorithms.

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41 Lagrangian Geometrical Model of the Rheonomic Mechanical Systems

Authors: Camelia Frigioiu, Katica (Stevanovic) Hedrih, Iulian Gabriel Birsan

Abstract:

In this paper we study the rheonomic mechanical systems from the point of view of Lagrange geometry, by means of its canonical semispray. We present an example of the constraint motion of a material point, in the rheonomic case.

Keywords: Lagrange's equations, mechanical system, non-linear connection, rheonomic Lagrange space.

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40 Solitons in Nonlinear Optical Lattices

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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39 Kinematic and Dynamic Analysis of a Lower Limb Exoskeleton

Authors: Tawakal Hasnain Baluch, Adnan Masood, Javaid Iqbal, Umer Izhar, Umar Shahbaz Khan

Abstract:

This paper will provide the kinematic and dynamic analysis of a lower limb exoskeleton. The forward and inverse kinematics of proposed exoskeleton is performed using Denevit and Hartenberg method. The torques required for the actuators will be calculated using Lagrangian formulation technique. This research can be used to design the control of the proposed exoskeleton.

Keywords: Dynamic Analysis, Exoskeleton, Kinematic Analysis, Lower Limb, Rehabilitation Robotics

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38 Simulation of the Large Hadrons Collisions Using Monte Carlo Tools

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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37 Searching the Efficient Frontier for the Coherent Covering Location Problem

Authors: Felipe Azocar Simonet, Luis Acosta Espejo

Abstract:

In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: Coherent covering location problem, efficient frontier, Lagrangian relaxation, data envelopment analysis.

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36 Study on the Particle Removal Efficiency of Multi Inner Stage Cyclone by CFD Simulation

Authors: Sang Won Han, Won Joo Lee, Sang Jun Lee

Abstract:

A new multi inner stage (MIS) cyclone was designed to remove the acidic gas and fine particles produced from electronic industry. To characterize gas flow in MIS cyclone, pressure and velocity distribution were calculated by means of CFD program. Also, the flow locus of fine particles and particle removal efficiency were analyzed by Lagrangian method. When outlet pressure condition was –100mmAq, the efficiency was the best in this study.

Keywords: Cyclone, SiO2 particle, Particle removal efficiency, CFD simulation

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35 Exterior Calculus: Economic Profit Dynamics

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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34 Computational Simulation of Imploding Current Sheath Trajectory at the Radial Phase of Plasma Focus Performance

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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33 Determination of Optimal Stress Locations in 2D–9 Noded Element in Finite Element Technique

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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32 Using Lagrange Equations to Study the Relative Motion of a Mechanism

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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31 Determination of Extreme Shear Stresses in Teaching Mechanics Using Freely Available Computer Tools

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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30 A Novel Slip Correction Factor for Spherical Aerosol Particles

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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29 Topological Quantum Diffeomorphisms in Field Theory and the Spectrum of the Space-Time

Authors: Francisco Bulnes

Abstract:

Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.

Keywords: Floer cohomology, Fukaya conjecture, Lagrangian submanifolds, spectrum of ring, topological quantum diffeomorphisms.

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28 Dynamic Analysis of Offshore 2-HUS/U Parallel Platform

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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