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Page will reload when a filter is selected or excluded.- "The extensive completed research and continuous study of pendulum is due to its scientific and engineering importance. The present study simulate the Poincare solutions of damped, nonlinear and harmonically driven pendulum using FORTRAN 90 coded form of the popular fourth and fifth order Runge-Kutta schemes with constant time step. Validation case studies were those reported by Gregory and Jerry (I 990) for two damping qualities q1,q2= 2,4), fixed drive amplitude and frequency (g = 1.5,ώD= 2/3). A novel graphic presentation of the displacement and velocity components of the Poincare solutions for 101-eases each drawn from the parameters spaces 2≤q≤4 and 0.9≤ g≤ 1.5 at 100-equal steps were characterised using the fractal disk dimension analysis. Corresponding validation results compare well with reported results of Gregory and Jerry (1990). There is observed quantitative variations in the corresponding consecutive Poincare solutions prescribed by Runge-Kutta schemes with increasing number of excitation period however the quality of the overall Poincare section is hard to discern. Non uniform variation of scatter plots per area of solutions space characterised chaotic and periodic responses as against average uniform variation for a random data set The plots of periodic response distribute restrictedly on the solutions space diagonal while probabilities of chaotic responses on the studied parameters space is between 21.5% and 70.6%. Estimated fractal disk dimension variation is in the range 0.00≤ Df≤ 1.8 I for studied cases. The study therefore has demonstrated the utility of the novel graphic plots as a dynamic systems characterising tool. " 1 results 1
- Both Engineering students and practicing Engineers are involved in the design and analysis associated with fluid mechanics and thermo-dynamics problems. For them to be very efficient and proficient in handling various problems there is need for scientific data and general information in forms of tables or graphs. These must be made available in a compact form. In this paper a successful attempt was made to make available this aforementioned data in respect of compressible flow. All the equations concerned are brought together in a simplified form and programmed to generate useful data for various gases of interest on compressible flows. Analysis of compressible fluid flow becomes very easy if one has access to information as presented in this paper. 1 results 1
- Chaos is one of the most important behavioural modes exhibited by dynamical systems and refers to the unpredictable, seemingly random, motion of trajectories of a dynamical system. In recent time, non-linear dynamics and chaos have become familiar in the technical vocabulary of most sciences and technology due to the various applications of chaos in these areas. Chaotic systems display chaotic behaviours only for specific range of values of their parameters. It is therefore important to understand the chaotic features as well as parameter values resulting in its emergence in systems. In this paper, the emergence of chaos in six chaotic systems was demonstrated using Simulink with specific initial conditions and parameter values. The simulation results obtained in form of time series illustrated noise-like waveforms which were unpredictable even after a long interval of time, while the phase portraits were irregular and sponge-like in appearance. The noise-like and unpredictable trajectories as well strange attractors observed clearly demonstrated the emergence of chaos the chosen parameter values. 1 results 1
- In 1973 the industrial countries of the world abandoned the Bretton – Wood adjustable - peg exchange rate system as a means of international payments, and embraced a floating exchange rate system. By the beginning of the 1980's some developing countries of the world joined the league of exchange rate-floaters. It was thought that a floating exchange rate system is intrinsically superior to a fixed one because it not only insulates an economy from the events in other economies but also provides automatic adjustment of the trade balance and the balance of payments. From the mid 1980's however there have been calls in the industrial countries for yet a change in the international payments system from a floating one back to the Bretton-Woods fixed system (Marris, 1984; Dunn, 1983) or to some other variant of a fixed system. The questions then are - is there an ideal exchange rate regime? - is there reason to believe that a given exchange rate regime enhances the performance of an economy better than another? These questions form the focus of this study. There have been several positions in the literature. While Mundell-Fleming (1960, 1962) maintain that a floating exchange system is better than a fixed one if a country tends to depend more on monetary policy, but that a fixed exchange rate regime is ideal when fiscal policy is the major instrument employed in an economy, Sohmen (1965) maintained that a floating regime is superior whatever the more dominant economic policy (fiscal or monetary). Demberg (1970) maintained that the performance of an economy does not depend on the exchange rate regime per-se but rather on the optimal mix of fiscal and monetary policy. In the developing world there is fear that a floating exchange regime would aggravate rather than reduce the problems of inflation. debt-service burden and balance of payments disequilibrium (Olofin, Akinkugbe, Ajayi 1986). This study therefore attempted to find out which of the positions in the literature really holds in the case of developing African economies. To find answers to the issues raised we chose three African economies who had experienced both fixed and floating exchange rate systems, Namely, Ghana. Nigeria and Uganda. We built a model of each economy in the manner of Rhomberg (1964) and Tullio 1981. Each model has two versions. The shorter version has seven stochastic equations and tries to capture the economy under a fixed system, while the longer version added two additional stochastic equations to the first set and endogenizes exchange rates and interest rates as obtains under a floating exchange system. Utilizing quarterly data for 1977 to 1990 for Nigeria and Ghana, and for 1981 to 1990 for Uganda and employing the Ordinary Least Squares technique we estimated the shorter version of the model for the period 1977:1- 1990:4 and the longer version for the period 1986:4-1990:4 for Ghana and Nigeria. In the case of Uganda we estimated the longer version for the period 1981:1 to 1990:4 and the shorter version for 1987:2 to 1990:4. Beyond the statistical tests of the individual equations and parameters, we attempted to carry out rigorous tests of the validity of our model(s) through dynamic simulation. Thus we solved our model(s) using the Time Series Processor (TSP) econometric Software (Version 4.0) developed by Hall in 1983. When we solved each model using the Gauss -Seidel iterative technique, each converged for each endogenous variable and for each year demonstrating that each model is internally consistent. Utilizing different policy scenarios we tried to find out the effects of monetary, fiscal and exchange rate policy changes on internal sectors' macroaggregates of prices, real demand for money and money supply, as well as on external sector's macroaggregates of exports, imports and the trade balance. The results of our estimation exercises reveal that in Ghana a floating exchange rate system does not fuel inflation as is suggested by casual empiricism; rather it is the money supply that is the major propeller of domestic prices, given an exchange rate elasticity of domestic prices of 2% which is statistically insignificant at the 5% level and a money supply elasticity of domestic prices of 19% that is statistically significant at the 5% level. In Uganda there is a remarkable pass through from nominal exchange rates onto prices which contradicts Elbadawi's (1990) position, that it is not nominal exchange rates that fuel inflation in Uganda but fiscal deficits. The exchange rate elasticity of domestic prices in Uganda is 11% and this is statistically significant at the 5% level. However even in Uganda, nominal money supply and nominal rates of interest proved to be greater propellers of prices hence they have more dominant impact on inflation than the nominal exchange rate. In Nigeria there is some degree of pass through from nominal exchange rates onto prices given an exchange rate elasticity of domestic prices of 5%, which is statistically significant at the 5% level. However as in Ghana and Uganda money supply was the greater propeller of prices in Nigeria. What is more- the estimation results also showed that nominal exchange rates in the three countries follow the money supply. This goes to show that the behavior of the money supply and hence monetary policy influences the direction and degree of variability in nominal exchange rates under a floating system. Hence it shows that monetary policy is crucial to the success of the floating exchange rate system. Further the money supply was shown to vary in response to government fiscal deficits which makes fiscal prudence or otherwise the major determinant of exchange rate movements. For the simulation experiments we tried to find in what ways our endogenous variables change if a given macroeconomic policy varies while the others are kept constant. Thus we increased the rate of growth of government expenditure while keeping monetary policy and exchange rate policy constant. Similarly when we increased the rate of growth of the money supply we assumed fiscal and exchange rate policies to be constant. Our results show that in the long-run (over a period of at least ten years) a floating exchange rate performs better than a fixed one in terms of ensuring expanded output which ensures declining prices which in turn results in rising real demand for money and hence in rising rates of interests. A floating exchange rate regime also expanded exports and higher positive trade balance. Overall however the success of the floating system depends on coordinated and prudent macroeconomic policies; in the words of Goldstein (1984) "the capacity of the exchange rate system per-se to do good or harm should not be overestimated... the importance of discipline and coordinated macroeconomic policies for the successful operation of floating exchange rate regime should not be underestimated". 1 results 1
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