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

Authors: L. Joseph, B. Farid, F. Ravelet

Abstract:

Fundamental studies were performed on bifurcation, instabilities and turbulence in Taylor-Couette flow and applied to many engineering applications like astrophysics models in the accretion disks, shrouded fans, and electric motors. Such rotating machinery performances need to have a better understanding of the fluid flow distribution to quantify the power losses and the heat transfer distribution. The present investigation is focused on high gap ratio of Taylor-Couette flow with high rotational speeds, for smooth and grooved surfaces. So far, few works has been done in a very narrow gap and with very high rotation rates and, to the best of our knowledge, not with this combination with grooved surface. We study numerically the turbulent flow between two coaxial cylinders where R1 and R2 are the inner and outer radii respectively, where only the inner is rotating. The gap between the rotor and the stator varies between 0.5 and 2 mm, which corresponds to a radius ratio η = R1/R2 between 0.96 and 0.99 and an aspect ratio Γ= L/d between 50 and 200, where L is the length of the rotor and d being the gap between the two cylinders. The scaling of the torque with the Reynolds number is determined at different gaps for different smooth and grooved surfaces (and also with different number of grooves). The fluid in the gap is air. Re varies between 8000 and 30000. Another dimensionless parameter that plays an important role in the distinction of the regime of the flow is the Taylor number that corresponds to the ratio between the centrifugal forces and the viscous forces (from 6.7 X 105 to 4.2 X 107). The torque will be first evaluated with RANS and U-RANS models, and compared to empirical models and experimental results. A mesh convergence study has been done for each rotor-stator combination. The results of the torque are compared to different meshes in 2D dimensions. For the smooth surfaces, the models used overestimate the torque compared to the empirical equations that exist in the bibliography. The closest models to the empirical models are those solving the equations near to the wall. The greatest torque achieved with grooved surface. The tangential velocity in the gap was always higher in between the rotor and the stator and not on the wall of rotor. Also the greater one was in the groove in the recirculation zones. In order to avoid endwall effects, long cylinders are used in our setup (100 mm), torque is measured by a co-rotating torquemeter. The rotor is driven by an air turbine of an automotive turbo-compressor for high angular velocities. The results of the experimental measurements are at rotational speed of up to 50 000 rpm. The first experimental results are in agreement with numerical ones. Currently, quantitative study is performed on grooved surface, to determine the effect of number of grooves on the torque, experimentally and numerically.

Keywords: Taylor-Couette flow, high gap ratio, grooved surface, high speed

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Authors: Liliana O. Martínez, Juan E González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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A serious game category mobile application called Math Dominoes is presented. The main objective of this applications is to strengthen the teaching-learning process of solving algebraic equations and is based on the board game "Double 6" dominoes. Math Dominoes allows the practice of solving first, second-, and third-degree algebraic equations. This application is aimed to students who seek to strengthen their skills in solving algebraic equations in a dynamic, interactive, and fun way, to reduce the risk of failure in subsequent courses that require mastery of this algebraic tool.

Keywords: algebra, equations, dominoes, serious games

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Kamel Al-Khaled

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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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Authors: Krolo Paulina

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The seismic response of moment-resisting steel frames depends on the behavior of the joints, especially when they are considered as ductile zones. The aim of this research is to provide a realistic assessment of the moment-resisting steel frame behavior under seismic loading using nonlinear static pushover analysis (N2 method). The hysteresis behavior of the joints in the frame model was described using a new hysteresis envelope model. The obtained seismic response was compared with the results of the seismic analysis obtained for the same steel frame that takes into account the monotonic model of the joints.

Keywords: beam-to-column joints, hysteresis envelope model, moment-resisting frame, nonlinear static pushover analysis, N2 method

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Authors: Keyvan Ramin

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The geometric nonlinearity of Off-Diagonal Bracing System (ODBS) could be a complementary system to covering and extending the nonlinearity of reinforced concrete material. Finite element modeling is performed for flexural frame, x-braced frame and the ODBS braced frame system at the initial phase. Then the different models are investigated along various analyses. According to the experimental results of flexural and x-braced frame, the verification is done. Analytical assessments are performed in according to three-dimensional finite element modeling. Non-linear static analysis is considered to obtain performance level and seismic behavior, and then the response modification factors calculated from each model’s pushover curve. In the next phase, the evaluation of cracks observed in the finite element models, especially for RC members of all three systems is performed. The finite element assessment is performed on engendered cracks in ODBS braced frame for various time steps. The nonlinear dynamic time history analysis accomplished in different stories models for three records of Elcentro, Naghan, and Tabas earthquake accelerograms. Dynamic analysis is performed after scaling accelerogram on each type of flexural frame, x-braced frame and ODBS braced frame one by one. The base-point on RC frame is considered to investigate proportional displacement under each record. Hysteresis curves are assessed along continuing this study. The equivalent viscous damping for ODBS system is estimated in according to references. Results in each section show the ODBS system has an acceptable seismic behavior and their conclusions have been converged when the ODBS system is utilized in reinforced concrete frame.

Keywords: FEM, seismic behaviour, pushover analysis, geometric nonlinearity, time history analysis, equivalent viscous damping, passive control, crack investigation, hysteresis curve

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Authors: Mark Daniel De Luna, Ma. Katreena Pillejera, Wei-Hsin Chen

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The raw bamboo (Phyllostachys mankinoi), with a moisture content of 13.54 % and a higher heating value (HHV) of 17.657 MJ/kg, was subjected to torrefaction under a high gravity (higee) environment using a rotating packed bed. The performance of the higee torrefaction was explored in two parts: (1) effect of rotation and temperature and (2) effect of duration on the solid yield, HHV and energy yield. By statistical analyses, the results indicated that the rotation, temperature and their interaction has a significant effect on the three responses. Same remarks on the effect of duration where when the duration (temperature and rotation) increases, the HHV increases, while the solid yield and energy yield decreases. Graphical interpretations showed that at 300 °C, the rotating speed has no evident effect on the responses. At 30-min holding time, the highest HHV reached (28.389 MJ/kg) was obtained in the most severe torrefaction condition (the rotating speed at 1800 rpm and temperature at 300 °C) with an enhancement factor of HHV corresponding to 1.61 and an energy yield of 63.51%. Upon inspection, the recommended operating condition under a 30-min holding time is at 255 °C-1800 rpm since the enhancement factor of HHV (1.53), HHV (26.988 MJ/kg), and energy yield (65.21%) values are relatively close to that of the aforementioned torrefaction condition. The Van Krevelen diagram of the torrefied biomass showed that the ratios decrease as the torrefaction intensifies, hence improving the hydrophobicity of the product. The spreads of the results of the solid yield, enhancement factor (EF) of HHV, energy yield, and H/C and O/C ratios were in accordance with the trends of the responses. Overall, from the results presented, it can be concluded that the quality of the product from the process is at par to that of coal (i.e. HHV of coal is 21-35 MJ/kg). The Fourier transform infrared (FTIR) spectroscopy results indicated that cellulose and lignin may have been degraded at a lower temperature accompanied with a high rotating speed. The results suggested that torrefaction under higee environment indicates promising process for the utilization of bamboo.

Keywords: heat transfer, high gravity environment, FTIR, rotation, rotating speed, torrefaction

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Authors: Hamid Fazlollahi, Behzad Rafezy, Hassan Afshin

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There masonry infill increases the stiffness of reinforced concrete frames, thus increasing the force of the earthquake also the interaction between the frame and infill, which can have devastating effects on structures. In contrast presence of infill to increase the structural strength and stability. What is seen in the construction and design of structures has largely ignored the effects of infill and regardless infill structure and its positive and negative effects analyzes and designs, that it is not economically justified and the positive effects of positive infill to be increased and almost all of the useful capacity of moment frames used for infill. In this paper, by using ABAQUS software, reinforced concrete frame with masonry infill will be modeled, then add a mechanical rubber element to modify the interaction between the frame and infill and thus reduce the losses caused by the presence of infill explains. Finally, by comparing the analytical curves, benefits of this approach we will study and to present the results of the interaction between the frame and infill masonry needs modification and methods it will provide.

Keywords: masonry infill, mechanical rubber, reinforced concrete frame, interaction, ductility

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Authors: Getachew T. Sedebo, Stephan V. Joubert, Michael Y. Shatalov

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Conventional configuration of the vibratory disc gyroscope is based on in-plane non-axisymmetric vibrations of the disc with a prescribed circumferential wave number. Due to the Bryan's effect, the vibrating pattern of the disc becomes sensitive to the axial component of inertial rotation of the disc. Rotation of the vibrating pattern relative to the disc is proportional to the inertial angular rate and is measured by sensors. In the present paper, the authors investigate a possibility of making a 3D sensor on the basis of both in-plane and bending vibrations of the disc resonator. We derive equations of motion for the disc vibratory gyroscope, where both in-plane and bending vibrations are considered. Hamiltonian variational principle is used in setting up equations of motion and the corresponding boundary conditions. The theory of thin shells with the linear elasticity principles is used in formulating the problem and also the disc is assumed to be isotropic and obeys Hooke's Law. The governing equation for a specific mode is converted to an ODE to determine the eigenfunction. The resulting ODE has exact solution as a linear combination of Bessel and Neumann functions. We demonstrate how to obtain an explicit solution and hence the eigenvalues and corresponding eigenfunctions for annular disc with fixed inner boundary and free outer boundary. Finally, the characteristics equations are obtained and the corresponding eigenvalues are calculated. The eigenvalues are used for the calculation of tuning conditions of the 3D disc vibratory gyroscope.

Keywords: Bryan’s effect, bending vibrations, disc gyroscope, eigenfunctions, eigenvalues, tuning conditions

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Authors: Van Thang Nguyen, Amelie Danlos, Richard Paridaens, Farid Bakir

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This article presents a study of the effect of a contra-rotating component on the efficiency of centrifugal compressors. A contra-rotating centrifugal compressor (CRCC) is constructed using two independent rotors, rotating in the opposite direction and replacing the single rotor of a conventional centrifugal compressor (REF). To respect the geometrical parameters of the REF one, two rotors of the CRCC are designed, based on a single rotor geometry, using the hub and shroud length ratio parameter of the meridional contour. Firstly, the first rotor is designed by choosing a value of length ratio. Then, the second rotor is calculated to be adapted to the fluid flow of the first rotor according aerodynamics principles. In this study, four values of length ratios 0.3, 0.4, 0.5, and 0.6 are used to create four configurations CF1, CF2, CF3, and CF4 respectively. For comparison purpose, the circumferential velocity at the outlet of the REF and the CRCC are preserved, which means that the single rotor of the REF and the second rotor of the CRCC rotate with the same speed of 16000rpm. The speed of the first rotor in this case is chosen to be equal to the speed of the second rotor. The CFD simulation is conducted to compare the performance of the CRCC and the REF with the same boundary conditions. The results show that the configuration with a higher length ratio gives higher pressure rise. However, its efficiency is lower. An investigation over the entire operating range shows that the CF1 is the best configuration in this case. In addition, the CRCC can improve the pressure rise as well as the efficiency by changing the speed of each rotor independently. The results of changing the first rotor speed show with a 130% speed increase, the pressure ratio rises of 8.7% while the efficiency remains stable at the flow rate of the design operating point.

Keywords: centrifugal compressor, contra-rotating, interaction rotor, vacuum

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Authors: A. Shooshtari, A. R. Masoodi, S. Heyrani Moghaddam

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Free vibration analysis of a gabled frame with elastic support and semi-rigid connections is performed by using a program in OpenSees software. Natural frequencies and mode shape details of frame are obtained for two states, which are semi-rigid connections and elastic supports, separately. The members of this structure are analyzed as a prismatic nonlinear beam-column element in software. The mass of structure is considered as two equal lumped masses at the head of two columns in horizontal and vertical directions. Note that the degree of freedom, allocated to all nodes, is equal to three. Furthermore, the mode shapes of frame are achieved. Conclusively, the effects of connections and supports flexibility on the natural frequencies and mode shapes of structure are investigated.

Keywords: natural frequency, mode shape, gabled frame, semi-rigid connection, elastic support, OpenSees software

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Authors: Li Xu, Yang Hong, T. Zhao Wen

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Experimental results of many RC beam-column subassemblage indicate that slippage of longitudinal beam rebar within the joint and the shear deformation of joint core have significant influence on seismic behavior of the subassemblage. However, rigid joint assumption has been generally used in the seismic response analysis of RC frames, in which two kinds of inelastic deformation of joint have been ignored. Based on OpenSees platform, ‘Super Joint Element Model’ with more detailed inelastic mechanism is used to simulate the inelastic response of joints. Two finite element models of typical RC plane frame, namely considering or ignoring the inelastic deformation of joint respectively, were established and analyzed under seven strong earthquake waves. The simulated global and local inelastic deformations of the RC plane frame is shown and discussed. The analyses also confirm the security of the earthquake-resistant frame designed according to Chinese codes.

Keywords: frame structure, beam-column joint, longitudinal bar slippage, shear deformation, nonlinear analysis

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Authors: H. Zou, B. Wang

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Thermal distortion of the machine tool plays a critical role in its machining accuracy. This study investigates the thermal performance of a high-precision machine frame with future-oriented mineral casting components. A thermo-mechanical finite element model (FEM) was established to evaluate the thermal behavior of the frame under environmental thermal fluctuations. The validity of the presented FEM model was confirmed experimentally by a series of laser interferometer tests. Good agreement between numerical and experimental results demonstrates that the proposed model can accurately predict the thermal deformation of the frame with thermo-mechanical coupling effect. The results also show that keeping the workshop in thermally stable conditions is crucial for improving the machine accuracy of the system with large scale components. The goal of this paper is to investigate the feasibility of innovative mineral casting material applied in high-precision drilling machine and to provide a strategy for machine tool industry seeking a perfect substitute for classic frame materials such as cast iron and granite.

Keywords: thermo-mechanical model, finite element method, laser interferometer, mineral casting frame

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Authors: Shah Nister Kabir

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This study examines the construction of the controversy surrounding the cartoons of the Prophet Muhammad, as it appeared in three New Zealand newspapers; the Otago Daily Times (ODT), the New Zealand Herald (NZH) and the Press. It discursively argues that these mainstream newspapers promote the Orientalist perception of a clash of civilizations between Islam and the West in their news frame, but, in most cases, the perceived clash was not apparent in editorials. This study also argues that the uniformity in news frame conflicts with editorials’ construction of the issue. Furthermore, while the construction of the issue in news frame and editorials in the Press remained similar, the other two newspapers—the ODT and NZH—both contradict their own news frame in their editorials and contradict the editorials appearing in the Press.

Keywords: clash of culture, discourse, Islam, media agenda, New Zealand, orientalism, the West

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

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The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: super harmonic resonances, non-linear vibration, axially moving beam, Galerkin method

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Authors: Li Zhou, Yanmei Fang

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With current technology, images and videos can be obtained more easily than ever. It is so easy to manipulate these digital multimedia information when obtained, and that the content or source of the image and video could be easily tampered. In this paper, we propose to identify the image and video frame by the texture-based approach, e.g. Markov Transition Probability (MTP), which is in space domain, DCT domain and DWT domain, respectively. In the experiment, image and video frame database is constructed, and is used to train and test the classifier Support Vector Machine (SVM). Experiment results show that the texture-based approach has good performance. In order to verify the experiment result, and testify the universality and robustness of algorithm, we build a random testing dataset, the random testing result is in keeping with above experiment.

Keywords: multimedia forensics, video frame, LBP, MTP, SVM

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Authors: Samuel David Dunstan

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An elementary observation of a laminar cylindrical Poiseulle-Couette flow profile reveals no distinction in the parabolic streamwise profile from one without a cross-stream flow in whatever reference frame the observation is made. This is because the laminar flow is in solid-body rotation, and there is no intrinsic fluid rotation. Hence the main streamwise Poiseuille flow is unaffected. However, in turbulent (unsteady) cylindrical Poiseuille-Couette flow, the rotational reference frame must be considered, and any observation from an external inertial reference frame can give outright incorrect results. A common misconception in the study of fluid mechanics is the position of the observer does not matter. In this DNS (direct numerical simulation) study, firstly, turbulent flow in a pipe with axial rotation is established. Then in turbulent flow in the concentric pipe, with inner wall rotation, it is shown how the wall streak direction is oriented by the rotational reference frame. The Coriolis force here is not so fictitious after all!

Keywords: concentric pipe, rotational and inertial frames, frame invariance, wall streaks, flow orientation

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Karchung, S. Ruangsinchaiwanich

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This paper presents open-loop vector control method of induction motor with space vector pulse width modulation (SVPWM) technique. Normally, the closed loop speed control is preferred and is believed to be more accurate. However, it requires a position sensor to track the rotor position which is not desirable to use it for certain workspace applications. This paper exhibits the performance of three-phase induction motor with the simplest control algorithm without the use of a position sensor nor an estimation block to estimate rotor position for sensorless control. The motor stator currents are measured and are transformed to synchronously rotating (d-q-axis) frame by use of Clarke and Park transformation. The actual control happens in this frame where the measured currents are compared with the reference currents. The error signal is fed to a conventional PI controller, and the corrected d-q voltage is generated. The controller outputs are transformed back to three phase voltages and are fed to SVPWM block which generates PWM signal for the voltage source inverter. The open loop vector control model along with SVPWM algorithm is modeled in MATLAB/Simulink software and is experimented and validated in TMS320F28335 DSP board.

Keywords: electric drive, induction motor, open-loop vector control, space vector pulse width modulation technique

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Authors: T. R. Sreekrishnan, Mukesh Khare, Dinesh Upadhyay

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In a Rotating Biological Contactor (RBC), the biological film responsible for removal of pollutants is formed on the surface of discs. Evaluation studies of a pilot RBC designed to treat sewage of 150 persons with BOD Loading Rate: 8.2–26.7 g/m2/d, Discharge: 57.6 – 115.2 m3/day, HRT 1.25 – 2.5 hrs, at STP Yamuna Vihar Delhi. Removal of organic materials through use of fixed film reactors such as RBC is accomplished by means of a biological film on the fixed media. May and June in Delhi are dry summer months where the ambient temperature is in the range of 35oC to 45oC. July is a wet monsoon month that receives occasional precipitation, cloud cover, high humidity, with ambient temperature in the range of 30oC to 35oC. The organic and inorganic loads to the RBC employed in this study are actual city sewage conditions. Average in fluent BOD concentrations have been 330 mg/l, 245 mg/l and 160 mg/l and the average COD concentrations have been 670 mg/l, 500 mg/l, and 275 mg/l. The city sewage also has high concentration of ammonia, phosphorous, total suspended solids (TSS). pH of the city sewage is near neutral. Overall, the substrate conditions of city sewage are conducive for biological treatment though aerobic process. The presentation is a part of the ongoing collaborative research initiative between IIT Delhi and Karlsruhe Institute of Technology, Germany which is going on for last 15 years or so in the treatment of sewage waste of Delhi using semi-decentralized treatment system based on Rotating Biological Contactor.

Keywords: Rotating Biological Contactor (RBC), COD, BOD, HRT, STP

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Youn-Hwan Kim, Jae-Won Moon, Hae-Joong Kim

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This paper introduces the study on the method of accelerated life test to electrical rotating system. In recent years, as well as efficiency for motors and generators, there is a growing need for research on the life expectancy. It is considered impossible to calculate the acceleration coefficient by increasing the rotational load or temperature load as the acceleration stress in the motor system because the temperature of the copper exceeds the wire thermal class rating. In this paper, the accelerated life test methods of the electrical rotating system are classified according to the application. This paper describes the development of the test procedure for the highly accelerated life test (HALT) of the 100kW permanent magnet synchronous motor (PMSM) of electric vehicle. Finally, it explains how to select acceleration load for vibration, temperature, bearing load, etc. for accelerated life test.

Keywords: acceleration coefficient, electric vehicle motor, HALT, life expectancy, vibration

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Authors: Elena M. Kopteva, Pavlina Jaluvkova, Zdenek Stuchlik

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The question of constructing a consistent model of the cosmological black hole remains to be unsolved and still attracts the interest of cosmologists as far as it is important in a wide set of research problems including the problem of the black hole horizon dynamics, the problem of interplay between cosmological expansion and local gravity, the problem of structure formation in the early universe etc. In this work, the model of the cosmological black hole is built on the basis of the exact solution of the Einstein equations for the spherically symmetric inhomogeneous dust distribution in the approach of the mass function use. Possible trajectories for massive particles and photons near the black hole immersed in the nonstatic dust cosmological background are investigated in frame of the obtained model. The reference system of distant galaxy comoving to cosmological expansion combined with curvature coordinates is used, so that the resulting metric becomes nondiagonal and involves both proper ‘cosmological’ time and curvature spatial coordinates. For this metric the geodesic equations are analyzed for the test particles and photons, and the respective trajectories are built.

Keywords: exact solutions for Einstein equations, Lemaitre-Tolman-Bondi solution, cosmological black holes, particle and photon trajectories

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Authors: Minto Rattan, Tania Bose, Neeraj Chamoli

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The present paper investigates the effect of linear thermal gradient on the steady-state creep behavior of rotating isotropic disc using threshold stress based Sherby’s creep law. The composite discs made of aluminum matrix reinforced with silicon carbide particulate has been taken for analysis. The stress and strain rate distributions have been calculated for discs rotating at linear thermal gradation using von Mises’ yield criterion. The material parameters have been estimated by regression fit of the available experimental data. The results are displayed and compared graphically in designer friendly format for the above said temperature profile with the disc operating under uniform temperature profile. It is observed that radial and tangential stresses show minor variation and the strain rates vary significantly in the presence of thermal gradation as compared to disc having uniform temperature.

Keywords: creep, isotropic, steady-state, thermal gradient

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Authors: Muhammad Omer Farooq Saeed

Abstract:

The purpose of the proposal is to find out what time actually is! And to understand the natural phenomenon of the behavior of time and light corresponding to the motion of the bodies at relatively high speeds. The utmost concern of the paper is to deal with the possible demerits in the equations of relativity, thereby providing some valuable extensions in those equations and concepts. The idea used develops the most basic conception of the relative motion of the body with respect to space and a real understanding of time and the variation of energy of the body in different frames of reference. The results show the development of a completely new understanding of time, relative motion and energy, along with some extensions in the equations of special relativity most importantly the time dilation and the mass-energy relationship that will explain all frames of a body, all in one go. The proposal also raises serious questions on the validity of the “Principle of Equivalence” on which the General Relativity is based, most importantly a serious case of the bending light that eventually goes against its own governing concepts of space-time being proposed in the theory. The results also predict the existence of a completely new field that explains the fact just how and why bodies acquire energy in space-time. This field explains the production of gravitational waves based on time. All in all, this proposal challenges the formulas and conceptions of Special and General Relativity, respectively.

Keywords: time, relative motion, energy, speed, frame of reference, photon, curvature, space-time, time –differentials

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: A. Bhandari, S. Mukherjee

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Two frames in a Hilbert space are called woven or weaving if all possible merge combinations between them generate frames of the Hilbert space with uniform frame bounds. Weaving frames are powerful tools in wireless sensor networks which require distributed data processing. Considering the practical applications, this article deals with finite woven frames. We provide methods of constructing finite woven frames, in particular, bounded linear operators are used to construct woven frames from a given frame. Several examples are discussed. We also introduce the notion of woven frame sequences and characterize them through the concepts of gaps and angles between spaces.

Keywords: frames, woven frames, gap, angle

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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