Search results for: navier-stokes equations in a rotating frame of refence

Authors: Boguslaw Schreyer

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In this paper, a general dynamical model is derived using the Lagrange formalism. The two masses: sprang and unsprang are included in a six-degree of freedom model for a sprung mass. The unsprung mass is included and shown only in a simplified model, although its equations have also been derived by an author. The simplified equations, more suitable for the computer model of robot’s dynamics are also shown.

Keywords: dynamics, mobile, robot, wheeled mobile robots

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Authors: Dnyanesh P. Mathur, Gregory L. Slater

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Gravitation and the expansion of the universe at a large scale are generally regarded as two completely distinct phenomena. Yet, in general, relativity theory, they both manifest as 'curvature' of spacetime. We propose a hypothesis which treats these two 'curvature-producing' phenomena as aspects of an underlying process. This process treats spacetime itself as composed of discrete units (Plancktons) and is 'dynamic' in the sense that these elements of spacetime are continually being both created and annihilated. It is these two complementary processes of Planckton creation and Planckton annihilation which manifest themselves as - 'cosmic expansion' on the one hand and as 'gravitational attraction’ on the other. The Planckton hypothesis treats spacetime as a perfect fluid in the same manner as the co-moving frame of reference of Friedman equations and the Gullstrand-Painleve metric; i.e.Planckton hypothesis replaces 'curvature' of spacetime by the 'flow' of Plancktons (spacetime). Here we discuss how this perspective may allow a unified description of both cosmological and gravitational acceleration as well as providing a mechanism for inducing an irreducible action at every point associated with the creation and annihilation of Plancktons, which could be identified as the zero point energy.

Keywords: discrete spacetime, spacetime flow, zero point energy, planktons

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Authors: Gong Kangming, Zhao Caiqi

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High-rise special-shaped structure, such as main frame structure of the statues, is one of the structure forms in irregular structure widely used. Due to the complex shape of the statue structure, with a large aspect ratio, its wind load value and the overall mechanical properties are very different from the high-rise buildings with the general rules. The paper taking a certain 48 meters high main frame structure of the statue located in Shuangyashan City, Heilongjiang Province, static and dynamic properties are analyzed by the finite element software. Through static and dynamic analysis, it got a number of useful conclusions that have a certain reference value for the analysis and design of the future similar structure.

Keywords: a Buddhism goddess Guanyin body, wind load, dynamic analysis, bolster, node design

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Authors: Keltoum Bouherine, Olivier Leroy

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The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.

Keywords: electron density, electric field, microwave plasma reactor, gas velocity, non-equilibrium plasma

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Authors: Tomasz Borowski, Dawid Sołoducha, Agata Markowska-Szczupak, Aneta Wesołowska, Marian Kordas, Rafał Rakoczy

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Essential oils (EOs) are fragrant volatile oils obtained from plants. These are used for cooking (for flavor and aroma), cleaning, beauty (e.g., rosemary essential oil is used to promote hair growth), health (e.g. thyme essential oil cures arthritis, normalizes blood pressure, reduces stress on the heart, cures chest infection and cough) and in the food industry as preservatives and antioxidants. Rosemary and thyme essential oils are considered the most eminent herbs based on their history and medicinal properties. They possess a wide range of activity against different types of bacteria and fungi compared with the other oils in both in vitro and in vivo studies. However, traditional uses of EOs are limited due to rosemary and thyme oils in high concentrations can be toxic. In light of the accessible data, the following hypothesis was put forward: Low frequency rotating magnetic field (RMF) increases the antimicrobial potential of EOs. The aim of this work was to investigate the antimicrobial activity of commercial Salvia Rosmarinus L. and Thymus vulgaris L. essential oil from Polish company Avicenna-Oil under Rotating Magnetic Field (RMF) at f = 25 Hz. The self-constructed reactor (MAP) was applied for this study. The chemical composition of oils was determined by gas chromatography coupled with mass spectrometry (GC-MS). Model bacteria Escherichia coli K12 (ATCC 25922) was used. Minimum inhibitory concentrations (MIC) against E. coli were determined for the essential oils. Tested oils in very small concentrations were prepared (from 1 to 3 drops of essential oils per 3 mL working suspensions). From the results of disc diffusion assay and MIC tests, it can be concluded that thyme oil had the highest antibacterial activity against E. coli. Moreover, the study indicates the exposition to the RMF, as compared to the unexposed controls causing an increase in the efficacy of antibacterial properties of tested oils. The extended radiation exposure to RMF at the frequency f= 25 Hz beyond 160 minutes resulted in a significant increase in antibacterial potential against E. coli. Bacteria were killed within 40 minutes in thyme oil in lower tested concentration (1 drop of essential oils per 3 mL working suspension). Rapid decrease (>3 log) of bacteria number was observed with rosemary oil within 100 minutes (in concentration 3 drops of essential oils per 3 mL working suspension). Thus, a method for improving the antimicrobial performance of essential oil in low concentrations was developed. However, it still remains to be investigated how bacteria get killed by the EOs treated by an electromagnetic field. The possible mechanisms relies on alteration in the permeability of ionic channels in ionic channels in the bacterial cell walls that transport in the cells was proposed. For further studies, it is proposed to examine other types of essential oils and other antibiotic-resistant bacteria (ARB), which are causing a serious concern throughout the world.

Keywords: rotating magnetic field, rosemary, thyme, essential oils, Escherichia coli

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Authors: M. H. Kazemi, D. Salac

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A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Mujde Turkkan, Nurkan Yagiz

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In this study an active controller is presented for vibration suppression of a full-bus model. The bus is modelled having seven degrees of freedom. Using the achieved model via Lagrange Equations the system equations of motion are derived. The suspensions of the bus model include air springs with two auxiliary chambers are used. Fuzzy logic controller is used to improve the ride comfort. The numerical results, verifies that the presented fuzzy logic controller improves the ride comfort.

Keywords: ride comfort, air spring, bus, fuzzy logic controller

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Authors: Denis Ushakov

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Cities are the main actors of global production and trade, and dominant share of international business activity is now concentrating within a frame of global urban net. This trend transforms mechanisms and patterns of market economy institutes’ (such as competition, division of labor, international movement of capital and labor force) functioning; stimulates an appearance of new economical (development of rural areas), social (urbanization) and political (political and economical unity of the big countries) problems. All these reasons identified relevance and importance of purpose of this study – to consider a modern role of cities’ business systems in the global economy, to identify sources for global urban competitive advantages, to clear inter-cities economic relationships and patterns of cities’ positioning within a frame of global net.

Keywords: globalization, urban business system, global city, transnationalization, networking

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Authors: Chivon Choeung, Heng Tang, Panha Soth, Vichet Huy

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This paper presents a robust control strategy for a single-phase DC-AC inverter with an output LC-filter. An all-pass filter is utilized to create an artificial β-signal so that the proposed controller can be simply used in dq-synchronous frame. The proposed robust controller utilizes a state feedback control with integral action in the dq-synchronous frame. A linear matrix inequality-based optimization scheme is used to determine stabilizing gains of the controllers to maximize the convergence rate to steady state in the presence of uncertainties. The uncertainties of the system are described as the potential variation range of the inductance and resistance in the LC-filter.

Keywords: single-phase inverter, linear matrix inequality, robust control, all-pass filter

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Authors: Amal Machtalay

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In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

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Authors: Takeru Furuawa, Kohei Takizawa, Daisuke Kuwahara, Shunjiro Shinohara

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In the field of a space propulsion, an electric propulsion system has been developed because its fuel efficiency is much higher than a conventional chemical one. However, the practical electric propulsion systems, e.g., an ion engine, have a problem of short lifetime due to a damage of generation and acceleration electrodes of the plasma. A helicon plasma thruster is proposed as a long-lifetime electric thruster which has non-direct contact electrodes. In this system, both generation and acceleration methods of a dense plasma are executed by antennas from the outside of a discharge tube. Development of the helicon plasma thruster has been conducting under the Helicon Electrodeless Advanced Thruster (HEAT) project. Our helicon plasma thruster has two important processes. First, we generate a dense source plasma using a helicon wave with an excitation frequency between an ion and an electron cyclotron frequencies, fci and fce, respectively, applied from the outside of a discharge using a radio frequency (RF) antenna. The helicon plasma source can provide a high-density (~1019 m-3), a high-ionization ratio (up to several tens of percent), and a high particle generation efficiency. Second, in order to achieve high thrust and specific impulse, we accelerate the dense plasma by the axial Lorentz force fz using the product of the induced azimuthal current jθ and the static radial magnetic field Br, shown as fz = jθ × Br. The HEAT project has proposed several kinds of electrodeless acceleration schemes, and in our particular case, a Rotating Magnetic Field (RMF) method has been extensively studied. The RMF scheme was originally developed as a concept to maintain the Field Reversed Configuration (FRC) in a magnetically confined fusion research. Here, RMF coils are expected to generate jθ due to a nonlinear effect shown below. First, the rotating magnetic field Bω is generated by two pairs of RMF coils with AC currents, which have a phase difference of 90 degrees between the pairs. Due to the Faraday’s law, an axial electric field is induced. Second, an axial current is generated by the effects of an electron-ion and an electron-neutral collisions through the Ohm’s law. Third, the azimuthal electric field is generated by the nonlinear term, and the retarding torque generated by the collision effects again. Then, azimuthal current jθ is generated as jθ = - nₑ er ∙ 2π fRMF. Finally, the axial Lorentz force fz for plasma acceleration is generated. Here, jθ is proportional to nₑ and frequency of RMF coil current fRMF, when Bω is fully penetrated into the plasma. Our previous study has achieved 19 % increase of ion velocity using the 5 MHz and 50 A of the RMF coil power supply. In this presentation, we will show the improvement of the ion velocity using the lower frequency and higher current supplied by RMF power supply. In conclusion, helicon high-density plasma production and electromagnetic acceleration by the RMF scheme with a concept of electrodeless condition have been successfully executed.

Keywords: electric propulsion, electrodeless thruster, helicon plasma, rotating magnetic field

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

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Authors: Sasibhushan Yengala, Nelson Muthu, Subramani Kanagaraj

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The abstract reports on the design related to a modular and affordable standing cum sitting device to meet the requirements of paraplegic patients of the different physiques. Paraplegic patients need the assistance of an external arrangement to the lower limbs and trunk to help patients adopt the correct posture while standing abreast gravity. This support can be from a tilt table or a standing frame which the patient can use to stay in a vertical posture. Standing frames are devices fitting to support a person in a weight-bearing posture. Commonly, these devices support and lift the end-user in shifting from a sitting position to a standing position. The merits of standing for a paraplegic patient with a spinal injury are numerous. Even when there is limited control on muscles that ordinarily support the user using the standing frame in a vertical position, the standing stance improves the blood pressure, increases bone density, improves resilience and scope of motion, and improves the user's feelings of well-being by letting the patient stand. One limitation with standing frames is that these devices are typically function definitely; cannot be used for different purposes. Therefore, users are often compelled to purchase more than one of these devices, each being purposefully built for definite activities. Another concern frequent in standing frames is manoeuvrability; it is crucial to provide a convenient adjustment scope for all users. Thus, there is a need to provide a standing frame with multiple uses that can be economical for a larger population. There is also a need to equip added readjustment means in a standing frame to lessen the shear and to accommodate a broad range of users. The proposed Versatile Standing cum Sitting Device (VSD) is designed to change from standing to a comfortable sitting position using a series of mechanisms. First, a locking mechanism is provided to lock the VSD in a standing stance. Second, a dampening mechanism is provided to make sure that the VSD shifts from a standing to a sitting position gradually when the lock mechanism gets disengaged. An adjustment option is offered for the height of the headrest via the use of lock knobs. This device can be used in clinics for rehabilitation purposes irrespective of patient's anthropometric data due to its modular adjustments. It can facilitate the patient's daily life routine while in therapy and giving the patient the comfort to sit when tired. The device also provides the availability of rehabilitation to a common person.

Keywords: paraplegic, rehabilitation, spinal cord injury, standing frame

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Authors: Lucas Wilman Crispim, Patrícia Hallack, Maikel Ballester

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This work aims at modeling electric discharges in gas mixtures. The mathematical model mimics the ignition process in a commercial spark-plug when a high voltage is applied to the plug terminals. A longitudinal unidimensional Cartesian domain is chosen for the simulation region. Energy and mass transfer are considered for a macroscopic fluid representation, while energy transfer in molecular collisions and chemical reactions are contemplated at microscopic level. The macroscopic model is represented by a set of uncoupled partial differential equations. Microscopic effects are studied within a discrete model for electronic and molecular collisions in the frame of ZDPlasKin, a plasma modeling numerical tool. The BOLSIG+ solver is employed in solving the electronic Boltzmann equation. An operator splitting technique is used to separate microscopic and macroscopic models. The simulation gas is a mixture of atomic Argon neutral, excited and ionized. Spatial and temporal evolution of such species and temperature are presented and discussed.

Keywords: CFD, electronic discharge, ignition, spark plug

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Authors: Rawhy Ismail

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Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity.

Keywords: curl operator, fractional calculus, fractional curl operators, Maxwell equations

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Authors: Ehsan Asgari, Meisam Afazeli, Nezhla Attarchian

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Post-earthquake fire is considered as a major threat in seismic areas. After an earthquake, fire is possible in structures. In this research, the effect of post-earthquake fire on steel moment frames with and without fireproofing coating is investigated. For this purpose, finite element method is employed. For the verification of finite element results, the results of an experimental study carried out by previous researchers are used, and the predicted FE results are compared with the test results, and good agreement is observed. After ensuring the accuracy of the predictions of finite element models, the effect of post-earthquake fire on the frames is investigated taking into account the parameters including the presence or absence of fire protection, frame design assumptions, earthquake type and different fire scenario. Ordinary fire and post-earthquake fire effect on the frames is also studied. The plastic hinges induced by earthquake in the structure are determined in the beam to the column connection and in panel zone. These areas should be accurately considered when providing fireproofing coatings. The results of the study show that the occurrence of fire beside corner columns is the most damaging scenario that results in progressive collapse of structure. It was also concluded that the behavior of structure in fire after a strong ground motion is significantly different from that in a normal fire.

Keywords: post earthquake fire, moment frame, finite element simulation, coupled temperature-displacement analysis, fire scenario

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Authors: Mahyar Maali, Merve Sagiroglu

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Steel, which is one of the base materials we prefer in the building construction, is the material with the highest ratio to weight of carrying capacity. Due to the carrying capacity, lighter and better quality steel in smaller sections and sizes has recently been used as a frame system in cold-formed steel structures. While light steel elements used as secondary frame elements during the past, they have nowadays started to be preferred as the main frame in low/middle story buildings and detached houses with advantages such as quick and easy installation, time-saving, and small amount of scrap. It is also economically ideal because the weight of structure is lighter than other steel profiles. Structural performances and failure modes of cold-formed structures are different from conventional ones due to their thin-walled structures. One of the most important elements of light steel structures to ensure stability is the connection. The screwed connections, which have self-drilling properties with special drilling tools, are widely used in the installation of cold-formed profiles. The length of the screw is selected according to the total thickness of the elements after the screw thickness is determined according to the elements of connections. The thickness of the material depends on the length of the drilling portion at the end of the screw. The shear tests of plates connected with self-drilling screws are carried out depending on the screw length, and their failure modes were evaluated in this study.

Keywords: cold-formed steel, screwed connection, connection, screw length

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Authors: Reut Lanyado, David Mendlovic

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Most biological methods for authentication require special equipment and, some of them are easy to fake. We proposed a method for authentication based on hand movement while typing a sentence with a regular camera. This technique uses the full video of the hand, which is harder to fake. In the first phase, we tracked the hand joints in each frame. Next, we represented a single frame for each individual using our Pose Agnostic Rotation and Movement (PARM) dimensional space. Then, we indicated a full video of hand movement in a fixed low dimensional space using this method: Fixed Dimension Video by Interpolation Statistics (FDVIS). Finally, we identified each individual in the FDVIS representation using unsupervised clustering and supervised methods. Accuracy exceeds 96% for 80 individuals by using supervised KNN.

Keywords: authentication, feature extraction, hand recognition, security, signal processing

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Authors: Ainul Haque, Ameeye Kumar Nayak

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Flow enhancement and species transport in a slit hydrophobic microchannel is studied for non-Newtonian fluids with the externally imposed electric field and pressure gradient. The incompressible Poisson-Nernst-Plank equations and the Navier-Stokes equations are approximated by lubrication theory to quantify the flow structure due to hydrophobic and hydrophilic surfaces. The analytical quantification of velocity and pressure of electroosmotic flow (EOF) is made with the numerical results due to the staggered grid based finite volume method for flow governing equations. The resistance force due to fluid friction and shear force along the surface are decreased by the hydrophobicity, enables the faster movement of fluid particles. The resulting flow enhancement factor Ef is increased with the low viscous fluid and provides maximum species transport. Also, the analytical comparison of EOF with pressure driven EOF justifies the flow enhancement due to hydrophobicity and shear impact on flow variation.

Keywords: electroosmotic flow, hydrophobic surface, power-law fluid, shear effect

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Authors: Y. M. Aiyesimi, G. T. Okedayo, O. W. Lawal

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The analysis has been carried out to study unsteady MHD thin film flow of a third grade fluid down an inclined plane with heat transfer when the slippage between the surface of plane and the lower surface of the fluid is valid. The governing nonlinear partial differential equations involved are reduced to linear partial differential equations using regular perturbation method. The resulting equations were solved analytically using method of separation of variable and eigenfunctions expansion. The solutions obtained were examined and discussed graphically. It is interesting to find that the variation of the velocity and temperature profile with the slip and magnetic field parameter depends on time.

Keywords: non-Newtonian fluid, MHD flow, thin film flow, third grade fluid, slip boundary condition, heat transfer, separation of variable, eigenfunction expansion

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Authors: Alex Fedoseyev

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This study explores Generalized Hydrodynamic Equations (GHE) for the simulation of turbulent flows. The GHE was derived from the Generalized Boltzmann Equation (GBE) by Alexeev (1994). GBE was obtained by first principles from the chain of Bogolubov kinetic equations and considered particles of finite dimensions, Alexeev (1994). The GHE has new terms, temporal and spatial fluctuations compared to the Navier-Stokes equations (NSE). These new terms have a timescale multiplier τ, and the GHE becomes the NSE when τ is zero. The nondimensional τ is a product of the Reynolds number and the squared length scale ratio, τ=Re*(l/L)², where l is the apparent Kolmogorov length scale, and L is a hydrodynamic length scale. The turbulence phenomenon is not well understood and is not described by NSE. An additional one or two equations are required for the turbulence model, which may have to be tuned for specific problems. We show that, in the case of the GHE, no additional turbulence model is needed, and the turbulent velocity profile is obtained from the GHE. The 2D turbulent channel and circular pipe flows were investigated using a numerical solution of the GHE for several cases. The solutions are compared with the experimental data in the circular pipes and 2D channels by Nicuradse (1932, Prandtl Lab), Hussain and Reynolds (1975), Wei and Willmarth (1989), Van Doorne (2007), theory by Wosnik, Castillo and George (2000), and the relevant experiments on Superpipe setup at Princeton, data by Zagarola (1996) and Zagarola and Smits (1998), the Reynolds number is from Re=7200 to Re=960000. The numerical solution data compared well with the experimental data, as well as with the approximate analytical solution for turbulent flow in channel Fedoseyev (2023). The obtained results confirm that the Alexeev generalized hydrodynamic theory (GHE) is in good agreement with the experiments for turbulent flows. The proposed approach is limited to 2D and 3D axisymmetric channel geometries. Further work will extend this approach by including channels with square and rectangular cross-sections.

Keywords: comparison with experimental data. generalized hydrodynamic equations, numerical solution, turbulent boundary layer, turbulent flow in channel

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Cailyn Green

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This research investigated the lack of standardization that exists in the field of polysubstance use. This standardization has to do with a uniform way of defining when and if polysubstance is taking place. This research is important to the field of substance abuse as it makes future researchers aware of this lack of uniformity in a commonly used word in the field. By investigating, we make researchers aware of these discrepancies to encourage a uniform definition to be created and used. The methodology for this research was a literary review. This literature review consisted of four peer-reviewed and published journal articles in four different journals. These articles focused on adolescents and their polysubstance use. The research question asked what time frame was used to determine if a client's substance use can be classified as polysubstance use when they reported using two or more substances. The results identify that there is no uniform working definition of the time frame for polysubstance to take place.

Keywords: addiction, adolescence, literary review, polysubstance

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Authors: Pablo Ampuero, Claudia Labarca

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The current research paper assesses how the narrative of Chilean businesspeople about China shapes a new Orientalism Analyses on the role of non-state actors in foreign policy that have hitherto theorized about Orientalism as a narrative of hegemonic power. Hence, it has been instrumental to the efforts of imperialist powers to justify their mission civilisatrice. However, such conceptualization can seldom explain new complexities of international interactions at the height of globalization. Hence, we assessed the case of Chile, a small Latin American country, and its relationship with China, its largest trading partner. Through a discourse analysis of interviews with Chilean businesspeople engaged in the Chinese market, we could determine that Chile is building an Orientalist image of China. This new business Orientalism reinforces a relation of alterity based on commercial opportunities, traditional values, and natural dispositions. Hence, the perception of the Chinese Other amongst Chilean business people frames a new set of representations as part of the essentially commercial nature of current bilateral relations. It differs from previous frames, such as the racial bias frame of the early 20^th century, or the anti-communist frame in reaction to Mao’s leadership. As in every narrative of alterity, there is not only a construction of the Other but also a definition of the Self. Consequently, this analysis constitutes a relevant case of the role of non-state actors in asymmetrical bilateral relations, where the non-state actors of the minor power build and act upon an Orientalist frame, which is not representative of its national status in the relation. This study emerges as a contribution on the relation amongst non-state actors in asymmetrical relations, where the smaller power’s business class acts on a negative prejudice of its interactions with its counterpart. The research builds upon the constructivist approach to international relations, linking the idea of Nation Branding with Orientalism in the case of Chile-China relations.

Keywords: new business Orientalism, small power, framing, Chile-China relations

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Authors: Said Algarni

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The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

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Authors: Minas Balyan

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

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

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Authors: Youb Said, Fourar Ali

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To describe the influence of bottom roughness on the free surface flows by numerical modeling, a two-dimensional model was developed. The equations of continuity and momentum (Naviers Stokes equations) are solved by the finite volume method. We considered a turbulent flow in an open channel with a bottom roughness. For our simulations, the K-ε model was used. After setting the initial and boundary conditions and solve the equations set, we were able to achieve the following results: vortex forming in the hollow causing substantial energy dissipation in the obstacle areas that form the bottom roughness. The comparison of our results with experimental ones shows a good agreement in terms of the results in the rough area. However, in other areas, differences were more or less important. These differences are in areas far from the bottom, especially the free surface area just after the bottom. These disagreements are probably due to experimental constants used by the k-ε model.

Keywords: modeling, free surface flow, turbulence, bottom roughness, finite volume, K-ε model, energy dissipation

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Authors: A. Abbasi Moshaii, M. Soltan Rezaee, M. Mohammadi Moghaddam

Abstract:

Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-RRR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-RRR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process.

Keywords: 3-RRR, dynamic equations, mechanisms control, structural uncertainty

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Authors: Youssef Abdelli, Rachid Nasri

Abstract:

The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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