Screening effect for excitonic spectrum of Coulomb coupling between two Dirac particles

The properties of screening effect for energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. The excitonic hamiltonian in the product base of the Dirac single-particle is used. The corresponding energy eigenvalue system of the first order ODE (radial equations) was solved using the finite difference method. This enables to determine the energy eigenvalues of the discrete excitonic spectrum and the wave functions. We compare the results for the energy spectrum and the corresponding eigen-functions forms for WS 2 and WSe 2 computed for two different potentials: pure Coulomb and screened Coulomb (Keldysh potential). It is demonstrated that excitonic energy levels for unscreened potential lie dipper, and the corresponding eigen-functions’ forms differ from those obtained for screened one.

Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles

The properties of the energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. In the multiband model, we use the excitonic Hamiltonian in the product base of the Dirac single-particle states at the conduction and valence band edges. Following the separation of variables, we decouple the corresponding energy eigenvalue system of the first-order ODE radial equations rigorously and solve the resulting second-order ODE self-consistently, using the finite difference method, thus we determine the energy eigenvalues of the discrete excitonic spectrum and the corresponding wave functions. We also developed a WKB approach to solve the same spectral problem in semiclassical approximation for the resulting ODE. We compare the results for the energy spectrum and the corresponding eigen-function forms for WS 2 and WSe 2 obtained by means of both methods. We also compare our results for the energy spectrum with other theoretical works for excitons, and with available experimental data.

Studi Kestabilan Generator Sistem Sulselrabar (Stability Study of Sulselrabar System Generator)

In the standard operating system, the input parameters such as changes in the mechanical torque of the turbine and changes in the field voltage of the amplifier from the exciter need to be considered. Some studies that can be done include the study of the dynamic stability of synchronous generators when dealing with small changes that occur using the eigenvalue approach which is the roots of the characteristic equations of the system state space equation. The eigenvalue can show information on system stability and is related to the response of time to changes in the system. The system used is in the Sulselrabar electrical system. From the simulation results show the characteristics of the system in terms of the frequency response and angle of the generator rotor. For the eigenvalue system value in the inter-area oscillation mode is -0.33293 + 4.0844i, for the oscillation mode it is -0.9043 + 7.9670i. While the generator frequency response, where oscillations occur before reaching steady state conditions. The biggest overshoot response occurs in Old Tello plants, with a maximum overshoot of 0.09124 pu and a minimum of -0.2227 pu. While the smallest overshoot response is found in the Bakaru hydroelectric power plant which is equal to 0.004681 maximum pu and -0.02563 minimum pu.

An Optimal Lower Eigenvalue System

An optimal lower eigenvalue system is studied, and main theorems including a series of necessary and suffcient conditions concerning existence and a Lipschitz continuity result concerning stability are obtained. As applications, solvability results to some von-Neumann-type input-output inequalities, growth, and optimal growth factors, as well as Leontief-type balanced and optimal balanced growth paths, are also gotten.

Differential Quadrature Element Method for the Analysis of Vibration of Frame Structures Having Nonprismatic Members Considering Warping Torsion

The differential quadrature element method (DQEM) and the extended differential quadrature (EDQ) have been proposed by the author. The EDQ is used to the DQEM vibration analysis frame structures. The element can be a nonprismatic beam considering the warping due to torsion. The EDQ technique is used to discretize the element-based differential eigenvalue equations, the transition conditions at joints and the boundary conditions on domain boundaries. An overall discrete eigenvalue system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the overall discrete eigenvalue system. Mathematical formulations for the EDQ-based DQEM vibration analysis of nonprismatic structures considering the effect of warping torsion are carried out. By using this DQEM model, accurate results of frame problems can efficiently be obtained.

Three-dimensional instabilities of nonlinear gravity-capillary waves

Linear three-dimensional instabilities of nonlinear two-dimensional uniform gravitycapillary waves are studied using numerical methods. The eigenvalue system for the stability problem is generated using a Galerkin method and differs in detail from techniques used to study the stability of pure gravity waves (McLean 1982) and pure capillary waves (Chen & Saffman 1985). It is found that instabilities develop in the neighbourhood of the linear (triad, quartet and quintet) resonance curves. Further, both sum and difference triad ressonances are unstable for sufficiently steep waves in consequence of which Hasselmann's (1967) theorem is restricted to weakly nonlinear waves. The appearance of a superharmonic two-dimensional instability and bifurcation to three-dimensional waves are noted.

The effect of a magnetic field and rotation acting simultaneously on the onset of stationary convection in a fluid layer with rigid boundaries

The simultaneous effect of rotation and a magnetic field on the onset of buoyancy-driven thermal convection in a horizontal layer of viscous fluid with finite electrical conductivity, confined between two rigid perfectly conducting or electrically non-conducting boundaries, and heated from below is investigated. Critical constants for the onset of cellular convection are obtained, by solving the differential eigenvalue system using both an initial value and a variational technique, for an extensive range of Taylor number and Chandrasekhar number values (non-dimensional measures of rotation rate and magnetic field strength, respectively). The theoretical values so obtained are presented mainly in diagrammatical form and a comparison is made on a quantitative basis with the experimental results of Nakagawa at the corresponding parameter values.