Search results for: Differential subordination

Authors: Nisha Goyal, R.K. Gupta

Abstract:

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Tahseen Al-Shaikhli, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin

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A concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. Furthermore, the objectives are to control the coordination problem which mainly depends on offset selection, and to estimate the uniform delay based on the offset choice at each signalized intersection. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show that the derived model minimizes the total uniform delay to almost half compared to conventional models; the mathematical objective function is robust; the algorithm convergence time is fast.

Keywords: Area traffic control, differential evolution, offset variable, sinusoidal periodic function, traffic flow, uniform delay.

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Authors: Mohd Agos Salim Nasir, Ahmad Izani Md. Ismail

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Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme is to find the compact approximations to the derivative terms by differentiating centrally the governing equations. Our primary interest is to study the performance of the new scheme when applied to two Goursat partial differential equations against the traditional finite difference scheme.

Keywords: Goursat problem, partial differential equation, finite difference scheme, compact finite difference

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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Authors: Sanjeeb Kumar Kar

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The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, C. Ardil

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In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.

Keywords: Reduced Order Modeling, Stability, Mihailov Stability Criterion, Continued Fraction Expansions, Differential Evolution, Integral Squared Error.

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Authors: Osama A. Marzouk

Abstract:

We propose a reduced-ordermodel for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform timeconsuming simulations and solving the partial differential equations (PDEs) governing the flow field.

Keywords: reduced-order model, wake oscillator, nonlinear, ODEsystem

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Authors: Majed Omar Al-Dwairi

Abstract:

This paper evaluate the multilevel modulation for different techniques such as amplitude shift keying (M-ASK), MASK, differential phase shift keying (M-ASK-Bipolar), Quaternary Amplitude Shift Keying (QASK) and Quaternary Polarization-ASK (QPol-ASK) at a total bit rate of 107 Gbps. The aim is to find a costeffective very high speed transport solution. Numerical investigation was performed using Monte Carlo simulations. The obtained results indicate that some modulation formats can be operated at 100Gbps in optical communication systems with low implementation effort and high spectral efficiency.

Keywords: Optical communication, multilevel amplitude shift keying (M-ASK), Differential phase shift keying (DPSK), Quaternary Amplitude Shift Keying (QASK), Quaternary Polarization-ASK (QPol-ASK).

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Authors: Leila Vafajoo, Farhad Khorasheh, Mehrnoosh Hamzezadeh Nakhjavani, Moslem Fattahi

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In the present study, a procedure was developed to determine the optimum reaction rate constants in generalized Arrhenius form and optimized through the Nelder-Mead method. For this purpose, a comprehensive mathematical model of a fixed bed reactor for dehydrogenation of heavy paraffins over Pt–Sn/Al2O3 catalyst was developed. Utilizing appropriate kinetic rate expressions for the main dehydrogenation reaction as well as side reactions and catalyst deactivation, a detailed model for the radial flow reactor was obtained. The reactor model composed of a set of partial differential equations (PDE), ordinary differential equations (ODE) as well as algebraic equations all of which were solved numerically to determine variations in components- concentrations in term of mole percents as a function of time and reactor radius. It was demonstrated that most significant variations observed at the entrance of the bed and the initial olefin production obtained was rather high. The aforementioned method utilized a direct-search optimization algorithm along with the numerical solution of the governing differential equations. The usefulness and validity of the method was demonstrated by comparing the predicted values of the kinetic constants using the proposed method with a series of experimental values reported in the literature for different systems.

Keywords: Dehydrogenation, Pt-Sn/Al2O3 Catalyst, Modeling, Nelder-Mead, Optimization

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Authors: Magdy G. Asaad

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The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N-soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.

Keywords: Bilinear operator, G-BKP equation, Integrable nonlinear PDEs, Jimbo-Miwa equation, Ma-Fan equation, N-soliton solutions, Pfaffian solutions.

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Authors: Changjin Xu, Qianhong Zhang

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In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: N. Outili, A-H. Meniai

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Modeling transfer phenomena in several chemical engineering operations leads to the resolution of partial differential equations systems. According to the complexity of the operations mechanisms, the equations present a nonlinear form and analytical solution became difficult, we have then to use numerical methods which are based on approximations in order to transform a differential system to an algebraic one.Finite element method is one of numerical methods which can be used to obtain an accurate solution in many complex cases of chemical engineering.The packed columns find a large application like contactor for liquid-liquid systems such solvent extraction. In the literature, the modeling of this type of equipment received less attention in comparison with the plate columns.A mathematical bidimensionnal model with radial and axial dispersion, simulating packed tower extraction behavior was developed and a partial differential equation was solved using the finite element method by adopting the Galerkine model. We developed a Mathcad program, which can be used for a similar equations and concentration profiles are obtained along the column. The influence of radial dispersion was prooved and it can-t be neglected, the results were compared with experimental concentration at the top of the column in the extraction system: acetone/toluene/water.

Keywords: finite element method, Galerkine method, liquidliquid extraction modelling, packed column simulation, two dimensional model

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Authors: Y. J. Zhou, G. Lu

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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: Analytical method, mechanical responses, spherical wave propagation, traumatic brain injury.

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Authors: Joon Ho Kim, Tae Kwon Ha

Abstract:

Effect of aging treatment on microstructural aspects of interfacial layers of the Cu/Al clad sheet produced by differential speed rolling (DSR) process were studied by electron back scattered diffraction (EBSD). Clad sheet of Al/Cu has been fabricated by using DSR, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100^oC with speed ratio of 2, in which the total thickness reduction was 45%. Interface layers of clad sheet were analyzed by EBSD after subsequent annealing at 400^oC for 30 to 120min. With increasing annealing time, thickness of interface layer and fraction of high angle grain boundary were increased and average grain size was decreased.

Keywords: Aluminum/Copper clad sheet, differential speed rolling, interface layer, microstructure, annealing, electron back scattered diffraction.

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Authors: Olga V. Kharchenko

Abstract:

Applicability of a KTA crystal-based laser system with optical parametric oscillators (OPO) generation to lidar sounding of the atmosphere in the spectral range 3–4 µm is studied in this work. A technique based on differential absorption lidar (DIAL) method and differential optical absorption spectroscopy (DOAS) is developed for lidar sounding of trace atmospheric gases (TAG). The DIAL-DOAS technique is tested to estimate its efficiency for lidar sounding of atmospheric trace gases.

Keywords: Atmosphere, lidar sounding, DIAL, DOAS, trace gases, nonlinear crystal.

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Authors: Wei Zhang, Xin Zhao, Yi-Fan Zhu, Xin-Jian Zhang

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Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, Green function, support vectorregression

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Authors: Alpana Agarwal, Akhil Sharma

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This work presents a fully differential CMOS amplifier consisting of two self-biased gain boosted inverter stages, that provides an alternative to the power hungry operational amplifier. The self-biasing avoids the use of external biasing circuitry, thus reduces the die area, design efforts, and power consumption. In the present work, regulated cascode technique has been employed for gain boosting. The Miller compensation is also applied to enhance the phase margin. The circuit has been designed and simulated in 1.8 V 0.18 µm CMOS technology. The simulation results show a high DC gain of 100.7 dB, Unity-Gain Bandwidth of 107.8 MHz, and Phase Margin of 66.7^o with a power dissipation of 286 μW and makes it suitable candidate for the high resolution pipelined ADCs.

Keywords: CMOS amplifier, gain boosting, inverter-based amplifier, self-biased inverter.

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

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This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: Differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control.

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: Boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation.

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Authors: T. G. Emam

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The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.

Keywords: Heat and mass transfer, stretching surface, chemical reaction, porus medium.

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

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The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.

Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.

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Authors: Edina Koch, Péter Hudacsek

Abstract:

In railways transition zone is present at the boundaries of zones with different stiffness. When a train rides from an embankment onto a stiff structure, such as a bridge, tunnel or culvert, an abrupt change in the support stiffness occurs possibly inducing differential settlements. This in long term can yield to the degradation of the tracks and foundations in the transition zones. A number of techniques have been proposed or implemented to provide gradual stiffness transition at the problem zones, such as methods to ensure gradually changing pad stiffness, application of long sleepers or installation of auxiliary rails in the transition zone. Aim of the research presented in this paper is to analyze the 3D and the dynamic effects induced by the passing train over an area where significant difference in the support stiffness exists. The effects were analyzed for different arrangements associated with certain differential settlement mitigation strategies of the transition zones.

Keywords: Culvert, dynamic load, HS small model, railway transition zone.

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Authors: N. Ghatwary, A. Ahmed, H. Jalab

Abstract:

In this paper, an approach for the liver tumor detection in computed tomography (CT) images is represented. The detection process is based on classifying the features of target liver cell to either tumor or non-tumor. Fractional differential (FD) is applied for enhancement of Liver CT images, with the aim of enhancing texture and edge features. Later on, a fusion method is applied to merge between the various enhanced images and produce a variety of feature improvement, which will increase the accuracy of classification. Each image is divided into NxN non-overlapping blocks, to extract the desired features. Support vector machines (SVM) classifier is trained later on a supplied dataset different from the tested one. Finally, the block cells are identified whether they are classified as tumor or not. Our approach is validated on a group of patients’ CT liver tumor datasets. The experiment results demonstrated the efficiency of detection in the proposed technique.

Keywords: Fractional differential (FD), Computed Tomography (CT), fusion.

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Authors: Zanariah Mohd Yusof, Siti Khuzaimah Soid, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

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Unsteady magnetohydrodynamics (MHD) boundary layer flow and heat transfer over a continuously stretching surface in the presence of radiation is examined. By similarity transformation, the governing partial differential equations are transformed to a set of ordinary differential equations. Numerical solutions are obtained by employing the Runge-Kutta-Fehlberg method scheme with shooting technique in Maple software environment. The effects of unsteadiness parameter, radiation parameter, magnetic parameter and Prandtl number on the heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases as the Prandtl number and unsteadiness parameter increase but decreases with magnetic and radiation parameter.

Keywords: Heat transfer, magnetohydrodynamics, radiation, unsteadiness.

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Authors: Jin Zhang, Wing Lon Ng

Abstract:

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Keywords: Copula Models, Student t Copula, Parameter Inference, Differential Evolution, Threshold Accepting.

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

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Taking into account that many problems of natural sciences and engineering are reduced to solving initial-value problem for ordinary differential equations, beginning from Newton, the scientists investigate approximate solution of ordinary differential equations. There are papers of different authors devoted to the solution of initial value problem for ODE. The Euler-s known method that was developed under the guidance of the famous scientists Adams, Runge and Kutta is the most popular one among these methods. Recently the scientists began to construct the methods preserving some properties of Adams and Runge-Kutta methods and called them hybrid methods. The constructions of such methods are investigated from the middle of the XX century. Here we investigate one generalization of multistep and hybrid methods and on their base we construct specific methods of accuracy order p = 5 and p = 6 for k = 1 ( k is the order of the difference method).

Keywords: Multistep and hybrid methods, initial value problem, degree and stability of hybrid methods

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Authors: N. Yuvaraj, V. B. Prakash, D. Venkatraj

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This paper may be considered as combination of both pervasive computing and Differential GPS (global positioning satellite) which relates to control automatic traffic signals in such a way as to pre-empt normal signal operation and permit lifesaving vehicles. Before knowing the arrival of the lifesaving vehicles from the signal there is a chance of clearing the traffic. Traffic signal preemption system includes a vehicle equipped with onboard computer system capable of capturing diagnostic information and estimated location of the lifesaving vehicle using the information provided by GPS receiver connected to the onboard computer system and transmitting the information-s using a wireless transmitter via a wireless network. The fleet management system connected to a wireless receiver is capable of receiving the information transmitted by the lifesaving vehicle .A computer is also located at the intersection uses corrected vehicle position, speed & direction measurements, in conjunction with previously recorded data defining approach routes to the intersection, to determine the optimum time to switch a traffic light controller to preemption mode so that lifesaving vehicles can pass safely. In case when the ambulance need to take a “U" turn in a heavy traffic area we suggest a solution. Now we are going to make use of computerized median which uses LINKED BLOCKS (removable) to solve the above problem.

Keywords: Ubiquitous computing, differential GPS, fleet management system, wireless transmitter and receiver computerized median i.e. linked blocks (removable).

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Exponentially shrinking sheet, magnetic field, mixed convection, suction.

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Authors: Phool Singh, Ashok Jangid, N.S. Tomer, Deepa Sinha

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The aim of this paper is to study the oblique stagnation point flow on vertical plate with uniform surface heat flux in presence of magnetic field. Using Stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained using Runge-Kutta Fehlberg method with the help of shooting technique. In the present work the effects of striking angle, magnetic field parameter, Grashoff number, the Prandtl number on velocity and heat transfer characteristics have been discussed. Effect of above mentioned parameter on the position of stagnation point are also studied.

Keywords: Heat flux, Oblique stagnation point, Mixedconvection, Magneto hydrodynamics

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Authors: Arpita Soni, Sapna Mittal

Abstract:

Austenite and Martensite indicate the phases of solids undergoing phase transformation which we usually associate with materials and not with living organisms. This article provides an overview of bacterial proteins and structures that are undergoing phase transformation and suggests its probable effect on mechanical behavior. The context is mainly within the role of phase transformations occurring in the flagellum of bacteria. The current knowledge of molecular mechanism leading to phase variation in living organisms is reviewed. Since in bacteria, each flagellum is driven by a separate motor, similarity to a Differential drive in case of four-wheeled vehicles is suggested. It also suggests the application of the mechanism in which bacteria changes its direction of movement to facilitate single point turning of a multi-wheeled vehicle. Finally, examples are presented to illustrate that the motion due to phase transformation of flagella in bacteria can start a whole new research on motion mechanisms.

Keywords: Flagella, Phase Transformation, Nanobots, Differential Drive, Single point turn, Biomimetics

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