Effect of the Density of Molten Metal on the Raining Phenomenon in Horizontal Centrifugal Casting

In this work the influence of the density of the molten metal on the emergence of the raining phenomenon in the horizontal centrifugal casting process is numerically studied. Transient 2D numerical simulations were carried out using Computational Fluid Dynamics software. Three molten metals with different density, namely aluminum, iron and lead, and three angular frequencies, namely 50, 66 and 77 rad/s were considered. It is found that the density of the molten metal significantly affects the emergence, transient or permanent, of the rain phenomenon. However, the magnitude and duration of the rain phenomenon depend on the angular frequency of the rotating mold. Likewise, since gravitational forces affect the metal according to its density, the value of the critical rotation speed of the mold is also affected.

Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton＇s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.

Directional Spectrum of Wind Waves: Part Ⅱ- Comparison and Confirmation

A model on the directional frequency spectrum of wind waves for deep water is introduced. The comparisons of the proposed model with other existing models show that the proposed model is very close to the JONSWAP model and DHH model for describing the developing waves under the normal spectral bandwidth, and has a better description for the transition of the unidirectional spectrum from ω -4 to ω -5 at a position around 3ω p, i.e., three time the peak frequency. Comparisons also show that the proposed model describes closely both field data measured by a four-frequency radar and a laser-optical sensor, and laboratory data measured by a laser slope gauge and an imaging optical method. The comparisons further demonstrate that the inverse spectral bandwidth as a new wave parameter is robust for describing the spectral steepness. Finally, the formula on the local spectral-peak angular frequency is confirmed using the observed two-dimensional spectra.

A New Theory on Electron Wave-Particle Duality

A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.

Directional Spectrum of Wind Waves: Part Ⅰ- Model and Derivation

A new model on the directional spectrum of wind waves for deep water is proposed based on the statistics of wind waves. This model contains three parameters: the wave age, the inverse spectral bandwidth and the local spectral-peak angular frequency. The inverse spectral bandwidth is a robust parameter for describing the spectral steepness of wind waves. Using the inverse spectral bandwidth parameter, the proposed model can well describe various observations obtained from the open ocean and laboratory tank.

Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

In the present paper, three complicated non- linear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method （AGM）. Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method （Runge-Kutte 4th）. Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.

A Novel Color Image Compression Algorithm Using the Human Visual Contrast Sensitivity Characteristics

In order to achieve higher image compression ratio and improve visual perception of the decompressed image, a novel color image compression scheme based on the contrast sensitivity characteristics of the human visual system （HVS） is proposed. In the proposed scheme, firstly the image is converted into the YCrCb color space and divided into sub-blocks. Afterwards, the discrete cosine transform is carried out for each sub-block, and three quantization matrices are built to quantize the frequency spectrum coefficients of the images by combining the contrast sensitivity characteristics of HVS. The Huffman algorithm is used to encode the quantized data. The inverse process involves decompression and matching to reconstruct the decompressed color image. And simulations are carried out for two color images. The results show that the average structural similarity index measurement （SSIM） and peak signal to noise ratio （PSNR） under the approximate compression ratio could be increased by 2.78% and 5.48%, respectively, compared with the joint photographic experts group （JPEG） compression. The results indicate that the proposed compression algorithm in the text is feasible and effective to achieve higher compression ratio under ensuring the encoding and image quality, which can fully meet the needs of storage and transmission of color images in daily life.

Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method （AGM）. Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.