Solution of the Bosonic and Algebraic Hamiltonians by using AIM

We apply the notion of asymptotic iteration method (AIM) to determine eigenvalues of the bosonic Hamiltonians that include a wide class of quantum optical models. We consider solutions of the Hamiltonians, which are even polynomials of the fourth order with the respect to Boson operators. We also demonstrate applicability of the method for obtaining eigenvalues of the simple Lie algebraic structures. Eigenvalues of the multi-boson Hamiltonians have been obtained by transforming in the form of the single boson Hamiltonian in the framework of AIM

Robert Kolej

Taha Toros Arşivi, Dosya Adı: Eğitimİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

MATCASC: A tool to analyse cascading line outages in power grids

Blackouts in power grids typically result from cascading failures. The key importance of the electric power grid to society encourages further research into sustaining power system reliability and developing new methods to manage the risks of cascading blackouts. Adequate software tools are required to better analyze, understand, and assess the consequences of the cascading failures. This paper presents MATCASC, an open source MATLAB based tool to analyse cascading failures in power grids. Cascading effects due to line overload outages are considered. The applicability of the MATCASC tool is demonstrated by assessing the robustness of IEEE test systems and real-world power grids with respect to cascading failures

Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems

We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($D\geq 2$) Schr\"{o}dinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.Comment: 13 page

A Topological Investigation of Phase Transitions of Cascading Failures in Power Grids

Cascading failures are one of the main reasons for blackouts in electric power transmission grids. The economic cost of such failures is in the order of tens of billion dollars annually. The loading level of power system is a key aspect to determine the amount of the damage caused by cascading failures. Existing studies show that the blackout size exhibits phase transitions as the loading level increases. This paper investigates the impact of the topology of a power grid on phase transitions in its robustness. Three spectral graph metrics are considered: spectral radius, effective graph resistance and algebraic connectivity. Experimental results from a model of cascading failures in power grids on the IEEE power systems demonstrate the applicability of these metrics to design/optimize a power grid topology for an enhanced phase transition behavior of the system

Unusual arterial supply of the segment IV with interlobar bridge and right replaced hepatic artery: a case report

A replaced right hepatic artery (RHA) arising from the superior mesenteric artery and an interlobar parenchymal bridge over the sagittal fissure have been observed on a 64-year-old formalin-fixed male cadaver in the anatomy laboratory. As we had followed a detailed segmental anatomy, we encountered an arterial distribution of segment IV featuring a different pattern from the literature so far. According to our observations, the segment I is supplied by both left (LHA) and middle (MHA) hepatic arteries; the segments II and III are supplied by the LHA while the segment IV is supplied by both the MHA and replaced RHA. The segments V–VIII are supplied only by the replaced RHA.  The case emphasizes the importance of arterial variations of liver in terms of the surgical procedures during the liver transplantation, hepatic resections, hepatic tumours, and etc. Our discussion focuses to the arterial supply of the segment IV and possible complications it may cause during/after the liver operations.