Search results for: quantum mechanics of spin dynamics.

Authors: Ollie Hall, Salma ElSayed

Abstract:

Affective adaptation is a creative way for game designers to add an extra layer of engagement to their productions. When player’s emotions are an explicit factor in mechanics design, endless possibilities for imaginative gameplay emerge. Whilst gaining popularity, existing affective game research mostly runs controlled experiments in restrictive settings and rely on one or more specialist devices for measuring player’s emotional state. These conditions albeit effective, are not necessarily realistic. Moreover, the simplified narrative and intrusive wearables may not be suitable for players. This exploratory study investigates delivering an immersive affective experience in the wild with minimal requirements, in an attempt for the average developer to reach the average player. A puzzle game is created with rich narrative and creative mechanics. It employs both explicit and implicit adaptation and only requires a web camera. Participants played the game on their own machines in various settings. Whilst it was rated feasible, very engaging and enjoyable, it remains questionable whether a fully immersive experience was delivered due to the limited sample size.

Keywords: affective games, dynamic adaptation, emotion recognition, game design

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: Mathematical modeling, ordinary differential equations, endocrine system, stability analysis.

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Authors: J. Mirzaei, H. Kazemi Kargar

Abstract:

This paper presents a new approach for setting frequency relays based on the dynamic of power system. A simplified model of the power system based on the load-frequency control loop will be developed to be used instead of the complete model of the power system. The effects of the equipments and their responses on the frequency variations of the power plant will be investigated and then a method for adaptive settings of frequency relays will be explained. The proposed method will be investigated by analyzing a simplified model of a power plant by MATLAB software.

Keywords: Adaptive Settings, Frequency Relay (FR), PowerSystem Dynamics, SFR model.

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Authors: J. M. B. Mendonça, M. V. S. Siqueira, A. Soares, M. A. F. Santos

Abstract:

The purpose of this article is to understand the dynamics of the increase in incivility through social relations (gender, race, class, sexual orientation, etc.), which hide inequalities in the form of treatment and opportunities within the organizational sphere. For this, we will examine works that address incivility at work, as well as studies that deviate from the mainstream, bringing more obscure organizational facets to light in connection with a critical approach to this issue. Next, some results of a bibliometric study shall be exposed, to analyze contributions connected to the theme and demonstrate gaps for future research. Then, models that facilitate reflection on the dynamics of violence shall be discussed. Finally, a broader concept of incivility in interpersonal relationships in the workplace shall be exposed considering the multiple approaches discussed.

Keywords: Incivility, inequalities, organization reflections, preventing violence.

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Authors: Asadullah I. Qazi, Mansoor Ahsan, Zahir Ashraf, Uzair Ahmad

Abstract:

System identification of an Unmanned Aerial Vehicle (UAV), to acquire its mathematical model, is a significant step in the process of aircraft flight automation. The need for reliable mathematical model is an established requirement for autopilot design, flight simulator development, aircraft performance appraisal, analysis of aircraft modifications, preflight testing of prototype aircraft and investigation of fatigue life and stress distribution etc.  This research is aimed at system identification of a fixed wing UAV by means of specifically designed flight experiment. The purposely designed flight maneuvers were performed on the UAV and aircraft states were recorded during these flights. Acquired data were preprocessed for noise filtering and bias removal followed by parameter estimation of longitudinal dynamics transfer functions using MATLAB system identification toolbox. Black box identification based transfer function models, in response to elevator and throttle inputs, were estimated using least square error   technique. The identification results show a high confidence level and goodness of fit between the estimated model and actual aircraft response.

Keywords: Black box modeling, fixed wing aircraft, least square error, longitudinal dynamics, system identification.

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Authors: Giovanni Incerti

Abstract:

In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.

Keywords: Belt drive, Vibrations, Startup, DC motor.

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Authors: Siddharth Ahuja, T. M. Muruganandam

Abstract:

An analytical investigation is performed to study the unsteady response of a one-dimensional, non-linear dynamic shock system to external downstream pressure perturbations in a supersonic flow in a varying area duct. For a given pressure ratio across a wind tunnel, the normal shock's location can be computed as per one-dimensional steady gas dynamics. Similarly, for some other pressure ratio, the location of the normal shock will change accordingly, again computed using one-dimensional gas dynamics. This investigation focuses on the small-time interval between the first steady shock location and the new steady shock location (corresponding to different pressure ratios). In essence, this study aims to shed light on the motion of the shock from one steady location to another steady location. Further, this study aims to create the foundation of the Unsteady Gas Dynamics field enabling further insight in future research work. According to the new pressure ratio, a pressure pulse, generated at the exit of the tunnel which travels and perturbs the shock from its original position, setting it into motion. During such activity, other numerous physical phenomena also happen at the same time. However, three broad phenomena have been focused on, in this study - Traversal of a Wave, Fluid Element Interactions and Wave Interactions. The above mentioned three phenomena create, alter and kill numerous waves for different conditions. The waves which are created by the above-mentioned phenomena eventually interact with the shock and set it into motion. Numerous such interactions with the shock will slowly make it settle into its final position owing to the new pressure ratio across the duct, as estimated by one-dimensional gas dynamics. This analysis will be extremely helpful in the prediction of inlet 'unstart' of the flow in a supersonic engine intake and its prominence with the incoming flow Mach number, incoming flow pressure and the external perturbation pressure is also studied to help design more efficient supersonic intakes for engines like ramjets and scramjets.

Keywords: Analytical investigation, compression and expansion waves, fluid element interactions, shock trajectory, supersonic flow, unsteady gas dynamics, varying area duct, wave interactions.

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

Abstract:

In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr¨odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Spin systems, equivalent counterparts, integrable reductions, self-consistent potentials.

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Authors: Wu Di, Yeo Khoon Seng, Lim Tee Tai

Abstract:

The typical insects employ a flapping-wing mode of flight. The numerical simulations on free flight of a model fruit fly (Re=143) including hovering and are presented in this paper. Unsteady aerodynamics around a flapping insect is studied by solving the three-dimensional Newtonian dynamics of the flyer coupled with Navier-Stokes equations. A hybrid-grid scheme (Generalized Finite Difference Method) that combines great geometry flexibility and accuracy of moving boundary definition is employed for obtaining flow dynamics. The results show good points of agreement and consistency with the outcomes and analyses of other researchers, which validate the computational model and demonstrate the feasibility of this computational approach on analyzing fluid phenomena in insect flight. The present modeling approach also offers a promising route of investigation that could complement as well as overcome some of the limitations of physical experiments in the study of free flight aerodynamics of insects. The results are potentially useful for the design of biomimetic flapping-wing flyers.

Keywords: Free hovering flight, flapping wings, fruit fly, insect aerodynamics, leading edge vortex (LEV), computational fluid dynamics (CFD), Navier-Stokes equations (N-S), fluid structure interaction (FSI), generalized finite-difference method (GFD).

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Authors: M. Zake, I. Barmina, A. Kolmickovs, R. Valdmanis

Abstract:

Experimental investigations of the DC electric field effect on thermal decomposition of biomass, formation of the axial flow of volatiles (CO, H2, CxHy), mixing of volatiles with swirling airflow at low swirl intensity (S ≈ 0.2-0.35), their ignition and on formation of combustion dynamics are carried out with the aim to understand the mechanism of electric field influence on biomass gasification, combustion of volatiles and heat energy production. The DC electric field effect on combustion dynamics was studied by varying the positive bias voltage of the central electrode from 0.6 kV to 3 kV, whereas the ion current was limited to 2 mA. The results of experimental investigations confirm the field-enhanced biomass gasification with enhanced release of volatiles and the development of endothermic processes at the primary stage of thermochemical conversion of biomass determining the field-enhanced heat energy consumption with the correlating decrease of the flame temperature and heat energy production at this stage of flame formation. Further, the field-enhanced radial expansion of the flame reaction zone correlates with a more complete combustion of volatiles increasing the combustion efficiency by 3% and decreasing the mass fraction of CO, H2 and CxHy in the products, whereas by 10% increases the average volume fraction of CO2 and the heat energy production downstream the combustor increases by 5-10% 

Keywords: Biomass, combustion, electrodynamic control, gasification.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the automatic choosing functions of gradient optimization type for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by minimizing the Hamiltonian with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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Authors: A. Omran, G. El-Bayiumi, M. Bayoumi, A. Kassem

Abstract:

Applicability of tuning the controller gains for Stewart manipulator using genetic algorithm as an efficient search technique is investigated. Kinematics and dynamics models were introduced in detail for simulation purpose. A PD task space control scheme was used. For demonstrating technique feasibility, a Stewart manipulator numerical-model was built. A genetic algorithm was then employed to search for optimal controller gains. The controller was tested onsite a generic circular mission. The simulation results show that the technique is highly convergent with superior performance operating for different payloads.

Keywords: Stewart kinematics, Stewart dynamics, task space control, genetic algorithm.

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Authors: Mahmood Reza Rahimi, Hajir Karimi

Abstract:

Downward turbulent bubbly flows in pipes were modeled using computational fluid dynamics tools. The Hydrodynamics, phase distribution and turbulent structure of twophase air-water flow in a 57.15 mm diameter and 3.06 m length vertical pipe was modeled by using the 3-D Eulerian-Eulerian multiphase flow approach. Void fraction, liquid velocity and turbulent fluctuations profiles were calculated and compared against experimental data. CFD results are in good agreement with experimental data.

Keywords: CFD, Bubbly flow, Vertical pipe, Population balance modeling, Gas void fraction, Liquid velocity, Normal turbulent stresses.

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Authors: Mliki Bouchmel, Abbassi Mohamed Ammar, Kamel Geudri, Chrigui Mouldi, Omri Ahmed

Abstract:

The objective of this work is to use the Fire Dynamics Simulator (FDS) to investigate the behavior of a kerosene small-scale fire. FDS is a Computational Fluid Dynamics (CFD) tool developed specifically for fire applications. Throughout its development, FDS is used for the resolution of practical problems in fire protection engineering. At the same time FDS is used to study fundamental fire dynamics and combustion. Predictions are based on Large Eddy Simulation (LES) with a Smagorinsky turbulence model. LES directly computes the large-scale eddies and the sub-grid scale dissipative processes are modeled. This technique is the default turbulence model which was used in this study. The validation of the numerical prediction is done using a direct comparison of combustion output variables to experimental measurements. Effect of the mesh size on the temperature evolutions is investigated and optimum grid size is suggested. Effect of width openings is investigated. Temperature distribution and species flow are presented for different operating conditions. The effect of the composition of the used fuel on atmospheric pollution is also a focus point within this work. Good predictions are obtained where the size of the computational cells within the fire compartment is less than 1/10th of the characteristic fire diameter.

Keywords: Large eddy simulation, Radiation, Turbulence, combustion, pollution.

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Authors: N. Daneshvar, S. Aber, M. S. Seyed Dorraji, A. R. Khataee, M. H. Rasoulifard

Abstract:

ZnO nanocrystals with mean diameter size 14 nm have been prepared by precipitation method, and examined as photocatalyst for the UV-induced degradation of insecticide diazinon as deputy of organic pollutant in aqueous solution. The effects of various parameters, such as illumination time, the amount of photocatalyst, initial pH values and initial concentration of insecticide on the photocatalytic degradation diazinon were investigated to find desired conditions. In this case, the desired parameters were also tested for the treatment of real water containing the insecticide. Photodegradation efficiency of diazinon was compared between commercial and prepared ZnO nanocrystals. The results indicated that UV/ZnO process applying prepared nanocrystalline ZnO offered electrical energy efficiency and quantum yield better than commercial ZnO. The present study, on the base of Langmuir-Hinshelwood mechanism, illustrated a pseudo first-order kinetic model with rate constant of surface reaction equal to 0.209 mg l-1 min-1 and adsorption equilibrium constant of 0.124 l mg-1.

Keywords: Zinc oxide nanopowder, Electricity consumption, Quantum yield, Nanoparticles, Photodegradation, Kinetic model, Insecticide.

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Authors: Sumit Kumar, Sunil Kumar, Chandan Deep Singh

Abstract:

This paper presents modeling and simulation of flexible robot in an underwater environment. The underwater environment completely contrasts with ground or space environment. The robot in an underwater situation is subjected to various dynamic forces like buoyancy forces, hydrostatic and hydrodynamic forces. The underwater robot is modeled as Rayleigh beam. The developed model further allows estimating the deflection of tip in two directions. The complete dynamics of the underwater robot is analyzed, which is the main focus of this investigation. The control of robot trajectory is not discussed in this paper. Simulation is performed using Symbol Shakti software.

Keywords: Bond graph modeling, dynamics. modeling, Rayleigh beam, underwater robot.

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Authors: B. Ghosh, H. Sahoo, K. K. Mondal

Abstract:

Propagation of arbitrary amplitude nonlinear Alfven waves has been investigated in low but finite β electron-positron-ion plasma including full ion dynamics. Using Sagdeev pseudopotential method an energy integral equation has been derived. The Sagdeev potential has been calculated for different plasma parameters and it has been shown that inclusion of ion parallel motion along the magnetic field changes the nature of slow shear Alfven wave solitons from dip type to hump type. The effects of positron concentration, plasma-β and obliqueness of the wave propagation on the solitary wave structure have also been examined.

Keywords: Alfven waves, Sagdeev potential, Solitary waves.

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Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb

Abstract:

The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.

Keywords: Discrete Fourier Transform (DFT), K-space Data, Magnetic Resonance (MR), Spin, Windows.

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Authors: K. Kamalanand, P. Mannar Jawahar

Abstract:

Methods of contemporary mathematical physics such as chaos theory are useful for analyzing and understanding the behavior of complex biological and physiological systems. The three dimensional model of HIV/AIDS is the basis of active research since it provides a complete characterization of disease dynamics and the interaction of HIV-1 with the immune system. In this work, the behavior of the HIV system is analyzed using the three dimensional HIV model and a chaotic measure known as the Hurst exponent. Results demonstrate that Hurst exponents of CD4, CD8 cells and viral load vary nonlinearly with respect to variations in system parameters. Further, it was observed that the three dimensional HIV model can accommodate both persistent (H>0.5) and anti-persistent (H<0.5) dynamics of HIV states. In this paper, the objectives of the study, methodology and significant observations are presented in detail.

Keywords: HIV/AIDS, mathematical model, chaos theory, Hurst exponent

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Authors: K. Jagannath, Akhilesh Kotian, S. S. Sharma, Achutha Kini U., P. R. Prabhu

Abstract:

Boiling process is characterized by the rapid formation of vapour bubbles at the solid–liquid interface (nucleate boiling) with pre-existing vapour or gas pockets. Computational fluid dynamics (CFD) is an important tool to study bubble dynamics. In the present study, CFD simulation has been carried out to determine the bubble detachment diameter and its terminal velocity. Volume of fluid method is used to model the bubble and the surrounding by solving single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. In the simulation, bubble is generated by allowing water-vapour to enter a cylinder filled with liquid water through an inlet at the bottom. After the bubble is fully formed, the bubble detaches from the surface and rises up during which the bubble accelerates due to the net balance between buoyancy force and viscous drag. Finally when these forces exactly balance each other, it attains a constant terminal velocity. The bubble detachment diameter and the terminal velocity of the bubble are captured by the monitor function provided in FLUENT. The detachment diameter and the terminal velocity obtained are compared with the established results based on the shape of the bubble. A good agreement is obtained between the results obtained from simulation and the equations in comparison with the established results.

Keywords: Bubble growth, computational fluid dynamics, detachment diameter, terminal velocity.

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Authors: Sajjad Seifoori

Abstract:

Impact behavior of striker on graphene sheet and carbon nanotube is investigated based on molecular dynamics (MD) simulations. A MD simulation is conducted to obtain the maximum dynamic deflections of a square and rectangular single-layered graphene sheets (SLGSs) with various values of side-length and striker parameter. Effect of (i) chirality, (ii) graphene side-length and nanotube length, (iii) striker mass on the maximum dynamic deflections of graphene and nanotube are investigated. The effect of different types of boundary condition on the maximum dynamic deflections is studied for zigzag and armchair SWCNTs with various aspect ratios (Length/Diameter).

Keywords: Impact, molecular dynamic, graphene, nanotube.

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Authors: M. F. Sung, Y.D. Kuan, R.J. Shyu, S.M. Lee

Abstract:

Tread design has evolved over the years to achieve the common tread pattern used in current vehicles. However, to meet safety and comfort requirements, tread design considers more than one design factor. Tread design must consider the grip and drainage, and the manner in which to reduce rolling noise, which is one of the main factors considered by manufacturers. The main objective of this study was the application the computational fluid dynamics (CFD) technique to simulate the contact surface of the tire and ground. The results demonstrated an air-Pumping and large pressure drop effect in the process of contact surface. The results also revealed that the pressure can be used to analyze sound pressure level (SPL).

Keywords: Air-pumping, computational fluid dynamics, sound pressure level, tire.

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Authors: Haowei Chen, Kaiqi Xiong

Abstract:

We have developed a better model for understanding the dynamics of malware spread in WMNs in this paper. The suggested model provides an insight into how viral propagation with energy exhaustion and various dispersed node densities might function. Based on a theoretical examination of the suggested model, we conclude that the threshold parameter could be used to identify the dynamics of viral spread globally. When the threshold is less than 1, the virus may be contained, but if it is greater than 1, a pandemic may result. Lastly, we discuss the various viral propagation strategies in relation to the distributed node densities and communication radii in WMNs. The aforementioned numerical simulation findings could serve as a guarantee of the theoretical analyses’ correctness.

Keywords: Bluetooth Security, Malware Propagation, Wireless Mesh Networks, Stability Analysis.

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Authors: Toshinori Nawata

Abstract:

In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designed the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Mofid Gorjibandpy, Mehdi Kazemi Sangsereki

Abstract:

In a bi-fuel diesel engine, the carburetor plays a vital role in switching from fuel gas to petrol mode operation and viceversa. The carburetor is the most important part of the fuel system of a diesel engine. All diesel engines carry variable venturi mixer carburetors. The basic operation of the carburetor mainly depends on the restriction barrel called the venturi. When air flows through the venturi, its speed increases and its pressure decreases. The main challenge focuses on designing a mixing device which mixes the supplied gas is the incoming air at an optimum ratio. In order to surmount the identified problems, the way fuel gas and air flow in the mixer have to be analyzed. In this case, the Computational Fluid Dynamics or CFD approach is applied in design of the prototype mixer. The present work is aimed at further understanding of the air and fuel flow structure by performing CFD studies using a software code. In this study for mixing air and gas in the condition that has been mentioned in continuance, some mixers have been designed. Then using of computational fluid dynamics, the optimum mixer has been selected. The results indicated that mixer with 12 holes can produce a homogenous mixture than those of 8-holes and 6-holes mixer. Also the result showed that if inlet convergency was smoother than outlet divergency, the mixture get more homogenous, the reason of that is in increasing turbulence in outlet divergency.

Keywords: Computational Fluid Dynamics, Venturi mixer, Air-fuel ratio, Turbulence.

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Authors: Maryam Momeni Feili, Mahvash Zandy Navgaran

Abstract:

The wave function at the origin is an important quantity in studying many physical problems concerning heavy quarkonia. This is because that it is using for calculating spin state hyperfine splitting and also crucial to evaluating the production and decay amplitude of the heavy quarkonium. In this paper, we present the variational method by using the single-parameter wave function to estimate the WFO for the ground state of heavy mesons.

Keywords: Wave function at the origin, heavy mesons, bound states, variational method, non-relativistic quark model, potential model, trial wave function.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the gradient optimization automatic choosing functions for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by expanding a stable region in the sense of Lyapunov with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: V.K. Mukhomorov

Abstract:

The solvated electron is self-trapped (polaron) owing to strong interaction with the quantum polarization field. If the electron and quantum field are strongly coupled then the collective localized state of the field and quasi-particle is formed. In such a formation the electron motion is rather intricate. On the one hand the electron oscillated within a rather deep polarization potential well and undergoes the optical transitions, and on the other, it moves together with the center of inertia of the system and participates in the thermal random walk. The problem is to separate these motions correctly, rigorously taking into account the conservation laws. This can be conveniently done using Bogolyubov-Tyablikov method of canonical transformation to the collective coordinates. This transformation removes the translational degeneracy and allows one to develop the successive approximation algorithm for the energy and wave function while simultaneously fulfilling the law of conservation of total momentum of the system. The resulting equations determine the electron transitions and depend explicitly on the translational velocity of the quasi-particle as whole. The frequency of optical transition is calculated for the solvated electron in ammonia, and an estimate is made for the thermal-induced spectral bandwidth.

Keywords: Canonical transformations, solvated electron, width of the optical spectrum.

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid.

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