Suitable Transformation Technique Research Articles

Wavelet investigation of Soret and Dufour effects on stagnation point fluid flow in two dimensions with variable thermal conductivity and diffusivity

The current analysis is devoted to observing the influence of Soret and Dufour effects on stagnation point fluid flow in two dimensions. The buoyancy effects, variable thermal conductivity and diffusivity are also considered in our study. The governing equations of flow are reduced to a nonlinear ordinary differential equation system via a suitable transformation technique. The numerical simulation is performed by means of a new algorithm based on the Chebyshev wavelet method (MCWM). A detailed assessment of outcomes obtained by MCWM with fourth-order Runge–Kutta technique is available to support our wavelet-based solution. The significant properties and effects of various physical parameters are presented graphically. It is noted that an increase in the values of magnetic parameters cause a decrease in the velocity profile for the assisting case while the behavior of velocity is the opposite for the opposing case. The effects of Soret and Dufour enhanced the temperature and concentration, respectively. The comparison and convergence analysis indicate that the proposed algorithm is an efficient tool and could be extended for other complex nature models in engineering and physics.

Using direct transformation approach as an alternative technique to fuse global digital elevation models with GPS/levelling measurements in Egypt

Abstract Open global digital elevation models (GDEMs) represent a free and important source of information that is available to any country. Fusion processing between global and national digital elevation models is neither easy nor inexpensive. Hence, an alternative solution to fuse a GDEM (GTOPO30 or SRTM 1) with national GPS/levelling measurements is adopted. Herein, a transformation process between the GDEMs and national GPS/levelling measurements is applied using parametric and non-parametric equations. Two solutions are implemented before and after the filtration of raw data from outliers to assess the ability of the generated corrector surface model to absorb the effect of the outliers’ existence. In addition, a reliability analysis is conducted to select the most suitable transformation technique. We found that when both the fitting and prediction properties have equal priority, least-squares collocation integrated with a least-squares support vector machine inherited with a linear or polynomial kernel function exhibits the most accurate behavior. For the GTOPO30 model, before filtration of the raw data, there is an improvement in the mean and root mean square of errors by 39.31 % and 68.67 %, respectively. For the SRTM 1 model, the improvement in mean and root mean square values reached 86.88 % and 75.55 %, respectively. Subsequently, after the filtration process, these values became 3.48 % and 36.53 % for GTOPO30 and 85.18 % and 47.90 % for SRTM 1. Furthermore, it is found that using a suitable mathematical transformation technique can help increase the precision of classic GDEMs, such as GTOPO30, making them to be equal or more accurate than newer models, such as SRTM 1, which are supported by more advanced technologies. This can help overcome the limitation of shortage of technology or restricted data, particularly in developed countries. Henceforth, the proposed direct transformation technique represents an alternative faster and more economical way to utilize unfiltered measurements of GDEMs to estimate national digital elevations in areas with limited data.

Stochastic stability of mode-dependent Markovian jump inertial neural networks

The problem of stochastic stability analysis for Markovian jump inertial neural networks with mode-dependent time-varying delay is considered in this paper. The time-delay is assumed to be mode-dependent and time-varying. Using the suitable transformation technique, the second-order inertial neural network model is transformed into a system of first-order differential equations model. Delay-dependent stochastic stability condition is formulated in terms of linear matrix inequalities through the construction of Lyapunov–Krasovskii functional candidate involving mode-dependent time-varying delay. An integral inequality technique is used in the process to find the bounds of some integral terms. Finally, a numerical example is illustrated to show the effectiveness of the derived theoretical results.

Multi-objective constraint optimizing IOL control of distillation column with nonlinear observer

Performance of input–output linearizing (IOL) controllers suffers due to constraints on input and output variables. This problem is successfully tackled by augmenting IOL controllers with quadratic dynamic matrix controller (QDMC). However, this has created a constraint-mapping problem for coupled MIMO systems like distillation column. A multi-objective optimization problem needs to be solved to map the constraints on inputs. A suitable transformation technique is proposed to convert this multi-objective optimization problem to a single objective one. This makes the controller less computationally intensive and easy to implement. This controller (IOL-QDMC) along with nonlinear observer is implemented on a binary distillation column for dual composition control. Its performance is evaluated against a quadratic dynamic matrix controller (QDMC) and input–output linearization with PI controller (IOL-PI).

The temperature analysis of the billet with phase change during continuous casting

In this paper, the problem of 3-D steady heat conduction including the influence of phase change on billets is turned into the 2-D transient problem by a suitable transformation technique. The effective specific heat has been employed to substitute for the effect of the phase change. The computational formulation of finite element has been presented. And the careful disposal of the phase change region has also been given.

Computer cryptographic techniques for processing and storage of confidential information†

This paper is concerned with basic techniques that are suitable for computational cryptography. The difficulties involved in constructing suitable crypto-programmes as well as the criteria for the choice of crypto-programmes are discussed. The relevant mathematical properties of transformations are worked out. On this basis, suitable transformation techniques such as arithmetical, logic, matrix, topological, functional and hierarchical schemes are described. Finally, a brief discussion is given on the system design for crypto -programming.

A new approach to the study of coupled nonlinear systems

In this paper, a new approach to the problem of nonlinear coupling has been presented. This approach is based on differential transformation techniques which have been successfully used elsewhere in the literature for the study of nonlinear systems in uncoupled form. Here, the object of these transformations is to reduce the given set of coupled ordinary differential equations to an equivalent set of uncoupled equations amenable to existing techniques. The method is illustrated with an example drawn from the field of space mechanics. T is well known that the governing differential equations in the field of linear mechanics can always be obtained in an uncoupled form, since the kinetic and potential energy quadratics can be simultaneousl y reduced to their normal form and the application of the Lag-range's equation leads to a system of uncoupled equations. A parallel method for systems in the nonlinear domain is not known. Also given a pair of coupled linear differential equations, suitable algebraic transformations of the variables, which result in uncoupling of the equations, can be thought of. But in general this is not a feasible proposition for nonlinear problems. One possible approach to the study of such coupled nonlinear systems, is to obtain a higher-order uncoupled system by differentiation and mutual substitution of the given set of coupled differential equations. But the main disadvantage of this approach is the difficulties, encountered in studying higher order, nonlinear systems, which are too well known. Hence, attempts were made to develop suitable transformation techniques for the study of coupled nonlinear systems and this paper sets out the results of the research pursued in this direction. 2. Analysis A coupled dynamical system in two variables, say x and #2, can, in general, be thought of as spanning a three-dimensional space (xi,X2,t). In the case of linear systems, the uncoupling of this coupled system is effected by obtaining the projection of this system on the two constituent planes (xijt) and (xzjt) of the space (x^xzf) considered earlier. This direct approach is not practicable in the case of nonlinear systems with or without variable parameters. This calls for a suitable alternate approach to the problem. One such approach is based on the idea of effecting the uncoupling through a study of the system in the third constituent plane, (xijXz) [of the three dimensional space (xi}Xz,t)] or its transformations. Once the relation between xi and #2 is established, the resulting uncoupled systems can be studied through known techniques. This relatively unconventional approach, though not universal in application, can be extended to cover a fairly wide range of problems, leading to coupled, nonlinear, nonautonomous systems, depending on the ingenuity of the user.