Mehmet Özer

B-spline method for solving Bratu's problem

In this paper, we propose a B-spline method for solving the one-dimensional Bratus problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur.

Large single-crystal growth and characterization of the narrow-gap semiconductor

is a narrow-gap semiconductor with a layered structure, isoelectronically analogous to PbS. Large single crystals were grown by the Bridgman - Stockbarger method from the melt and characterized by x-ray diffraction. The lattice parameters were determined and the discrepancy between those already reported was removed. From IR reflectivity measurements in the plasma region, the number of carriers was calculated. Also a strong anisotropy of the electrical conductivity was detected and the narrow-gap character of the material was supported by electrical measurements in the range of 10 - 300 K.

Chaos and Complex Systems

Springer Complexity is an interdisciplinary program publishing the best research and academiclevel teaching on both fundamental and applied aspects of complex systems – cutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine, neuroscience, social and computer science. Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous formation of distinctive temporal, spatial or functional structures. Models of such systems can be successfully mapped onto quite diverse “real-life” situations like the climate, the coherent emission of light from lasers, chemical reaction-diffusion systems, biological cellular networks, the dynamics of stock markets and of the internet, earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in social systems, to name just some of the popular applications. Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence. The three major book publication platforms of the Springer Complexity program are the monograph series “Understanding Complex Systems” focusing on the various applications of complexity, the “Springer Series in Synergetics”, which is devoted to the quantitative theoretical and methodological foundations, and the “SpringerBriefs in Complexity” which are concise and topical working reports, case-studies, surveys, essays and lecture notes of relevance to the field. In addition to the books in these two core series, the program also incorporates individual titles ranging from textbooks to major reference works.

Single crystal growth and characterization of narrow-gap - mixed crystals

Large single crystals of the family of layered compounds - were grown by the Bridgman-Stockbarger method for x = 0.0, 0.25, 0.50, 0.75 and 1.0. The structures of the as-grown single crystals were determined by x-ray diffraction and the lattice parameters and unit cell volumes were obtained. Infrared reflectivity measurements were also performed in the range 600-. From the analysis, the parameters , and were calculated. The electrical resistivities and (parallel and perpendicular to the layers, respectively) were measured as a function of temperature. From the measurements the plot of the Debye temperature versus x was calculated. An attempt was also made to correlate these physical properties with the compositional parameter x.

Fifth-degree B-spline solution for nonlinear fourth-order problems with separated boundary conditions

In this paper, we discussed a fifth-degree B-spline solution for the numerical solution to nonlinear fourth-order boundary value problems (BVPs) with separated boundary conditions. Two numerical examples are given to illustrate the efficiency and performance of the method. The method gives accurate results for both the linear and nonlinear cases.

The influence of Tl4Bi2S5 precipitates on the crystalline TlBiS2 properties

Crystalline TlBiS 2 having homogeneously distributed Tl 4 Bi 2 S 5 precipitates was grown by the vertical Bridgman technique in a two-step procedure. X-rays and Transmission Electron Microscopy (TEM) studies were used to identify the as-grown material whereas a Scanning Electron Microscopy (SEM) examination revealed its layered structure. The electrical conductivity σ was measured both along (σ | ) and across (σ⊥) its layers. IR reflectivity measurements were also performed and the plasma minimum was determined. Both electrical and optical characterization show properties similar to those of TlBiS 2 but a reduced N/m* ratio and an irregular voltage oscillation in the I-U characteristics were deduced. Combining the results from these investigations a possible explanation was proposed.

Impulsive Synchronization Between Double-Scroll Circuits

Two identical, double-scroll circuits, in their chaotic mode of operation, are unidirectionally connected via an externally triggered electronic switch. Thus, the case of impulsive synchronization is established. Their synchronization and its dependence on the switch on-off frequency and duty cycle is demonstrated.

A characterization of the dynamics of Newton’s derivative

In the present report the dynamic behaviour of the one dimensional family of maps \( F_{a,b,c} \left( x \right) = c\left[ {\left( {1 - a} \right)x - b} \right]^{\frac{1} {{1 - a}}} \) is examined, for different ranges of the control parametres a, b and c. These maps are of special interest, since they are solutions of N f ′ (x) = a, where N f ′ is the Newton’s method derivative. In literature only the case N f ′ (x) = 2 has been completely examined. Simultaneously, they may be viewed as solutions of normal forms of second order homogeneous equations, F″(x)+p(x)F(x) = 0, with immense applications in mechanics and electronics. The reccurent form of these maps, \( x_n = c\left[ {\left( {1 - a} \right)x_{n - 1} - b} \right]^{\frac{1} {{1 - a}}} \) , after excessive iterations, shows an oscillatory behaviour with amplitudes undergoing the period doubling route to chaos. This behaviour was confirmed by calculating the corresponding Lyapunov exponents.