Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion

General computational multibody system (MBS) algorithms allow for the linearization of the highly nonlinear equations of motion at different points in time in order to obtain the eigenvalue solution. This eigenvalue solution of the linearized equations is often used to shed light on the system stability at different configurations that correspond to different time points. Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion. As a consequence, the forms of the linearized equations and the eigenvalue solution obtained strongly depend on the set of orientation coordinates used. This paper addresses this fundamental issue by examining the effect of the use of different orientation parameters on the linearized equations of a gyroscope. The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters. In order to obtain a set of linearized equations that can be used to define the eigenvalue solution, the algebraic equations that describe the MBS constraints are systematically eliminated leading to a nonlinear form of the equations of motion expressed in terms of the system degrees of freedom. Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem. It is shown in this paper that the independent state equations formulated using Euler angles and Euler parameters lead to different eigenvalue solutions. This solution is also different from the solution obtained using a form of the Newton-Euler matrix equation expressed in terms of the angular accelerations and angular velocities. A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of orientation parameters and also to shed light on the important issue of using the eigenvalue analysis in the study of MBS stability. The validity of using the eigenvalue analysis based on the linearization of the nonlinear equations of motion in the study of the stability of railroad vehicle systems, which have known critical speeds, is examined. It is shown that such an eigenvalue analysis can lead to wrong conclusions regarding the stability of nonlinear systems.     

Informational analysis of seismic sequences by applying the Fisher Information Measure and the Shannon entropy: An application to the 2004–2010 seismicity of Aswan area (Egypt)

The interevent-time (IET) and interevent-distance (IED) series of seismic events occurred at Aswan area (Egypt) from 2004 to 2010 were investigated by means of the Fisher Information Measure and the Shannon entropy. The analysis was performed varying the depth and the magnitude thresholds. The results point out to an increase of level of organization and order with the decrease of magnitude threshold and the increase of depth threshold for the IET series, while the IED series are characterized by a level of uncertainty approximately constant with the threshold magnitude. The complexity measure, calculated as the product of the Fisher Information Measure and the Shannon entropy power, presents very similar pattern for both the types of seismic series, indicating an increasing complexity with the decrease of the threshold magnitude and the increase of the threshold depth.     

A nonlocal Levinson beam model for free vibration analysis of zigzag single-walled carbon nanotubes including thermal effects

A nonlocal Levinson beam model is developed to study the free vibrations of a zigzag single-walled carbon nanotube (SWCNT) in thermal environments. The equivalent Young’s modulus and shear modulus for a zigzag SWCNT are derived using an energy-equivalent model. The present study illustrates that the vibration characteristics of an SWCNT are strongly dependent on the temperature change and on the chirality of a zigzag carbon nanotube. The investigation of the chirality and temperature effects on free vibration of carbon nanotubes may be used as a useful reference for the application and the design of nanoelectronic and nanodrive devices, nano-oscillators, and nanosensors, in which carbon nanotubes act as basic elements.     

MCNP Dose Calculations in a CT Phantom for Therapeutic External Photon Beam

In this paper, we have addressed the problem of the radiation transport with the Monte Carlo N particle(MCNP) code. This is a general purpose Monte Carlo tool designed to transport neutron, photon and electron in three dimensional geometries. To examine the performance of MCNP5 code in the field of external radiotherapy, we performed the modeling of an Electron Density phantom (EDP) irradiated by photons from 60Co source. The model was used to calculate the Percent Depth Dose (PDD) at different depths in an EDP. One field size for PDD has been examined. A 60Co photons source placed at 80 cm source to surface distance (SSD). The results of calculations were compared to TPS data obtained at National Institute of Oncology of Rabat.     

Strong Band-Edge Emission from ZnS Quantum Dots Stabilized by Gum Arabic

ZnS quantum dots （QDs）, prepared by soft-condensation, exhibit robust structure of a quantum size equal 3.13 nm mediated two-dimensional gum Arabic surfactant as characterized by scan tunnelling microscope （STM）. Strong blue-shifted absorption and emission bands are depicted by optical characterization even for the sample stored under ambient condition for two weeks. These enhancements can be attributed to the completely passivated surface trap states by Gum Arabic.     

AC conductivity and dielectric studies of (C5H10N)2BiCl5 compound

The bis (3-dimethylammonium-1-propyne) pentachlorobismuthate (III) exhibits a structural phase transition at T₁?=?(337?±?2?K), which has been characterized by differential scanning calorimetric, X-ray powder analysis, AC conductivity and dielectric measurements. The dielectric dispersion yielded the real and imaginary parts of impedance of (C₅H₁₀N)₂BiCl₅ in the form of a semicircle in a complex plane. Besides, a Cole?CCole plot was observed at frequencies ranging from 209?Hz to 5?MHz, whose result was found to fit the theoretical resistor?Ccapacitor parallel circuit model. The temperature dependence of the electrical conductivity in the different phases follows the Arrhenius law. The frequency-dependent conductivity data were fitted in the modified power law: $ \sigma = {\sigma_{dc}} + {B_1}(T){\omega^{{s_1}}} + {B_2}(T){\omega^{{s_2}}} $ . The imaginary part of the permittivity constant is analyzed with the Cole?CCole formalism. With regard to the modulus plot, it can be characterized by full width at half height or in terms of a non-exponential decay function $ \phi (t) = \exp {\left( {\frac{{ - t}}{{{\tau_\sigma }}}} \right)^\beta } $ . Besides, the activation energy responsible for relaxation has been evaluated and found to be close the DC conductivity.