Mustafa Riza | Eastern Mediterranean University (original) (raw)
Papers by Mustafa Riza
Chaos: An Interdisciplinary Journal of Nonlinear Science
We investigate the transition to synchronization in a two-layer network of oscillators with time-... more We investigate the transition to synchronization in a two-layer network of oscillators with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the timescale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical oscillators in the layers, we observe a significant improvement in the system synchronizability; i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching time, the transition from the network state of low inter-layer synchronization to high inter-layer synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as shrinking and ultimately the disappearance of the basin of attraction of a desynchronized network state.
In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions... more In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions on the energy-levels of a charged isotropic harmonic oscillator in the presence of a uniform magnetic field in the z-direction. The extension of this problem to three dimensions proves to be non-trivial. We obtain the first-order corrections to the energy-levels in closed form in the low energy limit of weak noncommutativity. The most important result we can note is that all energy corrections due to noncommutativity are negative and their magnitude increase with increasing Quantum numbers and magnetic field.
Physical Review B - PHYS REV B, 1997
We develop a quantum mechanical scattering theory for electrons which tunnel out of (or into) the... more We develop a quantum mechanical scattering theory for electrons which tunnel out of (or into) the tip of a scanning tunneling microscope. The method is based on propagators (or Green functions) for quasistationary scattering with the tip being an electron source (or sink). The results for the tunneling current generalize the Tersoff-Hamann approach of scanning tunneling microscopy. In contrast to previous calculations the present theory relates the tunneling current to the potential distribution of the sample. Expressions for the corrugation are available through a simple perturbation expansion scheme. Analytical model calculations are presented and compared with existing results.
AIP Conference Proceedings
Backscattering of atomic beams above a given surface yields information similar to the one obtain... more Backscattering of atomic beams above a given surface yields information similar to the one obtained from scanning the same surface with a scanning tunneling microscope (STM): In both cases the experimentally accessible quantity is the local density of states (LDOS) n(r,E) of the surface. For the case of backscattering, the LDOS at the turning point of the atom is an important ingredient of the potential between atom and surface. In experiments performed with an STM, the LDOS at the apex of an atomically sharp tip can be determined directly. Probing surfaces locally by an STM allows for the study of basic phenomena in atomic physics, with tunneling of electrons in three dimensions being a central issue.
Numerical Algorithms, 2013
ABSTRACT Theory and applications of multiplicative and Volterra calculi have been evolving rapidl... more ABSTRACT Theory and applications of multiplicative and Volterra calculi have been evolving rapidly over the recent years. As numerical minimization methods have a wide range of applications in science and engineering, the idea of the design of minimization methods based on multiplicative and Volterra calculi is self-evident. In this paper, the well-known Newton minimization method for one and two variables is developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed minimization methods is exposed by examples, and the results are compared with the original minimization method. One of the striking results of the proposed method is that the rate of convergence and the range of initial values are considerably larger compared to the original method.
Physical Review A, 1999
Tunneling problems are characterized by different quantum time scales of motion. In this paper, w... more Tunneling problems are characterized by different quantum time scales of motion. In this paper, we identify a tunneling time scale, which is based on a simple variational principle. The method utilizes the stationary eigenfunctions for a given one-dimensional potential ...
Chaos: An Interdisciplinary Journal of Nonlinear Science
We investigate the transition to synchronization in a two-layer network of oscillators with time-... more We investigate the transition to synchronization in a two-layer network of oscillators with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the timescale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical oscillators in the layers, we observe a significant improvement in the system synchronizability; i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching time, the transition from the network state of low inter-layer synchronization to high inter-layer synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as shrinking and ultimately the disappearance of the basin of attraction of a desynchronized network state.
In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions... more In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions on the energy-levels of a charged isotropic harmonic oscillator in the presence of a uniform magnetic field in the z-direction. The extension of this problem to three dimensions proves to be non-trivial. We obtain the first-order corrections to the energy-levels in closed form in the low energy limit of weak noncommutativity. The most important result we can note is that all energy corrections due to noncommutativity are negative and their magnitude increase with increasing Quantum numbers and magnetic field.
Physical Review B - PHYS REV B, 1997
We develop a quantum mechanical scattering theory for electrons which tunnel out of (or into) the... more We develop a quantum mechanical scattering theory for electrons which tunnel out of (or into) the tip of a scanning tunneling microscope. The method is based on propagators (or Green functions) for quasistationary scattering with the tip being an electron source (or sink). The results for the tunneling current generalize the Tersoff-Hamann approach of scanning tunneling microscopy. In contrast to previous calculations the present theory relates the tunneling current to the potential distribution of the sample. Expressions for the corrugation are available through a simple perturbation expansion scheme. Analytical model calculations are presented and compared with existing results.
AIP Conference Proceedings
Backscattering of atomic beams above a given surface yields information similar to the one obtain... more Backscattering of atomic beams above a given surface yields information similar to the one obtained from scanning the same surface with a scanning tunneling microscope (STM): In both cases the experimentally accessible quantity is the local density of states (LDOS) n(r,E) of the surface. For the case of backscattering, the LDOS at the turning point of the atom is an important ingredient of the potential between atom and surface. In experiments performed with an STM, the LDOS at the apex of an atomically sharp tip can be determined directly. Probing surfaces locally by an STM allows for the study of basic phenomena in atomic physics, with tunneling of electrons in three dimensions being a central issue.
Numerical Algorithms, 2013
ABSTRACT Theory and applications of multiplicative and Volterra calculi have been evolving rapidl... more ABSTRACT Theory and applications of multiplicative and Volterra calculi have been evolving rapidly over the recent years. As numerical minimization methods have a wide range of applications in science and engineering, the idea of the design of minimization methods based on multiplicative and Volterra calculi is self-evident. In this paper, the well-known Newton minimization method for one and two variables is developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed minimization methods is exposed by examples, and the results are compared with the original minimization method. One of the striking results of the proposed method is that the rate of convergence and the range of initial values are considerably larger compared to the original method.
Physical Review A, 1999
Tunneling problems are characterized by different quantum time scales of motion. In this paper, w... more Tunneling problems are characterized by different quantum time scales of motion. In this paper, we identify a tunneling time scale, which is based on a simple variational principle. The method utilizes the stationary eigenfunctions for a given one-dimensional potential ...